Related papers: Mean Field Limit for Congestion Dynamics in One Di…
We present a mode-coupling theory for the dynamics of a tagged particle in a driven granular fluid close to the glass transition. The mean-squared displacement is shown to exhibit a plateau indicating structural arrest. In contrast to…
In this paper we study a two dimensional crowd model where pedestrian velocity consists of two elements: a non--local interaction term, modeling the effect of other walkers on each individual, and a control term. This latter term can be…
We consider deterministic particle dynamics with time evolving weights and their associated Kolmogorov equation and mean-field equation. We prove existence and unique- ness for the limit PDE alongside estimates on the growth of the…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…
The equation of the density field of an assembly of macroscopic particles advected by a hydrodynamic flow is derived from the microscopic description of the system. This equation allows to recognize the role and the relative importance of…
A recently introduced model describing -on a 1d lattice- the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but…
Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf {R}^m$ in the presence of a random environment and…
This study investigates the complex dynamic interactions between two typed populations coexisting within a shared space. We propose both theoretical and numerical study to analyze scenarios where one population (population $1$) must…
We study Mean Field stochastic control problems where the cost function and the state dynamics depend upon the joint distribution of the controlled state and the control process. We prove suitable versions of the Pontryagin stochastic…
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the perceived densities of the different groups present as well…
In this paper, we address the problem of modeling the traffic flow of a heritage city whose streets are represented by a network. We consider a mean field approach where the standard forward backward system of equations is also intertwined…
The exact evolution of a system coupled to a complex environment can be described by a stochastic mean-field evolution of the reduced system density. The formalism developed in Ref. [D.Lacroix, Phys. Rev. E77, 041126 (2008)] is illustrated…
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…
The recent emergence of navigational tools has changed traffic patterns and has now enabled new types of congestion-aware routing control like dynamic road pricing. Using the fundamental diagram of traffic flows - applied in macroscopic and…
In this paper, we study the numerical simulations for Euler system with maximal density constraint. This model is developed in [1, 3] with the constraint introduced into the system by a singular pressure law, which causes the transition of…
We introduce a family of glassy models having a parameter, playing the role of an interaction range, that may be varied continuously to go from a system of particles in d dimensions to a mean-field version of it. The mean-field limit is…
In this work, we derive first order continuum traffic flow models from a microscopic delayed follow-the-leader model. Those are applicable in the context of vehicular traffic flow as well as pedestrian traffic flow. The microscopic model is…
We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport,…
We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the…