This paper presents an analysis of the simultaneous incorporation of force and mass source terms into the multi-relaxation-time (MRT) collision operator. MRT force incorporation was obtained through Chapman-Enskog analysis. The numerical scheme was tested on different benchmark problems, including the decay of a shear wave with different bulk and kinematic viscosities and axisymmetric flow.

We present an algorithm for solving stochastic integer programming problems with recourse, based on a dual decomposition scheme and Lagrangian relaxation. The approach can be applied to multi-stage problems with mixed-integer variables in each time stage. Numerical experience is presented for some two-stage test problems.

The most commonly used theoretical models for describing chemical kinetics are accurate in two limits. When relaxation is fast with respect to reaction time scales, thermal transition state theory (TST) is the theoretical tool of choice. In the limit of slow relaxation, an energy resolved description like RRKM theory is more appropriate. For intermediate relaxation regimes, where much of the ch...

In vivo spin spin relaxation time (T2) heterogeneity of hyperpolarized [13C,15N2]urea in the rat kidney was investigated. Selective quenching of the vascular hyperpolarized 13C signal with a macromolecular relaxation agent revealed that a long-T2 component of the [13C,15N2]urea signal originated from the renal extravascular space, thus allowing the vascular and renal filtrate contrast agent poo...

The stress-strain relationship in shales is generally time-dependent. This concerns their long-term deformation unconventional reservoirs, and its influence on the situ stress state therein. paper presents an experimental investigation time-dependent of Longmaxi shale gas shale. A series creep experiments subject samples to long-term, multi-step triaxial compression. It found that exhibit varyi...

this paper presents a multi-criteria vehicle routing problem with soft time windows (vrpstw) to mini-mize fleet cost, routes cost, and violation of soft time windows penalty. in this case, the fleet is heterogene-ous. the vrpstw consists of a number of constraints in which vehicles are allowed to serve customers out of the desirable time window by a penalty. it is assumed that this relaxation a...

<p style='text-indent:20px;'>Cross-docking is a kind of process that products are unloaded in front the inbound doors, consolidated based on downstream demand, and then directly transferred to outbound doors without long storage during transportation. In this paper, multi-door cross-dock truck scheduling problem investigated which sequencing assignment trucks need be considered, with obje...