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An einigen CT-Modellkomplexen in verschiedenen Lösungsmitteln und bei Temperaturen von 113-300 K sollte der Einfluß der Umgebung auf die Form und Lage der Absorption von CT-Komplexen unterschiedlicher Bindungsfestigkeit untersucht werden.
Dazu wurden bekannte Bandenprofilfunktionen auf ihre Anwendbar-keit geprüft. Da eine optimale Anpassung nicht möglich war, wurde eine neue Profilfunktion entwickelt, die eine bessere Beschreibung ergab.
Nach der Bestimmung der Gleichgewichtskonstante und des Extink-tionskoeffizienten konnte mit der Profilfläche das Übergangsmoment berechnet werden.
Die Lösungsmittelabhängigkeit wurde bei verschiedenen Brechzahlen und Dielektrizitätskonstanten untersucht.
Für feste Komplexe wurde eine spezielle Präparationstechnik gewählt. Die beobachteten Feinstrukturen und der auftretende Streuuntergrund werden diskutiert.
Intermolekulare Desaktivierung zwischen einem angeregten Fluorophor und einem Löscher durch Elektronenübertragung kann mit dynamischer und statischer Löschung beschrieben werden. Es wird vorgeschlagen den dynamischen Löschprozess in Transport- und Wechselwirkungsphase einzuteilen. Ergebnisse der Löschung der N-Heteroarene durch Naphthalen bei hohen Löscherkonzentrationen werden mit der statischen Löschung beschrieben. Außerdem werden CT-Systeme untersucht. Nach einem Überblick über statische Modelle zum Resonanzenergietransfer wird ein aus der Treffertheorie abgeleitetes Modell vorgestellt und an Beispielen getestet. Die Experimente sind computergesteuert.
We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.
In the modern industrialized countries every year several hundred thousands of people die due to the sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, non-invasive diagnostic tools like Holter-monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyse the HRV. Especially, some complexity measures that are basing on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients.
We have studied bifurcation phenomena for the incompressable Navier-Stokes equations in two space dimensions with periodic boundary conditions. Fourier representations of velocity and pressure have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. Invariant sets, notably steady states, have been traced for varying Reynolds number or strength of the imposed forcing, respectively. A complete bifurcation sequence leading to chaos is described in detail, including the calculation of the Lyapunov exponents that characterize the resulting chaotic branch in the bifurcation diagram.
Aus dem Inhalt: 1. Einführung 2. Motivation für die nichtlineare Dynamik 3. Logistische Abbildung (Parabel-Abbildung) 4. Lorenz-Gleichungen 5. Fraktale Selbstähnlichkeit 6. Die Brownsche Bewegung 7. Stöße & Billards 8. Körper mit gravitativer Wechselwirkung 9. Glossar 10. Turbo-Pascal-Texte 11. IDL-Texte 12. Reduce-Texte
A novel atomic beam splitter, using reflection of atoms off an evanescent light wave, is investigated theoretically. The intensity or frequency of the light is modulated in order to create sidebands on the reflected de Broglie wave. The weights and phases of the various sidevands are calculated using three different approaches: the Born approximation, a semiclassical path integral approach, and a numerical solution of the time-dependent Schrdinger equation. We show how this modulated mirror could be used to build practical atomic interferometers.
We present a semiclassical perturbation method for the description of atomic diffraction by a weakly modulated potential. It proceeds in a way similar to the treatment of light diffraction by a thin phase grating, and consists in calculating the atomic wavefunction by means of action integrals along the classical trajectories of the atoms in the absence of the modulated part of the potential. The capabilities and the validity condition of the method are illustrated on the well-known case of atomic diffraction by a Gaussian standing wave. We prove that in this situation the perturbation method is equivalent to the Raman-Nath approximation, and we point out that the usually-considered Raman-Nath validity condition can lead to inaccuracies in the evaluation of the phases of the diffraction amplitudes. The method is also applied to the case of an evanescent wave reflection grating, and an analytical expression for the diffraction pattern at any incidence angle is obtained for the first time. Finally, the application of the method to other situations is briefly discussed.
A detailed theoretical investigation of the reflection of an atomic de Broglie wave at an evanescent wave mirror is presented. The classical and the semiclassical descriptions of the reflection process are reviewed, and a full wave-mechanical approach based on the analytical soution of the corresponding Schrödinger equation is presented. The phase shift at reflection is calculated exactly and interpreted in terms of instantaneous reflection of the atom at an effective mirror. Besides the semiclassical regime of reflection describable by the WKB method, a pure quantum regime of reflection is identified in the limit where the incident de Broglie wavelength is large compared to the evanescent wave decay length.
Strange nonchaotic attractors typically appear in quasiperiodically driven nonlinear systems. Two methods of their characterization are proposed. The first one is based on the bifurcation analysis of the systems, resulting from periodic approximations of the quasiperiodic forcing. Secondly, we propose th characterize their strangeness by calculating a phase sensitivity exponent, that measures the sensitivity with respect to changes of the phase of the external force. It is shown, that phase sensitivity appears if there is a non-zero probability for positive local Lyapunov exponents to occur.
Two deterministic processes leading to roughening interfaces are considered. It is shown that the dynamics of linear perturbations of turbulent regimes in coupled map lattices is governed by a discrete version of the Kardar-Parisi-Zhang equation. The asymptotic scaling behavior of the perturbation field is investigated in the case of large lattices. Secondly, the dynamics of an order-disorder interface is modelled with a simple two-dimensional coupled map lattice, possesing a turbulent and a laminar state. It is demonstrated, that in some range of parameters the spreading of the turbulent state is accompanied by kinetic roughening of the interface.
The Voyager 2 Photopolarimeter experiment has yielded the highest resolved data of Saturn's rings, exhibiting a wide variety of features. The B-ring region between 105000 km and 110000 km distance from Saturn has been investigated. It has a high matter density and contains no significance features visible by eye. Analysis with statistical methods has let us to the detection of two significant events. These features are correlated with the inner 3:2 resonances of the F-ring shepherd satellites Pandora and Prometheus, and may be evidence of large ring paricles caught in the corotation resonances.
The present paper is related to the problem of approximating the exact solution to the magnetohydrodynamic equations (MHD). The behaviour of a viscous, incompressible and resistive fluid is exemined for a long period of time. Contents: 1 The magnetohydrodynamic equations 2 Notations and precise functional setting of the problem 3 Existence, uniqueness and regularity results 4 Statement and Proof of the main theorem 5 The approximate inertial manifold 6 Summary
Projection methods based on wavelet functions combine optimal convergence rates with algorithmic efficiency. The proofs in this paper utilize the approximation properties of wavelets and results from the general theory of regularization methods. Moreover, adaptive strategies can be incorporated still leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguelette decompositions enable the realization of especially fast algorithms for certain operators.
Contents: I. Algorithms 1. Theoretical Backround 2. Numerical Procedures 3. Graph Representation of the Solutions 4. Applications and Example II. Users' Manual 5. About the Program 6. The Course of a Qualitative Analysis 7. The Model Module 8. Input description 9. Output Description 10. Example 11. Graphics
We report on bifurcation studies for the incompressible magnetohydrodynamic equations in three space dimensions with periodic boundary conditions and a temporally constant external forcing. Fourier reprsentations of velocity, pressure and magnetic field have been used to transform the original partial differential equations into systems of ordinary differential equations (ODE), to which then special numerical methods for the qualitative analysis of systems of ODE have been applied, supplemented by the simulative calculation of solutions for selected initial conditions. In a part of the calculations, in order to reduce the number of modes to be retained, the concept of approximate inertial manifolds has been applied. For varying (incereasing from zero) strength of the imposed forcing, or varying Reynolds number, respectively, time-asymptotic states, notably stable stationary solutions, have been traced. A primary non-magnetic steady state loses, in a Hopf bifurcation, stability to a periodic state with a non-vanishing magnetic field, showing the appearance of a generic dynamo effect. From now on the magnetic field is present for all values of the forcing. The Hopf bifurcation is followed by furhter, symmetry-breaking, bifurcations, leading finally to chaos. We pay particular attention to kinetic and magnetic helicities. The dynamo effect is observed only if the forcing is chosen such that a mean kinetic helicity is generated; otherwise the magnetic field diffuses away, and the time-asymptotic states are non-magnetic, in accordance with traditional kinematic dynamo theory.
We report on bifurcation studies for the incompressible Navier-Stokes equations in two space dimensions with periodic boundary conditions and an external forcing of the Kolmogorov type. Fourier representations of velocity and pressure have been used to approximate the original partial differential equations by a finite-dimensional system of ordinary differential equations, which then has been studied by means of bifurcation-analysis techniques. A special route into chaos observed for increasing Reynolds number or strength of the imposed forcing is described. It includes several steady states, traveling waves, modulated traveling waves, periodic and torus solutions, as well as a period-doubling cascade for a torus solution. Lyapunov exponents and Kaplan-Yorke dimensions have been calculated to characterize the chaotic branch. While studying the dynamics of the system in Fourier space, we also have transformed solutions to real space and examined the relation between the different bifurcations in Fourier space and toplogical changes of the streamline portrait. In particular, the time-dependent solutions, such as, e.g., traveling waves, torus, and chaotic solutions, have been characterized by the associated fluid-particle motion (Lagrangian dynamics).
The bifurcation behaviour of the 3D magnetohydrodynamic equations has been studied for external forcings of varying degree of helicity. With increasing strength of the forcing a primary non-magnetic steady state loses stability to a magnetic periodic state if the helicity exceeds a threshold value and to different non-magnetic states otherwise.
We demonstrate the occurrence of regimes with singular continuous (fractal) Fourier spectra in autonomous dissipative dynamical systems. The particular example in an ODE system at the accumulation points of bifurcation sequences associated to the creation of complicated homoclinic orbits. Two different machanisms responsible for the appearance of such spectra are proposed. In the first case when the geometry of the attractor is symbolically represented by the Thue-Morse sequence, both the continuous-time process and its descrete Poincaré map have singular power spectra. The other mechanism owes to the logarithmic divergence of the first return times near the saddle point; here the Poincaré map possesses the discrete spectrum, while the continuous-time process displays the singular one. A method is presented for computing the multifractal characteristics of the singular continuous spectra with the help of the usual Fourier analysis technique.
Anhand eines paradigmatischen Modellbeispiels werden die Konsequenzen der Koexistenz vieler Attraktoren auf die globale Dynamik schwach dissipativer Systeme studiert. Es wird gezeigt, dass diese Systeme eine sehr reichhaltige Dynamik besitzen und extrem sensitiv gegenüber Störungen in den Anfangsbedingungen sind. Diese Systeme zeichnen sich durch eine extrem hohe Flexibilität ihres Verhaltens aus.
The paper presents a method that determines, by standard numerical means, the type of mutual relations of fold and flip bifurcations (configured as a so-called communication area) of a map. Equation systems are developed for the computation of points where a transition between areas of different types occurs. Furthermore, it is shown that saddle area<->spring area transitions can exist which have not yet been considered in the literature. Analytical conditions of that transition are derived.
Using a special technique of data analysis, we have found out 34 grand minima of solar activity obtained from a 7,700 years long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we use a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of solar maxima resp. minima by Eddy [5], but constitute a considerable extension. Hence, it has become possible to look closer at the validity of models. This way, we have tested several models for solar activity, esp. the model of Barnes et al. [1]. There are hints for that the grand minima might solely be driven by the 209 year period found in the Δ14C record.
We have shown that the two-dimensional complex Ginzburg-Landau equation exhibits supertransient chaos in a certain parameter range. Using numerical methods this behavior is found near the transition line separating frozen spiral solutions from turbulence. Supertransient chaos seems to be a common phenomenon in extended spatiotemporal systems. These supertransients are characterized by an average transient lifetime which depends exponentially on the size of the system and are due to an underlying nonattracting chaotic set.
Contents: 1 Introduction 1.1 Tikhanov-Phillips Regularization of Ill-Posed Problems 1.2 A Compact Course to Wavelets 2 A Multilevel Iteration for Tikhonov-Phillips Regularization 2.1 Multilevel Splitting 2.2 The Multilevel Iteration 2.3 Multilevel Approach to Cone Beam Reconstuction 3 The use of approximating operators 3.1 Computing approximating families {Ah}
We have studied the bifurcations in a three-dimensional incompressible magnetofluid with periodic boundary conditions and an external forcing of the Arnold-Beltrami-Childress (ABC) type. Bifurcation-analysis techniques have been applied to explore the qualitative behavior of solution branches. Due to the symmetry of the forcing, the equations are equivariant with respect to a group of transformations isomorphic to the octahedral group, and we have paid special attention to symmetry-breaking effects. As the Reynolds number is increased, the primary nonmagnetic steady state, the ABC flow, loses its stability to a periodic magnetic state, showing the appearance of a generic dynamo effect; the critical value of the Reynolds number for the instability of the ABC flow is decreased compared to the purely hydrodynamic case. The bifurcating magnetic branch in turn is subject to secondary, symmetry-breaking bifurcations. We have traced periodic and quasi- periodic branches until they end up in chaotic states. In particular detail we have analyzed the subgroup symmetries of the bifurcating periodic branches, which are closely related to the spatial structure of the magnetic field.
We have numerically studied the bifurcation properties of a sheet pinch with impenetrable stress-free boundaries. An incompressible, electrically conducting fluid with spatially and temporally uniform kinematic viscosity and magnetic diffusivity is confined between planes at x1=0 and 1. Periodic boundary conditions are assumed in the x2 and x3 directions and the magnetofluid is driven by an electric field in the x3 direction, prescribed on the boundary planes. There is a stationary basic state with the fluid at rest and a uniform current J=(0,0,J3). Surprisingly, this basic state proves to be stable and apparently to be the only time-asymptotic state, no matter how strong the applied electric field and irrespective of the other control parameters of the system, namely, the magnetic Prandtl number, the spatial periods L2 and L3 in the x2 and x3 directions, and the mean values B¯2 and B¯3 of the magnetic-field components in these directions.
The dynamics of noisy bistable systems is analyzed by means of Lyapunov exponents and measures of complexity. We consider both the classical Kramers problem with additive white noise and the case when the barrier fluctuates due to additional external colored noise. In case of additive noise we calculate the Lyapunov exponents and all measures of complexity analytically as functions of the noise intensity resp. the mean escape time. For the problem of fluctuating barrier the usual description of the dynamics with the mean escape time is not sufficient. The application of the concept of measures of complexity allows to describe the structures of motion in more detail. Most complexity measures sign the value of correlation time at which the phenomenon of resonant activation occurs with an extremum.
The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.
We have studied the bifurcation structure of the incompressible two-dimensional Navier-Stokes equations with a special external forcing driving an array of 8×8 counterrotating vortices. The study has been motivated by recent experiments with thin layers of electrolytes showing, among other things, the formation of large-scale spatial patterns. As the strength of the forcing or the Reynolds number is raised the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. The bifurcations lead to several periodic branches, torus and chaotic solutions, and other stationary solutions. Most remarkable is the appearance of solutions characterized by structures on spatial scales large compared to the scale of the forcing. We also characterize the different dynamic regimes by means of tracers injected into the fluid. Stretching rates and Hausdorff dimensions of convected line elements are calculated to quantify the mixing process. It turns out that for time-periodic velocity fields the mixing can be very effective.
Two-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at top and bottom and periodic boundary conditions in the horizontal direction is investigated by means of numerical simulation and bifurcation-analysis techniques. As the bouyancy forces increase, the primary stationary and symmetric convection rolls undergo successive Hopf bifurcations, bifurcations to traveling waves, and phase lockings. We pay attention to symmetry breaking and its connection with the generation of large-scale horizontal flows. Calculations of Lyapunov exponents indicate that at a Rayleigh number of 2.3×105 no temporal chaos is reached yet, but the system moves nonchaotically on a 4-torus in phase space.
Three-dimensional bouyancy-driven convection in a horizontal fluid layer with stress-free boundary conditions at the top and bottom and periodic boundary conditions in the horizontal directions is investigated by means of numerical simulation and bifurcation-analysis techniques. The aspect ratio is fixed to a value of 2√2 and the Prandtl number to a value of 6.8. Two-dimensional convection rolls are found to be stable up to a Rayleigh number of 17 950, where a Hopf bifurcation leads to traveling waves. These are stable up to a Rayleigh number of 30 000, where a secondary Hopf bifurcation generates modulated traveling waves. We pay particular attention to the symmetries of the solutions and symmetry breaking by the bifurcations.
The usage of nonlinear Galerkin methods for the numerical solution of partial differential equations is demonstrated by treating an example. We desribe the implementation of a nonlinear Galerkin method based on an approximate inertial manifold for the 3D magnetohydrodynamic equations and compare its efficiency with the linear Galerkin approximation. Special bifurcation points, time-averaged values of energy and enstrophy as well as Kaplan-Yorke dimensions are calculated for both schemes in order to estimate the number of modes necessary to correctly describe the behavior of the exact solutions.
The stability of the quiescent ground state of an incompressible viscous fluid sheet bounded by two parallel planes, with an electrical conductivity varying across the sheet, and driven by an external electric field tangential to the boundaries is considered. It is demonstrated that irrespective of the conductivity profile, as magnetic and kinetic Reynolds numbers (based on the Alfvén velocity) are raised from small values, two-dimensional perturbations become unstable first.
We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.
Die Produktion von Polyrhythmen ist ein wichtiger experimenteller Zugang für die Untersuchung der menschlichen Motorik. Durch Variation des Tempos (externer Kontrollparameter) bei rhythmischen Bewegungsabläufen können qualitative Übergänge in der Koordinationsdynamik induziert werden. Diese Übergänge lassen sich mit der Methode der symbolischen Dynamik in experimentellen Zeitreihen nachweisen und sind ein wichtiger Hinweis darauf, dass die untersuchten Bewegungsabläufe nichtlinearen Kontrollprozessen unterliegen. Die theoretische Beschreibung bimanueller Rhythmusproduktion mit gekoppelten Differenzengleichungen führt auf ein Modell mit nichtlinearer Fehlerkontrolle. Es ist eine wichtige Eigenschaft der Kontrollprozesse, dass sie mit zeitverzögerter Rückkopplung arbeiten. Neben deterministischen Steuerungsmechanismen ist die Motorik des Menschen ausserdem von Fluktuationen auf zwei Ebenen gekennzeichnet, der kognitiven Kontrollebene und der Ebene der motorischen Systeme. Daher ist die Koordination von Bewegungen das Ergebnis von Wechselwirkungen zwischen nichtlinearen, zeitverzögerten Kontrollprozessen und stochastischen Fluktuationen.
The nonlinear interaction of waves excited by the modified two-stream instability (Farley-Buneman instability) is considered. It is found that, during the linear stage of wave growth, the enhanced pressure of the high-frequency part of the waves locally generates a ponderomotive force. This force acts on the plasma particles and redistributes them. Thus an additional electrostatic polarization field occurs, which influences the low-frequency part of the waves. Then, the low-frequency waves also cause a redistribution of the high-frequency waves. In the paper, a self-consistent system of equations is obtained, which describes the nonlinear interaction of the waves. It is shown that the considered mechanism of wave interaction causes a nonlinear stabilization of the high-frequency waves’ growth and a formation of local density structures of the charged particles. The density modifications of the charged particles during the non-linear stage of wave growth and the possible interval of aspect angles of the high-frequency waves are estimated.
We have numerically studied the bifurcations and transition to chaos in a two-dimensional fluid for varying values of the Reynolds number. These investigations have been motivated by experiments in fluids, where an array of vortices was driven by an electromotive force. In these experiments, successive changes leading to a complex motion of the vortices, due to increased forcing, have been explored [Tabeling, Perrin, and Fauve, J. Fluid Mech. 213, 511 (1990)]. We model this experiment by means of two-dimensional Navier-Stokes equations with a special external forcing, driving a linear chain of eight counter-rotating vortices, imposing stress-free boundary conditions in the vertical direction and periodic boundary conditions in the horizontal direction. As the strength of the forcing or the Reynolds number is raised, the original stationary vortex array becomes unstable and a complex sequence of bifurcations is observed. Several steady states and periodic branches and a period doubling cascade appear on the route to chaos. For increasing values of the Reynolds number, shear flow develops, for which the spatial scale is large compared to the scale of the forcing. Furthermore, we have investigated the influence of the aspect ratio of the container as well as the effect of no-slip boundary conditions at the top and bottom, on the bifurcation scenario.
This paper deals with the electrical conductivity problem in geophysics. It is formulated as an elliptic boundary value problem of second order for a large class of bounded and unbounded domains. A special boundary condition, the so called "Complete Electrode Model", is used. Poincaré inequalities are formulated and proved in the context of weighted Sobolev spaces, leading to existence and uniqueness statements for the boundary value problem. In addition, a parameter-to-solution operator arising from the inverse conductivity problem in medicine (EIT) and geophysics is investigated mathematically and is shown to be smooth and analytic.
The determination of the atmospheric aerosol size distribution is an inverse illposed problem. The shape and the material composition of the air-carried particles are two substantial model parameters. Present evaluation algorithms only used an approximation with spherical homogeneous particles. In this paper we propose a new numerically efficient recursive algorithm for inhomogeneous multilayered coated and absorbing particles. Numerical results of real existing particles show that the influence of the two parameters on the model is very important and therefore cannot be ignored.
Contents: 1 Introduction 2 Formation and destruction of sporadic E-layers 3 Temporal variations of parameters of sporadic E-layers during earthquake preparation 3.1 Temporal variations of fbEs with time-scales of a few hours 3.2 Study of fbEs variations with characteristic time-scales of 0.5-3 hours 3.3 Variations of the parameters of sporadic E-layers with characteristic time-scales of 15-45 minutes 3.4 Sporadic E-layer variations with characteristic time-scales of 2-15 minutes 4 On the spatial scales of sporadic E-layer disturbances related to seismic activity 5 Complex experimental researches of the ionosphere, electromagnetic noise and the geomagnetic field 5.1 Ionospheric and electromagnetic phenomena of the Kayraccum earthquake in 1985 5.2 Comparison of anomalies with characteristic time-scales of 2-3 hours for ionospheric E- and F-layers, and temporal behaviour of electromagnetic noise emission intensity 5.3 Night airglow emissions in the E-region before earthquakes and sporadic E-layer variations 6 Physical models of lithosphere-ionosphere links 6.1 Lithosphere-ionosphere links due to AGW 6.2 Electromagnetic models for the lithosphere-ionosphere coupling 6.3 Sporadic E-layers as current generators 7 Discussion and conclusion
In single photon emission computed tomography (SPECT) one is interested in reconstructing the activity distribution f of some radiopharmaceutical. The data gathered suffer from attenuation due to the tissue density µ. Each imaged slice incorporates noisy sample values of the nonlinear attenuated Radon transform (formular at this place in the original abstract) Traditional theory for SPECT reconstruction treats µ as a known parameter. In practical applications, however, µ is not known, but either crudely estimated, determined in costly additional measurements or plainly neglected. We demonstrate that an approximation of both f and µ from SPECT data alone is feasible, leading to quantitatively more accurate SPECT images. The result is based on nonlinear Tikhonov regularization techniques for parameter estimation problems in differential equations combined with Gauss-Newton-CG minimization.
The aim of this paper is to describe an efficient strategy for descritizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips-regularization χ^δ α = (a * a + α I)^-1 A * y ^δ with a finite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing A n compared with standard methods.
The stability of the quiescent ground state of an incompressible, viscous and electrically conducting fluid sheet, bounded by stress-free parallel planes and driven by an external electric field tangential to the boundaries, is studied numerically. The electrical conductivity varies as cosh–2(x1/a), where x1 is the cross-sheet coordinate and a is the half width of a current layer centered about the midplane of the sheet. For a <~ 0.4L, where L is the distance between the boundary planes, the ground state is unstable to disturbances whose wavelengths parallel to the sheet lie between lower and upper bounds depending on the value of a and on the Hartmann number. Asymmetry of the configuration with respect to the midplane of the sheet, modelled by the addition of an externally imposed constant magnetic field to a symmetric equilibrium field, acts as a stabilizing factor.
The bifurcations in a three-dimensional incompressible, electrically conducting fluid with an external forcing of the Roberts type have been studied numerically. The corresponding flow can serve as a model for the convection in the outer core of the Earth and is realized in an ongoing laboratory experiment aimed at demonstrating a dynamo effect. The symmetry group of the problem has been determined and special attention has been paid to symmetry breaking by the bifurcations. The nonmagnetic, steady Roberts flow loses stability to a steady magnetic state, which in turn is subject to secondary bifurcations. The secondary solution branches have been traced until they end up in chaotic states.
The dynamics of tail-like current sheets under the influence of small-scale plasma turbulence
(1999)
A 2D-magnetohydrodynamic model of current-sheet dynamics caused by anomalous electrical resistivity as result of small-scale plasma turbulence is proposed. The anomalous resistivity is assumed to be proportional to the square of the gradient of the magnetic pressure as may be valid for instance in the case of lower-hybrid-drift turbulence. The initial resistivity pulse is given. Then the temporal and spatial evolution of the magnetic and electric fields, plasma density, pressure, convection and resistivity are considered. The motion of the induced electric field is discussed as indicator of the plasma disturbances. The obtained results found using much improved numerical methods show a magnetic field evolution with x-line formation and plasma acceleration. Besides, in the current sheet, three types of magnetohydrodynamic waves occur, fast magnetoacoustic waves of compression and rarefaction as well as slow magnetoacoustic waves.
Die Arbeit stellt neu entwickelte Röntgenbeugungsmethoden vor, mit deren Hilfe der Verzerrungszustand des Kristallgitters von Halbleiter-Wafern und -Bauteilen im Detail charakterisiert werden kann. Hierzu werden die aussergewöhnlichen Eigenschaften der an modernen Synchrotrons wie der ESRF (Grenoble) verfügbaren Röntgenstrahlung genutzt. Im ersten Teil der Arbeit werden Röntgen-Diffraktometrie und -Topographie zu einer Untersuchungsmethode kombiniert, mit der die makroskopische Krümmung von Halbleiter-Wafern ebenso wie ihre mikroskopische Defektstruktur abgebildet werden kann. Der zweite Teil ist der Untersuchung von epitaktisch gewachsenen und geätzten Oberflächengittern mit Abmessungen im Submikrometer-Bereich gewidmet. Die unterschiedlichen Gitterkonstanten der beteiligten Halbleitermaterialien führen zu einem inhomogenen Verzerrungsfeld in der Probe, das sich im Röntgenbild durch eine charakteristische Verformung des Beugungsmusters in der Umgebung der Bragg-Reflexe äussert. Die Analyse der experimentell gemessenen Beugungsmuster geschieht mit Hilfe eines neu entwickelten Simulationsverfahrens, das Elastizitätstheorie und eine semi-kinematische Röntgenbeugungstheorie miteinander verbindet. Durch quantitativen Vergleich der Simulationsergebnisse mit den Messdaten kann auf den genauen Verlauf des Verzerrungsfeldes in den Proben zurückgeschlossen werden. Dieses Verfahren wird erfolgreich auf verschiedene Halbleiter-Probensysteme angewendet, und schliesslich auch auf die Untersuchung von akustischen Oberflächenwellen in Halbleiterkristallen übertragen.
Diese Arbeit beschäftigt sich mit der Annahme, dass den Erdbeben ein selbstorganisiert kritischer Zustand der Erdkruste zugrunde liegt. Mit Hilfe einer Erweiterung bisheriger Modelle wird gezeigt, dass ein solcher Zustand nicht nur für die Grössenverteilung der Erdbeben (Gutenberg-Richter Gesetz), sondern auch für das beobachtete raumzeitliche Auftreten, z.B. für das Omori-Gesetz für Nachbebenserien, verantwortlich sein kann. Desweiteren wird die Frage nach der Vorhersagbarkeit grosser Erdbeben in solchen Modellsimulationen untersucht.
Die vorliegende Arbeit beschäftigt sich mit der Charakterisierung von Seismizität anhand von Erdbebenkatalogen. Es werden neue Verfahren der Datenanalyse entwickelt, die Aufschluss darüber geben sollen, ob der seismischen Dynamik ein stochastischer oder ein deterministischer Prozess zugrunde liegt und was daraus für die Vorhersagbarkeit starker Erdbeben folgt. Es wird gezeigt, dass seismisch aktive Regionen häufig durch nichtlinearen Determinismus gekennzeichent sind. Dies schließt zumindest die Möglichkeit einer Kurzzeitvorhersage ein. Das Auftreten seismischer Ruhe wird häufig als Vorläuferphaenomen für starke Erdbeben gedeutet. Es wird eine neue Methode präsentiert, die eine systematische raumzeitliche Kartierung seismischer Ruhephasen ermöglicht. Die statistische Signifikanz wird mit Hilfe des Konzeptes der Ersatzdaten bestimmt. Als Resultat erhält man deutliche Korrelationen zwischen seismischen Ruheperioden und starken Erdbeben. Gleichwohl ist die Signifikanz dafür nicht hoch genug, um eine Vorhersage im Sinne einer Aussage über den Ort, die Zeit und die Stärke eines zu erwartenden Hauptbebens zu ermöglichen.
We investigate numerically the appearance of heteroclinic behavior in a three-dimensional, buoyancy-driven fluid layer with stress-free top and bottom boundaries, a square horizontal periodicity with a small aspect ratio, and rotation at low to moderate rates about a vertical axis. The Prandtl number is 6.8. If the rotation is not too slow, the skewed-varicose instability leads from stationary rolls to a stationary mixed-mode solution, which in turn loses stability to a heteroclinic cycle formed by unstable roll states and connections between them. The unstable eigenvectors of these roll states are also of the skewed-varicose or mixed-mode type and in some parameter regions skewed-varicose like shearing oscillations as well as square patterns are involved in the cycle. Always present weak noise leads to irregular horizontal translations of the convection pattern and makes the dynamics chaotic, which is verified by calculating Lyapunov exponents. In the nonrotating case, the primary rolls lose, depending on the aspect ratio, stability to traveling waves or a stationary square pattern. We also study the symmetries of the solutions at the intermittent fixed points in the heteroclinic cycle.
A numerical bifurcation analysis of the electrically driven plane sheet pinch is presented. The electrical conductivity varies across the sheet such as to allow instability of the quiescent basic state at some critical Hartmann number. The most unstable perturbation is the two-dimensional tearing mode. Restricting the whole problem to two spatial dimensions, this mode is followed up to a time-asymptotic steady state, which proves to be sensitive to three-dimensional perturbations even close to the point where the primary instability sets in. A comprehensive three-dimensional stability analysis of the two-dimensional steady tearing-mode state is performed by varying parameters of the sheet pinch. The instability with respect to three-dimensional perturbations is suppressed by a sufficiently strong magnetic field in the invariant direction of the equilibrium. For a special choice of the system parameters, the unstably perturbed state is followed up in its nonlinear evolution and is found to approach a three-dimensional steady state.
Polymers at membranes
(2000)
The surface of biological cells consists of a lipid membrane and a large amount of various proteins and polymers, which are embedded in the membrane or attached to it. We investigate how membranes are influenced by polymers, which are anchored to the membrane by one end. The entropic pressure exerted by the polymer induces a curvature, which bends the membrane away from the polymer. The resulting membrane shape profile is a cone in the vicinity of the anchor segment and a catenoid far away from it. The perturbative calculations are confirmed by Monte-Carlo simulations. An additional attractive interaction between polymer and membrane reduces the entropically induced curvature. In the limit of strong adsorption, the polymer is localized directly on the membrane surface and does not induce any pressure, i.e. the membrane curvature vanishes. If the polymer is not anchored directly on the membrane surface, but in a non-vanishing anchoring distance, the membrane bends towards the polymer for strong adsorption. In the last part of the thesis, we study membranes under the influence of non-anchored polymers in solution. In the limit of pure steric interactions between the membrane and free polymers, the membrane curves towards the polymers (in contrast to the case of anchored polymers). In the limit of strong adsorption the membrane bends away from the polymers.
In dieser Arbeit wurden zwei Themenbereiche bearbeitet: 1. Ellipsometrie an Adsorpionsschichten niedermolekularer Tenside an der Wasser/Luft-Grenzfläche (Ellipsometrie ist geeignet, adsorbierte Mengen von nicht- und zwitterionischen Tensiden zu messen, bei ionischen werden zusätzlich die Gegenionen mit erfaßt; Ellipsometrie mißt sich ändernde Gegenionenverteilung). 2. Ellipsometrische Untersuchung von endadsorbierten Polymerbürsten an der Wasser/Öl-Grenzfläche (Ellipsometrie ist nicht in der Lage, verschiedene Segmentkonzentrationsprofile innerhalb der Bürste aufzulösen, ist aber sehr wohl geeignet, Skalengesetze für Dicken und Drücke in Abhängigkeit von Ankerdichte und Kettenlänge der Polymere zu überprüfen; für in Heptan gequollene Poly-isobuten-Bürsten konnte gezeigt werden, daß sie sich entsprechend den theoretischen Vorhersagen für Bürsten in einem theta-Lösungsmittel verhalten)
A numerical MHD model is developed to investigate acceleration and heating of both thermal and auroral plasma. This is done for magnetospheric flux tubes in which intensive field aligned currents flow. To give each of these tubes, the empirical Tsyganenko model of the magnetospheric field is used. The parameters of the background plasma outside the flux tube as well as the strength of the electric field of magnetospheric convection are given. Performing the numerical calculations, the distributions of the plasma densities, velocities, temperatures, parallel electric field and current, and of the coefficients of thermal conductivity are obtained in a self-consistent way. It is found that EIC turbulence develops effectively in the thermal plasma. The parallel electric field develops under the action of the anomalous resistivity. This electric field accelerates both the thermal and the auroral plasma. The thermal turbulent plasma is also subjected to an intensive heating. The increase of the plasma of the Earth's ionosphere. Besides, studying the growth and dispersion properties of oblique ion cyclotron waves excited in a drifting magnetized plasma, it is shown that under non-stationary conditions such waves may reveal the properties of bursts of polarized transverse electromagnetic waves at frequencies near the patron gyrofrequency.
Basing on recent solar models, the excitation of ion-acoustic turbulence in the weaklycollisional, fully and partially-ionized regions of the solar atmosphere is investigated. Within the frame of hydrodynamics, conditions are found under which the heating of the plasma by ion-acoustic type waves is more effective than the Joule heating. Taking into account wave and Joule heating effects, a nonlinear differential equation is derived, which describes the evolution of nonlinear ion-acoustic waves in the collisional plasma.
In this paper an analysis of the excitation conditions of mirror waves is done, which propagate parallel to an external magnetic field. There are found analytical expressions for the dispersion relations of the waves in case of different plasma conditions. These relations may be used in future to develop the nonlinear theory of mirror waves. In comparison with former analytical works, in the study the inuence of the magnetic field and nite temperatures of the ions parallel to the magnetic field are taken into account. Application is done for the earth's magnetosheath.
In this thesis we use the gravitational lensing effect as a tool to tackle two rather different cosmological topics: the nature of the dark matter in galaxy halos, and the rotation of the universe. Firstly, we study the microlensing effect in the gravitational lens systems Q0957+561 and Q2237+0305. In these systems the light from the quasar shines directly through the lensing galaxy. Due to the relative motion of the quasar, the lensing galaxy, and the observer compact objects in the galaxy or galaxy halo cause brightness fluctuations of the light from the background quasar. We compare light curve data from a monitoring program of the double quasar Q0957+561 at the 3.5m telescope at Apache Point Observatory from 1995 to 1998 (Colley, Kundic & Turner 2000) with numerical simulations to test whether the halo of the lensing galaxy consists of massive compact objects (MACHOs). This test was first proposed by Gott (1981). We can exclude MACHO masses from 10^-6 M_sun up to 10^-2 M_sun for quasar sizes of less than 3x10^14 h_60^-0.5 cm if the MACHOs make up at least 50% of the dark halo. Secondly, we present new light curve data for the gravitationally lensed quadruple quasar Q2237+0305 taken at the 3.5m telescope at Apache Point Observatory from June 1995 to January 1998. Although the images were taken under variable, often poor seeing conditions and with coarse pixel sampling, photometry is possible for the two brighter quasar images A and B with the help from HST observations. We find independent evidence for a brightness peak in image A of 0.4 to 0.5 mag with a duration of at least 100 days, which indicates that microlensing has taken place in the lensing galaxy. Finally, we use the weak gravitational lensing effect to put limits on a class of Goedel-type rotating cosmologies described by Korotky & Obukhov (1996). In weak lensing studies the shapes of thousands of background galaxies are measured and averaged to reveal coherent gravitational distortions of the galaxy shapes by foreground matter distributions, or by the large-scale structure of space-time itself. We calculate the predicted shear as a function of redshift in Goedel-type rotating cosmologies and compare this to the upper limit on cosmic shear gamma_limit of approximately 0.04 from weak lensing studies. We find that Goedel-type models cannot have larger rotations omega than H_0=6.1x10^-11 h_60/year if this shear limit is valid for the whole sky.
We numerically investigate nonlinear asymmetric square patterns in a horizontal convection layer with up-down reflection symmetry. As a novel feature we find the patterns to appear via the skewed varicose instability of rolls. The time-independent nonlinear state is generated by two unstable checkerboard (symmetric square) patterns and their nonlinear interaction. As the bouyancy forces increase, the interacting modes give rise to bifurcations leading to a periodic alternation between a nonequilateral hexagonal pattern and the square pattern or to different kinds of standing oscillations.
Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook
Populärwissenschaftlicher Abstract: Bislang gibt es in der beobachtenden optischen Astronomie zwei verschiedene Herangehensweisen: Einerseits werden Objekte durch Kameras abbildend erfaßt, andererseits werden durch die wellenlängenabhängige Zerlegung ihres Lichtes Spektren gewonnen. Das Integral - Field - Verfahren ist eine relativ neue Technik, welche die genannten Beobachtungsmethoden vereint. Das Objektbild im Teleskopfokus wird in räumlich zerlegt und jedes Ortselement einem gemeinsamen Spektrografen zugeführt. Hierdurch wird das Objekt nicht nur zweidimensional räumlich erfaßt, sondern zusätzlich die spektrale Kompenente als dritte Dimension erhalten, weswegen das Verfahren auch als 3D-Methode bezeichnet wird. Anschaulich kann man sich das Datenresultat als eine Abbildung vorstellen, in der jeder einzelne Bildpunkt nicht mehr nur einen Intensitätswert enthält, sondern gleich ein ganzes Spektrum. Diese Technik ermöglicht es, ausgedehnte Objekte im Unterschied zu gängigen Spaltspektrografen komplett zu erfassen. Die besondere Stärke der Methode ist die Möglichkeit, die Hintergrundkontamination der unmittelbaren Umgebung des Objektes zu erfassen und in der Auswertung zu berücksichtigen. Durch diese Fähigkeit erscheint die 3D-Methode prädestiniert für den durch moderne Großteleskope erschlossenen Bereich der extragalaktischen Stellarastronomie. Die detaillierte Untersuchung aufgelöster stellare Populationen in nahegelegenen Galaxien ist erst seit kurzer Zeit dank der Fortschritte mit modernen Grossteleskopen und fortschrittlicher Instrumentierung möglich geworden. Wegen der Bedeutung für die Entstehung und Evolution von Galaxien werden diese Arbeiten zukünftig weiter an Bedeutung gewinnen. In der vorliegenden Arbeit wurde die Integral-Field-Spektroskopie an zwei planetarischen Nebeln in der nächstgelegenen großen Spiralgalaxie M31 (NGC 224) getestet, deren Helligkeiten und Koordinaten aus einer Durchmusterung vorlagen. Hierzu wurden Beobachtungen mit dem MPFS-Instrument am russischen 6m - Teleskop in Selentschuk/Kaukasus sowie mit INTEGRAL/WYFFOS am englischen William-Herschel-Teleskop auf La Palma gewonnen. Ein überraschendes Ergebnis war, daß eins der beiden Objekte falsch klassifiziert wurde. Sowohl die meßbare räumliche Ausdehnung des Objektes als auch das spektrale Erscheinungsbild schlossen die Identität mit einem planetarischen Nebel aus. Mit hoher Wahrscheinlichkeit handelt es sich um einen Supernovaüberrest, zumal im Rahmen der Fehler an gleicher Stelle eine vom Röntgensatelliten ROSAT detektierte Röntgenquelle liegt. Die in diesem Projekt verwendeten Integral-Field-Instrumente wiesen zwei verschiedene Bauweisen auf, die sich miteinander vergleichen ließen. Ein Hauptkritikpunkt der verwendeten Instrumente war ihre geringe Lichtausbeute. Die gesammelten Erfahrung fanden Eingang in das Konzept des derzeit in Potsdam in der Fertigung befindlichen 3D-Instruments PMAS (Potsdamer Multi - Apertur - Spektrophotometer), welcher zunächst für das 3.5m-Teleskop des Calar - Alto - Observatoriums in Südspanien vorgesehen ist. Um die Effizienz dieses Instrumentes zu verbessern, wurde in dieser Arbeit die Kopplung der zum Bildrasterung verwendeten Optik zu den Lichtleitfasern im Labor untersucht. Die Untersuchungen zur Maximierung von Lichtausbeute und Stabilität zeigen, daß sich die Effizienz durch Auswahl einer geeigneten Koppelmethode um etwa 20 Prozent steigern lässt.
Nonlinear multistable systems under the influence of noise exhibit a plethora of interesting dynamical properties. A medium noise level causes hopping between the metastable states. This attractorhopping process is characterized through laminar motion in the vicinity of the attractors and erratic motion taking place on chaotic saddles, which are embedded in the fractal basin boundary. This leads to noise-induced chaos. The investigation of the dissipative standard map showed the phenomenon of preference of attractors through the noise. It means, that some attractors get a larger probability of occurrence than in the noisefree system. For a certain noise level this prefernce achieves a maximum. Other attractors are occur less often. For sufficiently high noise they are completely extinguished. The complexity of the hopping process is examined for a model of two coupled logistic maps employing symbolic dynamics. With the variation of a parameter the topological entropy, which is used together with the Shannon entropy as a measure of complexity, rises sharply at a certain value. This increase is explained by a novel saddle merging bifurcation, which is mediated by a snapback repellor. Scaling laws of the average time spend on one of the formerly disconnected parts and of the fractal dimension of the connected saddle describe this bifurcation in more detail. If a chaotic saddle is embedded in the open neighborhood of the basin of attraction of a metastable state, the required escape energy is lowered. This enhancement of noise-induced escape is demonstrated for the Ikeda map, which models a laser system with time-delayed feedback. The result is gained using the theory of quasipotentials. This effect, as well as the two scaling laws for the saddle merging bifurcation, are of experimental relevance.
One of the rules-of-thumb of colloid and surface physics is that most surfaces are charged when in contact with a solvent, usually water. This is the case, for instance, in charge-stabilized colloidal suspensions, where the surface of the colloidal particles are charged (usually with a charge of hundreds to thousands of e, the elementary charge), monolayers of ionic surfactants sitting at an air-water interface (where the water-loving head groups become charged by releasing counterions), or bilayers containing charged phospholipids (as cell membranes). In this work, we look at some model-systems that, although being a simplified version of reality, are expected to capture some of the physical properties of real charged systems (colloids and electrolytes). We initially study the simple double layer, composed by a charged wall in the presence of its counterions. The charges at the wall are smeared out and the dielectric constant is the same everywhere. The Poisson-Boltzmann (PB) approach gives asymptotically exact counterion density profiles around charged objects in the weak-coupling limit of systems with low-valent counterions, surfaces with low charge density and high temperature (or small Bjerrum length). Using Monte Carlo simulations, we obtain the profiles around the charged wall and compare it with both Poisson-Boltzmann (in the low coupling limit) and the novel strong coupling (SC) theory in the opposite limit of high couplings. In the latter limit, the simulations show that the SC leads in fact to asymptotically correct density profiles. We also compare the Monte Carlo data with previously calculated corrections to the Poisson-Boltzmann theory. We also discuss in detail the methods used to perform the computer simulations. After studying the simple double layer in detail, we introduce a dielectric jump at the charged wall and investigate its effect on the counterion density distribution. As we will show, the Poisson-Boltzmann description of the double layer remains a good approximation at low coupling values, while the strong coupling theory is shown to lead to the correct density profiles close to the wall (and at all couplings). For very large couplings, only systems where the difference between the dielectric constants of the wall and of the solvent is small are shown to be well described by SC. Another experimentally relevant modification to the simple double layer is to make the charges at the plane discrete. The counterions are still assumed to be point-like, but we constraint the distance of approach between ions in the plane and counterions to a minimum distance D. The ratio between D and the distance between neighboring ions in the plane is, as we will see, one of the important quantities in determining the influence of the discrete nature of the charges at the wall over the density profiles. Another parameter that plays an important role, as in the previous case, is the coupling as we will demonstrate, systems with higher coupling are more subject to discretization effects than systems with low coupling parameter. After studying the isolated double layer, we look at the interaction between two double layers. The system is composed by two equally charged walls at distance d, with the counterions confined between them. The charge at the walls is smeared out and the dielectric constant is the same everywhere. Using Monte-Carlo simulations we obtain the inter-plate pressure in the global parameter space, and the pressure is shown to be negative (attraction) at certain conditions. The simulations also show that the equilibrium plate separation (where the pressure changes from attractive to repulsive) exhibits a novel unbinding transition. We compare the Monte Carlo results with the strong-coupling theory, which is shown to describe well the bound states of systems with moderate and high couplings. The regime where the two walls are very close to each other is also shown to be well described by the SC theory. Finally, Using a field-theoretic approach, we derive the exact low-density ("virial") expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). The free energy obtained is valid for systems where the diameters d_+ and d_- and the charge valences q_+ and q_- of positive and negative ions are unconstrained, i.e., the same expression can be used to treat dilute salt solutions (where typically d_+ ~ d_- and q_+ ~ q_-) as well as colloidal suspensions (where the difference in size and valence between macroions and counterions can be very large). We also discuss some applications of our results.
Chemisch dotiertes Polypyrrol gilt als Modellsubstanz für leitfähige Polymere mit nichtdegeneriertem Grundzustand. Das elektrische Transportverhalten in dotiertem Polypyrrol wird durch lokalisierte Ladungsträger, Bipolaronen und Polaronen, bestimmt. Es besteht dabei eine enge gegenseitige Wechselwirkung zwischen der Struktur der Polymerkette und den Eigenschaften der Ladungsträger. Die in dieser Arbeit vorgestellte Kombination von Hochdruckmethodik und optischer Spektroskopie vertieft das Verständnis der Beziehung zwischen der molekularen und supramolekularen Struktur und den elektronischen und optischen Eigenschaften. Durch spezifische Synthesemethoden lassen sich unterschiedliche Strukturen in der polymeren Probe induzieren, die sich durch den Anteil an hochgeordneten Polymerketten unterscheiden. Die gezielte Veränderung dieser Strukturen durch Druckexperimente ermöglicht das Studium des Einflusses der Synthesemethoden auf die Ladungsträgereigenschaften. Für diese Studien wurden herkömmlich synthetisierte Polypyrrol-Filme und Filme, die sich aus Polypyrrol-Nanoröhren zusammensetzen (Synthese in Kernspur-membranen, "Template-Synthese") bei ansonsten gleichen Syntheseparametern untersucht. Raman- und Infrarotspektroskopie sowie UV-Vis-NIR-Absorptionsspektroskopie, die jeweils für die Hochdruckmethodik adaptiert wurden, dienten der Charakterisierung der Proben. Zusätzlich wurden temperatur- und druckabhängige Messungen des elektrischen Widerstands an den Template-Proben durchgeführt. Die Morphologie template-synthetisierter Polypyrrol-Nanoröhren und die filmbildenden Eigenschaften sowie der mögliche Aufbau von Schichtarchitekturen wurden mit transmissions- und rasterelektronenmikroskopischen Techniken untersucht. Die aus den Hochdruckexperimenten gewonnenen Daten werden in der Arbeit im Hinblick auf die Stabilität der Ladungsträger interpretiert. Im Ergebnis bewirkt die Druckerhöhung eine Dissoziation der Bipolaronen in den untersuchten Proben. Das Ladungsträger-gleichgewicht verschiebt sich dadurch mit steigendem Druck zu Zuständen mit höherem Anteil an polaronischen Ladungsträgern. Die Template-Synthese bewirkt gegenüber herkömmlich synthetisierten Proben einen höheren Anteil an Polaronen bereits bei Normaldruck, und eine Lage des Systems näher bei einem Isolator-Metall-Übergang. Die Dissoziationsrate der Bipolaronen ist für Template- und herkömmlich synthetisierte Proben vergleichbar groß und unabhängig vom Initialzustand nach der Synthese. Dieses Verhalten der Ladungsträger wird weitergehend im Rahmen eines Modells untersucht, bei dem der Einfluß benachbarter Polymerketten und der Dotandionen berücksichtigt wird. Dementsprechend können sich die Wellenfunktionen der Ladungsträger unter bestimmten Bedingungen auch auf benachbarte Ketten erstrecken (transversale Polaronen bzw. Bipolaronen). Eine solche Ausdehnung der Wellenfunktionen unter Mitwirkung der Dotandionen wurde in den untersuchten Proben nicht festgestellt. Die Wellenfunktionen der Ladungsträger besitzen demnach hauptsächlich Komponenten entlang der Polymerkette (longitudinale Polaronen bzw. Bipolaronen). Aus der Änderungsrate druckabhängiger spektraler Charakteristiken lassen sich Aussagen über den Ordnungszustand der Probe ableiten. Diese auf experimentellem Wege gefundenen Ergebnisse liefern somit Hinweise für die bisher kontrovers diskutierte Koexistenz der beiden Ladungsträgerarten Polaronen und Bipolaronen und die Größe ihrer jeweiligen Bindungsenergien. Druckerhöhung und Template-Synthese bewirken analoge Änderungen der Polymerstruktur. Sowohl höherer Druck wie auch die Template-Synthese lassen sich mit einem höheren Ordnungsgrad in den Template-Proben korrelieren. Der Ladungstransport in den Proben kann durch ein Mott Variable Range Hopping-Modell mit druckabhängiger charakteristischer Dimension beschrieben werden. Die Erhöhung des Drucks bewirkt einen Anstieg der Dimension, eine bessere Überlappung der Wellenfunktionen der Ladungsträger und eine Vergrößerung der Lokalisierungslänge der Ladungsträger. Die druckinduzierte Dissoziation der Bipolaronen beeinflußt den Ladungstransport zusätzlich durch Erhöhung der Anzahl unabhängiger Ladungsträger und verbessert diesen aufgrund stärkerer Überlappung der Wellenfunktionen. Template-Proben niedriger Synthesetemperatur zeigen bei Normaldruck eine höhere Dimension des Mott Variable Range Hoppings und eine größere Lokalisierungslänge gegenüber bei Raumtemperatur synthetisierten Proben. Kürzere Synthesezeiten bewirken einen Anstieg der Dimension bei Normaldruck und eine Verschiebung des Dimensionscrossovers zu niedrigeren Temperaturen. Template-Proben kurzer Synthesezeit zeigen geringere druckinduzierte Änderungen als solche mit langer Synthesezeit. Es wurde ein kontinuierliches Ordnungsmodell der Polypyrrol-Nanoröhren entwickelt, das dieses Verhalten beschreibt. Die Morphologie und die mechanischen Eigenschaften der Nanoröhren werden durch spezifische Syntheseparameter, wie Temperatur und Dauer, beeinflußt und können mit Transmissions- und Rasterelektronenmikroskopie beobachtet werden. Die filmbildenden Eigenschaften der Röhren hängen stark von diesen mechanischen Eigenschaften ab. Die Struktur der Filme kann dabei von einer unregelmäßigen Anordnung der Röhren bis zu nahezu parallel ausgerichteten Röhren variieren. Es wurden Möglichkeiten untersucht, die Röhren in den Filmen zu orientieren und aus diesen Filmen durch Schichtung makroskopische Architekturen mit einem hohen Grad an orientierten Röhren aufzubauen. Solche Architekturen können für verschiedene Anwendungen, z.B. in elektronischen Bauteilen oder mikroskopischen Bioreaktoren, von Interesse sein.
Line driven winds are accelerated by the momentum transfer from photons to a plasma, by absorption and scattering in numerous spectral lines. Line driving is most efficient for ultraviolet radiation, and at plasma temperatures from 10^4 K to 10^5 K. Astronomical objects which show line driven winds include stars of spectral type O, B, and A, Wolf-Rayet stars, and accretion disks over a wide range of scales, from disks in young stellar objects and cataclysmic variables to quasar disks. It is not yet possible to solve the full wind problem numerically, and treat the combined hydrodynamics, radiative transfer, and statistical equilibrium of these flows. The emphasis in the present writing is on wind hydrodynamics, with severe simplifications in the other two areas. I consider three topics in some detail, for reasons of personal involvement. 1. Wind instability, as caused by Doppler de-shadowing of gas parcels. The instability causes the wind gas to be compressed into dense shells enclosed by strong shocks. Fast clouds occur in the space between shells, and collide with the latter. This leads to X-ray flashes which may explain the observed X-ray emission from hot stars. 2. Wind runaway, as caused by a new type of radiative waves. The runaway may explain why observed line driven winds adopt fast, critical solutions instead of shallow (or breeze) solutions. Under certain conditions the wind settles on overloaded solutions, which show a broad deceleration region and kinks in their velocity law. 3. Magnetized winds, as launched from accretion disks around stars or in active galactic nuclei. Line driving is assisted by centrifugal forces along co-rotating poloidal magnetic field lines, and by Lorentz forces due to toroidal field gradients. A vortex sheet starting at the inner disk rim can lead to highly enhanced mass loss rates.
One of the classical ways to describe the dynamics of nonlinear systems is to analyze theur Fourier spectra. For periodic and quasiperiodic processes the Fourier spectrum consists purely of discrete delta-functions. On the contrary, the spectrum of a chaotic motion is marked by the presence of the continuous component. In this work, we describe the peculiar, neither regular nor completely chaotic state with so called singular-continuous power spectrum. Our investigations concern various cases from most different fields, where one meets the singular continuous (fractal) spectra. The examples include both the physical processes which can be reduced to iterated discrete mappings or even symbolic sequences, and the processes whose description is based on the ordinary or partial differential equations.
Subject of this work is the investigation of generic synchronization phenomena in interacting complex systems. These phenomena are observed, among all, in coupled deterministic chaotic systems. At very weak interactions between individual systems a transition to a weakly coherent behavior of the systems can take place. In coupled continuous time chaotic systems this transition manifests itself with the effect of phase synchronization, in coupled chaotic discrete time systems with the effect of non-vanishing macroscopic mean field. Transition to coherence in a chain of locally coupled oscillators described with phase equations is investigated with respect to the symmetries in the system. It is shown that the reversibility of the system caused by these symmetries results to non-trivial topological properties of trajectories so that the system constructed to be dissipative reveals in a whole parameter range quasi-Hamiltonian features, i.e. the phase volume is conserved on average and Lyapunov exponents come in symmetric pairs. Transition to coherence in an ensemble of globally coupled chaotic maps is described with the loss of stability of the disordered state. The method is to break the self-consistensy of the macroscopic field and to characterize the ensemble in analogy to an amplifier circuit with feedback with a complex linear transfer function. This theory is then generalized for several cases of theoretic interest.
Subject of this work is the investigation of universal scaling laws which are observed in coupled chaotic systems. Progress is made by replacing the chaotic fluctuations in the perturbation dynamics by stochastic processes. First, a continuous-time stochastic model for weakly coupled chaotic systems is introduced to study the scaling of the Lyapunov exponents with the coupling strength (coupling sensitivity of chaos). By means of the the Fokker-Planck equation scaling relations are derived, which are confirmed by results of numerical simulations. Next, the new effect of avoided crossing of Lyapunov exponents of weakly coupled disordered chaotic systems is described, which is qualitatively similar to the energy level repulsion in quantum systems. Using the scaling relations obtained for the coupling sensitivity of chaos, an asymptotic expression for the distribution function of small spacings between Lyapunov exponents is derived and compared with results of numerical simulations. Finally, the synchronization transition in strongly coupled spatially extended chaotic systems is shown to resemble a continuous phase transition, with the coupling strength and the synchronization error as control and order parameter, respectively. Using results of numerical simulations and theoretical considerations in terms of a multiplicative noise partial differential equation, the universality classes of the observed two types of transition are determined (Kardar-Parisi-Zhang equation with saturating term, directed percolation).
Structural and spectroscopical study of crystals of 1,3,4-oxadiazole derivatives at high pressure
(2002)
In recent years the search for new materials of technological interest has given new impulses to the study of organic compounds. Organic substances possess a great number of advantages such as the possibility to adjust their properties for a given purpose by different chemical and physical techniques in the preparation process. Oxadiazole derivatives are interesting due to their use as material for light emitting diodes (LED) as well as scintillators. The physical properties of a solid depend on its structure. Different structures induce different intra- and intermolecular interactions. An advantageous method to modify the intra- as well as the intermolecular interactions of a given substance is the application of high pressure. Furthermore, using this method the chemical features of the compound are not influenced. We have investigated the influence of high pressure and high temperature on the super-molecular structure of several oxadiazole derivatives in crystalline state. From the results of this investigation an equation of state for these crystals was determined. Furthermore, the spectroscopical features of these materials under high pressure were characterized.
Deep convection is an essential part of the circulation in the North Atlantic Ocean. It influences the northward heat transport achieved by the thermohaline circulation. Understanding its stability and variability is therefore necessary for assessing climatic changes in the area of the North Atlantic. This thesis aims at improving the conceptual understanding of the stability and variability of deep convection. Observational data from the Labrador Sea show phases with and without deep convection. A simple two-box model is fitted to these data. The results suggest that the Labrador Sea has two coexisting stable states, one with regular deep convection and one without deep convection. This bistability arises from a positive salinity feedback that is due to the net freshwater input into the surface layer. The convecting state can easily become unstable if the mean forcing shifts to warmer or less saline conditions. The weather-induced variability of the external forcing is included into the box model by adding a stochastic forcing term. It turns out that deep convection is then switched "on" and "off" frequently. The mean residence time in either state is a measure of its stochastic stability. The stochastic stability depends smoothly on the forcing parameters, in contrast to the deterministic (non-stochastic) stability which may change abruptly. The mean and the variance of the stochastic forcing both have an impact on the frequency of deep convection. For instance, a decline in convection frequency due to a surface freshening may be compensated for by an increased heat flux variability. With a further simplified box model some stochastic stability features are studied analytically. A new effect is described, called wandering monostability: even if deep convection is not a stable state due to changed forcing parameters, the stochastic forcing can still trigger convection events frequently. The analytical expressions explicitly show how wandering monostability and other effects depend on the model parameters. This dependence is always exponential for the mean residence times, but for the probability of long nonconvecting phases it is exponential only if this probability is small. It is to be expected that wandering monostability is relevant in other parts of the climate system as well. All in all, the results demonstrate that the stability of deep convection in the Labrador Sea reacts very sensitively to the forcing. The presence of variability is crucial for understanding this sensitivity. Small changes in the forcing can already significantly lower the frequency of deep convection events, which presumably strongly affects the regional climate. ----Anmerkung: Der Autor ist Träger des durch die Physikalische Gesellschaft zu Berlin vergebenen Carl-Ramsauer-Preises 2003 für die jeweils beste Dissertation der vier Universitäten Freie Universität Berlin, Humboldt-Universität zu Berlin, Technische Universität Berlin und Universität Potsdam.
New polymers and low molecular compounds, suitable for organic light emitting devices and organic electronic applications, have been synthesised in this years in order to obtain electron transport characteristics compatible with requirements for applications in real plastic devices. However, despite of the technological importance and of the relevant progress in devices manufacture, fundamental physical properties of such class of materials are still not enough studied. In particular extensive presence of distributions of localised states inside the band gap has a deep impact on their electronic properties. Such presence of shallow traps as well as the influence of the sample preparation conditions on deep and shallow localised states have not been, until now, systematically explored. The thermal techniques are powerful tools in order to study localised levels in inorganic and organic materials. Thermally stimulated luminescence (TSL), thermally stimulated currents (TSC) and thermally stimulated depolarisation currents (TSDC) allow to deeply look to shallow and deep trap levels as well as they permit to study, in synergy with dielectric spectroscopy (DES), polarisation and depolarisation effects. We studied, by means of numerical simulations, the first and the second order kinetic equations characterised by negligible and strong re-trapping respectively. We included in the equations Gaussian, exponential and quasi-continuous distributions of localised states. The shapes of the theoretical peaks have been investigated by means of systematic variation of the two main parameters of the equations, i. e. the energy trap depth E and the frequency factor a and of the parameters regulating the distributions, in particular for a Gaussian distribution the distribution width s and the integration limits. The theoretical findings have been applied to experimental glow curves. Thin films of polymers and low molecular compounds. Polyphenylquinoxalines, trisphenylquinoxalines and oxadiazoles, studied because of their technological relevance, show complex thermograms, having several levels of localised states and depolarisation peaks. In particular well ordered films of an amphiphilic substituted 2-(p-nitrophenyl)-5-(p-undecylamidophenyl)-1,3,4-oxadiazole (NADPO) are characterised by rich TSL thermograms. A wide region of shallow traps, localised at Em = 4 meV, has been successfully fit by means of a first order kinetic equation having a Gaussian distribution of localised states. Two further peaks, having a different origin, have been characterised. The peaks at Tm = 221.5 K and Tm = 254.2 have activation energy of Em= 0.63 eV and Em = 0.66 eV, frequency factor s = 2.4x1012 s-1 and s = 1.85x1011 s-1, distribution width s = 0.045 eV and s = 0.088 eV respectively. Increasing the number of thermal cycle, a peak, probably connected with structural defects, appears at Tm = 197.7 K. The numerical analysis of this peak was performed by means of a first order equation containing a Gaussian distribution of traps. The activation energy of the trap level is centred at Em = 0.55 eV. The distribution is perfectly symmetric with a quite small width s = 0.028 eV. The frequency factor is s = 1.15 x 1012 s-1, resulting of the same order of magnitude of its neighbour peak at Tm = 221.5 K, having both, probably, the same origin. Furthermore the work demonstrates that the shape of the glow curves is strongly influenced by the excitation temperature and by the thermal cycles. For that reason Gaussian distributions of localised states can be confused with exponential distributions if the previous thermal history of the samples is not adequately considered.
In der nichtlinearen Datenreihenanalyse hat sich seit etwa 10 Jahren eine Monte-Carlo-Testmethode etabliert, die Theiler-surrogatmethode, mit Hilfe derer entschieden werden kann, ob eine Datenreihe nichtlinearen Ursprungs sei. Diese Methode wird kritisiert, modifiziert und verallgemeinert. Das, was Theiler untersuchen will braucht andere Surrogatmethoden, die hier konstruiert werden. Und das, was Theiler untersucht braucht gar keine Monte-Carlo-Methoden. Mit Hilfe des in der Arbeit eingeführten Begriffs des Phasensignals werden Testmöglichkeiten dargelegt und Beziehungen zwischen den nichtlinearen Eigenschaften der Zeitreihe und deren Phasenspektrum erforscht. Das Phasensignal wird aus dem Phasenspektrum der Zeitreihe hergeleitet und registriert außerordentliche Geschehnisse im Zeitbereich sowie Phasenkopplungen im Frequenzbereich. Die gewonnenen Erkenntnisse werden auf das Problem der Polbewegung angewendet. Die Hypothese einer nichtlinearen Beziehung zwischen der atmosphärischen Erregung und der Polbewegung wird untersucht. Eine nichtlineare Behandlung wird nicht für nötig gehalten.
Our every-day experience is connected with different acoustical noise or music. Usually noise plays the role of nuisance in any communication and destroys any order in a system. Similar optical effects are known: strong snowing or raining decreases quality of a vision. In contrast to these situations noisy stimuli can also play a positive constructive role, e.g. a driver can be more concentrated in a presence of quiet music. Transmission processes in neural systems are of especial interest from this point of view: excitation or information will be transmitted only in the case if a signal overcomes a threshold. Dr. Alexei Zaikin from the Potsdam University studies noise-induced phenomena in nonlinear systems from a theoretical point of view. Especially he is interested in the processes, in which noise influences the behaviour of a system twice: if the intensity of noise is over a threshold, it induces some regular structure that will be synchronized with the behaviour of neighbour elements. To obtain such a system with a threshold one needs one more noise source. Dr. Zaikin has analyzed further examples of such doubly stochastic effects and developed a concept of these new phenomena. These theoretical findings are important, because such processes can play a crucial role in neurophysics, technical communication devices and living sciences.
Highly collimated, high velocity streams of hot plasma – the jets – are observed as a general phenomenon being found in a variety of astrophysical objects regarding their size and energy output. Known as jet sources are protostellar objects (T Tauri stars, embedded IR sources), galactic high energy sources ("microquasars"), and active galactic nuclei (extragalactic radio sources and quasars). Within the last two decades our knowledge regarding the processes involved in astro-physical jet formation has condensed in a kind of standard model. This is the scenario of a magnetohydrodynamically accelerated and collimated jet stream launched from the innermost part of an accretion disk close to the central object. Traditionally, the problem of jet formation is divided in two categories. One is the question how to collimate and accelerate an uncollimated low velocity disk wind into a jet. The second is the question how to initiate that outflow from a disk, i.e. how to turn accretion of matter into an ejection as a disk wind. My own work is mainly related to the first question, the collimation and acceleration process. Due to the complexity of both, the physical processes believed to be responsible for the jet launching and also the spatial configuration of the physical components of the jet source, the enigma of jet formation is not yet completely understood. On the theoretical side, there has been a substantial advancement during the last decade from purely station-ary models to time-dependent simulations lead by the vast increase of computer power. Observers, on the other hand, do not yet have the instruments at hand in order to spatially resolve observe the very jet origin. It can be expected that also the next years will yield a substantial improvement on both tracks of astrophysical research. Three-dimensional magnetohydrodynamic simu-lations will improve our understanding regarding the jet-disk interrelation and the time-dependent character of jet formation, the generation of the magnetic field in the jet source, and the interaction of the jet with the ambient medium. Another step will be the combina-tion of radiation transfer computations and magnetohydrodynamic simulations providing a direct link to the observations. At the same time, a new generation of telescopes (VLT, NGST) in combination with new instrumental techniques (IR-interferometry) will lead to a "quantum leap" in jet observation, as the resolution will then be sufficient in order to zoom into the innermost region of jet formation.
Jets are highly collimated flows of matter. They are present in a large variety of astrophysical sources: young stars, stellar mass black holes (microquasars), galaxies with an active nucleus (AGN) and presumably also intense flashes of gamma-rays. In particular, the jets of microquasars, powered by accretion disks, are probably small-scale versions of the outflows from AGN. Beside observations of astrophysical jet sources, also theoretical considerations have shown that magnetic fields play an important role in jet formation, acceleration and collimation. Collimated jets seem to be systematically associated with the presence of an accretion disk around a star or a collapsed object. If the central object is a black hole, the surrounding accretion disk is the only possible location for a magnetic field generation. We are interested in the formation process of highly relativistic jets as observed from microquasars and AGN. We theoretically investigate the jet collimation region, whose physical dimensions are extremely tiny even compared to radio telescopes spatial resolution. Thus, for most of the jet sources, global theoretical models are, at the moment, the only possibility to gain information about the physical processes in the innermost jet region. For the first time, we determine the global two-dimensional field structure of stationary, axisymmetric, relativistic, strongly magnetized (force-free) jets collimating into an asymptotically cylindrical jet (taken as boundary condition) and anchored into a differentially rotating accretion disk. This approach allows for a direct connection between the accretion disk and the asymptotic collimated jet. Therefore, assuming that the foot points of the field lines are rotating with Keplerian speed, we are able to achieve a direct scaling of the jet magnetosphere in terms of the size of the central object. We find a close compatibility between the results of our model and radio observations of the M87 galaxy innermost jet. We also calculate the X-ray emission in the energy range 0.2--10.1\,keV from a microquasar relativistic jet close to its source of 5 solar masses. In order to do it, we apply the jet flow parameters (densities, velocities, temperatures of each volume element along the collimating jet) derived in the literature from the relativistic magnetohydrodynamic equations. We obtain theoretical thermal X-ray spectra of the innermost jet as composition of the spectral contributions of the single volume elements along the jet. Since relativistic effects as Doppler shift and Doppler boosting due to the motion of jets toward us might be important, we investigate how the spectra are affected by them considering different inclinations of the line of sight to the jet axis. Emission lines of highly ionized iron are clearly visible in our spectra, probably also observed in the Galactic microquasars GRS 1915+105 and XTE J1748-288. The Doppler shift of the emission lines is always evident. Due to the chosen geometry of the magnetohydrodynamic jet, the inner X-ray emitting part is not yet collimated. Ergo, depending on the viewing angle, the Doppler boosting does not play a major role in the total spectra. This is the first time that X-ray spectra have been calculated from the numerical solution of a magnetohydrodynamic jet.
Motivated by recent proposals on the experimental detectability of quantum gravity effects, the present thesis investigates assumptions and methods which might be used for the prediction of such effects within the framework of loop quantum gravity. To this end, a scalar field coupled to gravity is considered as a model system. Starting from certain assumptions about the dynamics of the coupled gravity-matter system, a quantum theory for the scalar field is proposed. Then, assuming that the gravitational field is in a semiclassical state, a "QFT on curved space-time limit" of this theory is defined. In contrast to ordinary quantum field theory on curved space-time however, in this limit the theory describes a quantum scalar field propagating on a (classical) random lattice. Then, methods to obtain the low energy limit of such a lattice theory, especially regarding the resulting modified dispersion relations, are discussed and applied to simple model systems. Finally, under certain simplifying assumptions, using the methods developed before as well as a specific class of semiclassical states, corrections to the dispersion relations for the scalar and the electromagnetic field are computed within the framework of loop quantum gravity. These calculations are of preliminary character, as many assumptions enter whose validity remains to be studied more thoroughly. However they exemplify the problems and possibilities of making predictions based on loop quantum gravity that are in principle testable by experiment.
Encounters with neighbours
(2003)
In this work, different aspects and applications of the recurrence plot analysis are presented. First, a comprehensive overview of recurrence plots and their quantification possibilities is given. New measures of complexity are defined by using geometrical structures of recurrence plots. These measures are capable to find chaos-chaos transitions in processes. Furthermore, a bivariate extension to cross recurrence plots is studied. Cross recurrence plots exhibit characteristic structures which can be used for the study of differences between two processes or for the alignment and search for matching sequences of two data series. The selected applications of the introduced techniques to various kind of data demonstrate their ability. Analysis of recurrence plots can be adopted to the specific problem and thus opens a wide field of potential applications. Regarding the quantification of recurrence plots, chaos-chaos transitions can be found in heart rate variability data before the onset of life threatening cardiac arrhythmias. This may be of importance for the therapy of such cardiac arrhythmias. The quantification of recurrence plots allows to study transitions in brain during cognitive experiments on the base of single trials. Traditionally, for the finding of these transitions the averaging of a collection of single trials is needed. Using cross recurrence plots, the existence of an El Niño/Southern Oscillation-like oscillation is traced in northwestern Argentina 34,000 yrs. ago. In further applications to geological data, cross recurrence plots are used for time scale alignment of different borehole data and for dating a geological profile with a reference data set. Additional examples from molecular biology and speech recognition emphasize the suitability of cross recurrence plots.
In this thesis the gravitational lensing effect is used to explore a number of cosmological topics. We determine the time delay in the gravitationally lensed quasar system HE1104-1805 using different techniques. We obtain a time delay Delta_t(A-B) Delta_t(A-B) =-310 +- 20 days (2 sigma errors) between the two components. We also study the double quasar Q0957+561 during a three years monitoring campaign. The fluctuations we find in the difference light curves are completely consistent with noise and no microlensing is needed to explain these fluctuations. Microlensing is also studied in the quadruple quasar Q2237+0305 during the GLITP collaboration (Oct.1999-Feb.2000). We use the absence of a strong microlensing signal to obtain an upper limit of v=600 km/s for the effective transverse velocity of the lens galaxy (considering microlenses with 0.1 solar masses). The distribution of dark matter in galaxy clusters is also studied in the second part of the thesis. In the cluster of galaxies Cl0024+1654 we obtain a mass-to-light ratio of M/L = 200 M_sun/L_sun (within a radius of 3 arcminutes). In the galaxy cluster RBS380 we find a relatively low X-ray luminosity for a massive cluster of L =2*10^(44) erg/s, but a rich distribution of galaxies in the optical band.
This thesis describes the development and application of the impacts module of the ICLIPS model, a global integrated assessment model of climate change. The presentation of the technical aspects of this model component is preceded by a discussion of the sociopolitical context for model-based integrated assessments, which defines important requirements for the specification of the model. Integrated assessment of climate change comprises a broad range of scientific efforts to support the decision-making about objectives and measures for climate policy, whereby many different approaches have been followed to provide policy-relevant information about climate impacts. Major challenges in this context are the large diversity of the relevant spatial and temporal scales, the multifactorial causation of many climate impacts', considerable scientific uncertainties, and the ambiguity associated with unavoidable normative evaluations. A hierarchical framework is presented for structuring climate impact assessments that reflects the evolution of their practice and of the underlying theory. Integrated assessment models of climate change (IAMs) are scientific tools that contain simplified representations of the relevant components of the coupled society-climate system. The major decision-analytical frameworks for IAMs are evaluated according to their ability to address important aspects of the pertinent social decision problem. The guardrail approach is presented as an inverse' framework for climate change decision support, which aims to identify the whole set of policy strategies that are compatible with a set of normatively specified constraints (guardrails'). This approach combines, to a certain degree, the scientific rigour and objectivity typical of predictive approaches with the ability to consider virtually all decision options that is at the core of optimization approaches. The ICLIPS model is described as the first IAM that implements the guardrail approach. The representation of climate impacts is a key concern in any IAM. A review of existing IAMs reveals large differences in the coverage of impact sectors, in the choice of the impact numeraire(s), in the consideration of non-climatic developments, including purposeful adaptation, in the handling of uncertainty, and in the inclusion of singular events. IAMs based on an inverse approach impose specific requirements to the representation of climate impacts. This representation needs to combine a level of detail and reliability that is sufficient for the specification of impact guardrails with the conciseness and efficiency that allows for an exploration of the complete domain of plausible climate protection strategies. Large-scale singular events can often be represented by dynamic reduced-form models. This approach, however, is less appropriate for regular impacts where the determination of policy-relevant results generally needs to consider the heterogeneity of climatic, environmental, and socioeconomic factors at the local or regional scale. Climate impact response functions (CIRFs) are identified as the most suitable reduced-form representation of regular climate impacts in the ICLIPS model. A CIRF depicts the aggregated response of a climate-sensitive system or sector as simulated by a spatially explicit sectoral impact model for a representative subset of plausible futures. In the CIRFs presented here, global mean temperature and atmospheric CO2 concentration are used as predictors for global and regional impacts on natural vegetation, agricultural crop production, and water availability. Application of a pattern scaling technique makes it possible to consider the regional and seasonal patterns in the climate anomalies simulated by several general circulation models while ensuring the efficiency of the dynamic model components. Efforts to provide quantitative estimates of future climate impacts generally face a trade-off between the relevance of an indicator for stakeholders and the exactness with which it can be determined. A number of non-monetary aggregated impact indicators for the CIRFs is presented, which aim to strike the balance between these two conflicting goals while taking into account additional constraints of the ICLIPS modelling framework. Various types of impact diagrams are used for the visualization of CIRFs, each of which provides a different perspective on the impact result space. The sheer number of CIRFs computed for the ICLIPS model precludes their comprehensive presentation in this thesis. Selected results referring to changes in the distribution of biomes in different biogeographical regions, in the agricultural potential of various countries, and in the water availability in selected major catchments are discussed. The full set of CIRFs is accessible via the ICLIPS Impacts Tool, a graphical user interface that provides convenient access to more than 100,000 impact diagrams developed for the ICLIPS model. The technical aspects of the software are described as well as the accompanying database of CIRFs. The most important application of CIRFs is in inverse' mode, where they are used to translate impact guardrails into simultaneous constraints for variables from the optimizing ICLIPS climate-economy model. This translation is facilitated by algorithms for the computation of reachable climate domains and for the parameterized approximation of admissible climate windows derived from CIRFs. The comprehensive set of CIRFs, together with these algorithms, enables the ICLIPS model to flexibly explore sets of climate policy strategies that explicitly comply with impact guardrails specified in biophysical units. This feature is not found in any other intertemporally optimizing IAM. A guardrail analysis with the integrated ICLIPS model is described that applies selected CIRFs for ecosystem changes. So-called necessary carbon emission corridors' are determined for a default choice of normative constraints that limit global vegetation impacts as well as regional mitigation costs, and for systematic variations of these constraints. A brief discussion of recent developments in integrated assessment modelling of climate change connects the work presented here with related efforts.
The present work investigates the structure formation and wetting in two dimensional (2D) Langmuir monolayer phases in local thermodynamic equilibrium. A Langmuir monolayer is an isolated 2D system of surfactants at the air/water interface. It exhibits crystalline, liquid crystalline, liquid and gaseous phases differing in positional and/or orientational order. Permanent electric dipole moments of the surfactants lead to a long range repulsive interaction and to the formation of mesoscopic patterns. An interaction model is used describing the structure formation as a competition between short range attraction (bare line tension) and long range repulsion (surface potentials) on a scale Delta. Delta has the meaning of a dividing length between the short and long range interaction. In the present work the thermodynamic equilibrium conditions for the shape of two phase boundary lines (Young-Laplace equation) and three phase intersection points (Young′s condition) are derived and applied to describe experimental data: The line tension is measured by pendant droplet tensiometry. The bubble shape and size of 2D foams is calculated numerically and compared to experimental foams. Contact angles are measured by fitting numerical solutions of the Young-Laplace equation on micron scale. The scaling behaviour of the contact angle allows to measure a lower limit for Delta. Further it is discussed, whether in biological membranes wetting transitions are a way in order to control reaction kinetics. Studies performed in our group are discussed with respect to this question in the framework of the above mentioned theory. Finally the apparent violation of Gibbs′ phase rule in Langmuir monolayers (non-horizontal plateau of the surface pressure/area-isotherm, extended three phase coexistence region in one component systems) is investigated quantitatively. It has been found that the most probable explanation are impurities within the system whereas finite size effects or the influence of the long range electrostatics can not explain the order of magnitude of the effect.
Concerns have been raised that anthropogenic climate change could lead to large-scale singular climate events, i.e., abrupt nonlinear climate changes with repercussions on regional to global scales. One central goal of this thesis is the development of models of two representative components of the climate system that could exhibit singular behavior: the Atlantic thermohaline circulation (THC) and the Indian monsoon. These models are conceived so as to fulfill the main requirements of integrated assessment modeling, i.e., reliability, computational efficiency, transparency and flexibility. The model of the THC is an interhemispheric four-box model calibrated against data generated with a coupled climate model of intermediate complexity. It is designed to be driven by global mean temperature change which is translated into regional fluxes of heat and freshwater through a linear down-scaling procedure. Results of a large number of transient climate change simulations indicate that the reduced-form THC model is able to emulate key features of the behavior of comprehensive climate models such as the sensitivity of the THC to the amount, regional distribution and rate of change in the heat and freshwater fluxes. The Indian monsoon is described by a novel one-dimensional box model of the tropical atmosphere. It includes representations of the radiative and surface fluxes, the hydrological cycle and surface hydrology. Despite its high degree of idealization, the model satisfactorily captures relevant aspects of the observed monsoon dynamics, such as the annual course of precipitation and the onset and withdrawal of the summer monsoon. Also, the model exhibits the sensitivity to changes in greenhouse gas and sulfate aerosol concentrations that are known from comprehensive models. A simplified version of the monsoon model is employed for the identification of changes in the qualitative system behavior against changes in boundary conditions. The most notable result is that under summer conditions a saddle-node bifurcation occurs at critical values of the planetary albedo or insolation. Furthermore, the system exhibits two stable equilibria: besides the wet summer monsoon, a stable state exists which is characterized by a weak hydrological cycle. These results are remarkable insofar, as they indicate that anthropogenic perturbations of the planetary albedo such as sulfur emissions and/or land-use changes could destabilize the Indian summer monsoon. The reduced-form THC model is employed in an exemplary integrated assessment application. Drawing on the conceptual and methodological framework of the tolerable windows approach, emissions corridors (i.e., admissible ranges of CO2- emissions) are derived that limit the risk of a THC collapse while considering expectations about the socio-economically acceptable pace of emissions reductions. Results indicate, for example, a large dependency of the width of the emissions corridor on climate and hydrological sensitivity: for low values of climate and/or hydrological sensitivity, the corridor boundaries are far from being transgressed by any plausible emissions scenario for the 21st century. In contrast, for high values of both quantities low non-intervention scenarios leave the corridor already in the early decades of the 21st century. This implies that if the risk of a THC collapse is to be kept low, business-as-usual paths would need to be abandoned within the next two decades. All in all, this thesis highlights the value of reduced-form modeling by presenting a number of applications of this class of models, ranging from sensitivity and bifurcation analysis to integrated assessment. The results achieved and conclusions drawn provide a useful contribution to the scientific and policy debate about the consequences of anthropogenic climate change and the long-term goals of climate protection. --- Anmerkung: Die Autorin ist Trägerin des von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Potsdam vergebenen Michelson-Preises für die beste Promotion des Jahres 2003/2004.
In a classical context, synchronization means adjustment of rhythms of self-sustained periodic oscillators due to their weak interaction. The history of synchronization goes back to the 17th century when the famous Dutch scientist Christiaan Huygens reported on his observation of synchronization of pendulum clocks: when two such clocks were put on a common support, their pendula moved in a perfect agreement. In rigorous terms, it means that due to coupling the clocks started to oscillate with identical frequencies and tightly related phases. Being, probably, the oldest scientifically studied nonlinear effect, synchronization was understood only in 1920-ies when E. V. Appleton and B. Van der Pol systematically - theoretically and experimentally - studied synchronization of triode generators. Since that the theory was well developed and found many applications. Nowadays it is well-known that certain systems, even rather simple ones, can exhibit chaotic behaviour. It means that their rhythms are irregular, and cannot be characterized only by one frequency. However, as is shown in the Habilitation work, one can extend the notion of phase for systems of this class as well and observe their synchronization, i.e., agreement of their (still irregular!) rhythms: due to very weak interaction there appear relations between the phases and average frequencies. This effect, called phase synchronization, was later confirmed in laboratory experiments of other scientific groups. Understanding of synchronization of irregular oscillators allowed us to address important problem of data analysis: how to reveal weak interaction between the systems if we cannot influence them, but can only passively observe, measuring some signals. This situation is very often encountered in biology, where synchronization phenomena appear on every level - from cells to macroscopic physiological systems; in normal states as well as in severe pathologies. With our methods we found that cardiovascular and respiratory systems in humans can adjust their rhythms; the strength of their interaction increases with maturation. Next, we used our algorithms to analyse brain activity of Parkinsonian patients. The results of this collaborative work with neuroscientists show that different brain areas synchronize just before the onset of pathological tremor. Morevoever, we succeeded in localization of brain areas responsible for tremor generation.
In-situ Wachstumsuntersuchungen beim reaktiven Anlassen von Cu, In Schichten in elementarem Schwefel
(2003)
In dieser Arbeit wurde das reaktive Anlassen von dünnen Kupfer-Indium-Schichten in elementarem Schwefel mittels energiedispersiver Röntgenbeugung untersucht. Durch die simultane Aufnahme der Röntgenspektren und der Messung der diffusen Reflexion von Laserlicht der Wellenlänge 635 nm an der Oberfläche der Probe während des Schichtwachstums von CuInS<SUB>2</SUB> konnte eine Methode zur Prozesskontrolle für ein Herstellungsverfahren von CuInS<SUB>2</SUB> etabliert werden. Die Bildung von CuInS<SUB>2</SUB> aus Kupfer-Indium-Vorläuferschichten wird dominiert von Umwandlungen der intermetallischen Phasen. CuInS<SUB>2</SUB> wächst innerhalb der Aufheizperiode ab einer Temperatur von ca. 200°C aus der Phase Cu11In9. Jedoch zerfällt letztere metallische Phase in Cu16In9 und flüssiges Indium bei einer Temperatur von ca. 310°C. Das flüssige Indium reagiert im Falle von Kupferarmut mit dem Schwefel und führt zu einem zusätzlichen Reaktionspfad über InS zu CuIn5S8. Unter Präparationsbedingungen mit Kupferüberschuss wird das Indium in einer intermetallischen Phase gebunden.Erstmals konnte die Phase Digenite bei Temperaturen über 240°C beobachtet werden. Beim Abkühlen auf Raumtemperatur wandelt sich diese Phase unter dem Verbrauch von Schwefel in Covellite um.Für Proben mit Kupferüberschuss konnte eine Wachstumskinetik proportional zur Temperatur beobachtet werden. Dieses Verhalten wurde durch eine stress-induzierte Diffusion als dominierenden Reaktionsmechanismus interpretiert. Dabei werden während der Bildung von CuInS<SUB>2</SUB> durch unterschiedliche Ausdehnungen der metallischen und sulfidischen Schichten eine Spannung in der CuInS<SUB>2</SUB>-Schicht induziert, die nach Überschreiten einer Grenzspannung zu Rissen in der CuInS2-Schicht führt. Entlang dieser Risse findet ein schneller Transport der Metalle zur Oberfläche, wo diese mit dem Schwefel reagieren können, statt. Die Risse heilen durch die Bildung neuen Sulfids wieder aus.
The theory of atomic Boson-Fermion mixtures in the dilute limit beyond mean-field is considered in this thesis. Extending the formalism of quantum field theory we derived expressions for the quasi-particle excitation spectra, the ground state energy, and related quantities for a homogenous system to first order in the dilute gas parameter. In the framework of density functional theory we could carry over the previous results to inhomogeneous systems. We then determined to density distributions for various parameter values and identified three different phase regions: (i) a stable mixed regime, (ii) a phase separated regime, and (iii) a collapsed regime. We found a significant contribution of exchange-correlation effects in the latter case. Next, we determined the shift of the Bose-Einstein condensation temperature caused by Boson-Fermion interactions in a harmonic trap due to redistribution of the density profiles. We then considered Boson-Fermion mixtures in optical lattices. We calculated the criterion for stability against phase separation, identified the Mott-insulating and superfluid regimes both, analytically within a mean-field calculation, and numerically by virtue of a Gutzwiller Ansatz. We also found new frustrated ground states in the limit of very strong lattices. ----Anmerkung: Der Autor ist Träger des durch die Physikalische Gesellschaft zu Berlin vergebenen Carl-Ramsauer-Preises 2004 für die jeweils beste Dissertation der vier Universitäten Freie Universität Berlin, Humboldt-Universität zu Berlin, Technische Universität Berlin und Universität Potsdam.
Transport processes in and of cells are of major importance for the survival of the organism. Muscles have to be able to contract, chromosomes have to be moved to opposing ends of the cell during mitosis, and organelles, which are compartments enclosed by membranes, have to be transported along molecular tracks. Molecular motors are proteins whose main task is moving other molecules.For that purpose they transform the chemical energy released in the hydrolysis of ATP into mechanical work. The motors of the cytoskeleton belong to the three super families myosin, kinesin and dynein. Their tracks are filaments of the cytoskeleton, namely actin and the microtubuli. Here, we examine stochastic models which are used for describing the movements of these linear molecular motors. The scale of the movements comprises the regime of single steps of a motor protein up to the directed walk along a filament. A single step bridges around 10 nm, depending on the protein, and takes about 10 ms, if there is enough ATP available. Our models comprise M states or conformations the motor can attain during its movement along a one-dimensional track. At K locations along the track transitions between the states are possible. The velocity of the protein depending on the transition rates between the single states can be determined analytically. We calculate this velocity for systems of up to four states and locations and are able to derive a number of rules which are helpful in estimating the behaviour of an arbitrary given system. Beyond that we have a look at decoupled subsystems, i.e., one or a couple of states which have no connection to the remaining system. With a certain probability a motor undergoes a cycle of conformational changes, with another probability an independent other cycle. Active elements in real transport processes by molecular motors will not be limited to the transitions between the states. In distorted networks or starting from the discrete Master equation of the system, it is possible to specify horizontal rates, too, which furthermore no longer have to fulfill the conditions of detailed balance. Doing so, we obtain unique, complete paths through the respective network and rules for the dependence of the total current on all the rates of the system. Besides, we view the time evolutions for given initial distributions. In enzymatic reactions there is the idea of a main pathway these reactions follow preferably. We determine optimal paths and the maximal flow for given networks. In order to specify the dependence of the motor's velocity on its fuel ATP, we have a look at possible reaction kinetics determining the connection between unbalanced transitions rates and ATP-concentration. Depending on the type of reaction kinetics and the number of unbalanced rates, we obtain qualitatively different curves connecting the velocity to the ATP-concentration. The molecular interaction potentials the motor experiences on its way along its track are unknown. We compare different simple potentials and the effects the localization of the vertical rates in the network model has on the transport coefficients in comparison to other models.
Movements of processive cytoskeletal motors are characterized by an interplay between directed motion along filament and diffusion in the surrounding solution. In the present work, these peculiar movements are studied by modeling them as random walks on a lattice. An additional subject of our studies is the effect of motor-motor interactions on these movements. In detail, four transport phenomena are studied: (i) Random walks of single motors in compartments of various geometries, (ii) stationary concentration profiles which build up as a result of these movements in closed compartments, (iii) boundary-induced phase transitions in open tube-like compartments coupled to reservoirs of motors, and (iv) the influence of cooperative effects in motor-filament binding on the movements. All these phenomena are experimentally accessible and possible experimental realizations are discussed.
This work incorporates three treatises which are commonly concerned with a stochastic theory of the Lyapunov exponents. With the help of this theory universal scaling laws are investigated which appear in coupled chaotic and disordered systems. First, two continuous-time stochastic models for weakly coupled chaotic systems are introduced to study the scaling of the Lyapunov exponents with the coupling strength (coupling sensitivity of chaos). By means of the the Fokker-Planck formalism scaling relations are derived, which are confirmed by results of numerical simulations. Next, coupling sensitivity is shown to exist for coupled disordered chains, where it appears as a singular increase of the localization length. Numerical findings for coupled Anderson models are confirmed by analytic results for coupled continuous-space Schrödinger equations. The resulting scaling relation of the localization length resembles the scaling of the Lyapunov exponent of coupled chaotic systems. Finally, the statistics of the exponential growth rate of the linear oscillator with parametric noise are studied. It is shown that the distribution of the finite-time Lyapunov exponent deviates from a Gaussian one. By means of the generalized Lyapunov exponents the parameter range is determined where the non-Gaussian part of the distribution is significant and multiscaling becomes essential.
Die heutige optische Informationsverarbeitung erfordert neue Materialien, die Licht effektiv verarbeiten, steuern und speichern können. Photorefraktive (PR) Materialien sind dafür sehr interessant. In diesen Materialien entsteht bei inhomogener Beleuchtung (z.B. mit einem Intererenzmuster) über Ladungsträgergenerierung und Einfang der Ladungsträger in Fallen ein Raumladungsfeld. Dieses wird über den elektrooptischen Effekt in eine räumliche Modulation des Brechungsindex umgesetzt. Letztendlich führt somit die inhomogene Beleuchtung eines PR-Materials zu einer räumlich variierenden Änderung des Brechungsindex. Vor ca. 10 Jahren wurde entdeckt, dass auch Polymere einen PR-Effekt aufweisen können. Die Ansprechzeit dieser Materialien wird dabei wesentlich durch die Dynamik der Ladungsträger (bestimmt durch Erzeugung, Transport, Einfang in Fallen etc.) begrenzt. Bis zu Beginn dieser Arbeit war es noch nicht gelungen, einen quantitativen Zusammenhang zwischen der Ladungsträgerdynamik und der Ansprechzeit des PR-Effekts experimentell nachzuweisen. In dieser Arbeit wird ein Weg aufgezeigt, durch photophysikalische Experimente unter verschiedenen Beleuchtungsbedingungen alle photophysikalischen Größen experimentell zu bestimmen, die den Aufbau des Raumladungsfelds in organischen photorefraktiven Materialien bestimmen. So konnte durch Experimente unter Beleuchtung mit kurzen Einzelpulsen sowohl die Beweglichkeit der freien Ladungsträger als auch die charakteristischen Parameter flacher Fallen ermittelt werden. Zur Bestimmung der Dichte tiefer Fallen wurde die Intensitätsabhängigkeit des stationären Photostroms untersucht. Durch die analytische Lösung des bestimmenden Gleichungssystems konnte gezeigt werden, dass die Sublinearität der Intensitätsabhängigkeit des Photostroms primär mit dem Verhältnis zwischen Entleerungs- und Einfangkoeffizienten tiefer Fallen korreliert. Zur unabhängigen Bestimmung des Entleerungskoeffizienten der tiefen Fallen wurden Doppelpulsexperimente mit variabler Verzögerungszeit zwischen den Pulsen verwendet. Mit den erhaltenen Parametern konnte dann das untere Limit der zum Aufbau des Raumladungsfelds notwendigen Zeit abgeschätzt werden. Diese Werte wurden mit den gemessenen photorefraktiven Ansprechzeiten verglichen. Es zeigt sich, dass weder die Photogeneration noch der Transport der Ladungsträger die Geschwindigkeit des Aufbaus des Raumladungsfeldes limitiert. Stattdessen konnte erstmals quantitativ nachgewiesen werden, dass die Dynamik des Raumladungsfelds in den hier untersuchten PR-Materialien durch das Füllen tiefer Fallen mit photogenerierten Ladungsträgern bestimmt wird. Dabei spielt das Verhältnis zwischen dem Einfang- und dem Rekombinationskoeffizienten eine wesentliche Rolle. Weiterhin wurde die Dynamik des Aufbaus des Raumladungsfelds bei unterschiedlichen Vorbeleuchtungsbedingungen quantitativ simuliert und mit den experimentellen PR-Transienten verglichen. Die gute Übereinstimmung zwischen den simulierten und gemessenen Transienten erlaubte es abschließend, die kritischen Parameter, die die Dynamik des PR-Effekts in den untersuchten Polymeren begrenzen, zu identifizieren.
Eine Nutzung der optischen Anisotropie dünner Schichten ist vor allem für die Displaytechnologie, die optische Datenspeicherung und für optische Sicherheitselemente von hoher Bedeutung. Diese Doktorarbeit befasst sich mit theoretischen und experimentellen Untersuchung von dreidimensionaler Anisotropie und dabei insbesondere mit der Untersuchung von lichtinduzierter dreidimensionaler Anisotropie in organischen dünnen Polymer-Schichten. Die gewonnenen Erkentnisse und entwickelten Methoden können wertvolle Beiträge für Optimierungsprozesse, wie bei der Kompensation der Blickwinkelabhängigkeit von Flüssigkristall-Displays, liefern. Die neue Methode der Immersions-Transmissions-Ellipsometrie (ITE) zur Untersuchung von dünneren Schichten wurde im Rahmen dieser Dissertation entwickelt. Diese Methode gestattet es, in Kombination mit konventioneller Reflexions- und Transmissionsellipsometrie, die absoluten dreidimensionalen Brechungsindices einer biaxialen Schicht zu bestimmen. Erstmals gelang es damit, das dreidimensionale Brechungsindexellipsoid von transparenten, dünneren (150 nm) Filmen hochgenau (drei Stellen hinter dem Komma) zu bestimmen. Die ITE-Methode hat demzufolge das Potential, auch bei noch dünneren Schichten mit Gewinn eingesetzt werden zu können. Die lichtinduzierte Generierung von dreidimensionaler Anisotropie wurde in dünnen Schichten von azobenzenhaltigen und zimtsäurehaltigen, amorphen und flüssig-kristallinen Homo- und Copolymeren untersucht. Erstmals wurden quantitative Untersuchungen zur Änderung von lichtinduzierten, dreidimensionalen Anisotropien in dünnen Schichten von azobenzenhaltigen und zimtsäurehaltigen Polymeren bei Tempern oberhalb der Glastemperatur durchgeführt. Bei vielen der untersuchten Polymere war die dreidimensionale Ordnung nach dem Bestrahlen mit polarisiertem Licht und anschließendem Tempern oberhalb der Glastemperatur scheinbar von der Schichtdicke abhängig. Die Ursache liegt wohl in der, mit der neuentwickelten ITE-Methode detektierten, planaren Ausgangsorientierung der aufgeschleuderten dünneren Schichten. Um Verkippungs-Gradienten in dickeren Polymerschichten in ihrem Verlauf zu bestimmen, wurde eine spezielle Methode unter Benutzung der Wellenleitermoden-Spektroskopie entwickelt. Quantenchemisch bestimmte, maximal induzierbare Doppelbrechungen in flüssig-kristallinen Polymeren wurden mit den experimentell gefundenen Ordnungen verglichen.
In festen azobenzenhaltigen Polymeren wurde bei Bestrahlung mit blauem Licht ein makroskopischer Materialtransport beobachtet. Um die Dynamik der Gitterentstehung zu verfolgen, wurde am Speicherring für Synchrotronstrahlung ein Gitterschreibaufbau errichtet. Damit konnte erstmals in dieser Arbeit die Gitterbildungsgeschwindigkeit in-situ simultan mit Röntgen- und Lichtstreuung untersucht werden. Mit Hilfe einer speziellen Anpassung der Röntgenstreutheorie konnten sehr gute Übereinstimmungen von theoretischen Berechnungen mit den Messergebnissen erzielt werden. Dabei konnte nachgewiesen werden, dass sich zeitgleich mit einem Oberflächengitter auch ein Dichtegitter entwickelt. Durch die Trennung beider Streuanteile ließ sich die Dynamik der Strukturentstehungen bestimmen. Des weiteren konnte erstmals mit Hilfe der Photoelektronenspektroskopie die molekulare Orientierung an der Oberfläche eines Oberflächengitters nachgewiesen werden. Die Bewegungsursache kann auf einen Impulsübertrag während der Isomerisierung zurückgeführt werden, während die Bewegungsrichtung durch den elektrischen Feldvektor festgelegt wird. Die Theorie der Gitterentstehung konnte verbessert werden.
Tätigkeitsbericht 1994-2000
(2004)
Das Interdisziplinäre Zentrum für Nichtlineare Dynamik an der Universität Potsdam verbindet theoretisch-methodische Untersuchungen in Mathematik und theoretischer Physik mit einer Vielzahl anderer Wissenschaften und zielt auf eine fruchtbare Wechselwirkung zwischen Theorie und Experiment. Unter Einbezug von Instituten und Großforschungseinrichtungen, die insbesondere im Potsdamer Raum angesiedelt sind, soll sich ein überregional bedeutender Schwerpunkt entwickeln, wie er an keiner anderen deutschen Universität in gleicher Weise interdisziplinär angelegt ist.
Robotic telescopes & Doppler imaging : measuring differential rotation on long-period active stars
(2004)
The sun shows a wide variety of magnetic-activity related phenomena. The magnetic field responsible for this is generated by a dynamo process which is believed to operate in the tachocline, which is located at the bottom of the convection zone. This dynamo is driven in part by differential rotation and in part by magnetic turbulences in the convection zone. The surface differential rotation, one key ingredient of dynamo theory, can be measured by tracing sunspot positions.To extend the parameter space for dynamo theories, one can extend these measurements to other stars than the sun. The primary obstacle in this endeavor is the lack of resolved surface images on other stars. This can be overcome by the Doppler imaging technique, which uses the rotation-induced Doppler-broadening of spectral lines to compute the surface distribution of a physical parameter like temperature. To obtain the surface image of a star, high-resolution spectroscopic observations, evenly distributed over one stellar rotation period are needed. This turns out to be quite complicated for long period stars. The upcoming robotic observatory STELLA addresses this problem with a dedicated scheduling routine, which is tailored for Doppler imaging targets. This will make observations for Doppler imaging not only easier, but also more efficient.As a preview of what can be done with STELLA, we present results of a Doppler imaging study of seven stars, all of which show evidence for differential rotation, but unfortunately the errors are of the same order of magnitude as the measurements due to unsatisfactory data quality, something that will not happen on STELLA. Both, cross-correlation analysis and the sheared image technique where used to double check the results if possible. For four of these stars, weak anti-solar differential rotation was found in a sense that the pole rotates faster than the equator, for the other three stars weak differential rotation in the same direction as on the sun was found.Finally, these new measurements along with other published measurements of differential rotation using Doppler imaging, were analyzed for correlations with stellar evolution, binarity, and rotation period. The total sample of stars show a significant correlation with rotation period, but if separated into antisolar and solar type behavior, only the subsample showing anti-solar differential rotation shows this correlation. Additionally, there is evidence for binary stars showing less differential rotation as single stars, as is suggested by theory. All other parameter combinations fail to deliver any results due to the still small sample of stars available.
The topic of synchronization forms a link between nonlinear dynamics and neuroscience. On the one hand, neurobiological research has shown that the synchronization of neuronal activity is an essential aspect of the working principle of the brain. On the other hand, recent advances in the physical theory have led to the discovery of the phenomenon of phase synchronization. A method of data analysis that is motivated by this finding - phase synchronization analysis - has already been successfully applied to empirical data. The present doctoral thesis ties up to these converging lines of research. Its subject are methodical contributions to the further development of phase synchronization analysis, as well as its application to event-related potentials, a form of EEG data that is especially important in the cognitive sciences. The methodical contributions of this work consist firstly in a number of specialized statistical tests for a difference in the synchronization strength in two different states of a system of two oscillators. Secondly, in regard of the many-channel character of EEG data an approach to multivariate phase synchronization analysis is presented. For the empirical investigation of neuronal synchronization a classic experiment on language processing was replicated, comparing the effect of a semantic violation in a sentence context with that of the manipulation of physical stimulus properties (font color). Here phase synchronization analysis detects a decrease of global synchronization for the semantic violation as well as an increase for the physical manipulation. In the latter case, by means of the multivariate analysis the global synchronization effect can be traced back to an interaction of symmetrically located brain areas.<BR> The findings presented show that the method of phase synchronization analysis motivated by physics is able to provide a relevant contribution to the investigation of event-related potentials in the cognitive sciences.
One of the most striking features of ecological systems is their ability to undergo sudden outbreaks in the population numbers of one or a small number of species. The similarity of outbreak characteristics, which is exhibited in totally different and unrelated (ecological) systems naturally leads to the question whether there are universal mechanisms underlying outbreak dynamics in Ecology. It will be shown into two case studies (dynamics of phytoplankton blooms under variable nutrients supply and spread of epidemics in networks of cities) that one explanation for the regular recurrence of outbreaks stems from the interaction of the natural systems with periodical variations of their environment. Natural aquatic systems like lakes offer very good examples for the annual recurrence of outbreaks in Ecology. The idea whether chaos is responsible for the irregular heights of outbreaks is central in the domain of ecological modeling. This question is investigated in the context of phytoplankton blooms. The dynamics of epidemics in networks of cities is a problem which offers many ecological and theoretical aspects. The coupling between the cities is introduced through their sizes and gives rise to a weighted network which topology is generated from the distribution of the city sizes. We examine the dynamics in this network and classified the different possible regimes. It could be shown that a single epidemiological model can be reduced to a one-dimensional map. We analyze in this context the dynamics in networks of weighted maps. The coupling is a saturation function which possess a parameter which can be interpreted as an effective temperature for the network. This parameter allows to vary continously the network topology from global coupling to hierarchical network. We perform bifurcation analysis of the global dynamics and succeed to construct an effective theory explaining very well the behavior of the system.
Recurrence plots, a rather promising tool of data analysis, have been introduced by Eckman et al. in 1987. They visualise recurrences in phase space and give an overview about the system's dynamics. Two features have made the method rather popular. Firstly they are rather simple to compute and secondly they are putatively easy to interpret. However, the straightforward interpretation of recurrence plots for some systems yields rather surprising results. For example indications of low dimensional chaos have been reported for stock marked data, based on recurrence plots. In this work we exploit recurrences or ``naturally occurring analogues'' as they were termed by E. Lorenz, to obtain three key results. One of which is that the most striking structures which are found in recurrence plots are hinged to the correlation entropy and the correlation dimension of the underlying system. Even though an eventual embedding changes the structures in recurrence plots considerably these dynamical invariants can be estimated independently of the special parameters used for the computation. The second key result is that the attractor can be reconstructed from the recurrence plot. This means that it contains all topological information of the system under question in the limit of long time series. The graphical representation of the recurrences can also help to develop new algorithms and exploit specific structures. This feature has helped to obtain the third key result of this study. Based on recurrences to points which have the same ``recurrence structure'', it is possible to generate surrogates of the system which capture all relevant dynamical characteristics, such as entropies, dimensions and characteristic frequencies of the system. These so generated surrogates are shadowed by a trajectory of the system which starts at different initial conditions than the time series in question. They can be used then to test for complex synchronisation.
The behaviour of an adhering cell is strongly influenced by the chemical, topographical and mechanical properties of the surface it attaches to. During recent years, it has been found experimentally that adhering cells actively sense the elastic properties of their environment by pulling on it through numerous sites of adhesion. The resulting build-up of force at sites of adhesion depends on the elastic properties of the environment and is converted into corresponding biochemical signals, which can trigger cellular programmes like growth, differentiation, apoptosis, and migration. In general, force is an important regulator of biological systems, for example in hearing and touch, in wound healing, and in rolling adhesion of leukocytes on vessel walls. In the habilitation thesis by Ulrich Schwarz, several theoretical projects are presented which address the role of forces and elasticity in cell adhesion. (1) A new method has been developed for calculating cellular forces exerted at sites of focal adhesion on micro-patterned elastic substrates. The main result is that cell-matrix contacts function as mechanosensors, converting internal force into protein aggregation. (2) A one-step master equation for the stochastic dynamics of adhesion clusters as a function of cluster size, rebinding rate and force has been solved both analytically and numerically. Moreover this model has been applied to the regulation of cell-matrix contacts, to dynamic force spectroscopy, and to rolling adhesion. (3) Using linear elasticity theory and the concept of force dipoles, a model has been introduced and solved which predicts the positioning and orientation of mechanically active cells in soft material, in good agreement with experimental observations for fibroblasts on elastic substrates and in collagen gels.
In this thesis, dynamical structures and manifolds in closed chaotic flows will be investigated. The knowledge about the dynamical structures (and manifolds) of a system is of importance, since they provide us first information about the dynamics of the system - means, with their help we are able to characterize the flow and maybe even to forecast it`s dynamics. The visualization of such structures in closed chaotic flows is a difficult and often long-lasting process. Here, the so-called 'Leaking-method' will be introduced, in examples of simple mathematical maps as the baker- or sine-map, with which we are able to visualize subsets of the manifolds of the system`s chaotic saddle. Comparisons between the visualized manifolds and structures traced out by chemical or biological reactions superimposed on the same flow will be done in the example of a kinematic model of the Gulf Stream. It will be shown that with the help of the leaking method dynamical structures can be also visualized in environmental systems. In the example of a realistic model of the Mediterranean Sea, the leaking method will be extended to the 'exchange-method'. The exchange method allows us to characterize transport between two regions, to visualize transport routes and their exchange sets and to calculate the exchange times. Exchange times and sets will be shown and calculated for a northern and southern region in the western basin of the Mediterranean Sea. Furthermore, mixing properties in the Earth mantle will be characterized and geometrical properties of manifolds in a 3dimensional mathematical model (ABC map) will be investigated.
Understanding stars, their magnetic activity phenomena and the underlying dynamo action is the foundation for understanding 'life, the universe and everything' - as stellar magnetic fields play a fundamental role for star and planet formation and for the terrestrial atmosphere and climate. Starspots are the fingerprints of magnetic field lines and thereby the most important sign of activity in a star's photosphere. However, they cannot be observed directly, as it is not (yet) possible to spacially resolve the surfaces of even the nearest neighbouring stars. Therefore, an indirect approach called 'Doppler imaging' is applied, which allows to reconstruct the surface spot distribution on rapidly rotating, active stars. In this work, data from 11 years of continuous spectroscopic observations of the active binary star EI Eridani are reduced and analysed. 34 Doppler maps are obtained and the problem of how to parameterise the information content of Doppler maps is discussed. Three approaches for parameter extraction are introduced and applied to all maps: average temperature, separated for several latitude bands; fractional spottedness; and, for the analysis of structural temperature distribution, longitudinal and latitudinal spot-occurrence functions. The resulting values do not show a distinct correlation with the proposed activity cycle as seen from photometric long-term observations, thereby suggesting that the photometric activity cycle is not accompanied by a spot cycle as seen on the Sun. The general morphology of the spot pattern on EI Eri remains persistent for the whole period of 11 years. In addition, a detailed parameter study is performed. Improved orbital parameters suggest that EI Eri might be complemented by a third star in a wide orbit of about 19 years. Preliminary differential rotation measurements are carried out, indicating an anti-solar orientation.
This work deals with the connection between two basic phenomena in Nonlinear Dynamics: synchronization of chaotic systems and recurrences in phase space. Synchronization takes place when two or more systems adapt (synchronize) some characteristic of their respective motions, due to an interaction between the systems or to a common external forcing. The appearence of synchronized dynamics in chaotic systems is rather universal but not trivial. In some sense, the possibility that two chaotic systems synchronize is counterintuitive: chaotic systems are characterized by the sensitivity ti different initial conditions. Hence, two identical chaotic systems starting at two slightly different initial conditions evolve in a different manner, and after a certain time, they become uncorrelated. Therefore, at a first glance, it does not seem to be plausible that two chaotic systems are able to synchronize. But as we will see later, synchronization of chaotic systems has been demonstrated. On one hand it is important to investigate the conditions under which synchronization of chaotic systems occurs, and on the other hand, to develop tests for the detection of synchronization. In this work, I have concentrated on the second task for the cases of phase synchronization (PS) and generalized synchronization (GS). Several measures have been proposed so far for the detection of PS and GS. However, difficulties arise with the detection of synchronization in systems subjected to rather large amounts of noise and/or instationarities, which are common when analyzing experimental data. The new measures proposed in the course of this thesis are rather robust with respect to these effects. They hence allow to be applied to data, which have evaded synchronization analysis so far. The proposed tests for synchronization in this work are based on the fundamental property of recurrences in phase space.
Adherent cells constantly collect information about the mechanical properties of their extracellular environment by actively pulling on it through cell-matrix contacts, which act as mechanosensors. In recent years, the sophisticated use of elastic substrates has shown that cells respond very sensitively to changes in effective stiffness in their environment, which results in a reorganization of the cytoskeleton in response to mechanical input. We develop a theoretical model to predict cellular self-organization in soft materials on a coarse grained level. Although cell organization in principle results from complex regulatory events inside the cell, the typical response to mechanical input seems to be a simple preference for large effective stiffness, possibly because force is more efficiently generated in a stiffer environment. The term effective stiffness comprises effects of both rigidity and prestrain in the environment. This observation can be turned into an optimization principle in elasticity theory. By specifying the cellular probing force pattern and by modeling the environment as a linear elastic medium, one can predict preferred cell orientation and position. Various examples for cell organization, which are of large practical interest, are considered theoretically: cells in external strain fields and cells close to boundaries or interfaces for different sample geometries and boundary conditions. For this purpose the elastic equations are solved exactly for an infinite space, an elastic half space and the elastic sphere. The predictions of the model are in excellent agreement with experiments for fibroblast cells, both on elastic substrates and in hydrogels. Mechanically active cells like fibroblasts could also interact elastically with each other. We calculate the optimal structures on elastic substrates as a function of material properties, cell density and the geometry of cell positioning, respectively, that allows each cell to maximize the effective stiffness in its environment due to the traction of all the other cells. Finally, we apply Monte Carlo simulations to study the effect of noise on cellular structure formation. The model not only contributes to a better understanding of many physiological situations. In the future it could also be used for biomedical applications to optimize protocols for artificial tissues with respect to sample geometry, boundary condition, material properties or cell density.
Die Untersuchung mikrogelinster astronomischer Objekte ermöglicht es, Informationen über die Größe und Struktur dieser Objekte zu erhalten. Im ersten Teil dieser Arbeit werden die Spektren von drei gelinsten Quasare, die mit dem Potsdamer Multi Aperture Spectrophotometer (PMAS) erhalten wurden, auf Anzeichen für Mikrolensing untersucht. In den Spektren des Vierfachquasares HE 0435-1223 und des Doppelquasares HE 0047-1756 konnten Hinweise für Mikrolensing gefunden werden, während der Doppelquasar UM 673 (Q 0142--100) keine Anzeichen für Mikrolensing zeigt. Die Invertierung der Lichtkurve eines Mikrolensing-Kausik-Crossing-Ereignisses ermöglicht es, das eindimensionale Helligkeitsprofil der gelinsten Quelle zu rekonstruieren. Dies wird im zweiten Teil dieser Arbeit untersucht. Die mathematische Beschreibung dieser Aufgabe führt zu einer Volterra'schen Integralgleichung der ersten Art, deren Lösung ein schlecht gestelltes Problem ist. Zu ihrer Lösung wird in dieser Arbeit ein lokales Regularisierungsverfahren angewendet, das an die kausale Strukture der Volterra'schen Gleichung besser angepasst ist als die bisher verwendete Tikhonov-Phillips-Regularisierung. Es zeigt sich, dass mit dieser Methode eine bessere Rekonstruktion kleinerer Strukturen in der Quelle möglich ist. Weiterhin wird die Anwendbarkeit der Regularisierungsmethode auf realistische Lichtkurven mit irregulärem Sampling bzw. größeren Lücken in den Datenpunkten untersucht.
My thesis is concerned with several new noise-induced phenomena in excitable neural models, especially those with FitzHugh-Nagumo dynamics. In these effects the fluctuations intrinsically present in any complex neural network play a constructive role and improve functionality. I report the occurrence of Vibrational Resonance in excitable systems. Both in an excitable electronic circuit and in the FitzHugh-Nagumo model, I show that an optimal amplitude of high-frequency driving enhances the response of an excitable system to a low-frequency signal. Additionally, the influence of additive noise and the interplay between Stochastic and Vibrational Resonance is analyzed. Further, I study systems which combine both oscillatory and excitable properties, and hence intrinsically possess two internal frequencies. I show that in such a system the effect of Stochastic Resonance can be amplified by an additional high-frequency signal which is in resonance with the oscillatory frequency. This amplification needs much lower noise intensities than for conventional Stochastic Resonance in excitable systems. I study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise-supported stochastic attractors. I show that the response of the coupled elements at different noise levels can be significantly enhanced or reduced by forcing some elements into resonance with these new frequencies which correspond to appropriate phase-relations. A noise-induced phase transition to excitability is reported in oscillatory media with FitzHugh-Nagumo dynamics. This transition takes place via noise-induced stabilization of a deterministically unstable fixed point of the local dynamics, while the overall phase-space structure of the system is maintained. The joint action of coupling and noise leads to a different type of phase transition and results in a stabilization of the system. The resulting noise-induced regime is shown to display properties characteristic of excitable media, such as Stochastic Resonance and wave propagation. This effect thus allows the transmission of signals through an otherwise globally oscillating medium. In particular, these theoretical findings suggest a possible mechanism for suppressing undesirable global oscillations in neural networks (which are usually characteristic of abnormal medical conditions such as Parkinson′s disease or epilepsy), using the action of noise to restore excitability, which is the normal state of neuronal ensembles.