Examples of mathematical models of somitogenesis include pattern formation models based on reaction-diffusion assumptions [25] [30] or various other mechanisms [31] [35] and cell-based models employing systems of ordinary differential equations (ODEs) [36] [40] or delay differential equations (DDEs) [1], [6], [21], [41] [45].
In case of the optically thin and diffusion less plasma assumption, the obtained electron temperature is rather high.
From Eq. (6), it is apparent that under the perfect sink assumption diffusion dominates the mass balance process.
The existence of such connections turns out to be important since, for instance in the case of linear diffusion, under certain assumptions on the initial datum the solutions to the PDE (2) converge, for (t to+infty), to suitable combinations of traveling wave-type solutions (see, e.g., [3, 4]).
At the potentials of −0.15 and −1.1 V the maximum surface concentration Γm, and the surface area occupied by one molecule, S, were derived from the diffusion-controlled adsorption behavior with the assumption of the diffusion coefficient.
The assumption of diffusion in fluid-saturated rocks (Shapiro et al. 1997) established a relationship between microseismic events and the water front (Shapiro et al. 2002).
Two differently detailed numerical simulation models have been developed, which are based on the assumption that diffusion into the storage particles is strongly affected by solid volume changes.
It considers the convection, migration and diffusion mechanisms under the assumption of a dilute solution, mass conservation, and local electro-neutrality.
However, in the case of a nearly microporous adsorbent, the diffusivity appears to be dependent on temperature to an extent which is not consistent with the assumption of diffusion in rigid, liquid-filled pores.
