Related papers: Mean Field Limit for Congestion Dynamics in One Di…
We investigate dynamical properties of traffic flow using the stochastic car-following model with modified optimal velocity on circular road. The safety distance following the two-second rule and autonomous vehicles, acting as agents,…
We consider a quantum mechanical system of N bosons with relativistic dispersion interacting through a mean field Coulomb potential (attractive or repulsive). We choose the initial wave function to describe a condensate, where the N bosons…
We study computationally the dynamics of forced, Brownian particles through a disordered system. As the concentration of mobile particles and/or fixed obstacles increase, we characterize the different regimes of flow and address how…
Objects driven through periodically modulated potential-energy landscapes in two dimensions can become locked in to symmetry-selected directions that are independent of the driving force's orientation. We investigate this problem in the…
Hard sphere systems in two dimensions are examined for arbitrary density. Simulation results are compared to the theoretical predictions for both the low and the high density limit, where the system is either disordered or ordered,…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
We prove that the highest density of non-overlapping translates of a given centrally symmetric convex domain relative to its outer parallel domain of given outer radius is attained by a lattice packing in the Euclidean plane. This…
We study the dynamics of a carrier, which performs a biased motion under the influence of an external field E, in an environment which is modeled by dynamic percolation and created by hard-core particles. The particles move randomly on a…
We study an optimal transport problem where, at some intermediate time, the mass is accelerated by either an external force field, or self-interacting. We obtain regularity of the velocity potential, intermediate density, and optimal…
This paper focuses on the role of a government of a large population of interacting agents as a mean field optimal control problem derived from deterministic finite agent dynamics. The control problems are constrained by a PDE of…
The interacting lattice gas model is used to simulate fluid flow through an open percolating porous medium with the fluid entering at the source-end and leaving from the opposite end. The shape of the steady-state concentration profile and…
This paper presents a macroscopic fundamental diagram model with volume-delay relationship (MFD-VD) for road traffic networks, by exploring two new data sources: license plate cameras (LPCs) and road congestion indices (RCIs). We derive a…
A two populations mean-field monomer-dimer model including both hard-core and attractive interactions between dimers is considered. The pressure density in the thermodynamic limit is proved to satisfy a three-dimensional variational…
The mean-field theory of Kinetically-Constrained-Models is developed by considering the Fredrickson-Andersen model on the Bethe lattice. Using certain properties of the dynamics observed in actual numerical experiments we derive asymptotic…
We consider transport networks with nodes scattered at random in a large domain. At certain local rates, the nodes generate traffic flowing according to some navigation scheme in a given direction. In the thermodynamic limit of a growing…
The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…
Highway vehicular traffic is an inherently multi-agent problem. Traffic jams can appear and disappear mysteriously. We develop a method for traffic flow control that is applied at the vehicular level via mean-field games. We begin this work…
The convective transport in a multicomponent isothermal compressible fluid subject to the mass continuity equations is considered. The velocity is proportional to the negative pressure gradient, according to Darcy's law, and the pressure is…
We consider a one-dimensional traffic model with a slow-to-start rule. The initial position of the cars in $\mathbb R$ is a Poisson process of parameter $\lambda$. Cars have speed 0 or 1 and travel in the same direction. At time zero the…
We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting…