Related papers: Mean Field Limit for Congestion Dynamics in One Di…
We study a non-exchangeable multi-agent system and rigorously derive a strong form of the mean-field limit. The convergence of the connection weights and the initial data implies convergence of large-scale dynamics toward a deterministic…
We conjecture that the current fluctuations in one-dimensional driven transport systems obey an upper bound determined by the mean current and the driving force. This inequality originates from repulsive interactions between transporting…
We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these…
These notes are devoted to a summary on the mean-field limit of large ensembles of interacting particles with applications in swarming models. We first make a summary of the kinetic models derived as continuum versions of second order…
The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly…
In this paper, we propose a macroscopic model that describes the influence of a slow moving large vehicle on road traffic. The model consists of a scalar conservation law with a non-local constraint on the flux. The constraint level depends…
In this paper we consider an optimal control problem for a large population of interacting agents with deterministic dynamics, aggregating potential and constraints on reciprocal distances, in dimension 1. We study existence and qualitative…
We derive a Maximum Principle for optimal control problems with constraints given by the coupling of a system of ODEs and a PDE of Vlasov-type. Such problems arise naturally as ${\Gamma}$-limits of optimal control problems subject to ODE…
We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modeling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an…
We study the phenomenon of real space condensation in the steady state of a class of one dimensional mass transport models. We derive the criterion for the occurrence of a condensation transition and analyse the precise nature of the shape…
We described the average traffic congestion in several populous cities around the world from a new concept, namely landscape percolation. The ratio of the residential area size to road width is a fundamental parameter that controls the…
In this paper we consider a mean field approach to modeling the agents flow over a transportation network. In particular, beside a standard framework of mean field games, with controlled dynamics by the agents and costs mass-distribution…
We introduce a new model of aggregation of particles where in addition to diffusion and aggregation upon contact, a single unit of mass can dissociate from a conglomerate. This dissociation move conserves the total mass and leads to a…
In this paper, a phase-field model is introduced to describe the evolution of a deformable, self-propelled object driven by surface-tension effects. The model couples an Allen-Cahn-type equation, which distinguishes the body from the…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
We derive the porous medium equation from an interacting particle system which belongs to the family of exclusion processes, with nearest neighbor exchanges. The particles follow a degenerate dynamics, in the sense that the jump rates can…
We recover the so-called field-road diffusion model as the hydrodynamic limit of an interacting particle system. The former consists of two parabolic PDEs posed on two sets of different dimensions (a "field" and a "road" in a population…
We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…
We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure…
We study a lattice gas of persistent walkers, in which each site is occupied by at most one particle and the direction each particle attempts to move to depends on its last step. We analyse the mean squared displacement (MSD) of the…