a)
kL

®L

(k ¡ 1)L

kL

(k + 1)L

L

(k + 1)L
kL

®L

(k ¡ 1)L

kL

(k + 1)L

L

(k + 1)L
a) O p en L oop

b) C l ose L oop
Maximizing Transport using Dynamic Programming
Maximizing Transport using Dynamic Programming
Maximizing Transport using Dynamic Programming
Maximizing Transport using Dynamic Programming
Maximizing Transport using Dynamic Programming
Maximizing Transport using Dynamic Programming
Maximizing Transport using Dynamic Programming
Maximizing Transport using Dynamic Programming
Maximizing Transport using Dynamic Programming
Maximizing Transport using Dynamic Programming
Maximizing Transport using Dynamic Programming
Maximizing Transport using Dynamic Programming
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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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