Related papers: Diffusion evolution of a pore in bounded particle …
In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion…
The radiative properties of interstellar dust are affected not only by the grain size distribution but also by the grain porosity. We develop a model for the evolution of size-dependent grain porosity and grain size distribution over the…
The diffusion of a pulse of small grains in an horizontal rotating drum is studied through discrete elements methods simulations. We present a theoretical analysis of the diffusion process in a one-dimensional confined space in order to…
In many environmental and industrial applications, the mass transfer of gases in liquid solvents is a fundamental process during the generation of bubbles for specific purposes or, vice versa, the removal of entrapped bubbles. We address…
A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface…
We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…
Thermally bistable fluid tends to self-organize into clouds of hot and cold material, which are internally uniform and separated by thin conduction fronts. The evolution of these clouds has been studied for isobaric systems, but when…
The dynamics and stability of a thin gas layer moving between two fluid layers moving in the same or opposite direction is studied. The linear evolutionary equations describing the spatial-temporal dynamics of the interface perturbations…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
Diffusion in a two-phase system is a classical problem discussed in the literature. The general solution of the one-dimensional case to this problem is revisited and a detailed derivation is proposed. The solution is discussed in…
Mineral dissolution in porous media is classically partitioned into static regimes within the Pe-Da plane, but this framework fails to capture the dissolution behavior of structurally complex rocks. Using three-dimensional micro-continuum…
Drop condensation and evaportation as a result of the gradient in vapor concentration are important in both engineering and natural systems. One of the interesting natural examples is transpiration on plant leaves. Most of water in the…
In this paper, we study some qualitative properties for an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains and, coupled in such a way that, the resulting evolution problem is the…
Mixing fronts form when fluids with different chemical compositions are brought into contact. They influence a large range of biogeochemical processes in hydrological systems. An important mechanism governing mixing rates in such fronts is…
A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures.…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
We model particle growth in a turbulent, viscously evolving protoplanetary nebula, incorporating sticking, bouncing, fragmentation, and mass transfer at high speeds. We treat small particles using a moments method and large particles using…
We study packings of bidispersed spherical particles on a spherical surface. The presence of curvature necessitates defects even for monodispersed particles; bidispersity either leads to a more disordered packing for nearly equal radii, or…
We investigate a reaction-diffusion problem in a two-component porous medium with a nonlinear interface condition between the different components. One component is connected and the other one is disconnected. The ratio between the…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…