TY - THES A1 - Hennig, Theresa T1 - Uranium migration in the Opalinus Clay quantified on the host rock scale with reactive transport simulations T1 - Uranmigration im Opalinuston quantifiziert für die Wirtsgesteinsskala mit reaktiven Transportsimulationen N2 - Humankind and their environment need to be protected from the harmful effects of spent nuclear fuel, and therefore disposal in deep geological formations is favoured worldwide. Suitability of potential host rocks is evaluated, among others, by the retention capacity with respect to radionuclides. Safety assessments are based on the quantification of radionuclide migration lengths with numerical simulations as experiments cannot cover the required temporal (1 Ma) and spatial scales (>100 m). Aim of the present thesis is to assess the migration of uranium, a geochemically complex radionuclide, in the potential host rock Opalinus Clay. Radionuclide migration in clay formations is governed by diffusion due to their low permeability and retarded by sorption. Both processes highly depend on pore water geochemistry and mineralogy that vary between different facies. Diffusion is quantified with the single-component (SC) approach using one diffusion coefficient for all species and the process-based multi-component (MC) option. With this, each species is assigned its own diffusion coefficient and the interaction with the diffuse double layer is taken into account. Sorption is integrated via a bottom-up approach using mechanistic surface complexation models and cation exchange. Therefore, reactive transport simulations are conducted with the geochemical code PHREEQC to quantify uranium migration, i.e. diffusion and sorption, as a function of mineralogical and geochemical heterogeneities on the host rock scale. Sorption processes are facies dependent. Migration lengths vary between the Opalinus Clay facies by up to 10 m. Thereby, the geochemistry of the pore water, in particular the partial pressure of carbon dioxide (pCO2), is more decisive for the sorption capacity than the amount of clay minerals. Nevertheless, higher clay mineral quantities compensate geochemical variations. Consequently, sorption processes must be quantified as a function of pore water geochemistry in contact with the mineral assemblage. Uranium diffusion in the Opalinus Clay is facies independent. Speciation is dominated by aqueous ternary complexes of U(VI) with calcium and carbonate. Differences in the migration lengths between SC and MC diffusion are with +/-5 m negligible. Further, the application of the MC approach highly depends on the quality and availability of the underlying data. Therefore, diffusion processes can be adequately quantified with the SC approach using experimentally determined diffusion coefficients. The hydrogeological system governs pore water geochemistry within the formation rather than the mineralogy. Diffusive exchange with the adjacent aquifers established geochemical gradients over geological time scales that can enhance migration by up to 25 m. Consequently, uranium sorption processes must be quantified following the identified priority: pCO2 > hydrogeology > mineralogy. The presented research provides a workflow and orientation for other potential disposal sites with similar pore water geochemistry due to the identified mechanisms and dependencies. With a maximum migration length of 70 m, the retention capacity of the Opalinus Clay with respect to uranium is sufficient to fulfill the German legal minimum requirement of a thickness of at least 100 m. N2 - Zum Schutz von Mensch und Umwelt vor den schädlichen Auswirkungen abgebrannter Brennelemente, wird weltweit die Endlagerung in tiefen geologischen Formationen favorisiert. Daher ist das Rückhaltevermögen potenzieller Wirtsgesteine gegenüber Radionukliden ein wichtiges Kriterium. Sicherheitsbewertungen basieren auf der Quantifizierung der Migration mit numerischen Simulationen, da Experimente die erforderlichen zeitlichen (1 Ma) und räumlichen Skalen (>100 m) nicht abdecken können. Ziel der Dissertation ist es, die Migration des geochemisch komplexen Radionuklids Uran im potenziellen Wirtsgestein Opalinuston zu bewerten. In Tonformationen wird die Radionuklidmigration aufgrund der geringen Durchlässigkeit von Diffusion bestimmt und durch Sorption verzögert. Beide Prozesse hängen stark von der Porenwassergeochemie und Mineralogie ab, die zwischen verschiedenen Fazies variieren. Die Diffusion wird mit dem Einkomponenten- (SC) und Mehrkomponentenansatz (MC) quantifiziert. Nach dem SC-Ansatz wird ein Diffusionskoeffizient für alle Spezies verwendet, wohingegen mit der MC-Option individuelle Werte zugewiesen und die Interaktion mit der diffusen Doppelschicht berücksichtigt wird. Die Sorption ist mit Hilfe mechanistischer Oberflächenkomplexierungsmodelle und Kationenaustausch integriert. Die Durchführung reaktiver Transportsimulationen mit dem Code PHREEQC ermöglicht die Quantifizierung der Uranmigration, d. h. Diffusion und Sorption, in Abhängigkeit der Mineralogie und Porenwassergeochemie für die Wirtsgesteinsskala. Sorptionsprozesse sind faziesabhängig. Die Migrationslängen variieren um bis zu 10 m zwischen den Fazies aufgrund von Unterschieden in der Porenwassergeochemie. Dabei ist insbesondere der Partialdruck des Kohlendioxids (pCO2) entscheidender für die Sorptionskapazität als die Menge an Tonmineralen. Allerdings kompensieren höhere Tonmineralmengen geochemische Schwankungen. Folglich müssen Sorptionsprozesse in Abhängigkeit der Porenwassergeochemie quantifiziert werden. Urandiffusion ist faziesunabhängig. Die Speziation wird durch aquatische ternäre Komplexe von U(VI) mit Kalzium und Karbonat dominiert. Die Unterschiede in den Migrationslängen zwischen SC- und MC-Diffusion sind mit +/-5 m vernachlässigbar. Die Anwendung des MC-Ansatzes hängt stark von der Qualität und Verfügbarkeit der zugrunde liegenden Daten ab. Diffusionsprozesse können also mit dem SC-Ansatz unter Verwendung experimentell ermittelter Diffusionskoeffizienten quantifiziert werden. Haupteinflussfaktor auf die Porenwassergeochemie ist das hydrogeologische System und nicht die Mineralogie. Der diffusive Austausch mit den angrenzenden Aquiferen hat über geologische Zeiträume geochemische Gradienten geschaffen, die die Migration um bis zu 25 m verlängern können. Folglich müssen Sorptionsprozesse nach der identifizierten Priorität quantifiziert werden: pCO2 > Hydrogeologie > Mineralogie. Die ermittelten Abhängigkeiten dienen als Orientierung für andere potenzielle Endlagerstandorte mit ähnlicher Porenwassergeochemie. Mit einer maximalen Migration von 70 m reicht das Rückhaltevermögen des Opalinustons gegenüber Uran aus, um die deutsche gesetzliche Mindestanforderung von 100 m Mächtigkeit zu erfüllen. KW - uranium KW - Opalinus Clay KW - PHREEQC KW - diffusion KW - sorption KW - nuclear waste disposal KW - reactive transport simulation KW - host rock scale KW - Opalinuston KW - PHREEQC KW - Diffusion KW - Wirtsgesteinsskala KW - Endlagerung nuklearer Abfälle KW - reaktive Transportsimulation KW - Sorption KW - Uran Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-552700 ER - TY - JOUR A1 - Sposini, Vittoria A1 - Grebenkov, Denis S. A1 - Metzler, Ralf A1 - Oshanin, Gleb A1 - Seno, Flavio T1 - Universal spectral features of different classes of random-diffusivity processes JF - New Journal of Physics N2 - Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations. KW - diffusion KW - power spectrum KW - random diffusivity KW - single trajectories Y1 - 2020 U6 - https://doi.org/10.1088/1367-2630/ab9200 SN - 1367-2630 VL - 22 IS - 6 PB - Dt. Physikalische Ges. CY - Bad Honnef ER - TY - GEN A1 - Sposini, Vittoria A1 - Grebenkov, Denis S. A1 - Metzler, Ralf A1 - Oshanin, Gleb A1 - Seno, Flavio T1 - Universal spectral features of different classes of random-diffusivity processes T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 999 KW - diffusion KW - power spectrum KW - random diffusivity KW - single trajectories Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-476960 SN - 1866-8372 IS - 999 ER - TY - JOUR A1 - Wang, Wei A1 - Seno, Flavio A1 - Sokolov, Igor M. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Unexpected crossovers in correlated random-diffusivity processes JF - New Journal of Physics N2 - The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion. KW - diffusion KW - anomalous diffusion KW - non-Gaussianity KW - fractional Brownian motion Y1 - 2020 U6 - https://doi.org/10.1088/1367-2630/aba390 SN - 1367-2630 VL - 22 PB - Dt. Physikalische Ges. CY - Bad Honnef ER - TY - GEN A1 - Wang, Wei A1 - Seno, Flavio A1 - Sokolov, Igor M. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Unexpected crossovers in correlated random-diffusivity processes N2 - The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1006 KW - diffusion KW - anomalous diffusion KW - non-Gaussianity KW - fractional Brownian motion Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-480049 SN - 1866-8372 IS - 1006 ER - TY - JOUR A1 - Beta, Carsten T1 - To turn or not to turn? JF - NEW JOURNAL OF PHYSICS N2 - Bacteria typically swim in straight runs, interruped by sudden turning events. In particular, some species are limited to a reversal in the swimming direction as the only turning maneuver at their disposal. In a recent article, Grossmann et al (2016 New J. Phys. 18 043009) introduce a theoretical framework to analyze the diffusive properties of active particles following this type of run-and-reverse pattern. Based on a stochastic clock model to mimic the regulatory pathway that triggers reversal events, they show that a run-and-reverse swimmer can optimize its diffusive spreading by tuning the reversal rate according to the level of rotational noise. With their approach, they open up promising new perspectives of how to incorporate the dynamics of intracellular signaling into coarse-grained active particle descriptions. KW - bacterial swimming KW - random walks KW - diffusion KW - stochastic models Y1 - 2016 U6 - https://doi.org/10.1088/1367-2630/18/5/051003 SN - 1367-2630 VL - 18 SP - 1 EP - 17 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Vinod, Deepak A1 - Aghion, Erez A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Time averaging, ageing and delay analysis of financial time series JF - New journal of physics N2 - We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics. KW - time averaging KW - diffusion KW - geometric Brownian motion KW - financial time series Y1 - 2017 U6 - https://doi.org/10.1088/1367-2630/aa7199 SN - 1367-2630 VL - 19 SP - 1 EP - 11 PB - IOP CY - London ER - TY - GEN A1 - Cherstvy, Andrey G. A1 - Vinod, Deepak A1 - Aghion, Erez A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Time averaging, ageing and delay analysis of financial time series N2 - We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 347 KW - diffusion KW - financial time series KW - geometric Brownian motion KW - time averaging Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-400541 ER - TY - JOUR A1 - Cherstvy, Andrey G. A1 - Vinod, Deepak A1 - Aghion, Erez A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Time averaging, ageing and delay analysis of financial time series JF - New journal of physics : the open-access journal for physics N2 - We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black-Scholes-Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics. KW - time averaging KW - diffusion KW - geometric Brownian motion KW - financial time series Y1 - 2017 U6 - https://doi.org/10.1088/1367-2630/aa7199 SN - 1367-2630 VL - 19 SP - 135 EP - 147 PB - IOP Publ. Ltd. CY - Bristol ER - TY - THES A1 - Sposini, Vittoria T1 - The random diffusivity approach for diffusion in heterogeneous systems N2 - The two hallmark features of Brownian motion are the linear growth < x2(t)> = 2Ddt of the mean squared displacement (MSD) with diffusion coefficient D in d spatial dimensions, and the Gaussian distribution of displacements. With the increasing complexity of the studied systems deviations from these two central properties have been unveiled over the years. Recently, a large variety of systems have been reported in which the MSD exhibits the linear growth in time of Brownian (Fickian) transport, however, the distribution of displacements is pronouncedly non-Gaussian (Brownian yet non-Gaussian, BNG). A similar behaviour is also observed for viscoelastic-type motion where an anomalous trend of the MSD, i.e., ~ ta, is combined with a priori unexpected non-Gaussian distributions (anomalous yet non-Gaussian, ANG). This kind of behaviour observed in BNG and ANG diffusions has been related to the presence of heterogeneities in the systems and a common approach has been established to address it, that is, the random diffusivity approach. This dissertation explores extensively the field of random diffusivity models. Starting from a chronological description of all the main approaches used as an attempt of describing BNG and ANG diffusion, different mathematical methodologies are defined for the resolution and study of these models. The processes that are reported in this work can be classified in three subcategories, i) randomly-scaled Gaussian processes, ii) superstatistical models and iii) diffusing diffusivity models, all belonging to the more general class of random diffusivity models. Eventually, the study focuses more on BNG diffusion, which is by now well-established and relatively well-understood. Nevertheless, many examples are discussed for the description of ANG diffusion, in order to highlight the possible scenarios which are known so far for the study of this class of processes. The second part of the dissertation deals with the statistical analysis of random diffusivity processes. A general description based on the concept of moment-generating function is initially provided to obtain standard statistical properties of the models. Then, the discussion moves to the study of the power spectral analysis and the first passage statistics for some particular random diffusivity models. A comparison between the results coming from the random diffusivity approach and the ones for standard Brownian motion is discussed. In this way, a deeper physical understanding of the systems described by random diffusivity models is also outlined. To conclude, a discussion based on the possible origins of the heterogeneity is sketched, with the main goal of inferring which kind of systems can actually be described by the random diffusivity approach. N2 - Die zwei grundlegenden Eigenschaften der Brownschen Molekularbewegung sind das lineare Wachstum < x2(t)> = 2Ddt der mittleren quadratischen Verschiebung (mean squared displacement, MSD) mit dem Diffusionskoeffizienten D in Dimension d und die Gauß Verteilung der räumlichen Verschiebung. Durch die zunehmende Komplexität der untersuchten Systeme wurden in den letzten Jahren Abweichungen von diesen zwei grundlegenden Eigenschaften gefunden. Hierbei, wurde über eine große Anzahl von Systemen berichtet, in welchen die MSD das lineare Wachstum der Brownschen Bewegung (Ficksches Gesetzt) zeigt, jedoch die Verteilung der Verschiebung nicht einer Gaußverteilung folgt (Brownian yet non-Gaussian, BNG). Auch in viskoelastischen Systemen Bewegung wurde ein analoges Verhalten beobachtet. Hier ist ein anomales Verhalten des MSD, ~ ta, in Verbindung mit einer a priori unerwarteten nicht gaußchen Verteilung (anomalous yet non-Gaussian, ANG). Dieses Verhalten, welches sowohl in BNG- als auch in ANG-Diffusion beobachtet wird, ist auf eine Heterogenität in den Systemen zurückzuführen. Um diese Systeme zu beschreiben, wurde ein einheitlicher Ansatz, basierend auf den Konzept der zufälligen Diffusivität, entwickelt. Die vorliegende Dissertation widmet sich ausführlich Modellen mit zufälligen Diffusivität. Ausgehend von einem chronologischen Überblick der grundlegenden Ansätze der Beschreibung der BNG- und ANG-Diffusion werden mathematische Methoden entwickelt, um die verschiedenen Modelle zu untersuchen. Die in dieser Arbeit diskutierten Prozesse können in drei Kategorien unterteil werden: i) randomly-scaled Gaussian processes, ii) superstatistical models und iii) diffusing diffusivity models, welche alle zu den allgemeinen Modellen mit zufälligen Diffusivität gehören. Der Hauptteil dieser Arbeit ist die Untersuchung auf die BNG Diffusion, welche inzwischen relativ gut verstanden ist. Dennoch werden auch viele Beispiele für die Beschreibung von ANG-Diffusion diskutiert, um die Möglichkeiten der Analyse solcher Prozesse aufzuzeigen. Der zweite Teil der Dissertation widmet sich der statistischen Analyse von Modellen mit zufälligen Diffusivität. Eine allgemeine Beschreibung basierend auf dem Konzept der momenterzeugenden Funktion wurde zuerst herangezogen, um grundsätzliche statistische Eigenschaften der Modelle zu erhalten. Anschließend konzentriert sich die Diskussion auf die Analyse der spektralen Leistungsdichte und der first passage Statistik für einige spezielle Modelle mit zufälligen Diffusivität. Diese Ergebnisse werden mit jenen der normalen Brownschen Molekularbewegung verglichen. Dadurch wird ein tiefergehendes physikalisches Verständnis über die Systeme erlangt, welche durch ein Modell mit zufälligen Diffusivität beschrieben werden. Abschließend, zeigt eine Diskussion mögliche Ursachen für die Heterogenität auf, mit dem Ziel darzustellen, welche Arten von Systemen durch den Zufalls-Diffusivitäts-Ansatz beschrieben werden können. N2 - Las dos características distintivas del movimiento Browniano son el crecimiento lineal < x2(t)> = 2Ddt del desplazamiento cuadrático medio (mean squared displacement}, MSD) con el coeficiente de difusión D en dimensiones espaciales d, y la distribución Gaussiana de los desplazamientos. Con los continuos avances en tecnologías experimentales y potencia de cálculo, se logra estudiar con mayor detalle sistemas cada vez más complejos y algunos sistemas revelan desviaciones de estas dos propiedades centrales. En los últimos años se ha observado una gran variedad de sistemas en los que el MSD presenta un crecimiento lineal en el tiempo (típico del transporte Browniano), no obstante, la distribución de los desplazamientos es pronunciadamente no Gaussiana (Brownian yet non-Gaussian diffusion}, BNG). Un comportamiento similar se observa asimismo en el caso del movimiento de tipo viscoelástico, en el que se combina una tendencia anómala del MSD, es decir, ~ ta, con a, con distribuciones inesperadamente no Gaussianas (Anomalous yet non-Gaussian diffusion, ANG). Este tipo de comportamiento observado en las difusiones BNG y ANG se ha relacionado con la presencia de heterogeneidades en los sistemas y se ha establecido un enfoque común para abordarlo: el enfoque de difusividad aleatoria. En la primera parte de esta disertación se explora extensamente el área de los modelos de difusividad aleatoria. A través de una descripción cronológica de los principales enfoques utilizados para caracterizar las difusiones BNG y ANG, se definen diferentes metodologías matemáticas para la resolución y el estudio de estos modelos. Los procesos expuestos en este trabajo, pertenecientes a la clase más general de modelos de difusividad aleatoria, pueden clasificarse en tres subcategorías: i) randomly-scaled Gaussian processes, ii) superstatistical models y iii) diffusing diffusivity models. Fundamentalmente el enfoque de este trabajo se centra en la difusión BNG, bien establecida y ampliamente estudiada en los últimos años. No obstante, múltiples ejemplos son examinados para la descripción de la difusión ANG, a fin de remarcar los diferentes modelos de estudio disponibles hasta el momento. En la segunda parte de la disertación se desarolla el análisis estadístico de los procesos de difusividad aleatoria. Inicialmente se expone una descripción general basada en el concepto de la función generadora de momentos para obtener las propiedades estadísticas estándar de los modelos. A continuación, la discusión aborda el estudio de la densidad espectral de potencia y la estadística del tiempo de primer paso para algunos modelos de difusividad aleatoria. Adicionalmente, los resultados del método de difusividad aleatoria se comparan junto a los de movimiento browniano estándar. Como resultado, se obtiene una mayor comprensión física de los sistemas descritos por los modelos de difusividad aleatoria. Para concluir, se presenta una discusión acerca de los posibles orígenes de la heterogeneidad, con el objetivo principal de inferir qué tipo de sistemas pueden describirse apropiadamente según el enfoque de la difusividad aleatoria. KW - diffusion KW - non-gaussianity KW - random diffusivity KW - power spectral analysis KW - first passage KW - Diffusion KW - zufälligen Diffusivität KW - spektrale Leistungsdichte KW - first passage KW - Heterogenität Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-487808 ER - TY - GEN A1 - Gallego-Llorente, Marcos A1 - Sarah, Connell A1 - Jones, Eppie R. A1 - Merrett, Deborah C. A1 - Jeon, Y. A1 - Eriksson, Anders A1 - Siska, Veronika A1 - Gamba, Cristina A1 - Meiklejohn, Christopher A1 - Beyer, Robert A1 - Jeon, Sungwon A1 - Cho, Yun Sung A1 - Hofreiter, Michael A1 - Bhak, Jong A1 - Manica, Andrea A1 - Pinhasi, Ron T1 - The genetics of an early Neolithic pastoralist from the Zagros, Iran T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - The agricultural transition profoundly changed human societies. We sequenced and analysed the first genome (1.39x) of an early Neolithic woman from Ganj Dareh, in the Zagros Mountains of Iran, a site with early evidence for an economy based on goat herding, ca. 10,000 BP. We show that Western Iran was inhabited by a population genetically most similar to hunter-gatherers from the Caucasus, but distinct from the Neolithic Anatolian people who later brought food production into Europe. The inhabitants of Ganj Dareh made little direct genetic contribution to modern European populations, suggesting those of the Central Zagros were somewhat isolated from other populations of the Fertile Crescent. Runs of homozygosity are of a similar length to those from Neolithic farmers, and shorter than those of Caucasus and Western Hunter-Gatherers, suggesting that the inhabitants of Ganj Dareh did not undergo the large population bottleneck suffered by their northern neighbours. While some degree of cultural diffusion between Anatolia, Western Iran and other neighbouring regions is possible, the genetic dissimilarity between early Anatolian farmers and the inhabitants of Ganj Dareh supports a model in which Neolithic societies in these areas were distinct. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 952 KW - whole-genome association KW - ancient KW - domestication KW - agriculture KW - mountains KW - diffusion KW - migration KW - admixture KW - patterns KW - sequence KW - archaeology KW - biological anthropology Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-439355 SN - 1866-8372 IS - 952 ER - TY - JOUR A1 - Pohlenz, Philipp A1 - Niedermeier, Frank T1 - The Bologna Process and the harmonisation of higher education systems in other world regions BT - a case from Southeast Asia JF - Innovation : the European journal of social sciences N2 - The Bologna Process has inspired harmonisation strategies for higher education systems in other parts of the world. However, developments in other contexts are not much under review in the European debate. The present article describes the case of Southeast Asia and the attempt to promote harmonisation of its higher education systems. It further compares the processes in ASEAN and the European Higher Education Area to then discuss open questions for future comparative research. To do so the authors re-contextualise data from a study in ASEAN against the background of future research needs in the field of higher education harmonisation. KW - ASEAN KW - Bologna Process KW - European Higher Education Area KW - higher education KW - quality assurance KW - harmonisation KW - regionalisation KW - diffusion KW - mobility Y1 - 2019 U6 - https://doi.org/10.1080/13511610.2019.1637248 SN - 1351-1610 SN - 1469-8412 VL - 32 IS - 4 SP - 481 EP - 494 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - GEN A1 - Shprits, Yuri A1 - Menietti, J. D. A1 - Drozdov, Alexander A1 - Horne, Richard B. A1 - Woodfield, Emma E. A1 - Groene, J. B. A1 - de Soria-Santacruz, M. A1 - Averkamp, T. F. A1 - Garrett, H. A1 - Paranicas, C. A1 - Gurnett, Don A. T1 - Strong whistler mode waves observed in the vicinity of Jupiter's moons T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - Understanding of wave environments is critical for the understanding of how particles are accelerated and lost in space. This study shows that in the vicinity of Europa and Ganymede, that respectively have induced and internal magnetic fields, chorus wave power is significantly increased. The observed enhancements are persistent and exceed median values of wave activity by up to 6 orders of magnitude for Ganymede. Produced waves may have a pronounced effect on the acceleration and loss of particles in the Jovian magnetosphere and other astrophysical objects. The generated waves are capable of significantly modifying the energetic particle environment, accelerating particles to very high energies, or producing depletions in phase space density. Observations of Jupiter's magnetosphere provide a unique opportunity to observe how objects with an internal magnetic field can interact with particles trapped in magnetic fields of larger scale objects. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 695 KW - electron acceleration KW - magnetic-field KW - diffusion KW - magnetosphere KW - Ganymede Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-426278 SN - 1866-8372 IS - 695 ER - TY - GEN A1 - Xu, Pengbo A1 - Zhou, Tian A1 - Metzler, Ralf A1 - Deng, Weihua T1 - Stochastic harmonic trapping of a Lévy walk: transport and first-passage dynamics under soft resetting strategies T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1262 KW - diffusion KW - anomalous diffusion KW - stochastic resetting KW - Levy walks Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-560402 SN - 1866-8372 SP - 1 EP - 28 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Xu, Pengbo A1 - Zhou, Tian A1 - Metzler, Ralf A1 - Deng, Weihua T1 - Stochastic harmonic trapping of a Lévy walk BT - transport and first-passage dynamics under soft resetting strategies JF - New journal of physics : the open-access journal for physics / Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics N2 - We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic. KW - diffusion KW - anomalous diffusion KW - stochastic resetting KW - Levy walks Y1 - 2022 U6 - https://doi.org/10.1088/1367-2630/ac5282 SN - 1367-2630 VL - 24 IS - 3 SP - 1 EP - 28 PB - Deutsche Physikalische Gesellschaft CY - Bad Honnef ER - TY - JOUR A1 - Palyulin, Vladimir V. A1 - Chechkin, Aleksei V. A1 - Metzler, Ralf T1 - Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias JF - Journal of statistical mechanics: theory and experiment N2 - Based on the space-fractional Fokker-Planck equation with a delta-sink term, we study the efficiency of random search processes based on Levy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the preference of the searcher based on prior experience. While Levy flights turn out to be efficient search processes when the target is upstream relative to the starting point, in the downstream scenario, regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Levy flights, due to which Levy flights typically overshoot a point or small interval. Studying the solution of the fractional Fokker-Planck equation, we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favours Levy flights over the regular Brownian search. Contrary to the common belief that Levy flights with a Levy index alpha = 1 (i.e. Cauchy flights) are optimal for sparse targets, we find that the optimal value for alpha may range in the entire interval (1, 2) and explicitly include Brownian motion as the most efficient search strategy overall. KW - driven diffusive systems (theory) KW - fluctuations (theory) KW - stochastic processes (theory) KW - diffusion Y1 - 2014 U6 - https://doi.org/10.1088/1742-5468/2014/11/P11031 SN - 1742-5468 PB - IOP Publ. Ltd. CY - Bristol ER - TY - GEN A1 - Sposini, Vittoria A1 - Metzler, Ralf A1 - Oshanin, Gleb T1 - Single-trajectory spectral analysis of scaled Brownian motion T2 - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe N2 - Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 753 KW - diffusion KW - anomalous diffusion KW - power spectral analysis KW - single trajectory analysis Y1 - 2019 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-436522 SN - 1866-8372 IS - 753 ER - TY - JOUR A1 - Sposini, Vittoria A1 - Metzler, Ralf A1 - Oshanin, Gleb T1 - Single-trajectory spectral analysis of scaled Brownian motion JF - New Journal of Physics N2 - Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement. KW - diffusion KW - anomalous diffusion KW - power spectral analysis KW - single trajectory analysis Y1 - 2019 U6 - https://doi.org/10.1088/1367-2630/ab2f52 SN - 1367-2630 VL - 21 PB - Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics CY - Bad Honnef und London ER - TY - JOUR A1 - Grätz, Fabio M. A1 - Seiß, Martin A1 - Schmidt, Jürgen A1 - Colwell, Joshua A1 - Spahn, Frank T1 - Sharp Gap Edges in Dense Planetary Rings BT - an Axisymmetric Diffusion Model JF - The astrophysical journal : an international review of spectroscopy and astronomical physics N2 - One of the most intriguing facets of Saturn's rings are the sharp edges of gaps in the rings where the surface density abruptly drops to zero. This is despite of the fact that the range over which a moon transfers angular momentum onto the ring material is much larger. Recent UVIS-scans of the edges of the Encke and Keeler gap show that this drop occurs over a range approximately equal to the rings' thickness. Borderies et al. show that this striking feature is likely related to the local reversal of the usually outward directed viscous transport of angular momentum in strongly perturbed regions. In this article we revise the Borderies et al. model using a granular flow model to define the shear and bulk viscosities, ν and ζ, and incorporate the angular momentum flux reversal effect into the axisymmetric diffusion model we developed for gaps in dense planetary rings. Finally, we apply our model to the Encke and Keeler division in order to estimate the shear and bulk viscosities in the vicinity of both gaps KW - celestial mechanics KW - diffusion KW - hydrodynamics KW - planets and satellites: rings KW - scattering Y1 - 2019 U6 - https://doi.org/10.3847/1538-4357/ab007e SN - 0004-637X SN - 1538-4357 VL - 872 IS - 2 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Singh, Rishu Kumar A1 - Metzler, Ralf A1 - Sandev, Trifce T1 - Resetting dynamics in a confining potential JF - Journal of physics : A, Mathematical and theoretical N2 - We study Brownian motion in a confining potential under a constant-rate resetting to a reset position x(0). The relaxation of this system to the steady-state exhibits a dynamic phase transition, and is achieved in a light cone region which grows linearly with time. When an absorbing boundary is introduced, effecting a symmetry breaking of the system, we find that resetting aids the barrier escape only when the particle starts on the same side as the barrier with respect to the origin. We find that the optimal resetting rate exhibits a continuous phase transition with critical exponent of unity. Exact expressions are derived for the mean escape time, the second moment, and the coefficient of variation (CV). KW - diffusion KW - resetting KW - barrier escape KW - first-passage Y1 - 2020 U6 - https://doi.org/10.1088/1751-8121/abc83a SN - 1751-8113 SN - 1751-8121 VL - 53 IS - 50 PB - IOP Publ. Ltd. CY - Bristol ER -