langevin - PHZ 5156 Final project Langevin dynamics This...

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PHZ 5156 Final project Langevin dynamics This problem builds on the molecular dynamics code to perform Langevin dynamics of a polymer. The polymer will be represented by a simple bead-spring model. In this model, only neighboring molecules along the polymer interact, with the potential energy of the chain given by, U = 1 2 k N X i =1 ( ~ r i - ~ r i - 1 ) 2 where ~ r i is a vector representing the coordinate of the ith bead along the polymer chain. Notice that only neighboring beads interact. At T = 0 the polymer chain has length zero. At finite temperature, the springs will begin to stretch, giving the polymer a finite length. While the bead-spring model is extremely simple and can even be explored analyt- ically, we will use Langevin dynamics to explore the equilibrium statistics and also transport properties. In Langevin dynamics, the solvent is modeled by including a dissipative force and a random force. In particular, the equation of motion for the nth bead is given by, m d 2 r i,μ
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langevin - PHZ 5156 Final project Langevin dynamics This...

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