Related papers: Diffusion in multi-dimensional solids using Forman…
Dissipative particle dynamics (DPD) is a novel particle method for mesoscale modeling of complex fluids. DPD particles are often thought to represent packets of real atoms, and the physical scale probed in DPD models are determined by the…
Many applications of porous media research involves high pressures and, correspondingly, exchange of thermal energy between the fluid and the matrix. While the system is relatively well understood for the case of non-moving porous media,…
Phase separation in a complex fluid with lamellar order has been studied in the case of cold thermal fronts propagating diffusively from external walls. The velocity hydrodynamic modes are taken into account by coupling the…
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially heterogeneous manner. Mathematical models of these…
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic…
In this paper we detail the mechanisms that drive substitutional binary diffusion and derive appropriate governing equations. We focus on the one-dimensional case with insulated boundary conditions. Asymptotic expansions are used in order…
We consider four different models of nonlinear diffusion equations involving fractional Laplacians and study the existence and properties of classes of self-similar solutions. Such solutions are an important tool in developing the general…
Vector fields and line fields, their counterparts without orientations on tangent lines, are familiar objects in the theory of dynamical systems. Among the techniques used in their study, the Morse--Smale decomposition of a (generic) field…
A theoretical approach to describing transport of an entire ensemble of clusters with different sizes as a single species in gas has been developed. The major assumption is an existence of local partial chemical equilibrium between the…
To integrate hydrodynamic fluctuations, namely thermal fluctuations of hydrodynamics, into dynamical models of high-energy nuclear collisions based on relativistic hydrodynamics, the property of the hydrodynamic fluctuations given by the…
We consider the system of Maxwell-Stefan equations which describe multicomponent diffusive fluxes in non-dilute solutions or gas mixtures. We apply the Perron-Frobenius theorem to the irreducible and quasi-positive matrix which governs the…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
Discrete mechanics makes it possible to formulate any problem of fluid mechanics or fluid-structure interaction in velocity and potentials of acceleration; the equation system consists of a single vector equation and potentials updates. The…
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…
In this paper we introduce a novel method to simulate lateral diffusion of inclusions in a fluctuating membrane. The regarded systems are governed by two dynamic processes: the height fluctuations of the membrane and the diffusion of the…
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…
The surrounding world surprises us by the beauty and variety of complex shapes that emerge from nanometric to macroscopic scales. Natural or manufactured materials (sandstones, sedimentary rocks and cement), colloidal solutions (proteins…
Motivated by compartmental analysis in engineering and biophysical systems, we present a variational framework for the nonequilibrium thermodynamics of systems involving both distributed and discrete (finite dimensional) subsystems by…
The multiscale flow structure in the solar convection zone - the coexistence of such features as the granules, mesogranules, supergranules and giant cells - has not yet been properly understood. Here, the possible role of one physical…