Related papers: Estimation of intrinsic diffusion coefficients in …
Based on recent calculations of the self-diffusion (SD) coefficient in amorphous silicon (a-Si) by classical Molecular Dynamics simulation [M. Posselt, H. Bracht, and D. Radi\'c, J. Appl. Phys. 131, 035102 (2022)] detailed investigations on…
The Cambrian explosion of easily accessible pre-trained diffusion models suggests a demand for methods that combine multiple different pre-trained diffusion models without incurring the significant computational burden of re-training a…
Predicting diffusion coefficients in mixtures is crucial for many applications, as experimental data remain scarce, and machine learning (ML) offers promising alternatives to established semi-empirical models. Among ML models, matrix…
In this paper a generalization of the Cahn-Hilliard theory of binary liquids is presented for multi-component incompressible liquid mixtures. First, a thermodynamically consistent convection-diffusion type dynamics is derived on the basis…
A method is proposed for the calculation of diffusion constants for one-dimensional maps exhibiting deterministic diffusion. The procedure is based on harmonic inversion and uses a known relation between the diffusion constant and the…
Driven-dissipative protocols are proposed to control and create nontrivial quantum many-body correlated states. Protocols conserving the number of particles stand apart. As well-known, in quantum systems with the unitary dynamics the…
We study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.
We consider the problem of inference for nonlinear, multivariate diffusion processes, satisfying It\^o stochastic differential equations (SDEs), using data at discrete times that may be incomplete and subject to measurement error. Our…
In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…
The static diffraction intensity distribution from large material system conceived as perfectly homogeneous system made inhomogeneous, though substitution of groups of atoms, small particles, by other groups of atoms, is explicitly…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
We introduce a Darcy-scale model to describe compressible multi-component flow in a fully saturated porous medium. In order to capture cross-diffusive effects between the different species correctly, we make use of the Maxwell--Stefan…
A review of solutions of solid-state diffusion problems in infinite and semi-infinite bodies is presented. Based on the identified solutions for the semi-infinite body a two-step diffusion problem is discussed in detail with the first step…
We introduce a new method for simulating photoemission spectra from bulk crystals in the ultra-violet energy range, within a three-step model. Our method explicitly accounts for transmission and matrix-element effects, as calculated from…
The mass flux of a low-density granular binary mixture obtained previously by solving the Boltzmann equation by means of the Chapman-Enskog method is considered further. As in the elastic case, the associated transport coefficients $D$,…
Analysis of signal fluctuations of a locally fixed probe, caused by molecules diffusing under the probe, can be used to determine diffusion coefficients. Theoretical treatments so far have been limited to point-like particles or to…
Quantitative phase analysis is one of the major applications of X-ray powder diffraction. The essential principle of quantitative phase analysis is that the diffraction intensity of a component phase in a mixture is proportional to its…
The topic of these notes could be easily expanded into a full one-semester course. Nevertheless, we shall try to give some flavour along with theoretical bases of spectral and pseudo-spectral methods. The main focus is made on Fourier-type…
Convenient variational formula for collective diffusion of many particles adsorbed at lattices of arbitrary geometry is formulated. The approach allows to find the expressions for the diffusion coefficient for any value of the system's…