@article{GrebenkovMetzlerOshanin2021, author = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb}, title = {A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes}, series = {New Journal of Physics (NJP)}, volume = {23}, journal = {New Journal of Physics (NJP)}, publisher = {IOP - Institute of Physics Publishing}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/ac1e42}, pages = {18}, year = {2021}, abstract = {We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.}, language = {en} } @misc{GrebenkovMetzlerOshanin2021, author = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb}, title = {A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes}, series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, issn = {1866-8372}, doi = {10.25932/publishup-52194}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-521942}, pages = {20}, year = {2021}, abstract = {We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.}, language = {en} } @article{SchwarzlGodecOshaninetal.2016, author = {Schwarzl, Maria and Godec, Aljaz and Oshanin, Gleb and Metzler, Ralf}, title = {A single predator charging a herd of prey: effects of self volume and predator-prey decision-making}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {49}, journal = {Journal of physics : A, Mathematical and theoretical}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8113/49/22/225601}, pages = {19}, year = {2016}, abstract = {We study the degree of success of a single predator hunting a herd of prey on a two-dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into directed escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics in terms of the mean distance between the predator and the nearest prey. It turns out that effectively the dynamics of this distance coordinate can be captured in terms of a simple Ornstein-Uhlenbeck picture. Reducing the many-body problem to a simple two-body problem by imagining predator and nearest prey to be connected by an effective Hookean bond, all features of the model such as prey density and sighting ranges merge into the effective binding constant.}, language = {en} } @article{GuggenbergerChechkinMetzler2022, author = {Guggenberger, Tobias and Chechkin, Aleksei and Metzler, Ralf}, title = {Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentials}, series = {New journal of physics : the open-access journal for physics}, volume = {24}, journal = {New journal of physics : the open-access journal for physics}, number = {7}, publisher = {Dt. Physikalische Ges.}, address = {[Bad Honnef]}, issn = {1367-2630}, doi = {10.1088/1367-2630/ac7b3c}, pages = {18}, year = {2022}, abstract = {We study the diffusive motion of a particle in a subharmonic potential of the form U(x) = |x|( c ) (0 < c < 2) driven by long-range correlated, stationary fractional Gaussian noise xi ( alpha )(t) with 0 < alpha <= 2. In the absence of the potential the particle exhibits free fractional Brownian motion with anomalous diffusion exponent alpha. While for an harmonic external potential the dynamics converges to a Gaussian stationary state, from extensive numerical analysis we here demonstrate that stationary states for shallower than harmonic potentials exist only as long as the relation c > 2(1 - 1/alpha) holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function. Moreover we discuss analogies of non-stationarity of Levy flights in shallow external potentials.}, language = {en} } @article{DoerriesChechkinMetzler2022, author = {Doerries, Timo J. and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching}, series = {Interface : journal of the Royal Society}, volume = {19}, journal = {Interface : journal of the Royal Society}, number = {192}, publisher = {Royal Society}, address = {London}, issn = {1742-5689}, doi = {10.1098/rsif.2022.0233}, pages = {14}, year = {2022}, abstract = {We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.}, language = {en} } @article{StojkoskiSandevKocarevetal.2022, author = {Stojkoski, Viktor and Sandev, Trifce and Kocarev, Ljupco and Pal, Arnab}, title = {Autocorrelation functions and ergodicity in diffusion with stochastic resetting}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {55}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {10}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/ac4ce9}, pages = {22}, year = {2022}, abstract = {Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc. What remains less explored is the two time point correlation functions whose evaluation is often daunting since it requires the implementation of the exact time dependent probability density functions of the resetting processes which are unknown for most of the problems. We adopt a different approach that allows us to write a stochastic solution for a single trajectory undergoing resetting. Moments and the autocorrelation functions between any two times along the trajectory can then be computed directly using the laws of total expectation. Estimation of autocorrelation functions turns out to be pivotal for investigating the ergodic properties of various observables for this canonical model. In particular, we investigate two observables (i) sample mean which is widely used in economics and (ii) time-averaged-mean-squared-displacement (TAMSD) which is of acute interest in physics. We find that both diffusion and drift-diffusion processes with resetting are ergodic at the mean level unlike their reset-free counterparts. In contrast, resetting renders ergodicity breaking in the TAMSD while both the stochastic processes are ergodic when resetting is absent. We quantify these behaviors with detailed analytical study and corroborate with extensive numerical simulations. Our results can be verified in experimental set-ups that can track single particle trajectories and thus have strong implications in understanding the physics of resetting.}, language = {en} } @article{ProkopovicVikulinaSustretal.2016, author = {Prokopovic, Vladimir Z. and Vikulina, Anna S. and Sustr, David and Duschl, Claus and Volodkin, Dmitry}, title = {Biodegradation-Resistant Multilayers Coated with Gold Nanoparticles. Toward a Tailor-made Artificial Extracellular Matrix}, series = {Journal of colloid and interface science}, volume = {8}, journal = {Journal of colloid and interface science}, publisher = {American Chemical Society}, address = {Washington}, issn = {1944-8244}, doi = {10.1021/acsami.6b10095}, pages = {24345 -- 24349}, year = {2016}, abstract = {Polymer multicomponent coatings such as multilayers mimic an extracellular, matrix (ECM) that attracts significant attention for the use of the multilayers as functional supports for advanced cell culture and tissue engineering. Herein, biodegradation and molecular transport in hyaluronan/polylysine multilayers coated with gold nanoparticles were described. Nanoparticle coating acts as a semipermeable barrier that governs molecular transport into/from the multilayers, and makes them biodegradation-resistant. Model protein lysozyme (mimics of ECM-soluble signals) diffuses into the multilayers as fast- and, slow-diffusing populations existing in an equilibrium,. Such a. composite system may have high potential to be exploited as degradation-resistant drug-delivery platforms suitable for cell-based applications.}, language = {en} } @phdthesis{Mulansky2012, author = {Mulansky, Mario}, title = {Chaotic diffusion in nonlinear Hamiltonian systems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-63180}, school = {Universit{\"a}t Potsdam}, year = {2012}, abstract = {This work investigates diffusion in nonlinear Hamiltonian systems. The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''. Its properties are studied on the example of one- or two-dimensional lattices of harmonic or nonlinear oscillators with nearest neighbor couplings. The fundamental observation is the spreading of energy for localized initial conditions. Methods of quantifying this spreading behavior are presented, including a new quantity called excitation time. This new quantity allows for a more precise analysis of the spreading than traditional methods. Furthermore, the nonlinear diffusion equation is introduced as a phenomenologic description of the spreading process and a number of predictions on the density dependence of the spreading are drawn from this equation. Two mathematical techniques for analyzing nonlinear Hamiltonian systems are introduced. The first one is based on a scaling analysis of the Hamiltonian equations and the results are related to similar scaling properties of the NDE. From this relation, exact spreading predictions are deduced. Secondly, the microscopic dynamics at the edge of spreading states are thoroughly analyzed, which again suggests a scaling behavior that can be related to the NDE. Such a microscopic treatment of chaotically spreading states in nonlinear Hamiltonian systems has not been done before and the results present a new technique of connecting microscopic dynamics with macroscopic descriptions like the nonlinear diffusion equation. All theoretical results are supported by heavy numerical simulations, partly obtained on one of Europe's fastest supercomputers located in Bologna, Italy. In the end, the highly interesting case of harmonic oscillators with random frequencies and nonlinear coupling is studied, which resembles to some extent the famous Discrete Anderson Nonlinear Schroedinger Equation. For this model, a deviation from the widely believed power-law spreading is observed in numerical experiments. Some ideas on a theoretical explanation for this deviation are presented, but a conclusive theory could not be found due to the complicated phase space structure in this case. Nevertheless, it is hoped that the techniques and results presented in this work will help to eventually understand this controversely discussed case as well.}, language = {en} } @article{MutothyaXuLietal.2021, author = {Mutothya, Nicholas Mwilu and Xu, Yong and Li, Yongge and Metzler, Ralf}, title = {Characterising stochastic motion in heterogeneous media driven by coloured non-Gaussian noise}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {54}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {29}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/abfba6}, pages = {31}, year = {2021}, abstract = {We study the stochastic motion of a test particle in a heterogeneous medium in terms of a position dependent diffusion coefficient mimicking measured deterministic diffusivity gradients in biological cells or the inherent heterogeneity of geophysical systems. Compared to previous studies we here investigate the effect of the interplay of anomalous diffusion effected by position dependent diffusion coefficients and coloured non-Gaussian noise. The latter is chosen to be distributed according to Tsallis' q-distribution, representing a popular example for a non-extensive statistic. We obtain the ensemble and time averaged mean squared displacements for this generalised process and establish its non-ergodic properties as well as analyse the non-Gaussian nature of the associated displacement distribution. We consider both non-stratified and stratified environments.}, language = {en} } @article{VilkAghionNathanetal.2022, author = {Vilk, Ohad and Aghion, Erez and Nathan, Ran and Toledo, Sivan and Metzler, Ralf and Assaf, Michael}, title = {Classification of anomalous diffusion in animal movement data using power spectral analysis}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {55}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {33}, publisher = {IOP Publishing}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/ac7e8f}, pages = {16}, year = {2022}, abstract = {The field of movement ecology has seen a rapid increase in high-resolution data in recent years, leading to the development of numerous statistical and numerical methods to analyse relocation trajectories. Data are often collected at the level of the individual and for long periods that may encompass a range of behaviours. Here, we use the power spectral density (PSD) to characterise the random movement patterns of a black-winged kite (Elanus caeruleus) and a white stork (Ciconia ciconia). The tracks are first segmented and clustered into different behaviours (movement modes), and for each mode we measure the PSD and the ageing properties of the process. For the foraging kite we find 1/f noise, previously reported in ecological systems mainly in the context of population dynamics, but not for movement data. We further suggest plausible models for each of the behavioural modes by comparing both the measured PSD exponents and the distribution of the single-trajectory PSD to known theoretical results and simulations.}, language = {en} }