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Thread: Mathematical Modelling ( steady states)

  1. #1 Mathematical Modelling ( steady states) 
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    non-dimensionalisation equation:
    \begin{equation} \frac {du}{d\tau}=\frac{\overline{\lambda}_{1} u}{u+1} -\overline{r}_{ab}uv -\overline{d}u
    \end{equation}
    where $\overline{\lambda}_{1}= \frac {\lambda_{1}}{\lambda_{2} K_{1}}$
    Another non-dimensionalisation equations
    \begin{equation} \frac {dv}{d\tau}=(1-v) -\overline{r}_{ba}uv
    \end{equation}
    THE REAL QUESTION IS: calculate the steady state $(u_4,v_4)$ and $(u_5,v_5)$? Discuss the occurrence of these steady-states in respect of any relationships between the non-dimensional. Note you are not required to determine the stability of these two states.

    =>
    I have already calculated the steady-states of $(u_4,v_4)$ and $(u_5,v_5)$ which are

    $(u_4,v_4)$ =($ \frac{\overline{\lambda}_{1} - \overline{d} -\overline{r}_{ab}}{\overline{r}_{ab} + \overline{d}} ,1)$

    $(u_5,v_5)$ =($ \frac{\overline{\lambda}_{1} - \overline{d} -\overline{r}_{ab}}{\overline{r}_{ab} + \overline{d}}$ ,$ 1 - \overline{r}_{ba} \frac{\overline{\lambda}_{1} - \overline{d} -\overline{r}_{ab}}{\overline{r}_{ab} + \overline{d}}$ )

    I HAVE ALREADY CALCULATED $(u_1,v_1)$ and $(u_2,v_2)$ and $(u_3,v_3)$ but i an not interested to talk about their steady-state with respect to non-dimensional parameters.

    here are the non-dimensional parameters which I have also determined:

    $\overline{\lambda}_{1}= \frac {\lambda_{1}}{\lambda_{2} K_{1}}$

    $\overline{d}= \frac{d}{\lambda_{2}}$

    $\overline{r}_{ab} = \frac{\overline{r}_{ab} K_{2}} {\lambda_{2}}$

    $\overline{r}_{ba} = \frac{\overline{r}_{ab} K_{1}} {\lambda_{2}}$

    can anyone please please help me in discussion of these steady states $(u_4,v_4)$ and $(u_5,v_5)$ with the above non-dimensional parameters .
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  2. #2  
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    why is it coming on latex form?
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  3. #3  
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    Quote Originally Posted by grandy View Post
    why is it coming on latex form?
    Write it in La Tex from the beginning.
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  4. #4  
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    Quote Originally Posted by Robittybob1 View Post
    Write it in La Tex from the beginning.
    its written la tex and paste it here
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  5. #5  
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    Quote Originally Posted by grandy View Post
    its written la tex and paste it here
    Do a little la Tex on the site and see what formatting parts you have missed.
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