A Galerkin approach for a class of multiscale reaction diffusion systems with nonlinear coupling between the microscopic and macroscopic variables is presented.
Finally, the significance of various macroscopic variables was determined by different types of crash risks using variable importance analysis.
In the transition flow regime, for Knudsen numbers of the order of unity or greater, a microscopic approach is required, wherein the trajectories of individual representative molecules are considered, and macroscopic variables are obtained from the statistical properties of their motions.
Note that not all macroscopic variables are macrostates.
All species that are not macroscopic variables are microscopic species (or microstates).
With the WENO reconstruction, a high-order moving-mesh multidimensional gas-kinetic method, with inclusion of both normal and tangential derivatives of macroscopic flow variables, is constructed.
Our results indicate that pressure, as an easily controlled macroscopic variable, can be used for both selective adsorption and chemical activation.
Scale separation is exploited so that the macroscopic variables can be evolved in macroscopic spatial/temporal scales using data that are estimated from molecular dynamics simulation on microscale spatial/temporal domains.
The vanishing of the second-order work, defined on the macroscopic scale from tensorial variables, is shown to play a fundamental role in detecting the occurrence of this type of bifurcation.
In the cylindrical coordinate system, the local time evolution of convection and source terms for the macroscopic and microscopic flow variables is fully coupled with particle free transport and collisions.
