Related papers: Homogenization of heat diffusion in a cracked medi…
This paper addresses the problem of generating textures for 3D mesh assets. Existing approaches often rely on image diffusion models to generate multi-view image observations, which are then transformed onto the mesh surface to produce a…
This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…
Different approaches are presented to investigate diffusion from a point source in a slab delimited by two absorbing boundaries consisting of parallel infinite planes. These approaches enable to consider the effect of absorption at the…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
We study the problem of lateral diffusion on a static, quasi-planar surface generated by a stationary, ergodic random field possessing rapid small-scale spatial fluctuations. The aim is to study the effective behaviour of a particle…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…
We develop a robust cut finite element method for a model of diffusion in fractured media consisting of a bulk domain with embedded cracks. The crack has its own pressure field and can cut through the bulk mesh in a very general fashion.…
In this paper we employ homogenization techniques to provide a rigorous derivation of the Darcy scale model for precipitation and dissolution in porous media proposed in [19]. The starting point is the pore scale model in [12], which is a…
We consider a reaction-diffusion-advection problem in a perforated medium, with nonlinear reactions in the bulk and at the microscopic boundary, and low diffusion scaling. The microstructure changes in time; the microstructural evolution is…
In this paper, diffusion in polymer solutions undergoing evaporation of solvent is modeled as a coupled heat and mass transfer problem with moving boundary condition within the framework of nonequilibrium thermodynamics. The proposed…
On the basis of a previous theoretical approach to the plastic flow of highly refined materials, a physical explanation for diffusion bonding is essayed, which yields closed--form equations relating the bonding progress with time,…
We consider acoustic waves propagating in an inviscid fluid interacting with a rigid periodically perforated plate in the presence of permanent flows. The paper presents a model of an acoustic interface obtained by the asymptotic…
When a flat sample of medium density fibreboard (MDF) is exposed to radiant heat in an inert atmosphere, primary crack patterns suddenly start to appear over the entire surface before pyrolysis and any charring occurs. Contrary to common…
The present paper deals with the homogenization of the heat conduction which takes place in a binary three-dimensional medium consisting of an ambiental phase having conductivity of unity order and a rectangular honeycomb structure formed…
Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the…
We investigate the dynamics of spreading of a small liquid droplet in gas in a one-component simple fluid, where the temperature is inhomogeneous around 0.9Tc and latent heat is released or generated at the interface upon evaporation or…
When water is present in a medium with pore sizes in a range around 10nm the corresponding freezing point depression will cause long range broadening of a melting front. Describing the freezing-point depression by the Gibbs-Thomson equation…
This work focuses on determining the coefficient of thermal diffusivity in a one-dimensional heat transfer process along a homogeneous and isotropic bar, embedded in a moving fluid with heat generation. A first type (Dirichlet) condition is…
In this paper a model for partial melts is constructed using two-scale homogenization theory. While this technique is well known to the mathematics and materials communities, it is relatively novel to problems in the solid Earth. This…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…