Related papers: Anomalous Diffusion and Emergent Universality in C…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
Axis-driven random walks were introduced by P. Andreoletti and P. Debs [AD23] to provide a rough description of the behaviour of a particle trapped in a localized force field. In contrast to their work, we examine the scenario where a…
The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations…
Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard…
Introducing a general class of one-dimensional single-file systems (meaning that particle crossings are prohibited) of interacting hardcore particles with internal degrees of freedom (called charge), we exhibit a novel type of dynamical…
We study the consumption behaviour of an asymmetric network of heterogeneous agents in the framework of discrete choice models with stochastic decision rules. We assume that the interactions among agents are uniquely specified by their…
In transport processes across materials like glasses, living cells, and porous media, the probability density function of displacements exhibits exponential decay rather than Gaussian behavior. We show that this universal behavior of rare…
In any ecosystem, the conditions of the environment and the characteristics of the species that inhabit it are entangled, co-evolving in space and time. We introduce a model that couples active agents with a dynamic environment, interpreted…
Using exact expressions for the persistence probability and for the leading eigenvalue of the Focker-Planck operator of a random walk in a random environment we establish a fundamental relation between the statistical properties of…
We present two complementary simulations that lead to an exploration of Anderson localization, a phenomenon in which wave diffusion is suppressed in disordered media by interference from multiple scattering. To build intuition, the first…
Collective behavior is commonly attributed to direct interactions among system components. Using a minimal stochastic model, we show that higher-order collective structure can instead emerge from shared stochastic environments, even in the…
We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals…
The evolutionary balance between innate and learned behaviors is highly intricate, and different organisms have found different solutions to this problem. We hypothesize that the emergence and exact form of learning behaviors is naturally…
Studies of the phase diagram of the coupled sine circle map lattice have identified the presence of two distinct universality classes of spatiotemporal intermittency viz. spatiotemporal intermittency of the directed percolation class with a…
Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…
Strong anomalous diffusion is {often} characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes $\xi$ and $\zeta$ for small and large moments, respectively, and by the critical…
Anomalous diffusion phenomenon is an intriguing process that tracer diffusion presents in numerous complex systems. Current experimental and theoretical investigations have reported the emergence of random diffusivity scenarios accompanied…
A topic of intense current investigation pursues the question how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of…
Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time…