in this paper, a higher order continuum model is presented based on the cosserat continuum theory in 3d numerical simulation of shear band localization. as the classical continuum models suffer from the pathological mesh-dependence in strain softening models, the governing equations are regularized by adding the rotational degrees-of-freedom to conventional degrees-of-freedom. the fundamental r...

In nonrelativistic quantum mechanics, we require that the free and interacting Hamiltonians be related by a unitary transformation, as has been done other authors. We then derive stationary perturbation theory for radial Schrödinger equation scattering from spherically symmetric potential. A resulting advantage over more commonly used Green function method is expression state vector normalized ...

Are extensions to continuum formulations for solving fluid dynamic problems in the transition-to-rarefied regimes viable alternatives to particle methods? It is well known that for increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier-Stokes equations lose accuracy. These inaccuracies are attributed primarily to the linear approximations of the stress ...

In an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 (2007)], to simulate non-equilibrium flows. In this paper, instead of using three temperatures in x−, y−, and z-directions, we are going to further define the translational temperature as a second-order symmetric tensor. Based on a multiple stage BGK-typ...

In an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 (2007)] to simulate nonequilibrium flows. In this paper, instead of using three temperatures in the x−, y−, and z-directions, we further define the translational temperature as a second-order symmetric tensor. Based on a multiple stage BGK-type collision...

In this paper, we develop two efficient numerical methods for a multiscale kinetic equation in the context of crowd dynamics with emotional contagion [A. Bertozzi, J. Rosado, M. Short and L. Wang, Contagion shocks in one dimension, J. Stat. Phys. 158 (2014) 647–664]. In the continuum limit, the mesoscopic kinetic equation produces a natural Eulerian limit with nonlocal interactions. However, su...

This paper analyzes the influence of an elastic plate on vibration wave propagation a pipe system. An impedance synthesis method is applied to establish governing equation pipe–plate coupled system by using force and boundary continuum. The natural frequency dynamic response are determined this method. validity theoretical derivation verified through comparisons with finite element model result...