A Galerkin approach for a class of multiscale reaction diffusion systems with nonlinear coupling between the microscopic and macroscopic variables is presented.
Another limitation is that the topics that have been used as the subject content contain direct mappings between microscopic and macroscopic variables (for example, electron motion with current).
The pdf (particle distribution function) (f s,v_{m},t)) is also related to macroscopic variables like the density and the fluid velocity (v_{f}) from its moments.
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.
This article establishes analytic, computational, and empirical support for the relations of evolutionary entropy with the macroscopic variables body size, metabolic rate, and life span.
When Knudsen number is small compared to unity (i.e. Kn ≤ 0.1), the fluid can be treated as a continuous medium and described in terms of the macroscopic variables such as velocity, density, pressure, and temperature.
The gas-kinetic scheme is designed for the updating of macroscopic variables, which include the conservative flow variables and the multiple temperature field.
Macroscopic variables such as speed, flow and density have been used in assessing the performance of pedestrian facilities and these variables constitute the Fundamental Diagrams (FDs) of pedestrian flow.
In layer-based modeling, signal flows occur between layers and can be represented by macroscopic variables, usually sums of species with phosphorylated binding sites x i and corresponding sums of species with occupied binding sites x i b.
