We describe a generalization of the tensorial slip boundary condition, originally justified for a thick (compared to texture period) channel, to any channel thickness. The eigenvalues of the effective slip-length tensor, however, in general case become dependent on the gap and cannot be viewed as a local property of the surface, being a global characteristic of the channel. To illustrate the us...

In this work, we consider the momentum transport of a incompressible fluid in like Beavers and Joseph (1967) system. For purpose, context volume averaging method, use one-domain approach (ODA). Thus, generalized equations (GTE), which are written terms position-dependent effective medium coefficients, valid everywhere system contains two Brinkman corrections addition to Darcy’s term. The ODA pr...

Existence of backward TE volume modes which are to be identified as Magnetostatic Wave (MSW) in anisotropic single-negative slab with partly negative permeability tensor component have already been revealed by present authors. In this paper, detailed modal analysis has been carried out for this kind of TE volume modes to find out their novel and peculiar properties. From these numerical results...

We propose sharp results on the numerical approximation of low-regularity electromagnetic fields by edge finite elements. We consider general geometrical settings, including topologically non-trivial domains or domains with a nonconnected boundary. In the model, the electric permittivity and magnetic permeability are symmetric, tensor-valued, piecewise smooth coefficients. In all cases, the err...

Diffusion anisotropy is the most fundamental and important parameter in the description of cardiac fibers using diffusion tensor magnetic resonance imaging (DTI), by reflecting the microstructure variation of the fiber. It is, however still not clear how the diffusion anisotropy is influenced by different contiguous structures (collagen, cardiac myocyte, etc.). In this paper, a virtual cardiac ...

This article is intended to provide clinical neurologists with an overview of the major techniques of advanced MRI of brain tumor: diffusion-weighted imaging, perfusion-weighted imaging, dynamic contrast-enhanced T1 permeability imaging, diffusion-tensor imaging, and magnetic resonance spectroscopy. These techniques represent a significant addition to conventional anatomic MRI T2-weighted image...

Introduction Diffusion MRI can give useful information on cellular structure and structural change (for a review see [1]). We show that the effective diffusion tensor obtained by mathematical homogenization theory (see e.g. [2,3]) is a good approximation to the long time apparent diffusion tensor under realistic DMR scanning conditions for both isotropic and anisotropic diffusion and general ge...

In the modelling of translational motion, the concepts of frequency-dependent (of the angular fluctuations of the velocity field) self-diffusion and the dispersion tensor are commonly used in its characterisation. Both of these parameters are related to velocity autocorrelation. An alternative means of modelling translational motion is via the equilibrium and nonequilibrium fluctuation-dissipat...

Viscous flow, effusion, and thermal transpiration are the main gas transport modalities for a rarefied gas in a macro-porous medium. They have been well quantified only in the case of simple geometries. This paper develops a model based on the homogenization of kinetic equations producing effective transport properties (permeability, Knudsen diffusivity, thermal transpiration ratio) in any poro...