The purpose of this paper is twofold. First, we give a derivation of the Lagrangian averaged Euler (LAE-α) and Navier-Stokes (LANS-α) equations. This theory involves a spatial scale α and the equations are designed to accurately capture the dynamics of the Euler and Navier-Stokes equations at length scales larger than α, while averaging the motion at scales smaller than α. The derivation involv...

the problem of propagation of plane wave including body and surface waves propagating in a transversely isotropic half-space with a depth-wise axis of material symmetry is investigated in details. using the advantage of representation of displacement fields in terms of two complete scalar potential functions, the coupled equations of motion are uncoupled and reduced to two independent equations...

in recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. these two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. in this paper i will consider the linear differential equations on the plane (phase diagram) and elements of nonl...

Naturally occurred soil deposits inherit heterogeneity and anisotropy in their strength properties. The main purpose of this paper is to model the soil stratum with anisotropy consideration and spatially varying undrained shear strength by using random field theory coupled with finite difference numerical analysis to evaluate their effect on the bearing capacity of the shallow foundations. In t...

in this paper, surface roughness of ht29 cancerous is determined using topography images obtained by atimic force microscopy (afm). the mean radiuses of cell and substrate surface asperities are determined, based on results of conducted roughness analysis and rabinovich roughness theory. these values have been applied in the equations of rough particle nanomanipulation dynamic model and the amo...