@article{ThapaWyłomańskaSikoraetal.2021, author = {Thapa, Samudrajit and Wyłomańska, Agnieszka and Sikora, Grzegorz and Wagner, Caroline E. and Krapf, Diego and Kantz, Holger and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories}, series = {New Journal of Physics}, volume = {23}, journal = {New Journal of Physics}, publisher = {Dt. Physikalische Ges. ; IOP}, address = {Bad Honnef ; London}, issn = {1367-2630}, doi = {10.1088/1367-2630/abd50e}, pages = {22}, year = {2021}, abstract = {Extensive time-series encoding the position of particles such as viruses, vesicles, or individualproteins are routinely garnered insingle-particle tracking experiments or supercomputing studies.They contain vital clues on how viruses spread or drugs may be delivered in biological cells.Similar time-series are being recorded of stock values in financial markets and of climate data.Such time-series are most typically evaluated in terms of time-averaged mean-squareddisplacements (TAMSDs), which remain random variables for finite measurement times. Theirstatistical properties are different for differentphysical stochastic processes, thus allowing us toextract valuable information on the stochastic process itself. To exploit the full potential of thestatistical information encoded in measured time-series we here propose an easy-to-implementand computationally inexpensive new methodology, based on deviations of the TAMSD from itsensemble average counterpart. Specifically, we use the upper bound of these deviations forBrownian motion (BM) to check the applicability of this approach to simulated and real data sets.By comparing the probability of deviations fordifferent data sets, we demonstrate how thetheoretical bound for BM reveals additional information about observed stochastic processes. Weapply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracerbeads measured in mucin hydrogels, and of geographic surface temperature anomalies. Ouranalysis shows how the large-deviation properties can be efficiently used as a simple yet effectiveroutine test to reject the BM hypothesis and unveil relevant information on statistical propertiessuch as ergodicity breaking and short-time correlations.}, language = {en} } @article{SposiniChechkinMetzler2018, author = {Sposini, Vittoria and Chechkin, Aleksei V. and Metzler, Ralf}, title = {First passage statistics for diffusing diffusivity}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {52}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {4}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/aaf6ff}, pages = {11}, year = {2018}, abstract = {A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law < r(2)(t)> similar or equal to Dt yet the distribution of particle displacements is strongly non-Gaussian. A central approach to describe this effect is the diffusing diffusivity (DD) model in which the diffusion coefficient itself is a stochastic quantity, mimicking heterogeneities of the environment encountered by the tracer particle on its path. We here quantify in terms of analytical and numerical approaches the first passage behaviour of the DD model. We observe significant modifications compared to Brownian-Gaussian diffusion, in particular that the DD model may have a faster first passage dynamics. Moreover we find a universal crossover point of the survival probability independent of the initial condition.}, language = {en} } @article{DybiecCapalaChechkinetal.2018, author = {Dybiec, Bartlomiej and Capala, Karol and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Conservative random walks in confining potentials}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {52}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {1}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/aaefc2}, pages = {25}, year = {2018}, abstract = {Levy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic systems, or even the dynamics in quantum systems such as cold atoms. In the simplest version Levy walks move with a finite speed. Here, we present an extension of the Levy walk scenario for the case when external force fields influence the motion. The resulting motion is a combination of the response to the deterministic force acting on the particle, changing its velocity according to the principle of total energy conservation, and random velocity reversals governed by the distribution of waiting times. For the fact that the motion stays conservative, that is, on a constant energy surface, our scenario is fundamentally different from thermal motion in the same external potentials. In particular, we present results for the velocity and position distributions for single well potentials of different steepness. The observed dynamics with its continuous velocity changes enriches the theory of Levy walk processes and will be of use in a variety of systems, for which the particles are externally confined.}, language = {en} } @article{GajdaWylomanskaKantzetal.2018, author = {Gajda, J. and Wylomanska, Agnieszka and Kantz, Holger and Chechkin, Aleksei V. and Sikora, Grzegorz}, title = {Large deviations of time-averaged statistics for Gaussian processes}, series = {Statistics \& Probability Letters}, volume = {143}, journal = {Statistics \& Probability Letters}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-7152}, doi = {10.1016/j.spl.2018.07.013}, pages = {47 -- 55}, year = {2018}, abstract = {In this paper we study the large deviations of time averaged mean square displacement (TAMSD) for Gaussian processes. The theory of large deviations is related to the exponential decay of probabilities of large fluctuations in random systems. From the mathematical point of view a given statistics satisfies the large deviation principle, if the probability that it belongs to a certain range decreases exponentially. The TAMSD is one of the main statistics used in the problem of anomalous diffusion detection. Applying the theory of generalized chi-squared distribution and sub-gamma random variables we prove the upper bound for large deviations of TAMSD for Gaussian processes. As a special case we consider fractional Brownian motion, one of the most popular models of anomalous diffusion. Moreover, we derive the upper bound for large deviations of the estimator for the anomalous diffusion exponent. (C) 2018 Elsevier B.V. All rights reserved.}, language = {en} } @article{MardoukhiChechkinMetzler2020, author = {Mardoukhi, Yousof and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Spurious ergodicity breaking in normal and fractional Ornstein-Uhlenbeck process}, series = {New Journal of Physics}, volume = {22}, journal = {New Journal of Physics}, publisher = {IOP}, address = {London}, issn = {1367-2630}, doi = {10.1088/1367-2630/ab950b}, pages = {18}, year = {2020}, abstract = {The Ornstein-Uhlenbeck process is a stationary and ergodic Gaussian process, that is fully determined by its covariance function and mean. We show here that the generic definitions of the ensemble- and time-averaged mean squared displacements fail to capture these properties consistently, leading to a spurious ergodicity breaking. We propose to remedy this failure by redefining the mean squared displacements such that they reflect unambiguously the statistical properties of any stochastic process. In particular we study the effect of the initial condition in the Ornstein-Uhlenbeck process and its fractional extension. For the fractional Ornstein-Uhlenbeck process representing typical experimental situations in crowded environments such as living biological cells, we show that the stationarity of the process delicately depends on the initial condition.}, language = {en} } @article{DelleSideNassisiPennettaetal.2017, author = {Delle Side, Domenico and Nassisi, Vincenzo and Pennetta, Cecilia and Alifano, Pietro and Di Salvo, Marco and Tala, Adelfia and Chechkin, Aleksei V. and Seno, Flavio and Trovato, Antonio}, title = {Bacterial bioluminescence onset and quenching: a dynamical model for a quorum sensing-mediated property}, series = {Royal Society Open Science}, volume = {4}, journal = {Royal Society Open Science}, publisher = {Royal Society}, address = {London}, issn = {2054-5703}, doi = {10.1098/rsos.171586}, pages = {12}, year = {2017}, abstract = {We present an effective dynamical model for the onset of bacterial bioluminescence, one of the most studied quorum sensing-mediated traits. Our model is built upon simple equations that describe the growth of the bacterial colony, the production and accumulation of autoinducer signal molecules, their sensing within bacterial cells, and the ensuing quorum activation mechanism that triggers bioluminescent emission. The model is directly tested to quantitatively reproduce the experimental distributions of photon emission times, previously measured for bacterial colonies of Vibrio jasicida, a luminescent bacterium belonging to the Harveyi clade, growing in a highly drying environment. A distinctive and novel feature of the proposed model is bioluminescence 'quenching' after a given time elapsed from activation. Using an advanced fitting procedure based on the simulated annealing algorithm, we are able to infer from the experimental observations the biochemical parameters used in the model. Such parameters are in good agreement with the literature data. As a further result, we find that, at least in our experimental conditions, light emission in bioluminescent bacteria appears to originate from a subtle balance between colony growth and quorum activation due to autoinducers diffusion, with the two phenomena occurring on the same time scale. This finding is consistent with a negative feedback mechanism previously reported for Vibrio harveyi.}, language = {en} } @article{PalyulinMantsevichKlagesetal.2017, author = {Palyulin, Vladimir V. and Mantsevich, Vladimir N. and Klages, Rainer and Metzler, Ralf and Chechkin, Aleksei V.}, title = {Comparison of pure and combined search strategies for single and multiple targets}, series = {The European physical journal : B, Condensed matter and complex systems}, volume = {90}, journal = {The European physical journal : B, Condensed matter and complex systems}, publisher = {Springer}, address = {New York}, issn = {1434-6028}, doi = {10.1140/epjb/e2017-80372-4}, pages = {20 -- 37}, year = {2017}, abstract = {We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with Levy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a Levy searcher.}, language = {en} } @article{PalyulinBlackburnLomholtetal.2019, author = {Palyulin, Vladimir V. and Blackburn, George and Lomholt, Michael A. and Watkins, Nicholas W. and Metzler, Ralf and Klages, Rainer and Chechkin, Aleksei V.}, title = {First passage and first hitting times of Levy flights and Levy walks}, series = {New journal of physics : the open-access journal for physics}, volume = {21}, journal = {New journal of physics : the open-access journal for physics}, number = {10}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/ab41bb}, pages = {23}, year = {2019}, abstract = {For both L{\´e}vy flight and L{\´e}vy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For L{\´e}vy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the L{\´e}vy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.}, language = {en} } @article{CherstvyThapaMardoukhietal.2018, author = {Cherstvy, Andrey G. and Thapa, Samudrajit and Mardoukhi, Yousof and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Time averages and their statistical variation for the Ornstein-Uhlenbeck process}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {98}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.98.022134}, pages = {15}, year = {2018}, abstract = {How ergodic is diffusion under harmonic confinements? How strongly do ensemble- and time-averaged displacements differ for a thermally-agitated particle performing confined motion for different initial conditions? We here study these questions for the generic Ornstein-Uhlenbeck (OU) process and derive the analytical expressions for the second and fourth moment. These quantifiers are particularly relevant for the increasing number of single-particle tracking experiments using optical traps. For a fixed starting position, we discuss the definitions underlying the ensemble averages. We also quantify effects of equilibrium and nonequilibrium initial particle distributions onto the relaxation properties and emerging nonequivalence of the ensemble- and time-averaged displacements (even in the limit of long trajectories). We derive analytical expressions for the ergodicity breaking parameter quantifying the amplitude scatter of individual time-averaged trajectories, both for equilibrium and outof-equilibrium initial particle positions, in the entire range of lag times. Our analytical predictions are in excellent agreement with results of computer simulations of the Langevin equation in a parabolic potential. We also examine the validity of the Einstein relation for the ensemble- and time-averaged moments of the OU-particle. Some physical systems, in which the relaxation and nonergodic features we unveiled may be observable, are discussed.}, language = {en} } @misc{PalyulinBlackburnLomholtetal.2019, author = {Palyulin, Vladimir V and Blackburn, George and Lomholt, Michael A and Watkins, Nicholas W and Metzler, Ralf and Klages, Rainer and Chechkin, Aleksei V.}, title = {First passage and first hitting times of L{\´e}vy flights and L{\´e}vy walks}, series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe}, number = {785}, issn = {1866-8372}, doi = {10.25932/publishup-43983}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-439832}, pages = {25}, year = {2019}, abstract = {For both L{\´e}vy flight and L{\´e}vy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For L{\´e}vy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the L{\´e}vy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.}, language = {en} } @article{CherstvyChechkinMetzler2014, author = {Cherstvy, Andrey G. and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity}, series = {Soft matter}, volume = {2014}, journal = {Soft matter}, number = {10}, publisher = {Royal Society of Chemistry}, issn = {2046-2069}, doi = {10.1039/c3sm52846d}, pages = {1591 -- 1601}, year = {2014}, abstract = {We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.}, language = {en} } @misc{CherstvyChechkinMetzler2014, author = {Cherstvy, Andrey G. and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity}, number = {168}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74021}, pages = {1591 -- 1601}, year = {2014}, abstract = {We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.}, language = {en} } @article{JeonChechkinMetzler2014, author = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion}, series = {Physical chemistry, chemical physics : PCCP}, volume = {30}, journal = {Physical chemistry, chemical physics : PCCP}, number = {16}, publisher = {The Royal Society of Chemistry}, address = {Cambridge}, doi = {10.1039/C4CP02019G}, pages = {15811 -- 15817}, year = {2014}, abstract = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.}, language = {en} } @misc{MardoukhiChechkinMetzler2020, author = {Mardoukhi, Yousof and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Spurious ergodicity breaking in normal and fractional Ornstein-Uhlenbeck process}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {981}, issn = {1866-8372}, doi = {10.25932/publishup-47487}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-474875}, pages = {20}, year = {2020}, abstract = {The Ornstein-Uhlenbeck process is a stationary and ergodic Gaussian process, that is fully determined by its covariance function and mean. We show here that the generic definitions of the ensemble- and time-averaged mean squared displacements fail to capture these properties consistently, leading to a spurious ergodicity breaking. We propose to remedy this failure by redefining the mean squared displacements such that they reflect unambiguously the statistical properties of any stochastic process. In particular we study the effect of the initial condition in the Ornstein-Uhlenbeck process and its fractional extension. For the fractional Ornstein-Uhlenbeck process representing typical experimental situations in crowded environments such as living biological cells, we show that the stationarity of the process delicately depends on the initial condition.}, language = {en} } @article{MardoukhiJeonChechkinetal.2018, author = {Mardoukhi, Yousof and Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Fluctuations of random walks in critical random environments}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {20}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {31}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/c8cp03212b}, pages = {20427 -- 20438}, year = {2018}, abstract = {Percolation networks have been widely used in the description of porous media but are now found to be relevant to understand the motion of particles in cellular membranes or the nucleus of biological cells. Random walks on the infinite cluster at criticality of a percolation network are asymptotically ergodic. On any finite size cluster of the network stationarity is reached at finite times, depending on the cluster's size. Despite of this we here demonstrate by combination of analytical calculations and simulations that at criticality the disorder and cluster size average of the ensemble of clusters leads to a non-vanishing variance of the time averaged mean squared displacement, regardless of the measurement time. Fluctuations of this relevant experimental quantity due to the disorder average of such ensembles are thus persistent and non-negligible. The relevance of our results for single particle tracking analysis in complex and biological systems is discussed.}, language = {en} } @article{PadashChechkinDybiecetal.2019, author = {Padash, Amin and Chechkin, Aleksei V. and Dybiec, Bartlomiej and Pavlyukevich, Ilya and Shokri, Babak and Metzler, Ralf}, title = {First-passage properties of asymmetric Levy flights}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {52}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {45}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/ab493e}, pages = {48}, year = {2019}, abstract = {L{\´e}vy flights are paradigmatic generalised random walk processes, in which the independent stationary increments—the 'jump lengths'—are drawn from an -stable jump length distribution with long-tailed, power-law asymptote. As a result, the variance of L{\´e}vy flights diverges and the trajectory is characterised by occasional extremely long jumps. Such long jumps significantly decrease the probability to revisit previous points of visitation, rendering L{\´e}vy flights efficient search processes in one and two dimensions. To further quantify their precise property as random search strategies we here study the first-passage time properties of L{\´e}vy flights in one-dimensional semi-infinite and bounded domains for symmetric and asymmetric jump length distributions. To obtain the full probability density function of first-passage times for these cases we employ two complementary methods. One approach is based on the space-fractional diffusion equation for the probability density function, from which the survival probability is obtained for different values of the stable index and the skewness (asymmetry) parameter . The other approach is based on the stochastic Langevin equation with -stable driving noise. Both methods have their advantages and disadvantages for explicit calculations and numerical evaluation, and the complementary approach involving both methods will be profitable for concrete applications. We also make use of the Skorokhod theorem for processes with independent increments and demonstrate that the numerical results are in good agreement with the analytical expressions for the probability density function of the first-passage times.}, language = {en} } @article{SliusarenkoVitaliSposinietal.2019, author = {Sliusarenko, Oleksii Yu and Vitali, Silvia and Sposini, Vittoria and Paradisi, Paolo and Chechkin, Aleksei V. and Castellani, Gastone and Pagnini, Gianni}, title = {Finite-energy Levy-type motion through heterogeneous ensemble of Brownian particles}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {52}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {9}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/aafe90}, pages = {27}, year = {2019}, abstract = {Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling x similar to t(delta) with delta not equal 1/2 in the probability density function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g. fractional Brownian motion, and power-law decaying distributions, e.g. Levy Flights or Levy Walks (LWs). Levy flights get anomalous scaling, but, being jumps of any size allowed even at short times, have infinite position variance, infinite energy and discontinuous paths. LWs, which are based on random trapping events, overcome these limitations: they resemble a Levy-type power-law distribution that is truncated in the large displacement range and have finite moments, finite energy and, even with discontinuous velocity, they are continuous. However, LWs do not take into account the role of strong heterogeneity in many complex systems, such as biological transport in the crowded cell environment. In this work we propose and discuss a model describing a heterogeneous ensemble of Brownian particles (HEBP). Velocity of each single particle obeys a standard underdamped Langevin equation for the velocity, with linear friction term and additive Gaussian noise. Each particle is characterized by its own relaxation time and velocity diffusivity. We show that, for proper distributions of relaxation time and velocity diffusivity, the HEBP resembles some LW statistical features, in particular power-law decaying PDF, long-range correlations and anomalous diffusion, at the same time keeping finite position moments and finite energy. The main differences between the HEBP model and two different LWs are investigated, finding that, even when both velocity and position PDFs are similar, they differ in four main aspects: (i) LWs are biscaling, while HEBP is monoscaling; (ii) a transition from anomalous (delta = 1/2) to normal (delta = 1/2) diffusion in the long-time regime is seen in the HEBP and not in LWs; (iii) the power-law index of the position PDF and the space/time diffusion scaling are independent in the HEBP, while they both depend on the scaling of the interevent time PDF in LWs; (iv) at variance with LWs, our HEBP model obeys a fluctuation-dissipation theorem.}, language = {en} } @article{WangCherstvyChechkinetal.2020, author = {Wang, Wei and Cherstvy, Andrey G. and Chechkin, Aleksei V. and Thapa, Samudrajit and Seno, Flavio and Liu, Xianbin and Metzler, Ralf}, title = {Fractional Brownian motion with random diffusivity}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {53}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {47}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/aba467}, pages = {34}, year = {2020}, abstract = {Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time tau characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on tau and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments.}, language = {en} } @article{KurilovichMantsevichStevensonetal.2020, author = {Kurilovich, Aleksandr A. and Mantsevich, Vladimir and Stevenson, Keith J. and Chechkin, Aleksei V. and Palyulin, V. V.}, title = {Complex diffusion-based kinetics of photoluminescence in semiconductor nanoplatelets}, series = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, volume = {22}, journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies}, number = {42}, publisher = {Royal Society of Chemistry}, address = {Cambridge}, issn = {1463-9076}, doi = {10.1039/d0cp03744c}, pages = {24686 -- 24696}, year = {2020}, abstract = {We present a diffusion-based simulation and theoretical models for explanation of the photoluminescence (PL) emission intensity in semiconductor nanoplatelets. It is shown that the shape of the PL intensity curves can be reproduced by the interplay of recombination, diffusion and trapping of excitons. The emission intensity at short times is purely exponential and is defined by recombination. At long times, it is governed by the release of excitons from surface traps and is characterized by a power-law tail. We show that the crossover from one limit to another is controlled by diffusion properties. This intermediate region exhibits a rich behaviour depending on the value of diffusivity. The proposed approach reproduces all the features of experimental curves measured for different nanoplatelet systems.}, language = {en} } @misc{ThapaWyłomańskaSikoraetal.2021, author = {Thapa, Samudrajit and Wyłomańska, Agnieszka and Sikora, Grzegorz and Wagner, Caroline E. and Krapf, Diego and Kantz, Holger and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1118}, issn = {1866-8372}, doi = {10.25932/publishup-49349}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-493494}, pages = {24}, year = {2021}, abstract = {Extensive time-series encoding the position of particles such as viruses, vesicles, or individualproteins are routinely garnered insingle-particle tracking experiments or supercomputing studies.They contain vital clues on how viruses spread or drugs may be delivered in biological cells.Similar time-series are being recorded of stock values in financial markets and of climate data.Such time-series are most typically evaluated in terms of time-averaged mean-squareddisplacements (TAMSDs), which remain random variables for finite measurement times. Theirstatistical properties are different for differentphysical stochastic processes, thus allowing us toextract valuable information on the stochastic process itself. To exploit the full potential of thestatistical information encoded in measured time-series we here propose an easy-to-implementand computationally inexpensive new methodology, based on deviations of the TAMSD from itsensemble average counterpart. Specifically, we use the upper bound of these deviations forBrownian motion (BM) to check the applicability of this approach to simulated and real data sets.By comparing the probability of deviations fordifferent data sets, we demonstrate how thetheoretical bound for BM reveals additional information about observed stochastic processes. Weapply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracerbeads measured in mucin hydrogels, and of geographic surface temperature anomalies. Ouranalysis shows how the large-deviation properties can be efficiently used as a simple yet effectiveroutine test to reject the BM hypothesis and unveil relevant information on statistical propertiessuch as ergodicity breaking and short-time correlations.}, language = {en} }