Related papers: Aggregation-diffusion in heterogeneous environment…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
Artificial ecosystems provide an additional experimental tool to support laboratory work, field work, and theoretical development in competitive exclusion research. A novel application of a spatiotemporal agent based model is presented…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…
Nonlocal aggregation-diffusion models, when coupled with a spatial map, can capture cognitive and memory-based influences on animal movement and population-level patterns. In this work, we study a one-dimensional…
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…
We study the propagation of sound waves in a three-dimensional, infinite ambient flow with weak random fluctuations of the mean particle velocity and speed of sound. We more particularly address the regime where the acoustic wavelengths are…
Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the…
Convenient variational formula for collective diffusion of many particles adsorbed at lattices of arbitrary geometry is formulated. The approach allows to find the expressions for the diffusion coefficient for any value of the system's…
We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…
Collective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from…
Excess pore pressure in granular--fluid mixtures can transiently suppress frictional contacts and dramatically enhance flow mobility, yet its evolution is commonly modeled using constant effective diffusivities. Here we show that the…
We study diffusion of colloids on a fluid-fluid interface using particle simulations and fluctuating hydrodynamics. Diffusion on a two-dimensional interface with three-dimensional hydrodynamics is known to be anomalous, with the collective…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
Many organisms in nature use local interactions to generate global cooperative phenomena. To unravel how the behavior of individuals generates effective interactions within a group, we introduce a simple model, wherein each agent senses the…
Reaction-diffusion equations describe various spatially extended processes that unfold as traveling fronts moving at constant velocity. We introduce and solve analytically a model that, besides such fronts, supports solutions advancing as…
Collective action and group formation are fundamental behaviors among both organisms cooperating to maximize their fitness, and people forming socioeconomic organizations. Researchers have extensively explored social interaction structures…
The process by which one may take a discrete model of a biophysical process and construct a continuous model based on it is of mathematical interest as well as being of practical use. In this paper, we first study the singular limit of a…
A simple three-dimensional model of a fluid whose constituent particles interact via a short range attractive and long range repulsive potential is used to model the aggregation into large spherical-like clusters made up of hundreds of…
Surface growth, by association or dissociation of material on the boundaries of a body, is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of 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…