Gray & Scott 1982

Key: gray1983autocatalytic

One of the two variable reaction-diffusion models presented in the article “Autocatalytic reactions in the isothermal, continuous stirred tank reactor: isolas and other forms of multistability”. Depending on the parameters, different patterns can be seen to form in its solutions.

It describes the chemical reactions:

\[\begin{split}U + 2V &\to 3V \\ V &\to P\end{split}\]

  • u, v: concentrations of \(U\), \(V\).

  • k: rate of conversion of \(V\) to \(P\).

  • f: rate of the process that feeds \(U\) and drains \(U\), \(V\), and \(P\).

References

  1. https://doi.org/10.1016/0009-2509(83)80132-8

Figure

Figure illustrating the Gray & Scott 1982 model.

Variables

  1. u = 1.0

  2. v = 0.0

Parameters

  • diffusivity_u = 1

  • diffusivity_v = 0.5

  • f = 0.055

  • k = 0.062

Source code

OpenCL kernel
const Real uvv = u * v * v;
const Real U = -uvv + f * (1 - u);
const Real V = uvv - (f + k) * v;

*_new_u = u + dt * (U + _diffuse_u);
*_new_v = v + dt * (V + _diffuse_v);

Additional metadata

keywords:
- pattern formation
example discretisation:
  dt: 0.1
  dx: 1.0
  stimulus: 0.4
units:
  t: 1
  x: 1
  u: 1