We describe the thermodynamic state of a single-phase fluid confined to porous medium with Hill’s thermodynamics small systems, also known as nanothermodynamics. This way defining system thermodynamics, separate set control variables, may be useful for study transport in non-deformable media, where presently no consensus exists on pressure computations. For fluid, we observe that there are two ...

• A theory for continuous multiscale upscaling of 3D flows is developed. General equations densities and fluxes are obtained. Upscaling the steady-state diffusion process in a heterogeneous medium studied. An equation coefficient obtained large class solutions. Depending on solution, an may be different. We describe procedure flow equations. Multiscale averaging necessary operation many applica...

A mathematical model is considered to investigate the behavior of horizontally polarized shear waves (SH-waves) in fluid saturated porous medium sandwiched between heterogeneous half-spaces. Heterogeneity in the upper half-space is due to linear variation of elastic parameters, whereas quadratic variation has been considered for lower half-space. The method of separation of variables and Whitta...

This paper concerned with the dispersion of Love wave in a fiber-reinforced medium lying over a heterogeneous half-space. The heterogeneity is caused by the consideration of quadratic variation in density and directional rigidity of lower half-space. The irregularity has been considered in the form of rectangle at the interface of the fiber-reinforced layer and heterogeneous half-space. The dis...

the present paper studies the possibility of propagation of torsional surface waves in an inhomogeneous anisotropic layer lying between two heterogeneous half-spaces (upper and lower half-space). both the half-spaces are assumed to be under compressive initial stress. the study reveals that under the assumed conditions, a torsional surface wave propagates in the medium. the dispersion relation ...

We consider solutions of a scalar reaction-diffusion equation of the ignition type with a random, stationary and ergodic reaction rate. We show that solutions of the Cauchy problem spread with a deterministic rate in the long time limit. We also establish existence of generalized random traveling waves and of transition fronts in general heterogeneous media.

A strongly heterogeneous strati ed elastic medium occupies a slab of nite thickness. The medium parameters vary randomly with correlation length of O( ). A pulse with O( ) wavelength enters the slab at one end. It travels coherently through the slab with a slowness near to that predicted by e ective medium theory. Relative to a certain realization-dependent co-moving frame of reference the puls...

In this PhD thesis, we consider heterogeneous Wireless Sensor Networks (WSNs) in which several sensing devices with different characteristics coexist. In contrast to a homogeneous sensor network, in heterogeneous networks different sensors may sense different physical phenomena generating traffic that have different characteristics such as monitoring temperature, pressure, and humidity. Moreove...

A distributed microstructure model is obtained by homogenization from an exact micro-model with continuous temperature and flux for heat diffusion through a periodically distributed highly-heterogeneous medium. This composite medium consists of two flow regions separated by a third region which forms the doubly-porous matrix structure. The homogenized system recognizes the multiple scale proces...