Related papers: Small inertia limit for coupled kinetic swarming m…
We overview recent developments in the study of alignment hydrodynamics, driven by a general class of symmetric communication kernels. A main question of interest is to characterize the emergent behavior of such systems, which we quantify…
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…
Recent years witnessed an extensive development of the theory of the critical point in two-dimensional statistical systems, which allowed to prove {\it existence} and {\it conformal invariance} of the {\it scaling limit} for two-dimensional…
We rigorously show the mean-field limit for a large class of swarming individual based models with local sharp sensitivity regions. For instance, these models include nonlocal repulsive-attractive forces locally averaged over sharp vision…
We introduce a kinetic model that couples the movement of a population of individuals with the dynamics of a pathogen in the same population. We consider that transmission occurs when a susceptible and an infectious individual are…
The concept of autonomy is fundamental for understanding biological organization and the evolutionary transitions of living systems. Understanding how a system constitutes itself as an individual, cohesive, self-organized entity is a…
We concentrate on kinetic models for swarming with individuals interacting through self-propelling and friction forces, alignment and noise. We assume that the velocity of each individual relaxes to the mean velocity. In our present case,…
One of the aims of systems biology is to build multiple layered and multiple scale models of living systems which can efficiently describe phenomena occurring at various level of resolution. Such models should consist of layers of various…
We study the existence of solutions arising from the modelling of elastic materials using generalized theories of continua. In view of some evidence from physics of meta-materials we focus our effort on two recent nonstandard relaxed…
This paper investigates a system of nonlocal continuity equations modelling the interaction of two species coupled through Riesz-type potentials. The model incorporates self- and cross-interaction kernels of possibly different fractional…
In this paper, we study convergence of coupled dynamical systems on convergent sequences of graphs to a continuum limit. We show that the solutions of the initial value problem for the dynamical system on a convergent graph sequence tend to…
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…
In this paper, we propose a numerical investigation of topological interactions in flocking dynamics. Starting from a microscopic description of the phenomena, mesoscopic and macroscopic models have been previously derived under specific…
We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…
We introduce a kinetic framework for modeling the time evolution of the statistical distributions of the population densities in the three compartments of susceptible, infectious, and recovered individuals, under epidemic spreading driven…
We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker--Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type…
We propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a…
We explore the self-organization dynamics of a set of entities by considering the interactions that affect the different subgroups conforming the whole. To this end, we employ the widespread example of coagulation kinetics, and characterize…
For the well-known model of a system of N particles with interaction (N-body problem), we consider the spatial problem of finding the minimum of the function of the kinetic energy of a system on its phase space under conditions on its size…
In this paper an optimal control problem for a large system of interacting agents is considered using a kinetic perspective. As a prototype model we analyze a microscopic model of opinion formation under constraints. For this problem a…