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Stochastic resetting models diverse phenomena across numerous scientific disciplines. Current understanding stems from the renewal framework, which relates systems subject to global resetting to their non-resetting counterparts. Yet, in…
We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…
We investigate a stochastic model hierarchy for pedestrian flow. Starting from a microscopic social force model, where the pedestrians switch randomly between the two states stop-or-go, we derive an associated macroscopic model of…
The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…
Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…
Stochastic power fluctuation in a fiber optic system due to the interplay among dispersion, nonlinearity and partial coherence of the source is investigated. An analytical expression for the power fluctuation of a signal pulse due to its…
Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We…
The pedestrian flow is one of the most complex systems, involving large populations of interacting agents. Models at microscopic and macroscopic scales offer different advantages for studying related problems. In general, microscopic models…
For the first time the phenomenon of cellular structure coarsening are consistently analysed from the positions of kinetic, hydrodynamic and stochastodynamic theories of nonequilibrium statistical systems. Thereby micro-, meso- and…
Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…
In this paper we review some recent results dealing with the transition between microscopic and macroscopic scales in different fields, including kinetic theory, cells movement in biology, chemotaxis, flocking phenomena and agent systems.…
The mean-field limit of systems of rank-based interacting diffusions is known to be described by a nonlinear diffusion process. We obtain a similar description at the level of stationary distributions. Our proof is based on explicit…
The dynamics of ecological as well as chemical systems may depend on heterogeneous configurations. Heterogeneity in reaction-diffusion systems often increase modelling and simulating difficulties when non-linear effects are present. One…
A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the $d$-dimensional Euclidean space with $d\geq 2$. Spheres arrive sequentially at…
When two surfaces are brought into contact and slide against each other, junctions are formed at the interface. The dynamics of formation, rupture and evolution of these junctions governs the tribological response of the macro-contact.…
Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on…
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the…
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…
This series of papers has two broader aims: 1) Construct a theory for multi-partite open quantum systems comprising several layers of structure with self-consistent back-actions. Develop the graded influence action formalism…
The aim of this paper is to study the derivation of appropriate meso- and macroscopic models for interactions as appearing in social processes. There are two main characteristics the models take into account, namely a network structure of…