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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…
We analyzed the stability of the uniform flow solution in the optimal velocity model for traffic and granular flow under the open boundary condition. It was demonstrated that, even within the linearly unstable region, there is a parameter…
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…
This paper discusses the effect of sequential conflict resolution maneuvers of an infinite aircraft flow through a finite control volume. Aircraft flow models are utilized to simulate traffic flows and determine stability. Pseudo-random…
The Gipps car-following model is a widely used tool for studying and simulation traffic dynamics. Despite its popularity an often disregarded property is that under heterogeneous parametrization on the individual vehicles in the traffic…
We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications, we allow for the the presence of space discontinuities both…
This paper studies steady-state traffic flow on a ring road with up- and down- slopes using a semi-discrete model. By exploiting the relations between the semi-discrete and the continuum models, a steady-state solution is uniquely…
Motivated by the formation of fingerprint patterns we consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. This class of models…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We study a car-following model of traffic flow which assumes only that a car's acceleration depends on its own speed, the headway ahead of it, and the rate of change of headway, with only minimal assumptions about the functional form of…
Stop-and-go waves in road traffic are complex collective phenomena with significant implications for traffic engineering, safety and the environment. Despite decades of research, understanding and controlling these dynamics remains…
The mathematical modeling and the stability analysis of multi-lane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynamics with lane changing, leading to a coupled system of…
Cooperative effects in oscillator networks are often associated with enhanced stability of phase-locked solutions, which increases with system size. We show that the stabilization of persistent currents in annular atomic superfluids with…
We explore the stability properties of multi-field solutions of assisted inflation type, where several fields collectively evolve to the same configuration. In the case of noninteracting fields, we show that the condition for such solutions…
Motivated by the observation of highly unstable flowing states in suspensions of microtubules and kinesin, we analyze a model of mutually-propelled filaments suspended in a solvent. The system undergoes a mean-field isotropic-nematic…
In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one…
We follow up an earlier work (briefly reviewed below) to investigate the temporal stability of an exact travelling front solution, constructed in the form of an integral expression, for a one-dimensional discrete Nagumo-like model without…
We present a general framework for modeling a wide selection of flocking scenarios under free boundary conditions. Several variants have been considered - including examples for the widely observed behavior of hierarchically interacting…
We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larger space of perturbation than previous results. Furthermore,…
We investigate the global in time stability of regular solutions with large velocity vectors to the evolutionary Navier-Stokes equation in ${\bf R}^3$. The class of stable flows contains all two dimensional weak solutions. The only…