Related papers: Solitons and kinks in a general car-following mode…
We have previously shown an analysis of our dimer model in the over-damped regime to show directed transport in equilibrium. Here we analyze the full model with inertial terms present to establish the same result. First we derive the…
An analytical framework for turbulent channel flow is developed based on the Alexeev hydrodynamic equations, focusing on the coupled behavior of streamwise and transverse velocity components. The mean streamwise velocity is represented as a…
This paper presents a new mathematical model of vehicular traffic, based on the methods of the generalized kinetic theory, in which the space of microscopic states (position and velocity) of the vehicles is genuinely discrete. While in the…
In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis…
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…
The problem of kink stability of isothermal spherical self-similar flow in newtonian gravity is revisited. Using distribution theory we first develop a general formula of perturbations, linear or non-linear, which consists of three sets of…
Evolution of perturbed embedded solitons in the general Hamiltonian fifth-order Korteweg--de Vries (KdV) equation is studied. When an embedded soliton is perturbed, it sheds a one-directional continuous-wave radiation. It is shown that the…
The Boltzmann kinetic equation for low-density granular suspensions under simple shear flow is considered to determine the velocity moments through the fourth degree. The influence of the interstitial gas on solid particles is modeled by a…
A nonlocal form of a two-layer fluid system is proposed by a simple symmetry reduction, then by applying multiple scale method to it a general nonlocal two place variable coefficient modified KdV (VCmKdV) equation with shifted space and…
It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by a novel variational method, where the velocity profile is assumed to be monotonic and analytic. Unstable eigenvalues of the Rayleigh…
Two different deterministic microscopic traffic flow models, which are in the context of the Kerner's there-phase traffic theory, are introduced. In an acceleration time delay model (ATD-model), different time delays in driver acceleration…
We prove a full asymptotic stability result for solitary wave solutions of the mKdV equation. We consider small perturbations of solitary waves with polynomial decay at infinity and prove that solutions of the Cauchy problem evolving from…
In this work, we primarily focus on the two-phase solutions and their stability to the focusing mKdV equation. By employing the algebro-geometric approach in combination with an effective integration method, we construct explicit two-phase…
We investigate the multi-soliton solutions to the generalized discrete KdV equation. In some cases a soliton with smaller amplitude moves faster than that with larger amplitude unlike the soliton solutions of the KdV equation. This…
Most car-following models show a transition from laminar to ``congested'' flow and vice versa. Deterministic models often have a density range where a disturbance needs a sufficiently large critical amplitude to move the flow from the…
The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena.…
The Hirota equation and the Sasa-Satsuma equation are U(1)-invariant integrable generalizations of the modified Korteweg-de Vries equation. These two generalizations admit oscillatory solitons, which describe harmonically modulated complex…
The generally held view that a model of large-scale structure, formed by collisionless matter in the Universe, can be based on the matter model ``dust'' fails in the presence of multi-stream flow, i.e., velocity dispersion. We argue that…
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…