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In this paper, we study the Cauchy problem of a time-dependent drift-diffusion-Poisson system for semiconductors. Existence and uniqueness of global weak solutions are proven for the system with a higher-order nonlinear…
We develop an iterative, numerically exact approach for the treatment of nonequilibrium quantum transport and dissipation problems that avoids the real-time sign problem associated with standard Monte Carlo techniques. The method requires a…
Aims. We present an implementation of an algorithm for 3D time-dependent Monte Carlo radiative transfer. It allows one to simulate temperature distributions as well as images and spectral energy distributions of the scattered light and…
We propose two efficient energetic spectral-element methods in time for marching nonlinear gradient systems with the phase-field Allen--Cahn equation as an example: one fully implicit nonlinear method and one semi-implicit linear method.…
This paper presents a kinetic model for the coupled evolution of radiation, electrons, and ions in a radiation plasma system. The model is solved using two methods. The gas-kinetic scheme (GKS) for electron and ion hydrodynamics and the…
An integrable nonlinear model for the time-dependent equilibration of a bosonic system that has been devised earlier is solved exactly with boundary conditions that are appropriate for a truncated Bose-Einstein distribution, and include the…
Studies of solar and stellar convection often employ simple polytropic setups using the diffusion approximation instead of solving the proper radiative transfer equation. This allows one to control separately the polytropic index of the…
We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on…
We study the non-linear current response of a Dirac model that is coupled to two time-periodic electro-magnetic fields with different frequencies. We distinguish between incommensurable and commensurable frequencies, the latter…
We derive a general integrodifferential equation for the transient behaviour of small-amplitude capillary waves on the planar surface of a viscous fluid in the presence of the Marangoni effect. The equation is solved for an insoluble…
Thermal Wave Model is used to study the strong self-consistent Plasma Wake Field interaction (transverse effects) between a strongly magnetized plasma and a relativistic electron/positron beam travelling along the external magnetic field,…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
Examination of equilibrium radiation in plasma media shows that the spectral energy distribution of such radiation is different from the Planck equilibrium radiation. Using the approach of quantum electrodynamics the general relation for…
By revising the application of the open quantum system approach to the early universe and extending it to the conditions beyond the Markovian approximation, we obtain a new non-Markovian quantum Boltzmann equation. Throughout the paper, we…
We provide a stochastic fractional diffusion equation description of energy transport through a finite one-dimensional chain of harmonic oscillators with stochastic momentum exchange and connected to Langevian type heat baths at the…
We derive a time-dependent density functional theory appropriate for calculating the near-edge X-ray absorption spectrum in molecules and condensed matter. The basic assumption is to increase the space of many-body wave functions from one…
Electrons accelerated by solar flares and observed as type III solar radio bursts are not only a crucial diagnostic tool for understanding electron transport in the inner heliosphere but also a possible early indication of potentially…
We consider systems of damped wave equations with a state-dependent damping coefficient and perturbed by a Gaussian multiplicative noise. Initially, we investigate their well-posedness, under quite general conditions on the friction.…
The present paper is concerned with the Cauchy-Dirichlet problem for fractional (and non-fractional) nonlinear diffusion equations posed in bounded domains. Main results consist of well-posedness in an energy class with no sign restriction…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonmagnetic, linearly polarized, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the…