Molecular dynamics: Hooke-Lennard-Jones hybrid method

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2012-05

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In this thesis we apply Hookes law and the Lennard-Jones potential together forming a hybrid potential energy function to model atomic interaction. These molecular dynamics simulations are then implemented in Matlab. For each simulation, we construct a cubic lattice of particles set at an equilibrium distance apart with most particles given an initial random velocity. The simulations are representative of generic solids. We observe how the system moves through time as the particles interact with one another. We are interested in investigating the e ciency of our Matlab implementation, evaluating the accuracy of the Runge-Kutta integration algorithm being used, and assessing the appropriateness of this hybrid potential to model cubic lattices.

This paper discusses the advantages and disadvantages of applying the fourth order Runge-Kutta (RK4) quadrature method to Newtons second law of motion in order to produce the trajectories of each particle in the system as they vary with time. Knowing that the RK4 method will not conserve energy, we observe how large our simulations can get before it produces too much error resulting in the loss or gain of energy. We also report on the run time performance of the code and suggest future improvements.

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