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We consider the dynamics of a parabolic and a hyperbolic equation coupled on a common interface and develop time-stepping schemes that can use different time-step sizes for each of the subproblems. The problem is formulated in a strongly…
We report measurements and Monte Carlo simulations of thermal conductivity of porous 100nm- thick silicon membranes, in which size, shape and position of the pores were varied randomly. Measurements using 2-laser Raman thermometry on both…
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…
Phonon modes and their dispersion relations in ultrathin homogenous dielectric membranes are calculated using elasticity theory. The approach differs from the previous ones by a rigorous account of the effect of the film surfaces on the…
We consider a moving boundary problem with kinetic condition that describes the diffusion of solvent into rubber and study semi-discrete finite element approximations of the corresponding weak solutions. We report on both a priori and a…
Recent studies have revealed that the symmetry of interparticle potential plays an important role in one-dimensional heat conduction problem. Here we demonstrate that by stretching or compressing the Fermi-Pasta-Ulam-\b{eta} lattice, one…
In this paper, we propose upper and lower error bounding techniques for reduced order modelling applied to the computational homogenisation of random composites. The upper bound relies on the construction of a reduced model for the stress…
This report describes a mathematical model of heat conduction. The differential equation for heat conduction in one dimensional rod has been derived. The explicit finite difference numerical method is used to solve this differential…
In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…
Accurate predictions of thermo-mechanically coupled process in metals can lead to a reduction of cost and an increase of productivity in manufacturing processes such as forming. For modeling these coupled processes with the finite element…
Context: Thermal conductivity provides important contributions to the energy evolution of the upper solar atmosphere, behaving as a non-linear concentration-dependent diffusion equation. Recently, different methods have been offered as…
Reflection and refraction of electromagnetic waves by artificial periodic composites (metamaterials) can be accurately modeled by an effective medium theory only if the boundary of the medium is explicitly taken into account and the two…
A multiphysics modeling approach for heat conduction in metal hydride powders is presented, including particle shape distribution, size distribution, granular packing structure, and effective thermal conductivity. A statistical geometric…
In this work, we initiate the study of the biharmonic heat equation in a spatial bounded domain subject to dynamic boundary conditions involving the bi-Laplace-Beltrami operator on the boundary. The boundary heat equation is coupled to the…
In this paper, we focus on multi-scale modeling and simulation of piezoelectric composite materials. A multi-scale model for piezoelectric composite materials under the framework of Heterogeneous Multi-scale Method(HMM) is proposed. For…
The paper reviews several topics associated with the homogenization of transport processed in historical masonry structures. Since these often experience an irregular or random pattern, we open the subject by summarizing essential steps in…
We provide operator-norm convergence estimates for solutions to a time-dependent equation of fractional elasticity in one spatial dimension, with rapidly oscillating coefficients that represent the material properties of a viscoelastic…
A finite-element method dependant adjoint-based procedure to determine the temperature field of structures based on measured displacements or strains and a set of standard loads is developed and tested. Given a series of force and…
Homogenization of a simultaneous heat and moisture flow in a masonry wall is presented in this paper. The principle objective is to examine an impact of the assumed imperfect hydraulic contact on the resulting homogenized properties. Such a…
We consider a self-adjoint non-negative operator $H$ in a Hilbert space $\mathsf{L}^2(X,{\rm d}\mu)$. We assume that the semigroup $(\mathrm{e}^{-t H})_{t>0}$ is defined by an integral kernel, $p$, which allows an estimate of the form…