We consider charge transport in a pore where the dielectric constant inside the pore is much greater than that in the surrounding material, so that the flux of the electric fields due to the charges is almost entirely confined to the pore. We develop exact solutions for the one component case...

With the aim of gaining insight into the notoriously difficult problem of energy and vorticity cascades in high dimensional incompressible flows, we take a simpler and very well understood low dimensional analog and approach it from a new perspective, using the Fourier transform. Specifically,...

We show that the critical mass Mc=8π of bacterial populations in two dimensions in the chemotactic problem is the counterpart of the critical temperature Tc=GMm/4kB of self-gravitating Brownian particles in two-dimensional gravity. We obtain these critical values by using the Virial theorem or...

A kinetic clustering of cars is analyzed using a limiting procedure and a reductive perturbation method. By using the limiting procedure, the difference–difference equation to describe the clustering is obtained. We derive the coarse-grained equation describing the hydrodynamic mode, using the...

We investigate the solutions of the Burgers equation ∂tu(x,t)=D∂x2u(x,t)−∂x[F(x,t)u(x,t)]−κu(x,t)∂xu(x,t)+Φ(x,t), where F(x,t) is an external force and Φ(x,t) represents a forcing term. This equation is first analyzed in the absence of the forcing term by taking...

A continuum version of the car-following full velocity difference model (FVDM) is developed using a series expansion of the headway in terms of the density. This continuum model obeys the equivalent stability criterion as its discrete counterpart, and the Burgers and Korteweg-de Vries equations...

A modified lattice hydrodynamic model of traffic flow is proposed by introducing the density difference between the leading and the following lattice. The stability condition of the modified model is obtained through the linear stability analysis. The results show that considering the density...

We study the formation of shockwaves from an initial condition of the pulse form in supercritical flow of traffic by using the optimal velocity model. The jam with the pulse form propagates with changing the initial form. The wave velocity is derived numerically and analytically. The dependence...

Solitary wave solutions exhibited at the onset of the phase transition in fluidized granular matter are perused. In the quasi-sonic limit the system is modeled by two Korteweg de Vries equations. We study the solitary wave interactions in order to understand the rich dynamics exhibited by the...