We propose a generalized polynomial chaos (gPC) based stochastic Galerkin methods for scalar hyperbolic balance laws with random geometric source terms or random initial data. This method is well-balanced (WB), in the sense that it captures the stochastic steady state solution with high order accuracy. The framework of the stochastic WB schemes is presented in details, along with several numeri...

The flowing material balance (FMB) method is widely used to evaluate geological reserves because it does not require shut-in wells and uses daily production data. original FMB based on a homogeneous medium model, but the reservoir often heterogeneous. In this study, equations are derived for radial composite reservoirs naturally fractured reservoirs, effect of parameters estimation analyzed. st...

this paper presents discrete galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. we use the generalized jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. numerical results are presented to demonstrate the effectiven...

In this paper, based on the homogeneous balance principle and two improved projective Riccati Equations, exact solutions to the general form of BBM equation and the generalized BBM-Burgers equation with nonlinear terms of any order are obtained, which include several kinds of solitary wave solutions and periodic wave solutions. Some of them are found for the first time.

ARTICLE OUTLINE Definition of the Subject and Importance Introduction Granular Matter and its Statistical Mechanics Nonequilibrium statistical mechanics Liouville equation Stationary homogeneous state Macroscopic Balance Equations ”Normal” States and Hydrodynamics Navier-Stokes Approximation Constitutive equations Green-Kubo expressions Hydrodynamic equations Discussion and Outlook Bibliography...

Chondrocytes are the living cells in articular cartilage (AC). They synthesize and maintain the extracellular matrix. Their activity is regulated by the interplay of genetic and environmental factors, such as soluble mediators, extracellular matrix composition, and mechanical factors. The mechanical environment of the chondrocytes has a significant influence on the health of the joint. In past ...

In the present paper, an asymptotic model is constructed for the short-time deformation of an articular cartilage layer modeled as transversely isotropic, transversely homogeneous (TITH) biphasic material. It is assumed that the layer thickness is relatively small compared with the characteristic size of the normal surface load applied to the upper surface of the cartilage layer, while the bott...