Difference between revisions of "Team:Aix-Marseille/Collaborations"
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\frac{\partial}{\partial t} W_\mathbf{z} (\mathbf{z},t) + \nabla_\mathbf{z}\cdot[(\beta\cdot\overline{\mathbf{R}}(\mathbf{z},c)W_\mathbf{z}(\mathbf{z},t))] = 2 \int \sigma (\mathbf{z',c}) p(\mathbf{z,z',c}) W_{\mathbf{Z}}(\mathbf{z'},t)\mathrm{d}v' - (D+\sigma (\mathbf{z,c})) W_{\mathbf{Z}}(\mathbf{z},t) (1) | \frac{\partial}{\partial t} W_\mathbf{z} (\mathbf{z},t) + \nabla_\mathbf{z}\cdot[(\beta\cdot\overline{\mathbf{R}}(\mathbf{z},c)W_\mathbf{z}(\mathbf{z},t))] = 2 \int \sigma (\mathbf{z',c}) p(\mathbf{z,z',c}) W_{\mathbf{Z}}(\mathbf{z'},t)\mathrm{d}v' - (D+\sigma (\mathbf{z,c})) W_{\mathbf{Z}}(\mathbf{z},t) (1) | ||
| − | + | \\ | |
\\ | \\ | ||
\frac{d\mathbf{c}}{dt} = D(\mathbf{c_f} - \mathbf{c} ) + \mathbf{\gamma}\cdotp \int \bar{\mathbf{R}}(\mathbf{z,c}) W_{\mathbf{Z}}(\mathbf{z},t)\mathrm{d}v (2) | \frac{d\mathbf{c}}{dt} = D(\mathbf{c_f} - \mathbf{c} ) + \mathbf{\gamma}\cdotp \int \bar{\mathbf{R}}(\mathbf{z,c}) W_{\mathbf{Z}}(\mathbf{z},t)\mathrm{d}v (2) | ||
| + | \\ | ||
| + | \\ | ||
| + | \begin{tabular}{p{0.10\linewidth}p{0.75\linewidth}} | ||
| + | |||
| + | $\mathbf{z} $& Vector for internal state of a bacteria.\\ | ||
| + | $\mathbf{c} $& Time dependant vector for conditions.\\ | ||
| + | $W_{\mathbf{Z}}(\mathbf{z},t) $& Distribution of bacteria in $\mathbf{z}$ space at time $t$.\\ | ||
| + | $\bar{\mathbf{R}}(\mathbf{z,c}) $& The expected value or the reaction rate vector function of $\mathbf{z}$ and $\mathbf{c}$.\\ | ||
| + | $\sigma (\mathbf{z',c}) $& Rate of fision for bacteria as a scalar function of $ \mathbf{z,c} $.\\ | ||
| + | $p(\mathbf{z,z',c}) $& Partitioning probability of generating a child in state $\mathbf{z}$ from a parent | ||
| + | in state $\mathbf{z'}$ given the conditions $\mathbf{c}$.\\ | ||
| + | $\nabla_{\mathbf{Z}}\cdot \mathbf{V} $& $\sum \frac{\partial}{\partial z_i}\mathbf{V}_i $\\ | ||
| + | $\textrm{d}v' $& Integral over state space $v'$ .\\ | ||
| + | $D $& Dilution rate of the culture (for fermenters). \\ | ||
| + | $\beta $& Stochiometric matrix for cellular substances.\\ | ||
| + | $\gamma $& Stochiometric matrix for extra-cellular substances.\\ | ||
| + | |||
| + | \end{tabular}\\ | ||
</div> | </div> | ||
