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LaTeX Math Block
anchorProxyBLSolution
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x_D(s) = \begin{cases}\dot f(s) \cdot t_D, & \mbox{if } s < s^*\\1 2 x^*_D- \dot f(s) \cdot t_D, & \mbox{if } s \geq s^*\end{cases}

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LaTeX Math Inline
body--uriencoded--s%5e*

critical saturation where fractional flow function reaches inflection point: 

LaTeX Math Inline
body--uriencoded--\ddot f(s%5e*) = 0

LaTeX Math Inline
body--uriencoded--\displaystyle \dot x%5e*_D= f(ss%5e*) = \frac%7Bd f%7D%7Bds%7D\cdot t_D%5e*

critical first derivative of the fractional flow function

LaTeX Math Inline
body--uriencoded--\displaystyle \dot f(s) = \frac%7Bd f%7D%7Bds%7D, \, \, \ddot f(s) = \frac%7Bd%5e2 f%7D%7Bds%5e2%7D

first and second derivative derivatives of the fractional flow function

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