Related papers: Diffusion-reaction approach to electronic relaxati…
In this paper, we propose a parallel-in-time algorithm for approximately solving parabolic equations. In particular, we apply the $k$-step backward differentiation formula, and then develop an iterative solver by using the waveform…
In this paper, we consider the asymptotic behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We prove that when the damping is effective, the solution is approximated by that of the corresponding…
The distribution function of relaxation times in disordered dielectrics has been calculated in the random field theory framework. For this purpose, we first consider the dynamics of single two-orientable impurity electric dipole in a random…
The reaction-diffusion equation is one of the cornerstones equations in applied science and engineering. In the present study, a deep neural network has been trained in order to predict the solution of the equation with different…
We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…
The dynamics of the electrons for a molecule in solution is coupled to the dynamics of its polarizable environment, i.e., the solvent. To theoretically investigate such electronic dynamics, we have recently developed equations of motion…
This paper is concerned with the connection between the properties of dielectric relaxation and ac (alternating-current) conduction in disordered dielectrics. The discussion is divided between the classical linear-response theory and a…
Enabling control over a spontaneous dynamic process is a very complicated task in practice because of its statistical nature, and electro-optic (E-O) relaxation dynamic in a nematic liquid crystal (NLC) system is not an exception.…
We consider a decision maker who must choose an action in order to maximize a reward function that depends also on an unknown parameter {\Theta}. The decision maker can delay taking the action in order to experiment and gather additional…
This paper is concerned with the numerical solution of porous-media flow and transport problems , i. e. heterogeneous, advection-diffusion problems. Its aim is to investigate numerical schemes for these problems in which different time…
We present an investigation into diffusion models for molecular generation, with the aim of better understanding how their predictions compare to the results of physics-based calculations. The investigation into these models is driven by…
We consider an initial-boundary value problem for $\partial_tu-\partial_t^{-\alpha}\nabla^2u=f(t)$, that is, for a fractional diffusion ($-1<\alpha<0$) or wave ($0<\alpha<1$) equation. A numerical solution is found by applying a…
Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this work, we show a priori rates of convergence of this…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…
We discuss the relaxation kinetics of a one-dimensional dimer adsorption model as recently proposed for the binding of biological dimers like kinesin on microtubules. The non-equilibrium dynamics shows several regimes: irreversible…
The energy relaxation in the spin-polarized disordered electron systems is studied in the diffusive regime. We derived the quantum kinetic equation in which the kernel of electron-electron collision integral explicitly depends on the…
In this paper, a recently developed numerical technique [{\em Tuncer E and Guba{\'n}ski S M, IEEE Trans Diel El Insul {\bf 8}(3)(2001) 310-320}] is applied to poly(propylene glycol) complex dielectric data to extract more information about…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…