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The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
Relativistic heat transport in electron-two-temperature plasmas with density gradients has been investigated. The Legendre expansion analysis of relativistically modified kinetic equations shows that strong inhibition of heat flux appears…
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is…
Heat radiation and near-field radiative heat transfer can be strongly manipulated by adjusting geometrical shapes, optical properties, or the relative positions of the objects involved. Typically these objects are considered as embedded in…
We study the diffusive dynamics of a Brownian particle in proximity of a flat surface under non-equilibrium conditions, which are created by an anisotropic thermal environment with different temperatures being active along distinct spatial…
We generalize Einstein's probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected…
Analytic solutions for cylindrical thermal waves in solid medium is given based on the nonlinear hyperbolic system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law is generalized where the…
This study presents a new turbulence model for isothermal compressible flows. The model is derived by combining the Favre averaging and the Conservation-dissipation formalism -- a newly developed thermodynamics theory. The latter provides a…
Using information theory we derive a thermodynamics for systems evolving under a collective motion, i.e. under a time-odd constraint. An illustration within the Lattice gas Model is given for two model cases: a collision between two complex…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
Geometric phases in particle diffusion systems, an intriguing aspect enlightened from thermal systems, offer a different understanding beyond traditional Brownian motion and Fick's laws. This concept introduces a phase factor with…
Since the thermal conduction equation has form invariance under coordinate transformation, one can design thermal metamaterials with novel functions by tailoring materials' thermal conductivities. In this work, we establish a different…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
Convection-diffusion equation is used to describe particle migration process in many fields, while it is proposed based on the empirical Fick's law. In this paper, with the help of the percolation model, we theoretically investigate the…
Mass transfer of gaseous components from rising bubbles to the ambient liquid can be described based on continuum mechanical sharp-interface balances of mass, momentum and species mass. In this context, the standard model consists of the…
We present the idea of intertwining of two diffusions by Feynman-Kac operators. We present some variations and implications of the method and give examples of its applications. Among others, it turns out to be a very useful tool for finding…
We investigate a simple model corresponding to particles driven in opposite directions and interacting via a repulsive potential. The particles move off-lattice on a periodic strip and are subject to random forces as well. We show that this…
Polyatomic gases find numerous applications across various scientific and technological fields, necessitating a quantitative understanding of their behavior in non-equilibrium conditions. In this study, we investigate the behavior of…