V

The dimensionless reaction diffusion system becomes, on dropping the asterisks for algebraic convenience, ut = y (a - u + u2v) + V2m = Yf (», v) + V2u, vt = Y(b - u2v) + dV2v = yg(u, v) + dV2v,

x where f and g are defined by these equations. We could incorporate y into new length and timescales by setting y 1/2r and y t for r and t respectively. This is equivalent to defining the length scale L such that y = 1; that is, L = (DA/k2)l/2. We retain the specific form (2.7) for reasons which become clear shortly as well as for the analysis in the next section and for the applications in the following chapters.

An appropriate nondimensionalisation of the reaction kinetics (2.4) and (2.5) give (see Exercise 1)

f (u, v) = a — bu +--, v f (u, v) = a — u — h(u, v), h(u, v) =

p uv

[u, v) = u — v, g(u, v) = a(b — v) — h(u, v),

0 0

Post a comment