The spectral formulation of the stochastic finite-element method is applied to the problem of heat conduction in a random medium. Specifically, the conductivity of the medium, as well as its heat capacity are treated as uncorrelated random processes with spatial random fluctuations. Using the spectral stochastic finiteelement method, this paper analyzes the sensitivity of heat conduction proble...

The electrical conductivity has been calculated 1 in the early universe at temperatures below as well as above the electroweak vacuum scale, Tc ≃ 100GeV. Debye and dynamical screening of electric and magnetic interactions leads to a finite conductivity, σel ∼ T/α ln(1/α), at temperatures well below Tc. At temperatures above, W charge-exchange processes – analogous to color exchange through gluo...

Realistic boundaries of finite heat conductivity for thermoconvection in a Rayleigh-Bénard setup with magnetized ferrofluids are investigated. A linear stability analysis of the conductive state is performed with a shooting method. It shows that the critical wave number is for any magnetic field stronly influenced by the conductivity of the boundaries. Linear as well as nonlinear coefficients o...

We investigated the thermal conductivity K of graphene ribbons and graphite slabs as the function of their lateral dimensions. Our theoretical model considered the anharmonic three-phonon processes to the second-order and included the angle-dependent phonon scattering from the ribbon edges. It was found that the long mean free path of the long-wavelength acoustic phonons in graphene can lead to...

This paper presents some weighted H-regularity estimates for a model Poisson problem with discontinuous coefficient at high contrast. The coefficient represents a random particle reinforced composite material, i.e., perfectly conducting circular particles are randomly distributed in some background material with low conductivity. Based on these regularity results we study the percolation of the...

Abstract. We present here complete mathematical proofs of the results annouced in cond-mat/0509688. We introduce a model whose thermal conductivity diverges in dimension 1 and 2, while it remains finite in dimension 3. We consider a system of harmonic oscillators perturbed by a stochastic dynamics conserving momentum and energy. We compute the current-current time correlation function and the t...

Thermal properties of organic semiconductors play a significant role in the performance and lifetime of organic electronic devices, especially for scaled-up large area applications. Here we employ silver nanoparticles (Ag NPs) to modify the thermal conductivity of the small molecule organic semiconductor, dinaphtho[2,3-b:2',3'-f]thieno[3,2-b]thiophene (DNTT). The differential 3-ω method was use...

In this paper, a three-dimensional finite element model has been developed to simulate the laser-TIG hybrid welding (HLAW) of stainless steel 1.4418 with thickness of 4 mm. Transient temperature profile and dimensions of the fusion zone and heat affected zone (HAZ) during welding process are calculatedusing finite element method (FEM) and were solved in the ABAQUS/Standard software.The heat sou...

The study of the effective properties of composite materials with anisotropic constituents and different inclusion shapes has motivated the development of the Mathematica 6.0 package “CompositeMaterials”. This package can be used to calculate the effective anisotropic conductivity tensor of two-phase composites. Any fiber cross section, even percolating ones, can be studied in the 2D composites...

Electrical Impedance Tomography (EIT) of closed conductive media is an ill-posed inverse problem. As regards the corresponding direct problem, the choice of a Finite Elements Method preserves the non linear dependence of the observation set upon the conductivity distribution. In this paper, we show that the Bayesian approach presented in (1) for linear inverse imaging problems is also valid for...