相关论文: Analysis of kinematic waves arising in diverging t…

We study the coupled complex Ginzburg-Landau (CGL) equations for traveling wave systems in the regime where sources and sinks separate patches of left and right-traveling waves. We show that sources and sinks are the important coherent…

In this work we investigate the existence of non-monotone traveling wave solutions to a reaction-diffusion system modeling social outbursts, such as rioting activity, originally proposed in arXiv:1502.04725v3. The model consists of two…

The slider-block Burridge-Knopoff model with the Coulomb friction law is studied as an excitable medium. It is shown that in the continuum limit the system admits solutions in the form of the self-sustained shock waves traveling with…

We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…

This paper continues the study of equilibria for flows over time in the fluid queueing model recently considered by Koch and Skutella [10]. We provide a constructive proof for the existence and uniqueness of equilibria in the case of a…

We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does not admit a fully conservative form, and we establish the…

Through a discussion of some typical unsteady hydrodynamic flows, we argue that the time averaged hydrodynamic functions at each point give a rather sparse filling of the local jet space. This situation then suggests a set of time dependent…

We show that keeping a constant lower limit on the net-time headway is the key mechanism behind the dynamics of pedestrian streams. There is a large variety in flow and speed as functions of density for empirical data of pedestrian streams,…

A noteworthy aspect in blood flow modeling is the definition of the mechanical interaction between the fluid flow and the biological structure that contains it, namely the vessel wall. It has been demonstrated that the addition of a viscous…

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…

Numerical simulations of classical pattern forming reaction-diffusion systems indicate that they often operate in the strongly nonlinear regime, with the final steady-state consisting of a spatially repeating pattern of localized spikes. In…

We consider several systems of nonlinear hyperbolic conservation laws describing the dynamics of nonlinear waves in presence of phase transition phenomena. These models admit under-compressive shock waves which are not uniquely determined…

In this paper, we examine how to build coarse-grain transport models consistently from the kinetic to fluid regimes. The internal energy of the gas particles is described through a state-to-state approach. A kinetic equation allows us to…

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent…

This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the…

In previous work, we developed a topological framework for solving Riemann initial-value problems for a system of conservation laws. Its core is a differentiable manifold, called the wave manifold, with points representing shock and…

We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic…

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…

We consider kinetic vehicular traffic flow models of BGK type. Considering different spatial and temporal scales, those models allow to derive a hierarchy of traffic models including a hydrodynamic description. In this paper, the kinetic…

We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a non-linear process: the particle current does not scale with the particle…