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# Maximizing Transport using Dynamic Programming

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• Add astumian referenceBrown color highlight that motion is possible only if switching is present
• Add astumian referenceBrown color highlight that motion is possible only if switching is present
• Add astumian referenceBrown color highlight that motion is possible only if switching is present
• Add astumian referenceBrown color highlight that motion is possible only if switching is present
• An intuition for this strategy is that as in this case if the potential is switched off, particle will travel $\dfrac{F_L}{\gamma}T_S$ distance toward the negative direction on an average. But if the potential is switched on, then the average \textit{maximum} distance it can travel toward negative direction is the amount the particle is away from the valley, is smaller than $\dfrac{F_L}{\gamma}T_S$. Once reaching the valley, it will be trapped.
• An intuition for this strategy is that as in this case if the potential is switched off, particle will travel $\dfrac{F_L}{\gamma}T_S$ distance toward the negative direction on an average. But if the potential is switched on, then the average \textit{maximum} distance it can travel toward negative direction is the amount the particle is away from the valley, is smaller than $\dfrac{F_L}{\gamma}T_S$. Once reaching the valley, it will be trapped.
• ### Maximizing Transport using Dynamic Programming

1. 1. a) kL ®L (k ¡ 1)L kL (k + 1)L L (k + 1)L
2. 2. kL ®L (k ¡ 1)L kL (k + 1)L L (k + 1)L
3. 3. a) O p en L oop b) C l ose L oop
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