Related papers: A rigorous derivation of multicomponent diffusion …
We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient…
A diffusion interface two-phase magnetohydrodynamic model has been used for matched densities in our previous work [1,2], which may limit the applications of the model. In this work, we derive a thermodynamically consistent diffuse…
We introduce a class of one dimensional deterministic models of energy-volume conserving interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive. We then modify the dynamics by adding a conservative…
Nonreciprocal interactions that violate Newton's law 'actio=reactio' are ubiquitous in nature and are currently intensively investigated in active matter, chemical reaction networks, population dynamics, and many other fields. An…
All possible linearly independent local conservation laws for $n$-dimensional diffusion--convection equations $u_t=(A(u))_{ii}+(B^i(u))_i$ were constructed using the direct method and the composite variational principle. Application of the…
This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…
We derive multicomponent relativistic second-order dissipative fluid dynamics from the Boltzmann equations for a reactive mixture of $N_{\text{spec}}$ particle species with $N_q$ intrinsic quantum numbers (e.g. electric charge, baryon…
We consider a dynamical system consisting of subsystems indexed by a lattice. Each subsystem has one conserved degree of freedom ("energy") the rest being uniformly hyperbolic. The subsystems are weakly coupled together so that the sum of…
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…
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…
We investigate diffusion in a polydisperse granular media. We derive mean-squared displacement of granular particles in a polydisperse granular gas in a homogeneous cooling state, containing arbitrary amount of species of different sizes…
We consider a system of partial differential equations describing mass transport in a multicomponent isothermal compressible fluid. The diffusion fluxes obey the Fick-Onsager or Maxwell-Stefan closure approach. Mechanical forces result into…
We investigate conservation laws of diffusion-convection equations to construct first-order potential systems corresponding to these equations. We do two iterations of the construction procedure, looking, in the second step, for the…
Studies of mesoscopic structures have now become a leading and rapidly evolving research field ranging from physics, chemistry, and mineralogy to life sciences. The increasing miniaturization of devices with length scales of a few…
This paper presents a thermodynamically consistent model for multicomponent electrolyte solutions. The first part of this paper derives the general governing equations for nonequilibrium systems within the theory of nonequilibrium…
Diffusion with multipole-moment conservation gives rise to transport laws that generalize Fick's law and has attracted growing attention following experimental advances in strongly tilted optical lattices. It was recently shown that…
Thermodynamic relations are derived from first principles of mechanics for non-equilibrium processes. Since the key role herein is played by the law of increase of entropy, the latter is analyzed at first. It is shown that its derivation…
We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…
Starting from the most general formulation of stochastic thermodynamics---i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs---, we define a procedure to identify the…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…