TY - GEN A1 - Ślęzak, Jakub A1 - Metzler, Ralf A1 - Magdziarz, Marcin T1 - Codifference can detect ergodicity breaking and non-Gaussianity T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 748 KW - diffusion KW - anomalous diffusion KW - stochastic time series Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436178 IS - 748 ER - TY - GEN A1 - Ślęzak, Jakub A1 - Metzler, Ralf A1 - Magdziarz, Marcin T1 - Superstatistical generalised Langevin equation BT - non-Gaussian viscoelastic anomalous diffusion N2 - Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 413 KW - anomalous diffusion KW - generalised langevin equation KW - superstatistics KW - non-Gaussian diffusion Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-409315 ER - TY - JOUR A1 - Ślęzak, Jakub A1 - Metzler, Ralf A1 - Magdziarz, Marcin T1 - Superstatistical generalised Langevin equation BT - non-Gaussian viscoelastic anomalous diffusion JF - New Journal of Physics N2 - Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations. KW - anomalous diffusion KW - generalised langevin equation KW - superstatistics KW - non-Gaussian diffusion Y1 - 2018 U6 - https://doi.org/10.1088/1367-2630/aaa3d4 SN - 1367-2630 VL - 20 IS - 023026 SP - 1 EP - 25 PB - Deutsche Physikalische Gesellschaft / Institute of Physics CY - Bad Honnef und London ER - TY - JOUR A1 - Ślęzak, Jakub A1 - Metzler, Ralf A1 - Magdziarz, Marcin T1 - Codifference can detect ergodicity breaking and non-Gaussianity JF - New Journal of Physics N2 - We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement. KW - diffusion KW - stochastic time series KW - anomalous diffusion Y1 - 2019 U6 - https://doi.org/10.1088/1367-2630/ab13f3 SN - 1367-2630 VL - 21 PB - Deutsche Physikalische Gesellschaft CY - Bad Honnef ER - TY - GEN A1 - Ślęzak, Jakub A1 - Burnecki, Krzysztof A1 - Metzler, Ralf T1 - Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 765 KW - diffusion KW - Langevin equation KW - Brownian yet non-Gaussian diffusion KW - diffusing diffusivity KW - superstatistics KW - autoregressive models KW - time series analysis KW - codifference Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-437923 SN - 1866-8372 IS - 765 ER - TY - JOUR A1 - Ślęzak, Jakub A1 - Burnecki, Krzysztof A1 - Metzler, Ralf T1 - Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems JF - New Journal of Physics N2 - Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion. KW - diffusion KW - Langevin equation KW - Brownian yet non-Gaussian diffusion KW - diffusing diffusivity KW - superstatistics KW - autoregressive models KW - time series analysis KW - codifference Y1 - 2019 U6 - https://doi.org/10.1088/1367-2630/ab3366 SN - 1367-2630 VL - 21 PB - Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics CY - Bad Honnef und London ER - TY - THES A1 - Zöller, Gert T1 - Critical states of seismicity : modeling and data analysis T1 - Kritische Zustände seismischer Dynamik : Modellierung und Datenanalyse N2 - The occurrence of earthquakes is characterized by a high degree of spatiotemporal complexity. Although numerous patterns, e.g. fore- and aftershock sequences, are well-known, the underlying mechanisms are not observable and thus not understood. Because the recurrence times of large earthquakes are usually decades or centuries, the number of such events in corresponding data sets is too small to draw conclusions with reasonable statistical significance. Therefore, the present study combines both, numerical modeling and analysis of real data in order to unveil the relationships between physical mechanisms and observational quantities. The key hypothesis is the validity of the so-called "critical point concept" for earthquakes, which assumes large earthquakes to occur as phase transitions in a spatially extended many-particle system, similar to percolation models. New concepts are developed to detect critical states in simulated and in natural data sets. The results indicate that important features of seismicity like the frequency-size distribution and the temporal clustering of earthquakes depend on frictional and structural fault parameters. In particular, the degree of quenched spatial disorder (the "roughness") of a fault zone determines whether large earthquakes occur quasiperiodically or more clustered. This illustrates the power of numerical models in order to identify regions in parameter space, which are relevant for natural seismicity. The critical point concept is verified for both, synthetic and natural seismicity, in terms of a critical state which precedes a large earthquake: a gradual roughening of the (unobservable) stress field leads to a scale-free (observable) frequency-size distribution. Furthermore, the growth of the spatial correlation length and the acceleration of the seismic energy release prior to large events is found. The predictive power of these precursors is, however, limited. Instead of forecasting time, location, and magnitude of individual events, a contribution to a broad multiparameter approach is encouraging. N2 - Das Auftreten von Erdbeben zeichnet sich durch eine hohe raumzeitliche Komplexität aus. Obwohl zahlreiche Muster, wie Vor- und Nachbeben bekannt sind, weiß man wenig über die zugrundeliegenden Mechanismen, da diese sich direkter Beobachtung entziehen. Die Zeit zwischen zwei starken Erdbeben in einer seismisch aktiven Region beträgt Jahrzehnte bis Jahrhunderte. Folglich ist die Anzahl solcher Ereignisse in einem Datensatz gering und es ist kaum möglich, allein aus Beobachtungsdaten statistisch signifikante Aussagen über deren Eigenschaften abzuleiten. Die vorliegende Arbeit nutzt daher numerische Modellierungen einer Verwerfungszone in Verbindung mit Datenanalyse, um die Beziehung zwischen physikalischen Mechanismen und beobachteter Seismizität zu studieren. Die zentrale Hypothese ist die Gültigkeit des sogenannten "kritischen Punkt Konzeptes" für Seismizität, d.h. starke Erdbeben werden als Phasenübergänge in einem räumlich ausgedehnten Vielteilchensystem betrachtet, ähnlich wie in Modellen aus der statistischen Physik (z.B. Perkolationsmodelle). Es werden praktische Konzepte entwickelt, die es ermöglichen, kritische Zustände in simulierten und in beobachteten Daten sichtbar zu machen. Die Resultate zeigen, dass wesentliche Eigenschaften von Seismizität, etwa die Magnitudenverteilung und das raumzeitliche Clustern von Erdbeben, durch Reibungs- und Bruchparameter bestimmt werden. Insbesondere der Grad räumlicher Unordnung (die "Rauhheit") einer Verwerfungszone hat Einfluss darauf, ob starke Erdbeben quasiperiodisch oder eher zufällig auftreten. Dieser Befund zeigt auf, wie numerische Modelle genutzt werden können, um den Parameterraum für reale Verwerfungen einzugrenzen. Das kritische Punkt Konzept kann in synthetischer und in beobachteter Seismizität verifiziert werden. Dies artikuliert sich auch in Vorläuferphänomenen vor großen Erdbeben: Die Aufrauhung des (unbeobachtbaren) Spannungsfeldes führt zu einer Skalenfreiheit der (beobachtbaren) Größenverteilung; die räumliche Korrelationslänge wächst und die seismische Energiefreisetzung wird beschleunigt. Ein starkes Erdbeben kann in einem zusammenhängenden Bruch oder in einem unterbrochenen Bruch (Vorbeben und Hauptbeben) stattfinden. Die beobachtbaren Vorläufer besitzen eine begrenzte Prognosekraft für die Auftretenswahrscheinlichkeit starker Erdbeben - eine präzise Vorhersage von Ort, Zeit, und Stärke eines nahenden Erdbebens ist allerdings nicht möglich. Die genannten Parameter erscheinen eher vielversprechend als Beitrag zu einem umfassenden Multiparameteransatz für eine verbesserte zeitabhängige Gefährdungsabschätzung. KW - Seismizität KW - Erdbebenvorhersage KW - statistische Physik KW - mathematische Modellierung KW - Datenanalyse KW - seismicity KW - earthquake prediction KW - statistical physics KW - mathematical modeling KW - data analysis Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-7427 ER - TY - THES A1 - Zöller, Gert T1 - Analyse raumzeitlicher Muster in Erdbebendaten N2 - Die vorliegende Arbeit beschäftigt sich mit der Charakterisierung von Seismizität anhand von Erdbebenkatalogen. Es werden neue Verfahren der Datenanalyse entwickelt, die Aufschluss darüber geben sollen, ob der seismischen Dynamik ein stochastischer oder ein deterministischer Prozess zugrunde liegt und was daraus für die Vorhersagbarkeit starker Erdbeben folgt. Es wird gezeigt, dass seismisch aktive Regionen häufig durch nichtlinearen Determinismus gekennzeichent sind. Dies schließt zumindest die Möglichkeit einer Kurzzeitvorhersage ein. Das Auftreten seismischer Ruhe wird häufig als Vorläuferphaenomen für starke Erdbeben gedeutet. Es wird eine neue Methode präsentiert, die eine systematische raumzeitliche Kartierung seismischer Ruhephasen ermöglicht. Die statistische Signifikanz wird mit Hilfe des Konzeptes der Ersatzdaten bestimmt. Als Resultat erhält man deutliche Korrelationen zwischen seismischen Ruheperioden und starken Erdbeben. Gleichwohl ist die Signifikanz dafür nicht hoch genug, um eine Vorhersage im Sinne einer Aussage über den Ort, die Zeit und die Stärke eines zu erwartenden Hauptbebens zu ermöglichen. KW - Erdbeben KW - nichtlineare Dynamik Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-0000122 ER - TY - JOUR A1 - Zuo, Guangzheng A1 - Shoaee, Safa A1 - Kemerink, Martijn A1 - Neher, Dieter T1 - General rules for the impact of energetic disorder and mobility on nongeminate recombination in phase-separated organic solar cells JF - Physical review applied N2 - State-of-the-art organic solar cells exhibit power conversion efficiencies of 18% and above. These devices benefit from the suppression of free charge recombination with regard to the Langevin limit of charge encounter in a homogeneous medium. It is recognized that the main cause of suppressed free charge recombination is the reformation and resplitting of charge-transfer (CT) states at the interface between donor and acceptor domains. Here, we use kinetic Monte Carlo simulations to understand the interplay between free charge motion and recombination in an energetically disordered phase-separated donor-acceptor blend. We identify conditions for encounter-dominated and resplitting-dominated recombination. In the former regime, recombination is proportional to mobility for all parameters tested and only slightly reduced with respect to the Langevin limit. In contrast, mobility is not the decisive parameter that determines the nongeminate recombination coefficient, k(2), in the latter case, where k2 is a sole function of the morphology, CT and charge-separated (CS) energetics, and CT-state decay properties. Our simulations also show that free charge encounter in the phase-separated disordered blend is determined by the average mobility of all carriers, while CT reformation and resplitting involves mostly states near the transport energy. Therefore, charge encounter is more affected by increased disorder than the resplitting of the CT state. As a consequence, for a given mobility, larger energetic disorder, in combination with a higher hopping rate, is preferred. These findings have implications for the understanding of suppressed recombination in solar cells with nonfullerene acceptors, which are known to exhibit lower energetic disorder than that of fullerenes. Y1 - 2021 U6 - https://doi.org/10.1103/PhysRevApplied.16.034027 SN - 2331-7019 VL - 16 IS - 3 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Zu, Fengshuo A1 - Wolff, Christian Michael A1 - Ralaiarisoa, Maryline A1 - Amsalem, Patrick A1 - Neher, Dieter A1 - Koch, Norbert T1 - Unraveling the Electronic Properties of Lead Halide Perovskites with Surface Photovoltage in Photoemission Studies JF - ACS applied materials & interfaces N2 - The tremendous success of metal-halide perovskites, especially in the field of photovoltaics, has triggered a substantial number of studies in understanding their optoelectronic properties. However, consensus regarding the electronic properties of these perovskites is lacking due to a huge scatter in the reported key parameters, such as work function (Φ) and valence band maximum (VBM) values. Here, we demonstrate that the surface photovoltage (SPV) is a key phenomenon occurring at the perovskite surfaces that feature a non-negligible density of surface states, which is more the rule than an exception for most materials under study. With ultraviolet photoelectron spectroscopy (UPS) and Kelvin probe, we evidence that even minute UV photon fluxes (500 times lower than that used in typical UPS experiments) are sufficient to induce SPV and shift the perovskite Φ and VBM by several 100 meV compared to dark. By combining UV and visible light, we establish flat band conditions (i.e., compensate the surface-state-induced surface band bending) at the surface of four important perovskites, and find that all are p-type in the bulk, despite a pronounced n-type surface character in the dark. The present findings highlight that SPV effects must be considered in all surface studies to fully understand perovskites’ photophysical properties. KW - lead halide perovskite films KW - ultraviolet photoelectron spectroscopy KW - Kelvin probe KW - surface band bending KW - surface photovoltage KW - surface states Y1 - 2019 U6 - https://doi.org/10.1021/acsami.9b05293 SN - 1944-8244 SN - 1944-8252 VL - 11 IS - 24 SP - 21578 EP - 21583 PB - American Chemical Society CY - Washington ER -