Difference between revisions of "Team:KU Leuven/Modeling/Top"
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The Keller segel model used is <sub> <a href="#ref1">[1] </a></sub>: | The Keller segel model used is <sub> <a href="#ref1">[1] </a></sub>: | ||
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$$\frac{\partial A}{\partial t} = D_a \bigtriangledown^2 A + k_A A(1 - \frac{A}{k_{p}}),$$ | $$\frac{\partial A}{\partial t} = D_a \bigtriangledown^2 A + k_A A(1 - \frac{A}{k_{p}}),$$ | ||
$$\frac{\partial B}{\partial t} = D_b \bigtriangledown^2 B + \bigtriangledown (X(B,H,R) \bigtriangledown R)+ k_B B(1 - \frac{B}{k_{p}}), $$ | $$\frac{\partial B}{\partial t} = D_b \bigtriangledown^2 B + \bigtriangledown (X(B,H,R) \bigtriangledown R)+ k_B B(1 - \frac{B}{k_{p}}), $$ | ||
$$ \frac{\partial R}{\partial t} = D_r \bigtriangledown^2 B + k_r A - k_lossH R $$ | $$ \frac{\partial R}{\partial t} = D_r \bigtriangledown^2 B + k_r A - k_lossH R $$ | ||
$$\frac{\partial H}{\partial t} = D_h \bigtriangledown^2 B + k_h A - k_lossR H . $$ | $$\frac{\partial H}{\partial t} = D_h \bigtriangledown^2 B + k_h A - k_lossR H . $$ | ||
| + | With: </br> | ||
| + | $$ X(B,H,R) = -B K_{c1} (K_{c2} H(t,:)/R(t,:)). $$ | ||
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When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are | When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are | ||
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$ | $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$ | ||
Revision as of 13:44, 23 July 2015
1-D continuous model
The Keller segel model used is [1] : $$\frac{\partial A}{\partial t} = D_a \bigtriangledown^2 A + k_A A(1 - \frac{A}{k_{p}}),$$ $$\frac{\partial B}{\partial t} = D_b \bigtriangledown^2 B + \bigtriangledown (X(B,H,R) \bigtriangledown R)+ k_B B(1 - \frac{B}{k_{p}}), $$ $$ \frac{\partial R}{\partial t} = D_r \bigtriangledown^2 B + k_r A - k_lossH R $$ $$\frac{\partial H}{\partial t} = D_h \bigtriangledown^2 B + k_h A - k_lossR H . $$ With: $$ X(B,H,R) = -B K_{c1} (K_{c2} H(t,:)/R(t,:)). $$ When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$
References
Reference 1
