Here a perturbation analysis is performed by comparing two curves as the difference in growth rate between the two increases.
The velocity fields are obtained using a perturbation analysis.
This result is arrived at using a perturbation analysis exactly as considered in the previous subsection.
92 (1990) 792] analyzed by a singular perturbation analysis.
Looking at Fig. 9, the corresponding shift in the s-value falls within the order of the singular perturbation parameter ε, as expected by a singular perturbation analysis.
By presenting a simple perturbation analysis, it is shown that some commonly applied MPS-based pressure gradient models are prone to increase the level of unphysical perturbations at the phase interface leading to numerical instabilities.
This is easily verified by performing a regular perturbation analysis in the small parameter 1/ k d as has been performed elsewhere.
We first briefly describe the deterministic aspects of this model, and build on the previous analysis by introducing a local perturbation analysis that leads to insights on how the initiation of polarisation depends on the parameters and on the total amount of molecules.
In this paper, the idealized case of a uniform and instantaneous scalar release across the channel is analytically explored by a two-scale perturbation analysis.
The results obtained by the proposed approach are compared to those obtained by perturbation analysis and by direct integration which we considered to the "exact solution".
