Difference between revisions of "Reaction-Diffusion Systems"
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=== Example 1: Simple Decay === | === Example 1: Simple Decay === | ||
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Suppose we have of chemical <math>P</math> which decays to <math>A</math>, i.e. | Suppose we have of chemical <math>P</math> which decays to <math>A</math>, i.e. | ||
<center> | <center> | ||
<math>P \to A</math> | <math>P \to A</math> | ||
</center> | </center> | ||
| + | with rate <math>k[P]</math> where <math>[P]</math> denotes concentration. Then if we | ||
| + | set <math>p=[P]</math> and <math>A = [A] </math> we obtain the equations | ||
| + | <center> | ||
| + | <math> \frac{dp}{dt} = kp\,\,\,\textrm{and}\,\,\, \frac{da}{dt} = kp</math> | ||
| + | </center> | ||
| + | |||
| − | [[Category | + | [[Category:Simple Nonlinear Waves]] |
Revision as of 22:38, 4 October 2009
We present here a brief theory of reaction diffusion waves.
Law of Mass Action
The law of mass action states that equation rates are proportional to the concentration of reacting species and the ratio in which they combined. It is discussed in detail in Billingham and King 2000. We will present here a few simple examples.
Example 1: Simple Decay
Suppose we have of chemical [math]\displaystyle{ P }[/math] which decays to [math]\displaystyle{ A }[/math], i.e.
[math]\displaystyle{ P \to A }[/math]
with rate [math]\displaystyle{ k[P] }[/math] where [math]\displaystyle{ [P] }[/math] denotes concentration. Then if we set [math]\displaystyle{ p=[P] }[/math] and [math]\displaystyle{ A = [A] }[/math] we obtain the equations
[math]\displaystyle{ \frac{dp}{dt} = kp\,\,\,\textrm{and}\,\,\, \frac{da}{dt} = kp }[/math]
