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In the present work, we study wave phenomena in strongly nonlinear lattices. Such lattices are characterized by the absence of classical linear waves. We demonstrate that compactons – strongly localized solitary waves with tails decaying faster than exponential – exist and that they play a major role in the dynamics of the system under consideration. We investigate compactons in different physical setups. One part deals with lattices of dispersively coupled limit cycle oscillators which find various applications in natural sciences such as Josephson junction arrays or coupled Ginzburg-Landau equations. Another part deals with Hamiltonian lattices. Here, a prominent example in which compactons can be found is the granular chain. In the third part, we study systems which are related to the discrete nonlinear Schrödinger equation describing, for example, coupled optical wave-guides or the dynamics of Bose-Einstein condensates in optical lattices. Our investigations are based on a numerical method to solve the traveling wave equation. This results in a quasi-exact solution (up to numerical errors) which is the compacton. Another ansatz which is employed throughout this work is the quasi-continuous approximation where the lattice is described by a continuous medium. Here, compactons are found analytically, but they are defined on a truly compact support. Remarkably, both ways give similar qualitative and quantitative results. Additionally, we study the dynamical properties of compactons by means of numerical simulation of the lattice equations. Especially, we concentrate on their emergence from physically realizable initial conditions as well as on their stability due to collisions. We show that the collisions are not exactly elastic but that a small part of the energy remains at the location of the collision. In finite lattices, this remaining part will then trigger a multiple scattering process resulting in a chaotic state.
In the present dissertation paper we study problems related to synchronization phenomena in the presence of noise which unavoidably appears in real systems. One part of the work is aimed at investigation of utilizing delayed feedback to control properties of diverse chaotic dynamic and stochastic systems, with emphasis on the ones determining predisposition to synchronization. Other part deals with a constructive role of noise, i.e. its ability to synchronize identical self-sustained oscillators. First, we demonstrate that the coherence of a noisy or chaotic self-sustained oscillator can be efficiently controlled by the delayed feedback. We develop the analytical theory of this effect, considering noisy systems in the Gaussian approximation. Possible applications of the effect for the synchronization control are also discussed. Second, we consider synchrony of limit cycle systems (in other words, self-sustained oscillators) driven by identical noise. For weak noise and smooth systems we proof the purely synchronizing effect of noise. For slightly different oscillators and/or slightly nonidentical driving, synchrony becomes imperfect, and this subject is also studied. Then, with numerics we show moderate noise to be able to lead to desynchronization of some systems under certain circumstances. For neurons the last effect means “antireliability” (the “reliability” property of neurons is treated to be important from the viewpoint of information transmission functions), and we extend our investigation to neural oscillators which are not always limit cycle ones. Third, we develop a weakly nonlinear theory of the Kuramoto transition (a transition to collective synchrony) in an ensemble of globally coupled oscillators in presence of additional time-delayed coupling terms. We show that a linear delayed feedback not only controls the transition point, but effectively changes the nonlinear terms near the transition. A purely nonlinear delayed coupling does not affect the transition point, but can reduce or enhance the amplitude of collective oscillations.
We present electrical impedance measurements of amoeboid cells on microelectrodes. The model organism Dictyostelium discoideum shows under starvation conditions a transition to collective behavior when chemotactic cells collect in multicellular aggregates. We show how impedance recordings give a precise picture of the stages of aggregation by tracing the dynamics of cell-substrate adhesion. Furthermore, we present for the first time systematic single cell measurements of wild type cells and four mutant strains that differ in their substrate adhesion strength. We recorded the projected cell area by time lapse microscopy and found a correlation between quasi-periodic oscillations in the kinetics of the projected area - the cell shape oscillation - and the long-term trend in the impedance signal. Typically, amoeboid motility advances via a cycle of membrane protrusion, substrate adhesion, traction of the cell body and tail retraction. This motility cycle results in the quasi-periodic oscillations of the projected cell area and the impedance. In all cell lines measured, similar periods were observed for this cycle, despite the differences in attachment strength. We observed that cell-substrate attachment strength strongly affects the impedance in that the deviations from mean (the magnitude of fluctuations) are enhanced in cells that effectively transmit forces, generated by the cytoskeleton, to the substrate. For example, in talA- cells, which lack the actin anchoring protein talin, the fluctuations are strongly reduced. Single cell force spectroscopy and results from a detachment assay, where adhesion is measured by exposing cells to shear stress, confirm that the magnitude of impedance fluctuations is a correct measure for the strength of substrate adhesion. Finally, we also worked on the integration of cell-substrate impedance sensors into microfluidic devices. A chip-based electrical chemotaxis assay is designed which measures the speed of chemotactic cells migrating over microelectrodes along a chemical concentration gradient.
In the living cell, the organization of the complex internal structure relies to a large extent on molecular motors. Molecular motors are proteins that are able to convert chemical energy from the hydrolysis of adenosine triphosphate (ATP) into mechanical work. Being about 10 to 100 nanometers in size, the molecules act on a length scale, for which thermal collisions have a considerable impact onto their motion. In this way, they constitute paradigmatic examples of thermodynamic machines out of equilibrium. This study develops a theoretical description for the energy conversion by the molecular motor myosin V, using many different aspects of theoretical physics. Myosin V has been studied extensively in both bulk and single molecule experiments. Its stepping velocity has been characterized as a function of external control parameters such as nucleotide concentration and applied forces. In addition, numerous kinetic rates involved in the enzymatic reaction of the molecule have been determined. For forces that exceed the stall force of the motor, myosin V exhibits a 'ratcheting' behaviour: For loads in the direction of forward stepping, the velocity depends on the concentration of ATP, while for backward loads there is no such influence. Based on the chemical states of the motor, we construct a general network theory that incorporates experimental observations about the stepping behaviour of myosin V. The motor's motion is captured through the network description supplemented by a Markov process to describe the motor dynamics. This approach has the advantage of directly addressing the chemical kinetics of the molecule, and treating the mechanical and chemical processes on equal grounds. We utilize constraints arising from nonequilibrium thermodynamics to determine motor parameters and demonstrate that the motor behaviour is governed by several chemomechanical motor cycles. In addition, we investigate the functional dependence of stepping rates on force by deducing the motor's response to external loads via an appropriate Fokker-Planck equation. For substall forces, the dominant pathway of the motor network is profoundly different from the one for superstall forces, which leads to a stepping behaviour that is in agreement with the experimental observations. The extension of our analysis to Markov processes with absorbing boundaries allows for the calculation of the motor's dwell time distributions. These reveal aspects of the coordination of the motor's heads and contain direct information about the backsteps of the motor. Our theory provides a unified description for the myosin V motor as studied in single motor experiments.
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.
This work explores the equilibrium structure and thermodynamic phase behavior of complexes formed by charged polymer chains (polyelectrolytes) and oppositely charged spheres (macroions). Polyelectrolyte-macroion complexes form a common pattern in soft-matter physics, chemistry and biology, and enter in numerous technological applications as well. From a fundamental point of view, such complexes are interesting in that they combine the subtle interplay between electrostatic interactions and elastic as well as entropic effects due to conformational changes of the polymer chain, giving rise to a wide range of structural properties. This forms the central theme of theoretical studies presented in this thesis, which concentrate on a number of different problems involving strongly coupled complexes, i.e. complexes that are characterized by a large adsorption energy and small chain fluctuations. In the first part, a global analysis of the structural phase behavior of a single polyelectrolyte-macroion complex is presented based on a dimensionless representation, yielding results that cover a wide range of realistic system parameters. Emphasize is made on the interplay between the effects due to the polyelectrolytes chain length, salt concentration and the macroion charge as well as the mechanical chain persistence length. The results are summarized into generic phase diagrams characterizing the wrapping-dewrapping behavior of a polyelectrolyte chain on a macroion. A fully wrapped chain state is typically obtained at intermediate salt concentrations and chain lengths, where the amount of polyelectrolyte charge adsorbed on the macroion typically exceeds the bare macroion charge leading thus to a highly overcharged complex. Perhaps the most striking features occur when a single long polyelectrolyte chain is complexed with many oppositely charged spheres. In biology, such complexes form between DNA (which carries the cell's genetic information) and small oppositely charged histone proteins serving as an efficient mechanism for packing a huge amount of DNA into the micron-size cell nucleus in eucaryotic cells. The resultant complex fiber, known as the chromatin fiber, appears with a diameter of 30~nm under physiological conditions. Recent experiments indicate a zig-zag spatial arrangement for individual DNA-histone complexes (nucleosome core particles) along the chromatin fiber. A numerical method is introduced in this thesis based on a simple generic chain-sphere cell model that enables one to investigate the mechanism of fiber formation on a systematic level by incorporating electrostatic and elastic contributions. As will be shown, stable complex fibers exhibit an impressive variety of structures including zig-zag, solenoidal and beads-on-a-string patterns, depending on system parameters such as salt concentration, sphere charge as well as the chain contour length (per sphere). The present results predict fibers of compact zig-zag structure within the physiologically relevant regime with a diameter of about 30~nm, when DNA-histone parameters are adopted. In the next part, a numerical method is developed in order to investigate the role of thermal fluctuations on the structure and thermodynamic phase behavior of polyelectrolyte-macroion complexes. This is based on a saddle-point approximation, which allows to describe the experimentally observed reaction (or complexation) equilibrium in a dilute solution of polyelectrolytes and macroions on a systematic level. This equilibrium is determined by the entropy loss a single polyelectrolyte chain suffers as it binds to an oppositely charged macroion. This latter quantity can be calculated from the spectrum of polyelectrolyte fluctuations around a macroion, which is determined by means of a normal-mode analysis. Thereby, a stability phase diagram is obtained, which exhibits qualitative agreement with experimental findings. At elevated complex concentrations, one needs to account for the inter-complex interactions as well. It will be shown that at small separations, complexes undergo structural changes in such a way that positive patches from one complex match up with negative patches on the other. Furthermore, one of the polyelectrolyte chains may bridge between the two complexes. These mechanisms lead to a strong inter-complex attraction. As a result, the second virial coefficient associated with the inter-complex interaction becomes negative at intermediate salt concentrations in qualitative agreement with recent experiments on solutions of nucleosome core particles.
In view of the importance of charge storage in polymer electrets for electromechanical transducer applications, the aim of this work is to contribute to the understanding of the charge-retention mechanisms. Furthermore, we will try to explain how the long-term storage of charge carriers in polymeric electrets works and to identify the probable trap sites. Charge trapping and de-trapping processes were investigated in order to obtain evidence of the trap sites in polymeric electrets. The charge de-trapping behavior of two particular polymer electrets was studied by means of thermal and optical techniques. In order to obtain evidence of trapping or de-trapping, charge and dipole profiles in the thickness direction were also monitored. In this work, the study was performed on polyethylene terephthalate (PETP) and on cyclic-olefin copolymers (COCs). PETP is a photo-electret and contains a net dipole moment that is located in the carbonyl group (C = O). The electret behavior of PETP arises from both the dipole orientation and the charge storage. In contrast to PETP, COCs are not photo-electrets and do not exhibit a net dipole moment. The electret behavior of COCs arises from the storage of charges only. COC samples were doped with dyes in order to probe their internal electric field. COCs show shallow charge traps at 0.6 and 0.11 eV, characteristic for thermally activated processes. In addition, deep charge traps are present at 4 eV, characteristic for optically stimulated processes. PETP films exhibit a photo-current transient with a maximum that depends on the temperature with an activation energy of 0.106 eV. The pair thermalization length (rc) calculated from this activation energy for the photo-carrier generation in PETP was estimated to be approx. 4.5 nm. The generated photo-charge carriers can recombine, interact with the trapped charge, escape through the electrodes or occupy an empty trap. PETP possesses a small quasi-static pyroelectric coefficient (QPC): ~0.6 nC/(m²K) for unpoled samples, ~60 nC/(m²K) for poled samples and ~60 nC/(m²K) for unpoled samples under an electric bias (E ~10 V/µm). When stored charges generate an internal electric field of approx. 10 V/µm, they are able to induce a QPC comparable to that of the oriented dipoles. Moreover, we observe charge-dipole interaction. Since the raw data of the QPC-experiments on PETP samples is noisy, a numerical Fourier-filtering procedure was applied. Simulations show that the data analysis is reliable when the noise level is up to 3 times larger than the calculated pyroelectric current for the QPC. PETP films revealed shallow traps at approx. 0.36 eV during thermally-stimulated current measurements. These energy traps are associated with molecular dipole relaxations (C = O). On the other hand, photo-activated measurements yield deep charge traps at 4.1 and 5.2 eV. The observed wavelengths belong to the transitions in PETP that are analogous to the π - π* benzene transitions. The observed charge de-trapping selectivity in the photocharge decay indicates that the charge detrapping is from a direct photon-charge interaction. Additionally, the charge de-trapping can be facilitated by photo-exciton generation and the interaction of the photo-excitons with trapped charge carriers. These results indicate that the benzene rings (C6H4) and the dipolar groups (C = O) can stabilize and share an extra charge carrier in a chemical resonance. In this way, this charge could be de-trapped in connection with the photo-transitions of the benzene ring and with the dipole relaxations. The thermally-activated charge release shows a difference in the trap depth to its optical counterpart. This difference indicates that the trap levels depend on the de-trapping process and on the chemical nature of the trap site. That is, the processes of charge detrapping from shallow traps are related to secondary forces. The processes of charge de-trapping from deep traps are related to primary forces. Furthermore, the presence of deep trap levels causes the stability of the charge for long periods of time.
Tremendous progress in the development of thin film solar cell techniques has been made over the last decade. The field of organic solar cells is constantly developing, new material classes like Perowskite solar cells are emerging and different types of hybrid organic/inorganic material combinations are being investigated for their physical properties and their applicability in thin film electronics. Besides typical single-junction architectures for solar cells, multi-junction concepts are also being investigated as they enable the overcoming of theoretical limitations of a single-junction. In multi-junction devices each sub-cell operates in different wavelength regimes and should exhibit optimized band-gap energies. It is exactly this tunability of the band-gap energy that renders organic solar cell materials interesting candidates for multi-junction applications. Nevertheless, only few attempts have been made to combine inorganic and organic solar cells in series connected multi-junction architectures. Even though a great diversity of organic solar cells exists nowadays, their open circuit voltage is usually low compared to the band-gap of the active layer. Hence, organic low band-gap solar cells in particular show low open circuit voltages and the key factors that determine the voltage losses are not yet fully understood. Besides open circuit voltage losses the recombination of charges in organic solar cells is also a prevailing research topic, especially with respect to the influence of trap states.
The exploratory focus of this work is therefore set, on the one hand, on the development of hybrid organic/inorganic multi-junctions and, on the other hand, on gaining a deeper understanding of the open circuit voltage and the recombination processes of organic solar cells.
In the first part of this thesis, the development of a hybrid organic/inorganic triple-junction will be discussed which showed at that time (Jan. 2015) a record power conversion efficiency of 11.7%. The inorganic sub-cells of these devices consist of hydrogenated amorphous silicon and were delivered by the Competence Center Thin-Film and Nanotechnology for Photovoltaics in Berlin. Different recombination contacts and organic sub-cells were tested in conjunction with these inorganic sub-cells on the basis of optical modeling predictions for the optimal layer thicknesses to finally reach record efficiencies for this type of solar cells.
In the second part, organic model systems will be investigated to gain a better understanding of the fundamental loss mechanisms that limit the open circuit voltage of organic solar cells. First, bilayer systems with different orientation of the donor and acceptor molecules were investigated to study the influence of the donor/acceptor orientation on non-radiative voltage loss. Secondly, three different bulk heterojunction solar cells all comprising the same amount of fluorination and the same polymer backbone in the donor component were examined to study the influence of long range electrostatics on the open circuit voltage. Thirdly, the device performance of two bulk heterojunction solar cells was compared which consisted of the same donor polymer but used different fullerene acceptor molecules. By this means, the influence of changing the energetics of the acceptor component on the open circuit voltage was investigated and a full analysis of the charge carrier dynamics was presented to unravel the reasons for the worse performance of the solar cell with the higher open circuit voltage. In the third part, a new recombination model for organic solar cells will be introduced and its applicability shown for a typical low band-gap cell. This model sheds new light on the recombination process in organic solar cells in a broader context as it re-evaluates the recombination pathway of charge carriers in devices which show the presence of trap states. Thereby it addresses a current research topic and helps to resolve alleged discrepancies which can arise from the interpretation of data derived by different measurement techniques.
This thesis discusses heat and charge transport phenomena in single-crystalline Silicon penetrated by nanometer-sized pores, known as mesoporous Silicon (pSi). Despite the extensive attention given to it as a thermoelectric material of interest, studies on microscopic thermal and electronic transport beyond its macroscopic characterizations are rarely reported. In contrast, this work reports the interplay of both.
PSi samples synthesized by electrochemical anodization display a temperature dependence of specific heat 𝐶𝑝 that deviates from the characteristic 𝑇^3 behaviour (at 𝑇<50𝐾). A thorough analysis reveals that both 3D and 2D Einstein and Debye modes contribute to this specific heat. Additional 2D Einstein modes (~3 𝑚𝑒𝑉) agree reasonably well with the boson peak of SiO2 in pSi pore walls. 2D Debye modes are proposed to account for surface acoustic modes causing a significant deviation from the well-known 𝑇^3 dependence of 𝐶𝑝 at 𝑇<50𝐾.
A novel theoretical model gives insights into the thermal conductivity of pSi in terms of porosity and phonon scattering on the nanoscale. The thermal conductivity analysis utilizes the peculiarities of the pSi phonon dispersion probed by the inelastic neutron scattering experiments. A phonon mean-free path of around 10 𝑛𝑚 extracted from the presented model is proposed to cause the reduced thermal conductivity of pSi by two orders of magnitude compared to p-doped bulk Silicon. Detailed analysis indicates that compound averaging may cause a further 10-50% reduction. The percolation threshold of 65% for thermal conductivity of pSi samples is subsequently determined by employing theoretical effective medium models.
Temperature-dependent electrical conductivity measurements reveal a thermally activated transport process. A detailed analysis of the activation energy 𝐸𝐴𝜎 in the thermally activated transport exhibits a Meyer Neldel compensation rule between different samples that originates in multi-phonon absorption upon carrier transport. Activation energies 𝐸𝐴𝑆 obtained from temperature-dependent thermopower measurements provide further evidence for multi-phonon assisted hopping between localized states as a dominant charge transport mechanism in pSi, as they systematically differ from the determined 𝐸𝐴𝜎 values.
Auf der Grundlage von Sonnenphotometermessungen an drei Messstationen (AWIPEV/ Koldewey in Ny-Ålesund (78.923 °N, 11.923 °O) 1995–2008, 35. Nordpol Driftstation – NP-35 (84.3–85.5 °N, 41.7–56.6 °O) März/April 2008, Sodankylä (67.37 °N, 26.65 °O) 2004–2007) wird die Aerosolvariabilität in der europäischen Arktis und deren Ursachen untersucht. Der Schwerpunkt liegt dabei auf der Frage des Zusammenhanges zwischen den an den Stationen gemessenen Aerosolparametern (Aerosol optische Dicke, Angström Koeffizient, usw.) und dem Transport des Aerosols sowohl auf kurzen Zeitskalen (Tagen) als auch auf langen Zeitskalen (Monate, Jahre). Um diesen Zusammenhang herzustellen, werden für die kurzen Zeitskalen mit dem Trajektorienmodell PEP-Tracer 5-Tage Rückwärtstrajektorien in drei Starthöhen (850 hPa, 700 hPa, 500 hPa) für die Uhrzeiten 00, 06, 12 und 18 Uhr berechnet. Mit Hilfe der nicht-hierarchischen Clustermethode k-means werden die berechneten Rückwärtstrajektorien dann zu Gruppen zusammengefasst und bestimmten Quellgebieten und den gemessenen Aerosol optischen Dicken zugeordnet. Die Zuordnung von Aerosol optischer Dicke und Quellregion ergibt keinen eindeutigen Zusammenhang zwischen dem Transport verschmutzter Luftmassen aus Europa oder Russland bzw. Asien und erhöhter Aerosol optischer Dicke. Dennoch ist für einen konkreten Einzelfall (März 2008) ein direkter Zusammenhang von Aerosoltransport und hohen Aerosol optischen Dicken nachweisbar. In diesem Fall gelangte Waldbrandaerosol aus Südwestrussland in die Arktis und konnte sowohl auf der NP-35 als auch in Ny-Ålesund beobachtet werden. In einem weiteren Schritt wird mit Hilfe der EOF-Analyse untersucht, inwieweit großskalige atmosphärische Zirkulationsmuster für die Aerosolvariabilität in der europäischen Arktis verantwortlich sind. Ähnlich wie bei der Trajektorienanalyse ist auch die Verbindung der atmosphärischen Zirkulation zu den Photometermessungen an den Stationen in der Regel nur schwach ausgeprägt. Eine Ausnahme findet sich bei der Betrachtung des Jahresganges des Bodendruckes und der Aerosol optischen Dicke. Hohe Aerosol optische Dicken treten im Frühjahr zum einen dann auf, wenn durch das Islandtief und das sibirische Hochdruckgebiet Luftmassen aus Europa oder Russland/Asien in die Arktis gelangen, und zum anderen, wenn sich ein kräftiges Hochdruckgebiet über Grönland und weiten Teilen der Arktis befindet. Ebenso zeigt sich, dass der Übergang zwischen Frühjahr und Sommer zumindest teilweise bedingt ist durch denWechsel vom stabilen Polarhoch im Winter und Frühjahr zu einer stärker von Tiefdruckgebieten bestimmten arktischen Atmosphäre im Sommer. Die geringere Aerosolkonzentration im Sommer kann zum Teil mit einer Zunahme der nassen Deposition als Aerosolsenke begründet werden. Für Ny-Ålesund wird neben den Transportmustern auch die chemische Zusammensetzung des Aerosols mit Hilfe von Impaktormessungen an der Zeppelinstation auf dem Zeppelinberg (474m ü.NN) nahe Ny-Ålesund abgeleitet. Dabei ist die positive Korrelation der Aerosoloptischen Dicke mit der Konzentration von Sulfationen und Ruß sehr deutlich. Beide Stoffe gelangen zu einem Großteil durch anthropogene Emissionen in die Atmosphäre. Die damit nachweisbar anthropogen geprägte Zusammensetzung des arktischen Aerosols steht im Widerspruch zum nicht eindeutig herstellbaren Zusammenhang mit dem Transport des Aerosols aus Industrieregionen. Dies kann nur durch einen oder mehrere gleichzeitig stattfindende Transformationsprozesse (z. B. Nukleation von Schwefelsäurepartikeln) während des Transportes aus den Quellregionen (Europa, Russland) erklärt werden.
Over the past decades, there has been a growing interest in ‘extreme events’ owing to the increasing threats that climate-related extremes such as floods, heatwaves, droughts, etc., pose to society. While extreme events have diverse definitions across various disciplines, ranging from earth science to neuroscience, they are characterized mainly as dynamic occurrences within a limited time frame that impedes the normal functioning of a system. Although extreme events are rare in occurrence, it has been found in various hydro-meteorological and physiological time series (e.g., river flows, temperatures, heartbeat intervals) that they may exhibit recurrent behavior, i.e., do not end the lifetime of the system. The aim of this thesis to develop some
sophisticated methods to study various properties of extreme events.
One of the main challenges in analyzing such extreme event-like time series is that they have large temporal gaps due to the paucity of the number of observations of extreme events. As a result, existing time series analysis tools are usually not helpful to decode the underlying
information. I use the edit distance (ED) method to analyze extreme event-like time series in their unaltered form. ED is a specific distance metric, mainly designed to measure the similarity/dissimilarity between point process-like data. I combine ED with recurrence plot techniques to identify the recurrence property of flood events in the Mississippi River in the United States. I also use recurrence quantification analysis to show the deterministic properties
and serial dependency in flood events.
After that, I use this non-linear similarity measure (ED) to compute the pairwise dependency in extreme precipitation event series. I incorporate the similarity measure within the framework of complex network theory to study the collective behavior of climate extremes. Under this architecture, the nodes are defined by the spatial grid points of the given spatio-temporal climate dataset. Each node is associated with a time series corresponding to the temporal evolution
of the climate observation at that grid point. Finally, the network links are functions of the pairwise statistical interdependence between the nodes. Various network measures, such as degree, betweenness centrality, clustering coefficient, etc., can be used to quantify the network’s topology. We apply the methodology mentioned above to study the spatio-temporal coherence pattern of extreme rainfall events in the United States and the Ganga River basin, which reveals its relation to various climate processes and the orography of the region.
The identification of precursors associated with the occurrence of extreme events in the near future is extremely important to prepare the masses for an upcoming disaster and mitigate the potential risks associated with such events. Under this motivation, I propose an in-data prediction recipe for predicting the data structures that typically occur prior to extreme events using the Echo state network, a type of Recurrent Neural Network which is a part of the reservoir
computing framework. However, unlike previous works that identify precursory structures in the same variable in which extreme events are manifested (active variable), I try to predict these structures by using data from another dynamic variable (passive variable) which does not show large excursions from the nominal condition but carries imprints of these extreme events. Furthermore, my results demonstrate that the quality of prediction depends on the magnitude
of events, i.e., the higher the magnitude of the extreme, the better is its predictability skill. I show quantitatively that this is because the input signals collectively form a more coherent pattern for an extreme event of higher magnitude, which enhances the efficiency of the machine to predict the forthcoming extreme events.
We investigate properties of quantum mechanical systems in the light of quantum information theory. We put an emphasize on systems with infinite-dimensional Hilbert spaces, so-called continuous-variable systems'', which are needed to describe quantum optics beyond the single photon regime and other Bosonic quantum systems. We present methods to obtain a description of such systems from a series of measurements in an efficient manner and demonstrate the performance in realistic situations by means of numerical simulations. We consider both unconditional quantum state tomography, which is applicable to arbitrary systems, and tomography of matrix product states. The latter allows for the tomography of many-body systems because the necessary number of measurements scales merely polynomially with the particle number, compared to an exponential scaling in the generic case. We also present a method to realize such a tomography scheme for a system of ultra-cold atoms in optical lattices. Furthermore, we discuss in detail the possibilities and limitations of using continuous-variable systems for measurement-based quantum computing. We will see that the distinction between Gaussian and non-Gaussian quantum states and measurements plays an crucial role. We also provide an algorithm to solve the large and interesting class of naturally occurring Hamiltonians, namely frustration free ones, efficiently and use this insight to obtain a simple approximation method for slightly frustrated systems. To achieve this goals, we make use of, among various other techniques, the well developed theory of matrix product states, tensor networks, semi-definite programming, and matrix analysis.
In this work, binding interactions between biomolecules were analyzed by a technique that is based on electrically controllable DNA nanolevers. The technique was applied to virus-receptor interactions for the first time. As receptors, primarily peptides on DNA nanostructures and antibodies were utilized. The DNA nanostructures were integrated into the measurement technique and enabled the presentation of the peptides in a controllable geometrical order. The number of peptides could be varied to be compatible to the binding sites of the viral surface proteins.
Influenza A virus served as a model system, on which the general measurability was demonstrated. Variations of the receptor peptide, the surface ligand density, the measurement temperature and the virus subtypes showed the sensitivity and applicability of the technology. Additionally, the immobilization of virus particles enabled the measurement of differences in oligovalent binding of DNA-peptide nanostructures to the viral proteins in their native environment.
When the coronavirus pandemic broke out in 2020, work on binding interactions of a peptide from the hACE2 receptor and the spike protein of the SARS-CoV-2 virus revealed that oligovalent binding can be quantified in the switchSENSE technology. It could also be shown that small changes in the amino acid sequence of the spike protein resulted in complete loss of binding. Interactions of the peptide and inactivated virus material as well as pseudo virus particles could be measured. Additionally, the switchSENSE technology was utilized to rank six antibodies for their binding affinity towards the nucleocapsid protein of SARS-CoV-2 for the development of a rapid antigen test device.
The technique was furthermore employed to show binding of a non-enveloped virus (adenovirus) and a virus-like particle (norovirus-like particle) to antibodies. Apart from binding interactions, the use of DNA origami levers with a length of around 50 nm enabled the switching of virus material. This proved that the technology is also able to size objects with a hydrodynamic diameter larger than 14 nm.
A theoretical work on diffusion and reaction-limited binding interactions revealed that the technique and the chosen parameters enable the determination of binding rate constants in the reaction-limited regime.
Overall, the applicability of the switchSENSE technique to virus-receptor binding interactions could be demonstrated on multiple examples. While there are challenges that remain, the setup enables the determination of affinities between viruses and receptors in their native environment. Especially the possibilities regarding the quantification of oligo- and multivalent binding interactions could be presented.
This work investigates diffusion in nonlinear Hamiltonian systems. The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''. Its properties are studied on the example of one- or two-dimensional lattices of harmonic or nonlinear oscillators with nearest neighbor couplings. The fundamental observation is the spreading of energy for localized initial conditions. Methods of quantifying this spreading behavior are presented, including a new quantity called excitation time. This new quantity allows for a more precise analysis of the spreading than traditional methods. Furthermore, the nonlinear diffusion equation is introduced as a phenomenologic description of the spreading process and a number of predictions on the density dependence of the spreading are drawn from this equation. Two mathematical techniques for analyzing nonlinear Hamiltonian systems are introduced. The first one is based on a scaling analysis of the Hamiltonian equations and the results are related to similar scaling properties of the NDE. From this relation, exact spreading predictions are deduced. Secondly, the microscopic dynamics at the edge of spreading states are thoroughly analyzed, which again suggests a scaling behavior that can be related to the NDE. Such a microscopic treatment of chaotically spreading states in nonlinear Hamiltonian systems has not been done before and the results present a new technique of connecting microscopic dynamics with macroscopic descriptions like the nonlinear diffusion equation. All theoretical results are supported by heavy numerical simulations, partly obtained on one of Europe's fastest supercomputers located in Bologna, Italy. In the end, the highly interesting case of harmonic oscillators with random frequencies and nonlinear coupling is studied, which resembles to some extent the famous Discrete Anderson Nonlinear Schroedinger Equation. For this model, a deviation from the widely believed power-law spreading is observed in numerical experiments. Some ideas on a theoretical explanation for this deviation are presented, but a conclusive theory could not be found due to the complicated phase space structure in this case. Nevertheless, it is hoped that the techniques and results presented in this work will help to eventually understand this controversely discussed case as well.
Changes in extratropical storm track activity and their implications for extreme weather events
(2016)
The Casimir-Polder interaction between a single neutral atom and a nearby surface, arising from the (quantum and thermal) fluctuations of the electromagnetic field, is a cornerstone of cavity quantum electrodynamics (cQED), and theoretically well established. Recently, Bose-Einstein condensates (BECs) of ultracold atoms have been used to test the predictions of cQED. The purpose of the present thesis is to upgrade single-atom cQED with the many-body theory needed to describe trapped atomic BECs. Tools and methods are developed in a second-quantized picture that treats atom and photon fields on the same footing. We formulate a diagrammatic expansion using correlation functions for both the electromagnetic field and the atomic system. The formalism is applied to investigate, for BECs trapped near surfaces, dispersion interactions of the van der Waals-Casimir-Polder type, and the Bosonic stimulation in spontaneous decay of excited atomic states. We also discuss a phononic Casimir effect, which arises from the quantum fluctuations in an interacting BEC.
Noise is ubiquitous in nature and usually results in rich dynamics in stochastic systems such as oscillatory systems, which exist in such various fields as physics, biology and complex networks. The correlation and synchronization of two or many oscillators are widely studied topics in recent years.
In this thesis, we mainly investigate two problems, i.e., the stochastic bursting phenomenon in noisy excitable systems and synchronization in a three-dimensional Kuramoto model with noise. Stochastic bursting here refers to a sequence of coherent spike train, where each spike has random number of followers due to the combined effects of both time delay and noise. Synchronization, as a universal phenomenon in nonlinear dynamical systems, is well illustrated in the Kuramoto model, a prominent model in the description of collective motion.
In the first part of this thesis, an idealized point process, valid if the characteristic timescales in the problem are well separated, is used to describe statistical properties such as the power spectral density and the interspike interval distribution. We show how the main parameters of the point process, the spontaneous excitation rate, and the probability to induce a spike during the delay action can be calculated from the solutions of a stationary and a forced Fokker-Planck equation. We extend it to the delay-coupled case and derive analytically the statistics of the spikes in each neuron, the pairwise correlations between any two neurons, and the spectrum of the total output from the network.
In the second part, we investigate the three-dimensional noisy Kuramoto model, which can be used to describe the synchronization in a swarming model with helical trajectory. In the case without natural frequency, the Kuramoto model can be connected with the Vicsek model, which is widely studied in collective motion and swarming of active matter. We analyze the linear stability of the incoherent state and derive the critical coupling strength above which the incoherent state loses stability. In the limit of no natural frequency, an exact self-consistent equation of the mean field is derived and extended straightforward to any high-dimensional case.
We study buckling instabilities of filaments in biological systems. Filaments in a cell are the building blocks of the cytoskeleton. They are responsible for the mechanical stability of cells and play an important role in intracellular transport by molecular motors, which transport cargo such as organelles along cytoskeletal filaments. Filaments of the cytoskeleton are semiflexible polymers, i.e., their bending energy is comparable to the thermal energy such that they can be viewed as elastic rods on the nanometer scale, which exhibit pronounced thermal fluctuations. Like macroscopic elastic rods, filaments can undergo a mechanical buckling instability under a compressive load. In the first part of the thesis, we study how this buckling instability is affected by the pronounced thermal fluctuations of the filaments. In cells, compressive loads on filaments can be generated by molecular motors. This happens, for example, during cell division in the mitotic spindle. In the second part of the thesis, we investigate how the stochastic nature of such motor-generated forces influences the buckling behavior of filaments. In chapter 2 we review briefly the buckling instability problem of rods on the macroscopic scale and introduce an analytical model for buckling of filaments or elastic rods in two spatial dimensions in the presence of thermal fluctuations. We present an analytical treatment of the buckling instability in the presence of thermal fluctuations based on a renormalization-like procedure in terms of the non-linear sigma model where we integrate out short-wavelength fluctuations in order to obtain an effective theory for the mode of the longest wavelength governing the buckling instability. We calculate the resulting shift of the critical force by fluctuation effects and find that, in two spatial dimensions, thermal fluctuations increase this force. Furthermore, in the buckled state, thermal fluctuations lead to an increase in the mean projected length of the filament in the force direction. As a function of the contour length, the mean projected length exhibits a cusp at the buckling instability, which becomes rounded by thermal fluctuations. Our main result is the observation that a buckled filament is stretched by thermal fluctuations, i.e., its mean projected length in the direction of the applied force increases by thermal fluctuations. Our analytical results are confirmed by Monte Carlo simulations for buckling of semiflexible filaments in two spatial dimensions. We also perform Monte Carlo simulations in higher spatial dimensions and show that the increase in projected length by thermal fluctuations is less pronounced than in two dimensions and strongly depends on the choice of the boundary conditions. In the second part of this work, we present a model for buckling of semiflexible filaments under the action of molecular motors. We investigate a system in which a group of motors moves along a clamped filament carrying a second filament as a cargo. The cargo-filament is pushed against the wall and eventually buckles. The force-generating motors can stochastically unbind and rebind to the filament during the buckling process. We formulate a stochastic model of this system and calculate the mean first passage time for the unbinding of all linking motors which corresponds to the transition back to the unbuckled state of the cargo filament in a mean-field model. Our results show that for sufficiently short microtubules the movement of kinesin-I-motors is affected by the load force generated by the cargo filament. Our predictions could be tested in future experiments.
One of the most exciting predictions of Einstein's theory of gravitation that have not yet been proven experimentally by a direct detection are gravitational waves. These are tiny distortions of the spacetime itself, and a world-wide effort to directly measure them for the first time with a network of large-scale laser interferometers is currently ongoing and expected to provide positive results within this decade. One potential source of measurable gravitational waves is the inspiral and merger of two compact objects, such as binary black holes. Successfully finding their signature in the noise-dominated data of the detectors crucially relies on accurate predictions of what we are looking for. In this thesis, we present a detailed study of how the most complete waveform templates can be constructed by combining the results from (A) analytical expansions within the post-Newtonian framework and (B) numerical simulations of the full relativistic dynamics. We analyze various strategies to construct complete hybrid waveforms that consist of a post-Newtonian inspiral part matched to numerical-relativity data. We elaborate on exsisting approaches for nonspinning systems by extending the accessible parameter space and introducing an alternative scheme based in the Fourier domain. Our methods can now be readily applied to multiple spherical-harmonic modes and precessing systems. In addition to that, we analyze in detail the accuracy of hybrid waveforms with the goal to quantify how numerous sources of error in the approximation techniques affect the application of such templates in real gravitational-wave searches. This is of major importance for the future construction of improved models, but also for the correct interpretation of gravitational-wave observations that are made utilizing any complete waveform family. In particular, we comprehensively discuss how long the numerical-relativity contribution to the signal has to be in order to make the resulting hybrids accurate enough, and for currently feasible simulation lengths we assess the physics one can potentially do with template-based searches.