In this paper we describe a semianalytical approach to computing the temperature and thermal stress inside a III-V compound grown with the Czochralski technique. An analysis of the growing conditions indicates that the crystal growth occurs on the conductive time scale. A perturbation method for the temperature field is developed for an arbitrary crystal profile using the Biot number as a (smal...

While Biot theory can successfully account for the dispersion observed in sand sediments, the attenuation at high frequencies has been observed to increase more rapidly than Biot theory would predict. In an effort to account for this additional loss, perturbation theory is applied to Biot's poroelastic equations to model the loss due to the scattering of energy from heterogeneities in the sedim...

It is well known that the incompressible Euler equations in two dimensions have globally regular solutions. The inviscid surface quasi-geostrophic (SQG) equation has a Biot-Savart law which is one derivative less regular than in the Euler case, and the question of global regularity for its solutions is still open. We study here the patch dynamics in the half-plane for a family of active scalars...

Compressional and shear velocities of rocks are dependent on frequency and this dispersion may be significant even within the seismic band. The amount and position of dispersion will be largely a function of fluid properties, distribution, and motion in the pores. Velocities are thus directly coupled to rock permeability and pore compliance. Propagation often will be in the high frequency regim...

Abstract. We are concerned with the Barenblatt-Biott model in the theory of poroelasticity. We derive a guaranteed estimate of the difference between exact and approximate solutions expressed in a combined norm that encompasses errors for the pressure fields computed from the diffusion part of the model and errors related to stresses (strains) of the elastic part. Estimates do not contain gener...

This paper presents a didactic mathematical method to evaluate the self-inductance of a nonmagnetic core single-layer cylindrical and helicoidal coil presenting voids between turns. This type of calculation, using Biot–Savart Law, is not usually presented in the traditional electromagnetic text books, but constitutes an excellent tool to show to the students how to apply the very important Biot...