for arbitrary time t and arbitrary λ > 0, where ψ is a smooth bump function supported in [−2, 2] if λ < 1 and supported in [1, 2] if λ ≥ 1. This generalizes previous results in [MT]. We also prove pointwise estimates for the gradient of these convolution kernels. As a corollary, we reprove basic multiplier estimates from [HS] and [V1] and derive Sobolev estimates for the solutions to the wave e...

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 contact is characterized by a certain mismatching resistance allowing us to represent a discontinuous evolution of temperature and moisture fields across th...

In this work we study an r-species mixture of gases within the relativistic kinetic theory point of view. We use the relativistic covariant Boltzmann equation and incorporate the Schwarzschild metric. The method of solution of the Boltzmann equation is a combination of the Chapman-Enskog and Grad representations. The thermodynamic four-fluxes are expressed as functions of the thermodynamic forc...

Heat conduction in a ne scale mixture of two conductors is examined in the presence of a contact resistance between phases. The problem is studied rigorously in the context of periodic homogenization. Unlike the case of perfect heat transmission between phases, the temperature elds studied here may converge weakly in L to the homogenized temperature. The temperature gradients converge weakly as...

A theoretical framework is developed to generate tokamak equilibrium configurations for which, on one hand, the current results entirely from the bootstrap current source driven by the pressure gradient while, on the other hand, the pressure gradient is determined from the thermal conduction equation with a thermal diffusivity constructed to have properties observed in confinement experiments: ...

A novel stability-indicating gradient reverse phase ultra-performance liquid chromatographic (RP-UPLC) method was developed for the determination of purity of desloratadine in presence of its impurities and forced degradation products. The method was developed using Waters Aquity BEH C18 column with mobile phase containing a gradient mixture of solvents A and B. The eluted compounds were monito...

The recent popularity of 3D IC technology stems from its enhanced performance capabilities and reduced wiring length. However, wire congestion and thermal issues are exacerbated due to the compact nature of these layered technologies. In this paper, we develop techniques to reduce global the temperature gradient and local and global congestions of 3D circuit designs without compromising total i...

Motivated by recent experiments by Yuse and Sano (Nature, 362, 329 (1993)), we propose a discrete model of linear springs for studying fracture in thin and elastically isotropic brittle films. The method enables us to draw a map of the stresses in the material. Cracks generated by the model, imposing a moving thermal gradient in the material, can branch or wiggle depending on the driving parame...