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Team:ETH Zurich/Modeling/Analytical Approximations
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<h1> Kolmogorov-Petrovsky-Piskounov Equation </h1> | <h1> Kolmogorov-Petrovsky-Piskounov Equation </h1> | ||
A reaction–diffusion equation concerning the concentration of a single molecule in one spatial dimension is known as the Kolmogorov-Petrovsky-Piskounov Equation. In our case, the equation for AHL has the following general structure: | A reaction–diffusion equation concerning the concentration of a single molecule in one spatial dimension is known as the Kolmogorov-Petrovsky-Piskounov Equation. In our case, the equation for AHL has the following general structure: | ||
| + | |||
| + | \begin{align} | ||
| + | \frac{\partial AHL(\textbf{r},t)}{\partial t} = Diff(AHL(\textbf{r},t),\textbf{r}) + R(AHL(\textbf{r},t)) | ||
| + | \end{align} | ||
| + | |||
| + | And a less general form, as derived for the reaction-diffusion model for AHL: | ||
<br clear="all"/> | <br clear="all"/> | ||
{{:Team:ETH_Zurich/templates/footer}} | {{:Team:ETH_Zurich/templates/footer}} | ||
Revision as of 19:50, 24 October 2013
Steady State AHL Gradient Approximation
In the reaction-diffusion model we have formalized the gradient establishment and we solved the resulting partial differential equation numerically. Now, the aim is to derive a suitable analytical approximation.
Kolmogorov-Petrovsky-Piskounov Equation
A reaction–diffusion equation concerning the concentration of a single molecule in one spatial dimension is known as the Kolmogorov-Petrovsky-Piskounov Equation. In our case, the equation for AHL has the following general structure:
\begin{align} \frac{\partial AHL(\textbf{r},t)}{\partial t} = Diff(AHL(\textbf{r},t),\textbf{r}) + R(AHL(\textbf{r},t)) \end{align}
And a less general form, as derived for the reaction-diffusion model for AHL:
