Related papers: Co-evolving agents subject to local versus nonloca…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
The dynamics of minority games with agents trading on different time scales is studied via dynamical mean-field theory. We analyze the case where the agents' decision-making process is deterministic and its stochastic generalization with…
Most classical work on the hydrodynamics of low-Reynolds-number swimming addresses deterministic locomotion in quiescent environments. Thermal fluctuations in fluids are known to lead to a Brownian loss of the swimming direction. As most…
Locally interacting dynamical systems, such as epidemic spread, rumor propagation through crowd, and forest fire, exhibit complex global dynamics originated from local, relatively simple, and often stochastic interactions between dynamic…
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…
We analyze the dynamics of agent--based models (ABMs) from a Markovian perspective and derive explicit statements about the possibility of linking a microscopic agent model to the dynamical processes of macroscopic observables that are…
We consider general stochastic systems of interacting particles with noise which are relevant as models for the collective behavior of animals, and rigorously prove that in the mean-field limit the system is close to the solution of a…
Finding reduced models of spatially-distributed chemical reaction networks requires an estimation of which effective dynamics are relevant. We propose a machine learning approach to this coarse graining problem, where a maximum entropy…
Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
Despite the advanced stage of epidemic modeling, there is a major demand for methods to incorporate behavioral responses to the spread of a disease such as social distancing and adoption of prevention methods. Mobility plays an important…
We develop an agent-based model of the motion and pattern formation of vesicles. These intracellular particles can be found in four different modes of (undirected and directed) motion and can fuse with other vesicles. While the size of…
In this paper, we derive the mean-field limit of a collective dynamics model with time-varying weights, for weight dynamics that preserve the total mass of the system as well as indistinguishability of the agents. The limit equation is a…
We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…
Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
We introduce a new and robust approach for characterizing spatially and temporally heterogeneous behavior within a system based on the evolution of dynamic fuctuations once averaged over different space lengths and time scales. We apply it…
We analyze a non-Markovian mean field interacting spin system, related to the Curie--Weiss model. We relax the Markovianity assumption by replacing the memoryless distribution of the waiting times of a classical spin-flip dynamics with a…
We argue that the stochastic dynamics of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process akin to aging in complex materials. Specifically, our study uses extensive computer simulations of…
We present a stochastic, time-discrete boolean model which mimics the mesoscopic dynamics of the desorption reactions $A+A\to A+S$ and $A+A\to S+S$ in a 1D lattice. In the continuous-time limit, we derive a hierarchy of dynamical equations…