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We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…
The system of hydrodynamic-type equations, derived by two-side distribution function for a stratified gas in gravity field is applied to a problem of ultrasound. The theory is based on Gross-Jackson kinetic equation, which solution is built…
The experimental density dependence of gas (argon and nitrogen) permeability of partially densified silica aerogels in the Knudsen regime is quantitatively accounted for by a computer model. The model simulates both the structure of the…
We present a brief introduction to the relativistic kinetic theory of gases with emphasis on the underlying geometric and Hamiltonian structure of the theory. Our formalism starts with a discussion on the tangent bundle of a Lorentzian…
Hydrogen embrittlement in metals is strongly governed by hydrogen diffusion and trapping, yet predicting these effects in polycrystalline systems remains challenging. This work introduces a multiscale modeling framework that links atomistic…
Vapor condensation is a physical phenomenon that finds application in heat removal systems. The traditional design of these systems involves round tubes but experience shows that this geometry is not optimal for heat transfer. Flattened…
The aim of the thesis is to present and analyze two particular problems of transport in porous media flow. The first of them is related to the process of saturation of porous building materials. Recently, M. K\"untz and P. Laval\'ee, using…
We study in this work the transport properties of an impurity immersed in a granular gas under stationary nonlinear Couette flow. The starting point is a kinetic model for low-density granular mixtures recently proposed by the authors [Vega…
This work extends previous 1D irreversible port-Hamiltonian system (IPHS) formulations to boundary-controlled ND distributed parameter systems describing conduction-diffusion fluid phenomena. Within a unified and thermodynamically…
Relativistic transport phenomena are important from both theoretical and practical point of view. Accordingly, hydrodynamics of relativistic gas has been extensively studied theoretically. Here, we introduce a three-dimensional canonical…
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
In last years a great interest was brought to molecular transport problems at nanoscales, such as surface diffusion or molecular flows in nano or sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J.…
In last years a great interest was brought to molecular transport problems at nanoscales, such as surface diffusion or molecular flows in nano or sub-nano-channels. In a series of papers V. D. Borman, S. Y. Krylov, A. V. Prosyanov and J. J.…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
Despite the fact that conserved currents have dimensions that are determined solely by dimensional analysis (and hence no anomalous dimensions), Nature abounds in examples of anomalous diffusion in which $L\propto t^\gamma$, with $\gamma\ne…
We calculate a collective number of thermodynamic quantities in a one-dimensional gas of hard elongated objects (such as needles) whose centers mobile on a line. Our formalism uses an approximation for the probabilities of contact between…
In this paper we demonstrate that using a mathematical physics approach (focusing the attention to the physics and using mathematics as a tool) it is possible to visualize the formation of the transverse modes inside a cylindrical…
We present the first direct numerical simulations of particle-laden turbulent flow in concentric annuli to investigate the effects of transverse curvature over a range of Stokes numbers. The results demonstrate that transverse curvature…
Channel-mediated transport is ubiquitous in biology. A series of works by different theoreticians have sought to determine how the diffusive flux through a channel depends on (a) stochastic gating, (b) channel geometry, and (c)…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…