Related papers: Two-species system with nonlocal interactions driv…
We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or…
This note concerns the problem of minimizing a certain family of non-local energy functionals over measures on $\mathbb{R}^n$, subject to a mass constraint, in a strong attraction limit. In these problems, the total energy is an integral…
We prove the well-posedness of entropy solutions for a wide class of nonlocal transport equations with nonlinear mobility in one spatial dimension. The solution is obtained as the limit of approximations constructed via a deterministic…
We introduce a new interacting particle system intended to model an example of ecological succession involving two species: the bracken and the european beech. The objective is to exhibit phase transitions by proving that there exist three…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
We present a new proof of the turnpike property for nonlinear optimal control problems, when the running target is a steady control-state pair of the underlying system. Our strategy combines the construction of quasi-turnpike controls via…
A general class of hybrid models has been introduced recently, gathering the advantages multiscale descriptions. Concerning biological applications, the particular coupled structure fits to collective cell migrations and pattern formation…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
Interacting particle system (IPS) models have proven to be highly successful for describing the spatial movement of organisms. However, it has proven challenging to infer the interaction rules directly from data. In the field of equation…
The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous…
We introduce a general method to determine the large scale non-equilibrium steady-state properties of one-dimensional multi-species driven diffusive systems with open boundaries, generalizing thus the max-min current principle known for…
In this paper we review some recent results on nonlocal interaction problems. The focus is on interaction kernels that are anisotropic variants of the classical Coulomb kernel. In other words, while preserving the same singularity at zero…
Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality…
A unified theory for the current through a nanoscale region of interacting electrons connected to two leads which can be either ferromagnet or superconductor is presented, yielding Meir-Wingreen-type formulas when applied to specific…
In the present work we deal with the existence of solutions for optimal control problems associated to transport equations. The behaviour of a population of individuals will be influenced by the presence of a population of control agents…
Dynamical systems across many disciplines are modeled as interacting particles or agents, with interaction rules that depend on a very small number of variables (e.g. pairwise distances, pairwise differences of phases, etc...), functions of…
In this paper, we consider a family of seamlessly coupled nonlocal models associated with transmission conditions across an interface. The models are derived from the variation of a parameterized family of energies consisting of a…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
We propose an upwind finite volume method for a system of two kinetic equations in one dimension that are coupled through nonlocal interaction terms. These cross-interaction systems were recently obtained as the mean-field limit of a…
We prove existence, uniqueness and several qualitative properties for evolution equations that combine local and nonlocal diffusion operators acting in different subdomains and coupled in such a way that the resulting evolution equation is…