Related papers: Nonlinear Model of non-Debye Relaxation
Understanding how systems respond to external perturbations is a fundamental challenge in physics, particularly for non-equilibrium and non-stationary processes. The fluctuation-dissipation theorem provides a complete framework for…
In this paper we study the effect of rotation on nonlinear wave phenomena in weakly dispersive media modeled by the Korteweg-de Vries equation on the real line. It is well known that smoothing in the case of the KdV equation with periodic…
A simplified transient energy-transport system for semiconductors subject to mixed Dirichlet-Neumann boundary conditions is analyzed. The model is formally derived from the non-isothermal hydrodynamic equations in a particular vanishing…
New non-linear, spatially periodic, long wavelength electrostatic modes of an electron fluid oscillating against a motionless ion fluid (Langmuir waves) are given, with viscous and resistive effects included. The cold plasma approximation…
Open-system approaches are gaining traction in the simulation of charge transport in nanoscale and molecular electronic devices. In particular, "extended reservoir" simulations, where explicit reservoir degrees of freedom are present, allow…
The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an…
In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model…
There has been great interest in applying the results of statistical mechanics to single molecule experiements. Recent work has highlighted so-called non-equilibrium work-energy relations and Fluctuation Theorems which take on an…
A general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is…
We study analytically and numerically a frequency downshifting due to power-type frequency-dependent decay of surface waves in the ocean covered by ice floes. The downshifting is obtained both within the linear model and within the…
We investigate a semilinear wave equation with energy-critical nonlinearity and a nonlinear damping mechanism driven by the total energy of the system. The model combines the quintic defocusing term with a time-dependent dissipation of the…
The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory and astrophysical plasmas, can be described by the Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a…
Based on the momentum-resolved Boltzmann equation, we provide self-consistent numerical calculations of the dynamics of conduction electrons in thin noble metal films after linear and non-linear optical excitations with infrared and…
In this paper we study a Cauchy problem for the nonlinear damped wave equations for a general positive operator with discrete spectrum. We derive the exponential in time decay of solutions to the linear problem with decay rate depending on…
Porous electrodes{made of hierarchically nanostructured materials{are omnipresent in various electrochemical energy technologies from batteries and supercapacitors to sensors and electrocatalysis. Modeling the system-level macroscopic…
Flutter stability is a dominant design constraint of modern gas and steam turbines. To further increase the feasible design space, flutter-tolerant designs are currently explored, which may undergo Limit Cycle Oscillations (LCOs) of…
In this article we study the pointwise decay properties of solutions to the wave equation on a class of nonstationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form…
Thermodynamic nonequilibrium effects play a central role in momentum and energy transport in compressible flows. In conventional BGK kinetic models, the relaxation time $\tau$ is taken as a constant, which neglects the dependence of the…
This note has no new results and is therefore not intended to be submitted to a "research" journal in the foreseeable future, but to be available to the numerous individuals who are interested in this issue. The Debye-Waller factor is the…
We present a dynamical description of slow relaxation processes based on the extension of Onsager's fluctuation theory to systems in local quasi-equilibrium. A non-Markovian Fokker-Planck equation for the conditional probability density is…