Furthermore, it was assumed that the regulatory mechanisms modeled represented suitable (macroscopic) approximations to the underlying molecular mechanism, thus, altenative network models were not explored.
We also demonstrate the use of such projective integrators in a shooting boundary value problem formulation for the computation of "coarse limit cycles" of the macroscopic behavior, and the approximation of their stability through estimates of the leading "coarse Floquet multipliers".
Linear stability analysis and high-accuracy numerical simulations are employed to analyze the ability of macroscopic continuum equations to provide a consistent approximation of the displacement process.
Exploiting the special structure of the models, the functions spaces used for the approximation of the solution are chosen as tensor products of spaces on the macroscopic domain and on the standard cell associated to the microstructure.
SDEs provide a good approximation of molecular population systems when one can assume that there is a macroscopic time scale for which (i) the event rates can be regarded as constant and (ii) there are many events of each type.
The approach uses a laminate approximation of the underlying microscopic structure to specify an expression for the continuous spatial dependence of the effective macroscopic material properties.
You have an approximation of marriage.
Random walk approximation of diffusions.
3. Approximation of classical kinetics.
It was an approximation of sobbing.
