The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As is well known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equa...

Nonlinear evolution equations are widely used to describe complex phenomena in various sciences such as fluid physics, condensed matter, biophysics, plasma physics, nonlinear optics, quantum field theory and particle physics, etc. In recent years, various powerful methods have been presented for finding exact solutions of the nonlinear evolution equations in mathematical physics, such as, tanh ...

The gate dependence of a Coulomb attractive random telegraph signal is observed in a single-walled carbon nanotube field effect transistor for temperatures varying from 0.32 to 24 K. The mechanism of the Coulomb attractive random telegraph signal is attributed to the carrier tunneling between the carbon nanotube and the Coulomb attractive defect. The random telegraph signal is also studied unde...

A maximum principle is proved for the weak solutions uALNðR TÞ of the telegraph equation in space dimension three utt Dxu þ cut þ lu 1⁄4 f ðt; xÞ; when c40; lAð0; c=4 and fALNðR TÞ (Theorem 1). The result is extended to a solution and a forcing belonging to a suitable space of bounded measures (Theorem 2). Those results provide a method of upper and lower solutions for the semilinear equation u...

We propose a new numerical scheme for linear transport equations. It is based on a decomposition of the distribution function into equilibrium and non-equilibrium parts. We also use a projection technique that allows to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the non-equilibrium part. By using a suita...