Difference between revisions of "Team:Paris Saclay/Modeling"

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<p>In order to be considered for the <a href="https://2015.igem.org/Judging/Awards#SpecialPrizes">Best Model award</a>, you must fill out this page.</p>
 
<p>In order to be considered for the <a href="https://2015.igem.org/Judging/Awards#SpecialPrizes">Best Model award</a>, you must fill out this page.</p>
 
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The diffusion of particules is based on Fick's first law which is given by:
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\begin{equation}
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\textbf{j} = -D \, \bf{\nabla} n
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\label{eq:fick}
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\end{equation}
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In this equation, $\textbf{j}$ is the diffusion flux, $D$ the diffusion coefficient and $n$ the concentration of particles.
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This equation can be coupled with the continuity equation $\partial_t n = \mathbf{\nabla} \cdot \mathrm{j} \quad (+\sigma)$ expressing the conservation of the total number of diffusing particles. $\sigma$ is the net particle production rate.
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It is however interesting to study to what extent the porous medium used to allow diffusion of molecules is permissive, given the thickness of silica around the alginate beads that contain our working bacteria.
 
It is however interesting to study to what extent the porous medium used to allow diffusion of molecules is permissive, given the thickness of silica around the alginate beads that contain our working bacteria.
  
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START OF MODELING
  
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The diffusion of particules is based on Fick's first law which is given by:
+
 
−
\begin{equation}
+
 
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\textbf{j} = -D \, \bf{\nabla} n
+
 
−
\label{eq:fick}
+
 
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\end{equation}
+
 
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In this equation, $\textbf{j}$ is the diffusion flux, $D$ the diffusion coefficient and $n$ concentration of particles.
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--------------------------------
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It can be coupled with the continuity equation stating the number  second law
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physical containment method based on silica presented
 
physical containment method based on silica presented
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Equation de continuité -> conservation nombre de particules
 
Equation de continuité -> conservation nombre de particules
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\begin{equation}
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\partial_t n = \mathbf{\nabla} \cdot \mathrm{j} \, (+\sigma)
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\label{eq:continuity_eq}
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\end{equation}
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Eq. \ref{eq:fick} + Eq. \ref{eq:continuity_eq} : $\partial_t n = D \, \triangle n \, (+\sigma)$
 
Eq. \ref{eq:fick} + Eq. \ref{eq:continuity_eq} : $\partial_t n = D \, \triangle n \, (+\sigma)$
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$n(r,t) = \frac{\mathrm{e}^{-\lambda D^2 t}}{\sqrt{r}} \, \sqrt{\frac{2}{\lambda \pi}} \Big[C_1 \sin(\lambda r) - C_2 \cos(\lambda r) \Big]$
 
$n(r,t) = \frac{\mathrm{e}^{-\lambda D^2 t}}{\sqrt{r}} \, \sqrt{\frac{2}{\lambda \pi}} \Big[C_1 \sin(\lambda r) - C_2 \cos(\lambda r) \Big]$
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Revision as of 02:27, 19 September 2015

Modeling

Note

In order to be considered for the Best Model award, you must fill out this page.

The diffusion of particules is based on Fick's first law which is given by: \begin{equation} \textbf{j} = -D \, \bf{\nabla} n \label{eq:fick} \end{equation} In this equation, $\textbf{j}$ is the diffusion flux, $D$ the diffusion coefficient and $n$ the concentration of particles. This equation can be coupled with the continuity equation $\partial_t n = \mathbf{\nabla} \cdot \mathrm{j} \quad (+\sigma)$ expressing the conservation of the total number of diffusing particles. $\sigma$ is the net particle production rate.
Contact
eigem.parissaclay AT gmail DOT com
t@iGEMParisSaclay
aUniversité Paris Sud
a91405 Orsay, France Copyright © 2015 iGEM Paris Saclay. All rights reserved All inspirations encouraged.
*This wiki was conceived during long nights of work and a great coffee experience in the beautiful Orsay, France.