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In nonlinear dispersive evolution equations, the competing effects of nonlinearity and dispersion make a number of interesting phenomena possible. In the current work, the focus is on the numerical approximation of traveling-wave solutions…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…
This paper proposes an improved cellular automaton traffic flow model based on the brake light model, which takes into account that the desired time gap of vehicles is remarkably larger than one second. Although the hypothetical steady…
Gaseous flows under an external force are intrinsically defined by their multi-scale nature due to the large variation of densities along the forcing direction. Devising a numerical method capable of accurately and efficiently solving…
Several new families of nonlinear three-dimensional travelling wave solutions to the Navier-Stokes equation, also known as exact coherent states, are computed for Newtonian plane Poiseuille flow. The symmetries and streak/vortex structures…
In this work we extend a recent kinetic traffic model to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary…
Flow structures beneath a moving disturbance along a water free surface in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. We compute the exact two branches of…
It is shown that a variety of deterministic cellular automaton models of highway traffic flow obey a variational principle which states that, for a given car density, the average car flow is a non-decreasing function of time. This result is…
This paper presents an interactive bathtub model for describing the traffic dynamics of ride-sourcing vehicles including non-shared taxis and ride-pooling cars. A city with a network of undifferentiated streets and solely served by…
We use probabilistic methods to study properties of mean-field models, arising as large-scale limits of certain particle systems with mean-field interaction. The underlying particle system is such that $n$ particles move forward on the real…
We study a generalized Follow-the-Leader model where the driver considers the position of an arbitrary but finite number of vehicles ahead, as well as the position of the vehicle directly behind the driver. It is proved that this model…
This paper is concerned with the traveling wave solutions of delayed reaction-diffusion systems. By using Schauder's fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower…
The Whitham equation is a model for the evolution of small-amplitude, unidirectional waves of all wavelengths on shallow water. It has been shown to accurately model the evolution of waves in laboratory experiments. We compute…
We present a new analytical description of the cellular automaton model for single-lane traffic. In contrast to previous approaches we do not use the occupation number of sites as dynamical variable but rather the distance between…
Analytical solutions are constructed for an assembly of any finite number of bubbles in steady motion in a Hele-Shaw channel. The solutions are given in the form of a conformal mapping from a bounded multiply connected circular domain to…
A physically-based method to derive well-posed instances of the two-fluid transport equations for two-phase flow, from the Hamilton principle, is presented. The state of the two-fluid flow is represented by the superficial velocity and the…
A bottleneck situation in one-lane traffic-flow is typically modelled with a constant demand of entering cars. However, in practice this demand may depend on the density of cars in the bottleneck. The present paper studies a simple bimodal…
In this paper, we study dynamical optimal transport on a connected graph from the perspective of the Benamou-Brenier formulation, where densities are assigned to vertices and velocities to edges. However, directly using Newton's method on…
This paper aims at providing a first step toward a qualitative theory for a new class of chemotaxis models derived from the celebrated Keller-Segel system, with the main novelty being that diffusion is nonlinear with flux delimiter…
We propose and study a nonlocal conservation law modelling traffic flow in the existence of inter-vehicle communication. It is assumed that the nonlocal information travels at a finite speed and the model involves a space-time nonlocal…