Refine
Has Fulltext
- no (156) (remove)
Year of publication
- 2006 (156) (remove)
Document Type
- Article (135)
- Doctoral Thesis (13)
- Other (5)
- Monograph/Edited Volume (3)
Is part of the Bibliography
- yes (156)
Keywords
- 1,3,4-oxadiazole (1)
- CDA (1)
- Cassini (1)
- Deimos (1)
- E-ring (1)
- Mars (1)
- Trypanosoma cruzi (1)
- X-rays : stars (1)
- anatomical connectivity (1)
- bifurcation analysis (1)
Institute
- Institut für Physik und Astronomie (156) (remove)
We develop a model of stochastic radiation pressure for rotating non-spherical particles and apply the model to circumplanetary dynamics of dust grains. The stochastic properties of the radiation pressure are related to the ensemble-averaged characteristics of the rotating particles, which are given in terms of the rotational time-correlation function of a grain. We investigate the model analytically and show that an ensemble of particle trajectories demonstrates a diffusion-like behaviour. The analytical results are compared with numerical simulations, performed for the motion of the dusty ejecta from Deimos in orbit around Mars. We find that the theoretical predictions are in a good agreement with the simulation results. The agreement however deteriorates at later time, when the impact of non-linear terms, neglected in the analytic approach, becomes significant. Our results indicate that the stochastic modulation of the radiation pressure can play an important role in the circumplanetary dynamics of dust and may in case of some dusty systems noticeably alter an optical depth. (c) 2006 Elsevier Ltd. All rights reserved.
The velocity distribution function of granular gases in the homogeneous cooling state as well as some heated granular gases decays for large velocities as f proportional to exp(-const x nu). That is, its high-energy tail is overpopulated as compared with the Maxwell distribution. At the present time, there is no theory to describe the influence of the tail on the kinetic characteristics of granular gases. We develop an approach to quantify the overpopulated tail and analyze its impact on granular gas properties, in particular on the cooling coefficient. We observe and explain anomalously slow relaxation of the velocity distribution function to its steady state.
Context. Very massive stars pass through the Wolf-Rayet (WR) stage before they finally explode. Details of their evolution have not yet been safely established, and their physics are not well understood. Their spectral analysis requires adequate model atmospheres, which have been developed step by step during the past decades and account in their recent version for line blanketing by the millions of lines from iron and iron-group elements. However, only very few WN stars have been re-analyzed by means of line-blanketed models yet. Aims. The quantitative spectral analysis of a large sample of Galactic WN stars with the most advanced generation of model atmospheres should provide an empirical basis for various studies about the origin, evolution, and physics of the Wolf-Rayet stars and their powerful winds. Methods. We analyze a large sample of Galactic WN stars by means of the Potsdam Wolf-Rayet (PoWR) model atmospheres, which account for iron line blanketing and clumping. The results are compared with a synthetic population, generated from the Geneva tracks for massive star evolution. Results. We obtain a homogeneous set of stellar and atmospheric parameters for the GalacticWN stars, partly revising earlier results. Conclusions. Comparing the results of our spectral analyses of the Galactic WN stars with the predictions of the Geneva evolutionary calculations, we conclude that there is rough qualitative agreement. However, the quantitative discrepancies are still severe, and there is no preference for the tracks that account for the effects of rotation. It seems that the evolution of massive stars is still not satisfactorily understood.
This paper discusses translocation features of the 20S proteasome in order to explain typical proteasome length distributions. We assume that the protein transport depends significantly on the fragment length with some optimal length which is transported most efficiently. By means of a simple one-channel model, we show that this hypothesis can explain both the one- and the three-peak length distributions found in experiments. A possible mechanism of such translocation is provided by so-called fluctuation-driven transport.
Three methods for the determination of the surface tension of liquids based on force measurements namely, the vertical plate method of Wilhelmy, the frame method of Lenard and the ring method of du Nouy are compared and studied in respect of a common principle of correction. It is shown that these three most important force-based methods allow the determination of the surface tension under static conditions. The force components of the corresponding liquid column below the measuring wire obtained for the straight part of the withdrawal curve up to the transition in its curved part provides exact surface tension values. The experimentally accessible value of the force component describes the physical background of the measured value correction contrary to the approximate equations obtained by mathematical way. Usually the determination of surface tension of liquids is based merely at the vertical plate method on exact equations thermodynamically derived whereas in the case of the frame and ring methods correction factors in approximate equations are used. At usual application of the force-based methods under the non-static condition of the withdrawal of a liquid column, the force maximum measured at withdrawal of the measuring object (plate, frame, or ring) is the basis for the determination of surface tension. In these cases, the measured surface tension values are compensated by correction equations for the frame and ring methods which are based on an correction factor and correction tables empirically obtained. The surface tension values obtained in this usual way agree with those obtained by using the force component of the corresponding liquid column below the measuring wire for the straight part of the withdrawal curve up to the transition in its curved part. Problems arising at the force measurements with increasing thickness of the measuring wires inside and outside the rings are discussed.
Recurrence plot analyses suggest a novel reference system involved in newborn spontaneous movements
(2006)
The movements of newborns have been thoroughly studied in terms of reflexes, muscle synergies, leg coordination, and target-directed arm/hand movements. Since these approaches have concentrated mainly on separate accomplishments, there has remained a clear need for more integrated investigations. Here, we report an inquiry in which we explicitly concentrated on taking such a perspective and, additionally, were guided by the methodological concept of home base behavior, which Ilan Golard developed for studies of exploratory behavior in animals. Methods from nonlinear dynamics, such as symbolic dynamics and recurrence plot analyses of kinematic data received from audiovisual newborn recordings, yielded new insights into the spatial and temporal organization of limb movements. In the framework of home base behavior, our approach uncovered a novel reference system of spontaneous newborn movements.
Experimental results show that the polymerization of pyrrole in the presence of beta-naphthalenesulfonic acid and different fluorosurfactants like perfluorooctanesulfonic acid, perfluorooctyldiethanolamide, and ammonium perfluorooctanoate leads to polypyrrole with special morphologies, such as rings or disks and rectangular frames or plates. The formation of these unusually shaped particles of polymer dispersions is explained by the chemical and colloidal peculiarities of the oxidative pyrrole polymerization with ammonium peroxodisulfate in aqueous medium.
Structural and spectroscopical study of a 2,5-diphenyl-1,3,4-oxadiazole polymorph under compression
(2006)
The x-ray pattern and the Raman and luminescence spectra of crystalline 2,5-diphenyl-1,3,4-oxadiazole in one of its polymorphic forms (DPO II) have been investigated under pressure up to 5 GPa. The behaviour of the lattice parameters under compression was determined and it was found that the Murnaghan equation of state provides a good description of the volume-pressure relationship of DPO II. The values for the bulk modulus and its pressure derivative are K-0 = 8.6 GPa and K-0' = 7.2. The analysis of the Raman spectrum under compression clearly shows the pressure- induced shift of the Raman modes to higher frequencies. The mode Gruneisen parameters for the lattice modes were determined. Additionally, it was found that the emission spectrum of DPO II moves to lower energies and that the luminescence intensity decreases when pressure is applied
The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an ad hoc partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed
We report time-dependent configuration interaction singles calculations for the ultrafast laser driven many- electron dynamics in a polyatomic molecule, N-methyl-6-quinolone. We employ optimal control theory to achieve a nearly state-selective excitation from the S-0 to the S-1 state, on a time scale of a few (approximate to 6) femtoseconds. The optimal control scheme is shown to correct for effects opposing a state-selective transition, such as multiphoton transitions and other, nonlinear phenomena, which are induced by the ultrashort and intense laser fields. In contrast, simple two-level pi pulses are not effective in state-selective excitations when very short pulses are used. Also, the dependence of multiphoton and nonlinear effects on the number of states included in the dynamical simulations is investigated.
Der Klimawandel
(2006)
Offener Physikunterricht
(2006)
Die Nanowelt
(2006)
Chaosphysik
(2006)
Triplet energy back transfer in conjugated polymers with pendant phosphorescent iridium complexes
(2006)
The nature of Dexter triplet energy transfer between bonded systems of a red phosphorescent iridium complex 13 and a conjugated polymer, polyfluorene, has been investigated in electrophosphorescent organic light-emitting diodes. Red- emitting phosphorescent iridium complexes based on the [Ir(btp)2(acac)]fragment (where btp is 2-(2 '- benzo[b]thienyl)pyridinato and acac is acetylacetonate) have been attached either directly (spacerless) or through a - (CH2)(8)-chain (octamethylene-tethered) at the 9-position of a 9-octylfluorene host. The resulting dibromo- functionalized spacerless (8) or octamethylene-tethered (12) fluorene monomers were chain extended by Suzuki polycondensations using the bis(boronate)-terminated fluorene macromonomers 16 in the presence of end-capping chlorobenzene solvent to produce the statistical spacerless (17) and octamethylene-tethered ( 18) copolymers containing an even dispersion of the pendant phosphorescent fragments. The spacerless monomer 12 adopts a face-to-face conformation with a separation of only 3.6 angstrom between the iridium complex and fluorenyl group, as shown by X-ray analysis of a single crystal, and this facilitates intramolecular triplet energy transfer in the spacerless copolymers 17. The photo- and electroluminescence efficiencies of the octamethylene-tethered copolymers 18 are double those of the spacerless copolymers 17, and this is consistent with suppression of the back transfer of triplets from the red phosphorescent iridium complex to the polyfluorene backbone in 18. The incorporation of a -(CH2)(8)- chain between the polymer host and phosphorescent guest is thus an important design principle for achieving higher efficiencies in those electrophosphorescent organic light-emitting diodes for which the triplet energy levels of the host and guest are similar
We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can describe a class of systems which share a similar structure. Despite this generality, the proposed approach allows us to study the dynamical properties of generalized models efficiently in the framework of local bifurcation theory. The approach is based on a normalization procedure that is used to identify natural parameters of the system. The Jacobian in a steady state is then derived as a function of these parameters. The analytical computation of local bifurcations using computer algebra reveals conditions for the local asymptotic stability of steady states and provides certain insights on the global dynamics of the system. The proposed approach yields a close connection between modelling and nonlinear dynamics. We illustrate the investigation of generalized models by considering examples from three different disciplines of science: a socioeconomic model of dynastic cycles in china, a model for a coupled laser system and a general ecological food web
Recent theoretical studies have shown contrasting effects of temporal correlation of environmental fluctuations ( red noise) on the risk of population extinction. It is still debated whether and under which conditions red noise increases or decreases extinction risk compared with uncorrelated ( white) noise. Here, we explain the opposing effects by introducing two features of red noise time series. On the one hand, positive autocorrelation increases the probability of series of poor environmental conditions, implying increasing extinction risk. On the other hand, for a given time period, the probability of at least one extremely bad year ("catastrophe") is reduced compared with white noise, implying decreasing extinction risk. Which of these two features determines extinction risk depends on the strength of environmental fluctuations and the sensitivity of population dynamics to these fluctuations. If extreme ( catastrophic) events can occur ( strong noise) or sensitivity is high ( overcompensatory density dependence), then temporal correlation decreases extinction risk; otherwise, it increases it. Thus, our results provide a simple explanation for the contrasting previous findings and are a crucial step toward a general understanding of the effect of noise color on extinction risk
Past studies have shown that the initiation of symbiosis between the Red-Sea soft coral Heteroxenia fuscescens and its symbiotic dinoflagellates occurs due to the chemical attraction of the motile algal cells to substances emanating from the coral polyps. However, the resulting swimming patterns of zooxanthellae have not been previously studied. This work examined algal swimming behaviour, host location and navigation capabilities under four conditions: (1) still water, (2) in still water with waterborne host attractants, (3) in flowing water, and (4) in flow with host attractants. Algae were capable of actively and effectively locating their host in still water as well as in flow. When in water containing host attractants, swimming became slower, motion patterns straighter and the direction of motion was mainly towards the host-even if this meant advancing upstream against flow velocities of up to 0.5 mm s(-1)supercript stop. Coral-algae encounter probability decreased the further downstream of the host algae were located, probably due to diffusion of the chemical signal. The results show how the chemoreceptive zooxanthellae modify their swimming pattern, direction, velocity, circuity and turning rate to accommodate efficient navigation in changing environmental conditions
We investigated the spectral properties of light-emitting diodes based on a deep blue-emitting pyrazoloquinoline dye doped into a poly(N-vinylcarbazole)-based matrix. Even though the electroluminescence (EL) of the host is redshifted and broadened with respect to the emission of the dye, the EL spectrum becomes fully dominated by the dye emission at concentrations of ca. 2 wt %. This is attributed to a competition of exciplex formation on the matrix and exciton formation on the dye.
In this Letter, we show that coherence and phase synchronization analysis are sensitive but not specific in detecting the correct class of underlying dynamics. We propose procedures to increase specificity and demonstrate the power of the approach by application to paradigmatic dynamic model systems. (c) 2006 Elsevier B.V. All rights reserved
We present a detailed, realistic analysis of the implementation of a proposal for a quantum phase gate based on atomic vibrational states, specializing it to neutral rubidium atoms on atom chips. We show how to create a double-well potential with static currents on the atom chips, using for all relevant parameters values that are achieved with present technology. The potential barrier between the two wells can be modified by varying the currents in order to realize a quantum phase gate for qubit states encoded in the atomic external degree of freedom. The gate performance is analyzed through numerical simulations; the operation time is similar to 10 ms with a performance fidelity above 99.9%. For storage of the state between the operations the qubit state can be transferred efficiently via Raman transitions to two hyperfine states, where its decoherence is strongly inhibited. In addition we discuss the limits imposed by the proximity of the surface to the gate fidelity.
High cw power using an external cavity for spectral beam combining of diode laser-bar emission
(2006)
In extension to known concepts of wavelength-multiplexing diode laser arrays, a new external cavity is presented. The setup simultaneously improves the beam quality of each single emitter of a standard 25 emitter broad-area stripe laser bar and spectrally superimposes the 25 beams into one. By using this external resonator in an "off-axis" arrangement, beam qualities of M-slow(2) < 14 and M-fast(2) < 3 with optical powers in excess of 10 W in cw operation are obtained.
We study thermally induced birefringence in crystalline Nd:YAG zigzag slab lasers and the associated depolarization losses. The optimum crystallographic orientation of the zigzag slab within the Nd:YAG boule and photoelastic effects in crystalline Nd:YAG slabs are briefly discussed. The depolarization is evaluated using the temperature and stress distributions, calculated using a finite element model, for realistically pumped and cooled slabs of finite dimensions. Jones matrices are then used to calculate the depolarization of the zigzag laser mode. We compare the predictions with measurements of depolarization, and suggest useful criteria for the design of the gain media for such lasers.
We report that the performances of blue polymer electrophosphorescent devices are crucially depending on the choice of the electron transporting material incorporated into the emissive layer. Devices with 1,3-bis[(4-tert- butylphenyl)-1,3,4-oxidiazolyl]phenylene (OXD-7) doped at similar to 40 wt% into a poly(vinylcarbazole) matrix exhibited significantly higher efficiencies than those with 2-(4-biphenylyl)-5-(4-tert-butylphenyl)-1,3,4-oxadiazole (PBD), yielding maximum luminous and power efficiency values of 18.2 Cd/A and 8.8 lm/W, respectively. Time resolved photoluminescence measurements revealed a long lifetime phosphorescence component in layers with PBD, which we assign to significant triplet harvesting by this electron-transporting component. (c) 2006 American Institute of Physics
Experimental evidence of anomalous phase synchronization in two diffusively coupled Chua oscillators
(2006)
We study the transition to phase synchronization in two diffusively coupled, nonidentical Chua oscillators. In the experiments, depending on the used parameterization, we observe several distinct routes to phase synchronization, including states of either in-phase, out-of-phase, or antiphase synchronization, which may be intersected by an intermediate desynchronization regime with large fluctuations of the frequency difference. Furthermore, we report the first experimental evidence of an anomalous transition to phase synchronization, which is characterized by an initial enlargement of the natural frequency difference with coupling strength. This results in a maximal frequency disorder at intermediate coupling levels, whereas usual phase synchronization via monotonic decrease in frequency difference sets in only for larger coupling values. All experimental results are supported by numerical simulations of two coupled Chua models
We study theoretically the coherent and correlated motion of many fermions inside an infinite square well potential. We will look at electrons and He-3 atoms, which behave very differently not only because of their masses, but also because of their different interaction potential. Also, the level of theory and the role of approximations in the solution of the time-dependent Schrodinger equation will be discussed
We establish a quantitative relationship between the entanglement content of a single quantum chain at a critical point and the corresponding entropy of entanglement. We find that, surprisingly, the leading critical scaling of the single-copy entanglement with respect to any bipartitioning is exactly one-half of the entropy of entanglement, in a general setting of conformal field theory and quasifree systems. Conformal symmetry imposes that the single-copy entanglement scales as E-1(rho(L))=(c/6)ln L-(c/6)(pi(2)/ln L)+O(1/L), where L is the number of constituents in a block of an infinite chain and c denotes the central charge. This shows that from a single specimen of a critical chain, already half the entanglement can be distilled compared to the rate that is asymptotically available. The result is substantiated by a quantitative analysis for all translationally invariant quantum spin chains corresponding to all isotropic quasifree fermionic models. An example of the XY spin chain shows that away from criticality the above relation is maintained only near the quantum phase transition
Spatial recurrence plots
(2006)
We propose an extension of the recurrence plot concept to perform quantitative analyzes of roughness and disorder of spatial patterns at a fixed time. We introduce spatial recurrence plots (SRPs) as a graphical representation of the pointwise correlation matrix, in terms of a two-dimensional spatial return plot. This technique is applied to the study of complex patterns generated by coupled map lattices, which are characterized by measures of complexity based on SRPs. We show that the complexity measures we propose for SRPs provide a systematic way of investigating the distribution of spatially coherent structures, such as synchronization domains, in lattice profiles. This approach has potential for many more applications, e.g., in surface roughness analyzes
We analyse the relationship of longitudinal and transversal increment statistics measured in isotropic small- scale turbulence. This is done by means of the theory of Markov processes leading to a phenomenological Fokker - Planck equation for the two increments from which a generalized K arm an equation is derived. We discuss in detail the analysis and show that the estimated equation can describe the statistics of the turbulent cascade. A remarkable result is that the main differences between longitudinal and transversal increments can be explained by a simple rescaling symmetry, namely the cascade speed of the transverse increments is 1.5 times faster than that of the longitudinal increments. Small differences can be found in the skewness and in a higher order intermittency term. The rescaling symmetry is compatible with the Kolmogorov constants and the K arm an equation and gives new insight into the use of extended self- similarity (ESS) for transverse increments. Based on the results we propose an extended self-similarity for the transverse increments (ESST)
In side pumped laser head geometries good extraction of energy has to be weighted against diffraction effects of the amplified beam. Beam clipping at the aperture of laser rods can be avoided by using an undoped cladding around the doped core. The wings of e. g. Gaussian beams can be accommodated in the cladding. Phase distortion by the refractive index step of the rod can be compensated by a phase conjugating mirror in double pass configuration. In our proof of principle experiment the brightness of the beam from core doped amplifier rods was shown to be doubled compared to a conventional rod of the same outer diameter. (c) 2006 Optical Society of America
The parameters of the nutations are now known with a good accuracy, and the theory accounts for most of their values. Dissipative friction at the core-mantle boundary (CMB) and at the inner core boundary is an important ingredient of the theory. Up to now, viscous coupling at a smooth interface and electromagnetic coupling have been considered. In some cases they appear hardly strong enough to account for the observations. We advocate here that the CMB has a small- scale roughness and estimate the dissipation resulting from the interaction of the fluid core motion with this topography. We conclude that it might be significant
In planetary rings, binary collisions and mutual gravity are the predominant particle interactions. Based on a viscoelastic contact model we implement the concept of static adhesion. We discuss the collision dynamics and obtain a threshold velocity for restitution or agglomeration to occur. The latter takes place within a range of a few cm s(-1) for icy grains at low temperatures. The stability of such two-body agglomerates bound by adhesion and gravity in a tidal environment is discussed and applied to the saturnian system. A maximal agglomerate size for a given orbit location is obtained. In this way we are able to resolve the borderline of the zone where agglomerates can exist as a function of the agglomerate size and thus gain an alternative to the classical Roche limit. An increasing ring grain size with distance to Saturn as observed by the VIMS-experiment on board the Cassini spacecraft can be found by our estimates and implications for the saturnian system will be addressed.
The averaged dynamics of various two-phase systems in a high-frequency vibration field is studied theoretically. The continuum approach is applied to describe such systems as solid particle suspensions, emulsions, bubbly fluids, when the volume concentration of the disperse phase is small and gravity is insignificant. The dynamics of the disperse system is considered by means of the method of averaging, when the fast pulsation and slow averaged motion can be treated separately. Two averaged models for both nondeformable and deformable particles, when the compressibility of the disperse phase becomes important, are obtained. A criterion when the compressibility of bubbles cannot be neglected is figured out. For both cases the developed models are applied to study the averaged dynamics of the disperse media in an infinite plane layer under the action of transversal vibration. (C) 2006 American Institute of Physics
Objective Pre-eclampsia is a serious complication of pregnancy with high morbidity and mortality and an incidence of 3-5% in all pregnancies. Early prediction is still insufficient in clinical practice. Although most pre- eclamptic patients have pathological uterine perfusion in the second trimester, perfusion disturbance has a positive predictive accuracy (PPA) only of approximately 30%. Methods Non-invasive continuous blood pressure recordings were taken simultaneously via a finger cuff for 30 min. Time series of systolic as well as diastolic beat-to-beat pressure values were extracted to analyse heart rate and blood pressure variability and baroreflex sensitivity in 102 second- trimester pregnancies, to assess predictability for pre-eclampsia (n = 16). All women underwent Doppler investigations of the uterine arteries. Results We identified a combination of three variability and baroreflex parameters to best predict pre-eclampsia several weeks before clinical manifestation. The discriminant function of these three parameters classified patients with later pre-eclampsia with a sensitivity of 87.5%, a specificity of 83.7%, and a PPA of 50.0%. Combined with Doppler investigations of uterine arteries, PPA increased to 71.4%. Conclusions This technique of incorporating one-stop clinical assessment of uterine perfusion and variability parameters in the second trimester produces the most effective prediction of pre-eclampsia to date
Polymeric electrophosphorescent LEDs with internal quantum efficiencies approaching unity have been fabricated. Such performance levels are previously unknown for OLEDs. The key to this success is redox chemically doped oxetane- crosslinkable hole-transporting layers with multilayer capability (see figure). They improve hole injection and act as electron-blocking layers, without the need to include exciton-or hole-blocking layers
Wachsende Filamentbündel
(2006)
An approach is presented for coupled chaotic systems with weak coherent motion, from which we estimate the upper bound value for the absolute phase difference in phase synchronous states. This approach shows that synchronicity in phase implies synchronicity in the time of events, a characteristic explored to derive an equation to detect phase synchronization, based on the absolute difference between the time of these events. We demonstrate the potential use of this approach for the phase coherent and the funnel attractor of the Rossler system, as well as for the spiking/bursting Rulkov map.
A series of novel platinum-containing carbazole monomers and polymers was synthesized and fully characterized by UV-VIS absorption, luminescence, and photoinduced absorption studies. In these compounds, a carbazole unit is incorporated into the main chain via either a para- or a meta-linkage. We discuss the effects of linkage and polymerization on the energy levels of S-1, T-1, and T-n. The S-1-T-1 splitting observed for the meta-linked monomer (0.4 eV) is only half of that in the para-linked monomer (0.8 eV). Upon polymerization, the exchange energy in the para- linked compound reduces, yet still remains larger than in the meta-linked polymer. We attribute the difference in exchange energy to the difference in wave function overlap between electron and hole in these compounds. (c) 2006 American Institute of Physics
This article presents recent progress in the field of polymeric surfactants made of permanently amphiphilic block copolymers or of stimulus-sensitive ones. We highlight key points in the design of amphiphilic macromolecules, to yield polymer surfactants with tailor-made properties, as well as recently developed and still challenging application fields for this new class of surfactants. The efficiency boosting of amphiphilic block copolymers as co-surfactants in microemulsions is discussed, as are surface modification by polymer surfactants, and stabilization of dispersions. Moreover, the use of block copolymers in nanosciences is presented, for instance as a tool for nanomaterial fabrication, or for biomedical and cosmetic applications in bio-nanotechnology. Finally, self-assembly and applications of some newly developed "exotic" amphiphilic block copolymer structures as new surface-active materials will be highlighted
The velocity distribution of a granular gas is analyzed in terms of the Sonine polynomials expansion. We derive an analytical expression for the third Sonine coefficient a(3). In contrast to frequently used assumptions this coefficient is of the same order of magnitude as the second Sonine coefficient a(2). For small inelasticity the theoretical result is in good agreement with numerical simulations. The next-order Sonine coefficients a(4), a(5) and a(6) are determined numerically. While these coefficients are negligible for small dissipation, their magnitude grows rapidly with increasing inelasticity for 0 < epsilon less than or similar to 0.6. We conclude that this behavior of the Sonine coefficients manifests the breakdown of the Sonine polynomial expansion caused by the increasing impact of the overpopulated high-energy tail of the distribution function
Clear-water phase (CWP) is an important event in seasonal plankton succession. We examined the influence of all herbivorous zooplankton on its initiation under different weather and climatic conditions using up to 19 years of observations from the large, deep Lake Constance (Europe) and estimates of relative clearance rates. A CWP occurred regularly, even if daphnid biomass was still very low. CWP was attributed to strong grazing either by a daphnid- dominated zooplankton community or by a diverse assemblage consisting of micro- and meso-zooplankton. Both types of zooplankton communities occurred with approximately the same frequency. The timing of the CWP was unrelated to the North Atlantic Oscillation (NAO) but correlated with the wind-dependent intensity of deep vertical mixing 3 months earlier, during early spring. Less mixing enabled early growth of phytoplankton, ciliates and rotifers despite low temperatures, which prevented daphnid development at this time. This resulted in enhanced grazing of ciliates and rotifers, which increased the importance of phytoplankton less edible for most ciliates, rotifers and daphnids. Ciliates clearly dominated the grazing pressure on phytoplankton throughout spring, maintaining high biomasses together with the phytoplankton for up to 2 months. A CWP was observed when herbivores grazing on larger phytoplankton developed in addition to ciliates
We present UVES observations of the log N(H I) = 21.7 damped Lyman-alpha system at z(abs) = 2.03954 towards the quasar PKS 0458-020. Hi Lyman-alpha emission is detected in the center of the damped Lyman-alpha absorption trough. Metallicities are derived for Mg II, Si II, P II, Cr II, Mn II, Fe II and Zn II and are found to be -1.21 +/- 0.12, - 1.28 +/- 0.20, -1.54 +/- 0.11, -1.66 +/- 0.10, -2.05 +/- 0.11, -1.87 +/- 0.11, -1.22 +/- 0.10, respectively, relative to solar. The depletion factor is therefore of the order of [Zn/Fe] = 0.65. We observe metal absorption lines to be blueshifted compared to the Lyman-alpha emission up to a maximum of similar to 100 and 200 km s(-1) for low and high- ionization species respectively. This can be interpreted either as the consequence of rotation in a large (similar to 7 kpc) disk or as the imprint of a galactic wind. The star formation rate (SFR) derived from the Lyman-alpha emission, 1.6 M-circle dot yr(-1), is compared with that estimated from the observed C II* absorption. No molecular hydrogen is detected in our data, yielding a molecular fraction log f < -6.52. This absence of H-2 can be explained as the consequence of a high ambient UV flux which is one order of magnitude larger than the radiation field in the ISM of our Galaxy and originates in the observed emitting region
In this work, we reanalyze the heart rate variability (HRV) data from the 2002 Computers in Cardiology (CiC) Challenge using the concept of large-scale dimension densities and additionally apply this technique to data of healthy persons and of patients with cardiac diseases. The large-scale dimension density (LASDID) is estimated from the time series using a normalized Grassberger-Procaccia algorithm, which leads to a suitable correction of systematic errors produced by boundary effects in the rather large scales of a system. This way, it is possible to analyze rather short, nonstationary, and unfiltered data, such as HRV. Moreover, this method allows us to analyze short parts of the data and to look for differences between day and night. The circadian changes in the dimension density enable us to distinguish almost completely between real data and computer-generated data from the CiC 2002 challenge using only one parameter. In the second part we analyzed the data of 15 patients with atrial fibrillation (AF), 15 patients with congestive heart failure (CHF), 15 elderly healthy subjects (EH), as well as 18 young and healthy persons (YH). With our method we are able to separate completely the AF (rho(mu)(ls)=0.97 +/- 0.02) group from the others and, especially during daytime, the CHF patients show significant differences from the young and elderly healthy volunteers (CHF, 0.65 +/- 0.13; EH, 0.54 +/- 0.05; YH, 0.57 +/- 0.05; p < 0.05 for both comparisons). Moreover, for the CHF patients we find no circadian changes in rho(mu)(ls) (day, 0.65 +/- 0.13; night, 0.66 +/- 0.12; n.s.) in contrast to healthy controls (day, 0.54 +/- 0.05; night, 0.61 +/- 0.05; p=0.002). Correlation analysis showed no statistical significant relation between standard HRV and circadian LASDID, demonstrating a possibly independent application of our method for clinical risk stratification
We present a technique that identifies truly interacting subsystems of a complex system from multichannel data if the recordings are an unknown linear and instantaneous mixture of the true sources. The method is valid for arbitrary noise structure. For this, a blind source separation technique is proposed that diagonalizes antisymmetrized cross- correlation or cross-spectral matrices. The resulting decomposition finds truly interacting subsystems blindly and suppresses any spurious interaction stemming from the mixture. The usefulness of this interacting source analysis is demonstrated in simulations and for real electroencephalography data
We propose a new autonomous dynamical system of dimension N=4 that demonstrates the regime of stable two- frequency motions and period-doubling bifurcations of a two-dimensional torus. It is shown that the period-doubling bifurcation of the two-dimensional torus is not followed by the resonance phenomenon, and the two-dimensional ergodic torus undergoes a period-doubling bifurcation. The interaction of two generators is also analyzed. The phenomenon of external and mutual synchronization of two-frequency oscillations is observed, for which winding number locking on a two- dimensional torus takes place
Starting from an initial wiring of connections, we show that the synchronizability of a network can be significantly improved by evolving the graph along a time dependent connectivity matrix. We consider the case of connectivity matrices that commute at all times, and compare several approaches to engineer the corresponding commutative graphs. In particular, we show that synchronization in a dynamical network can be achieved even in the case in which each individual commutative graphs does not give rise to synchronized behavior
In this paper we show that delay embedding produces spurious structures in a recurrence plot (RP) that are not present in the real attractor. We analyze typical sets of simulated data, such as white noise and data from the chaotic Rossler system to show the relevance of this effect. In the second part of the paper we show that the second order Renyi entropy and the correlation dimension are dynamical invariants that can be estimated from Recurrence Plots with arbitrary embedding dimension and delay
In the present paper, two kinds of dynamical complex networks are considered. The first is that elements of every node have different time delays but all nodes in Such networks have the same time-delay vector. The second is that different nodes have different time-delay vectors, and the elements of each node also have different time delays. Corresponding synchronization theorems are established. Numerical examples show the efficiency of the derived theorems.
We present the results of phase-referenced VLBA+Effelsberg observations at five frequencies of the double-image gravitational lens WAS B0218+357, made to establish the precise registration of the A and B lensed image positions. The motivation behind these observations is to investigate the anomalous variation of the image flux-density ratio (A[B) with frequency - this ratio changes by almost a factor of two over a frequency range from 1.65 GHz to 15.35 GHz. We investigate whether frequency dependent image positions, combined with a magnification gradient across the image field, could give rise to the anomaly. Our observations confirm the variation of image flux-density ratio with frequency. The results from Our phase-reference astrometry, taken together with the lens mass model of Wucknitz et al. (2004, MNRAS, 349, 14), show that shifts of the image peaks and centroids are too small to account for the observed frequency- dependent ratio
We demonstrate that the entropy of entanglement and the distillable entanglement of regions with respect to the rest of a general harmonic-lattice system in the ground or a thermal state scale at most as the boundary area of the region. This area law is rigorously proven to hold true in noncritical harmonic-lattice systems of arbitrary spatial dimension, for general finite-ranged harmonic interactions, regions of arbitrary shape, and states of nonzero temperature. For nearest-neighbor interactions-corresponding to the Klein-Gordon case-upper and lower bounds to the degree of entanglement can be stated explicitly for arbitrarily shaped regions, generalizing the findings of Phys. Rev. Lett. 94, 060503 (2005). These higher-dimensional analogs of the analysis of block entropies in the one-dimensional case show that under general conditions, one can expect an area law for the entanglement in noncritical harmonic many-body systems. The proofs make use of methods from entanglement theory, as well as of results on matrix functions of block- banded matrices. Disordered systems are also considered. We moreover construct a class of examples for which the two- point correlation length diverges, yet still an area law can be proven to hold. We finally consider the scaling of classical correlations in a classical harmonic system and relate it to a quantum lattice system with a modified interaction. We briefly comment on a general relationship between criticality and area laws for the entropy of entanglement
We investigate the relationship between the gap between the energy of the ground state and the first excited state and the decay of correlation functions in harmonic lattice systems. We prove that in gapped systems, the exponential decay of correlations follows for both the ground state and thermal states. Considering the converse direction, we show that an energy gap can follow from algebraic decay and always does for exponential decay. The underlying lattices are described as general graphs of not necessarily integer dimension, including translationally invariant instances of cubic lattices as special cases. Any local quadratic couplings in position and momentum coordinates are allowed for, leading to quasi-free ( Gaussian) ground states. We make use of methods of deriving bounds to matrix functions of banded matrices corresponding to local interactions on general graphs. Finally, we give an explicit entanglement-area relationship in terms of the energy gap for arbitrary, not necessarily contiguous regions on lattices characterized by general graphs
Many real-world networks are characterized by adaptive changes in their topology depending on the state of their nodes. Here we study epidemic dynamics on an adaptive network, where the susceptibles are able to avoid contact with the infected by rewiring their network connections. This gives rise to assortative degree correlation, oscillations, hysteresis, and first order transitions. We propose a low-dimensional model to describe the system and present a full local bifurcation analysis. Our results indicate that the interplay between dynamics and topology can have important consequences for the spreading of infectious diseases and related applications
There is strong observational evidence of shocks and clumping in radiation-driven stellar winds from hot, luminous stars. The resulting non nous monotonic velocity law allows for radiative coupling between distant locations, which is so far not accounted for in hydrodynamic wind simulations. In the present paper, we determine the Sobolev source function and radiative line force in the presence of radiative coupling in spherically symmetric flows, extending the geometry-free formalism of Rybicki & Hummer (1978, ApJ, 219, 654) to the case of three-point coupling, which can result from, e. g., corotating interaction regions, wind shocks, or mass overloading. For a simple model of an overloaded wind, we find that, surprisingly, the flow decelerates at all radii above a certain height when nonlocal radiative coupling is accounted for. We discuss whether radiation-driven winds might in general not be able to re- accelerate after a non monotonicity has occurred in the velocity law
We report a noise-memory induced phase transition in an array of oscillatory neural systems, which leads to the suppression of synchronous oscillations and restoration of excitable dynamics. This phenomenon is caused by the systematic contributions of temporally correlated parametric noise, i.e., possessing a memory, which stabilizes a deterministically unstable fixed point. Changing the noise correlation time, a reentrant phase transition to noise- induced excitability is observed in a globally coupled array. Since noise-induced excitability implies the restoration of the ability to transmit information, associated spatiotemporal patterns are observed afterwards. Furthermore, an analytic approach to predict the systematic effects of exponentially correlated noise is presented and its results are compared with the simulations
Kopplung von Polyelektrolyten und geladenen Lipid-Monoschichten an der Wasser / Luft-Grenzflächen
(2006)
The work presents low signal dielectric spectra of gold/copper phthalocyanine/magnesium and gold/copper phthalocyanine/gold sandwich systems in the 25 Hz-1 MHz frequency range. The performed analysis enables us to distinguish the electrode resistance and the lattice polarization from processes related with electric transport, such as charge carrier relaxation at space charge region of a barrier and charge carrier injection in dielectric response.
Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated
Dynamical organization of connection weights is studied in scale-free networks of chaotic oscillators, where the coupling strength of a node from its neighbors develops adaptively according to the local synchronization property between the node and its neighbors. We find that when complete synchronization is achieved, the coupling strength becomes weighted and correlated with the topology due to a hierarchical transition to synchronization in heterogeneous networks. Importantly, such an adaptive process enhances significantly the synchronizability of the networks, which could have meaningful implications in the manipulation of dynamical networks
Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters
The results of the theoretical consideration of stochastic resonance in overdamped bistable oscillators are given. These results are founded not on the model of two states as in [McNamara B, Wiesenfeld K. Theory of stochastic resonance. Phys Rev A 1989;39:4854-69], but on splitting of motion into regular and random and the rigorous solution of the Fokker-Planck equation for the random component. We show that this resonance is caused by a change, under the influence of noise, of the system's effective stiffness and damping factor contained in the equation for the regular component. For a certain value of the noise intensity the effective stiffness is minimal, and this fact causes non-monotonic change of the output signal amplitude as the noise intensity changes. It is important that the location of the minimum and its value depend essentially on the signal frequency.
We show many versatile phase synchronous configurations that emerge in an array of coupled chaotic elements due to the presence of a periodic stimulus. Then, we explain the relevance of these configurations to the understanding of how information about such a. stimulus is transmitted from one side to the other in this array. The stimulus actively creates the ways to be transmitted, by making the chaotic elements to phase synchronize
A key technology for large eddy simulation (LES) of complex flows is an appropriate wall modeling strategy. In this paper we apply for the first time a fully nonparametric procedure for the estimation of generalized additive models (GAM) by conditional statistics. As a database, we use DNS and wall-resolved LES data of plane channel flow for Reynolds numbers, Re = 2800, 4000 (DNS) and 10,935, 22,776 (LES). The statistical method applied is a quantitative tool for the identification of important model terms, allowing for an identification of some of the near-wall physics. The results are given as nonparametric functions which cannot be attained by other methods. We investigated a generalized model which includes Schumann's and Piomelli et al.'s model. A strong influence of the pressure gradient in the viscous sublayer is found; for larger wall distances the spanwise pressure gradient even dominates the tau(w,zy). component. The first a posteriori LES results are given.
The spin probes 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO), 4-hydroxy-2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPOL), and 2,2,6,6-tetramethyl-4-trimethylammoniumpiperidine-1-oxyllodide (CAT-1) are examined in a number of ionic liquids based on substituted imidazolium cations and tetrafluoroborate and hexafluorophosphate anions, respectively. The reorientation correlation times tau(R) of the spin probes in these systems have been determined by complete spectra simulation and, for rapid reortientation, by analysis of the intensities of the hyperfine lines of the electron spin resonance (ESR) spectra. A comparison of the results with those from the model system glycerol/water and selected organic solvents is made. Additions of diamagnetic and paramagnetic ions allow the conclusion that salt effects and spin exchange are present, and that both are superimposed by motional effects. Specific interactions in the ionic liquids, as well as between the spin-probe molecules and the constituents of the ionic liquids are reflected in the spectra of the spin probes, depending on their molecular structure
We study synchronization behavior in networks of coupled chaotic oscillators with heterogeneous connection degrees. Our focus is on regimes away from the complete synchronization state, when the coupling is not strong enough, when the oscillators are under the influence of noise or when the oscillators are nonidentical. We have found a hierarchical organization of the synchronization behavior with respect to the collective dynamics of the network. Oscillators with more connections (hubs) are synchronized more closely by the collective dynamics and constitute the dynamical core of the network. The numerical observation of this hierarchical synchronization is supported with an analysis based on a mean field approximation and the master stability function. (C) 2006 American Institute of Physics
In the favoured core-accretion model of formation of planetary systems, solid planetesimals accumulate to build up planetary cores, which then accrete nebular gas if they are sufficiently massive. Around M-dwarf stars ( the most common stars in our Galaxy), this model favours the formation of Earth-mass (M+) to Neptune-mass planets with orbital radii of 1 to 10 astronomical units (AU), which is consistent with the small number of gas giant planets known to orbit M-dwarf host stars(1-4). More than 170 extrasolar planets have been discovered with a wide range of masses and orbital periods, but planets of Neptune's mass or less have not hitherto been detected at separations of more than 0.15 AU from normal stars. Here we report the discovery of a 5.5(-2.7)(+5.5)M(+) planetary companion at a separation of 2.6(- 0.6)(+1.5) AU from a 0.22(-0.11)(+0.21)M(.) M-dwarf star, where M-. refers to a solar mass. (We propose to name it OGLE- 2005-BLG-390Lb, indicating a planetary mass companion to the lens star of the microlensing event.) The mass is lower than that of GJ876d (ref. 5), although the error bars overlap. Our detection suggests that such cool, sub-Neptune-mass planets may be more common than gas giant planets, as predicted by the core accretion theory.
We present ground-based and Hubble Space Telescope optical observations of the X-ray flash ( XRF) 020903, covering 300 days. The afterglow showed a very rapid rise in the first day, followed by a relatively slow decay in the next few days. There was a clear bump in the light curve after similar to 25 days, accompanied by a drastic change in the spectral energy distribution. The light curve and the spectral energy distribution are naturally interpreted as describing the emergence and subsequent decay of a supernova ( SN), similar to SN 1998bw. At peak luminosity, the SN is estimated to be 0.8 +/- 0.1 mag fainter than SN 1998bw. This argues in favor of the existence of a SN associated with this XRF. A spectrum obtained 35 days after the burst shows emission lines from the host galaxy. We use this spectrum to put an upper limit on the oxygen abundance of the host at [O/H] <= 0.6 dex. We also discuss a possible trend between the softness of several bursts and the early behavior of the optical afterglow, in the sense that XRFs and X-ray-rich gamma- ray bursts ( GRBs) seem to have a plateau phase or even a rising light curve. This can be naturally explained in models in which XRFs are similar to GRBs but are seen off the jet axis.
The paper provides an introduction and survey of conservative discretization methods for Hamiltonian partial differential equations. The emphasis is on variational, symplectic and multi-symplectic methods. The derivation of methods as well as some of their fundamental geometric properties are discussed. Basic principles are illustrated by means of examples from wave and fluid dynamics
Six Earth system models of intermediate complexity that are able to simulate interaction between atmosphere, ocean, and land surface, were forced with a scenario of land cover changes during the last millennium. In response to historical deforestation of about 18 million sq km, the models simulate a decrease in global mean annual temperature in the range of 0.13-0.25 degrees C. The rate of this cooling accelerated during the 19th century, reached a maximum in the first half of the 20th century, and declined at the end of the 20th century. This trend is explained by temporal and spatial dynamics of land cover changes, as the effect of deforestation on temperature is less pronounced for tropical than for temperate regions, and reforestation in the northern temperate areas during the second part of the 20th century partly offset the cooling trend. In most of the models, land cover changes lead to a decline in annual land evapotranspiration, while seasonal changes are rather equivocal because of spatial shifts in convergence zones. In the future, reforestation might be chosen as an option for the enhancement of terrestrial carbon sequestration. Our study indicates that biogeophysical mechanisms need to be accounted for in the assessment of land management options for climate change mitigation
We apply linear and nonlinear methods to study the properties of surfaces generated by a laser beam melt ablation process. As a result we present a characterization and ordering of the surfaces depending on the adjusted process parameters. Our findings give some insight into the performance of two widely applied multifractal analysis methods-the detrended fluctuation analysis and the wavelet transform modulus maxima method-on short real world data
Two metal tetrapyrroles containing gallium, gallium hydroxyl tetratolylporphyrin and 13(2)-demethoxycarbonyl- (gallium hydroxyl)methyl pheophorbide a (Ga-(OH)-chlorin), were synthesized from their respective free bases using Ga(III)-acetylacetonate in a phenol melt. Their photophysical properties were investigated and the quantum yields of different monomolecular deactivation processes were determined. For Ga-(OH)-porphyrin S-2-fluorescence was observed and quantified. In contrast. for Ga-(OH)-chlorin no S-2-fluorescence was observed. Both compounds should be useful as efficient photosensitizers in photodynamic therapy.
The velocity distributions of the laser-induced desorption of NO molecules from an epitaxially grown film of NiO(100) on Ni(100) have been studied [ Mull et al., J. Chem. Phys., 1992, 96, 7108]. A pronounced bimodality of velocity distributions has been found, where the NO molecules desorbing with higher velocities exhibit a coupling to the rotational quantum states J. In this article we present simulations of state resolved velocity distributions on a full ab initio level. As a basis for this quantum mechanical treatment a 4D potential energy surface (PES) was constructed for the electronic ground and a representative excited state, using a NiO5Mg1318+ cluster. The PESs of the electronic ground and an excited state were calculated at the CASPT2 and the configuration interaction (CI) level of theory, respectively. Multi-dimensional quantum wave packet simulations on these two surfaces were performed for different sets of degrees of freedom. Our key finding is that at least a 3D wave packet simulation, in which the desorption coordinate Z, polar angle theta and lateral coordinate X are included, is necessary to allow the simulation of experimental velocity distributions. Analysis of the wave packet dynamics demonstrates that essentially the lateral coordinate, which was neglected in previous studies [Kluner et al., Phys. Rev. Lett. 1998, 80, 5208], is responsible for the experimentally observed bimodality. An extensive analysis shows that the bimodality is due to a bifurcation of the wave packet on the excited state PES, where the motion of the molecule parallel to the surface plays a decisive role
Results of a high pressure x-ray study of 2,5-di(4-pyridyl)-1,3,4-oxadiazole up to 2.5 GPa are presented and discussed. Parameters for the Murnaghan equation of state are derived. The bulk modulus amounts to K-0 = 4.6 +/- 0.3 GPa and its pressure derivative to K-0' = 7.4 +/- 0.6. These values are comparable to values of other diphenyl-1,3,4- oxadiazoles. The anisotropy of the compression is analysed using the strain tensor and discussed based on the anisotropy of the intermolecular interactions
To test the consequences of decreased diversity and exclusion of keystone species, we compared the planktonic food webs in two acidic (pH <= 3), species-poor mining lakes with those in two species-rich, neutral lakes. The ratio of heterotrophic to autotrophic biomass (HIA) was similar in acidic and neutral lakes with comparable productivity. However, food webs in both acidic lakes were largely restricted to two trophic levels in contrast to the four levels found in neutral lakes. This restriction in food chain length was attributed to the absence of efficient secondary consumers, rather than to productivity or lake size which resulted in unusually low predator-prey weight ratios, with small top predators hardly exceeding their pry in size. In contrast to the neutral lakes, plankton biomass size spectra of acidic lakes were discontinuous due to a lack of major functional groups. The unique size-dependence of feeding modes in pelagic food webs, with bacteria in the smallest size classes followed by autotrophs, herbivores and carnivores, was maintained for bacteria but the other feeding modes strongly overlapped in size. Thus, their characteristic succession along the size gradient was roughly preserved under extreme conditions but the flow of energy along the size gradient was truncated in the acidic lakes. For most but not all attributes studied, differences were larger between acidic and neutral lakes than between neutral lakes of different trophic state
We describe effects of the asymmetry of cycles and non-stationarity in time series on the phase synchronization method which may lead to artifacts. We develop a modified method that overcomes these effects and apply it to study parkinsonian tremor. Our results indicate that there is synchronization between two different hands and provide information about the time delay separating their dynamics. These findings suggest that this method may be useful for detecting and quantifying weak synchronization between two non-stationary signals.
The development of surface relief and density patterns in azobenzene polymer films was studied by diffraction at two different wavelengths. We used x-ray diffraction of synchrotron radiation at 0.124 nm in combination with visible light diffraction at a wavelength of 633 nm. In contrast to visible light scattering x-ray diffraction allows the separation of a surface relief and a density grating contribution due to the different functional dependence of the scattering power. Additionally, the x-ray probe is most sensitive for the onset of the surface grating formation