Related papers: Small inertia limit for coupled kinetic swarming m…
We study a general class of interacting particle systems over a countable state space $V$ where on each site $x \in V$ the particle mass $\eta(x) \geq 0$ follows a stochastic differential equation. We construct the corresponding Markovian…
We introduce a mathematical description of the impact of sociality in the spread of infectious diseases by integrating an epidemiological dynamics with a kinetic modeling of population-based contacts. The kinetic description leads to study…
The Keller-Segel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form, it is a conservative drift-diffusion equation for the cell density coupled to an…
A relation between a class of stationary points of the energy landscape of continuous spin models on a lattice and the configurations of a Ising model defined on the same lattice suggests an approximate expression for the microcanonical…
We study the limits of linear modeling of swarm behavior by characterizing the inflection point beyond which linear models of swarm collective behavior break down. The problem we consider is a central place object gathering task. We design…
We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies…
Current engineering wear models are often based on empirical parameters rather than built upon physical considerations. Here, we look for a physical description of adhesive wear at the microscale, at which the interaction between two…
We propose a statistical model for static and sliding friction between rough surfaces. Approximating the contact between rough surfaces by the contact of an ensemble of one-dimensional viscoelastic elements with a rough rigid surface, we…
In this work, we study the inertial Kuramoto model, which is a second-order extension of the classical first-order Kuramoto model, as an inertial perturbation of the first-order Kuramoto model. We develop a quantitative Tikhonov theorem,…
We consider a random model of diffusion and coagulation. A large number of small particles are randomly scattered at an initial time. Each particle has some integer mass and moves in a Brownian motion whose diffusion rate is determined by…
We consider stochastic systems of interacting particles or agents, with dynamics determined by an interaction kernel which only depends on pairwise distances. We study the problem of inferring this interaction kernel from observations of…
The kinetic equations describing irreversible aggregation and the scaling approach developed to describe them in the limit of large times and large sizes are tersely reviewed. Next, a system is considered in which aggregates can only react…
We consider a system of two coupled parabolic PDEs introduced in [1] to model motility of eukaryotic cells. We study the asymptotic behavior of solutions in the limit of a small parameter related to the width of the interface in phase field…
We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the…
In this thesis, we investigate the emergence of kinetic processes in finite quantum systems. We first generalize the Redfield theory to describe the dynamics of a small quantum system weakly interacting with an environment of finite heat…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity…
We study invariant measures of continuous contact model in small dimensional spaces ($d =1,2$). Under general conditions we prove that in the critical regime this system has the one-parameter set of invariant measures parametrized by the…
We investigate the kinetics of many-species systems with aggregation of similar species clusters and annihilation of opposite species clusters. We find that the interplay between aggregation and annihilation leads to rich kinetic behaviors…
It has been recently shown that small subsystems of finite quantum systems generically equilibrate. We extend these results to infinite-dimensional Hilbert spaces of field theories and matrix models. We consider a quench setup, where…