The transport and continuum equations exhibit a number of conservation laws. For example, scalar multiplication is conserved by the transport equation, while positivity of probabilities is conserved by the continuum equation. Certain discretization techniques, such as particle based methods, conserve these properties, but converge slower than spectral discretization methods on smooth data. Stan...

The Kardar-Parisi-Zhang ~KPZ! equation @1# has been very successful in describing a class of dynamic nonlinear phenomena. It is applied to a wide range of topics including vapor deposition, bacterial colony growth, directed polymers, and flux lines in superconductors @2,3#. Computational studies have mostly concentrated on simulations of discrete models such as ballistic deposition models, soli...

in this paper, three dimensional (3d) static and dynamic analysis of thick plates based on the meshless local petrov-galerkin (mlpg) is presented. using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. a weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a uni...

A procedure suggested by Vvedensky for obtaining continuum equations as the coarse-grained limit of discrete models is applied to the restricted solid-on-solid model with both adsorption and desorption. Using an expansion of the master equation, discrete Langevin equations are derived; these agree quantitatively with direct simulation of the model. From these, a continuum differential equation ...

Incorporating the velocity slip effect of the gas flow at the solid boundary, the performance and dynamic response of a micro gas-bearing-rotor system are investigated in this paper. For the characteristic length scale of the micro gas bearing, the gas flow in the bearing resides in the slip regime rather than in the continuum regime. The modified Reynolds equations of different slip models are...

The Rayleigh-Plesset equation is used extensively to model spherical bubble dynamics, yet it has been shown that it cannot correctly capture damping effects due to mass and thermal diffusion. Full single bubble models have been successfully used to study these diffusion effects, but these are too computationally expensive to implement into the continuum model for bubbly cavitating flows since t...

a new type of backbone robot is presented in this paper. the core idea is to use a cross shape mechanism with the principle of functioning of the scissors linkages, known as a pantograph. although this continuum arm acts quite similar to tendon-driven robot, this manipulator does not include any tendon in its structure. this design does not suffer from the weaknesses of the continuum design suc...

The equation of the density field of an assembly of macroscopic particles advected by a hydro-dynamic flow is derived from the microscopic description of the system. This equation allows one to recognize the role and the relative importance of the different microscopic processes implicit in the model: the driving of the external flow, the inertia of the particles, and the collisions among them....