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Unformatted text preview: I These are defined as: P = X i p i L = X i r i × p i = X i r i × m i ˙ r i (13) I For a completely isolated system: I P and L are conserved I Hamiltonian H is independent on time , i.e., d H / d t = 0 (total energy is constant). I Further, the equations of motion are reversible in time . I I.e., by changing the signs of all momenta, particles would retrace their trajectories. I A successfull atomistic simulation reproduces all these features! Notes S MD A Notes MD, G C I The natural system to model is the socalled microcanonical ensemble ( NVE ). I This is closest to a real system because it’s a true solution for the Nbody problem, and corresponds to the real atomic motion (but only for a completely isolated system). I Current limit is ∼ 10 9 atoms in dynamical calculations for simulation times of a few ns with spatially parallelized codes. I For a Natomic system, one in principle needs to care about N 2 interactions for each time step Δ t ....
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 Winter '12
 Kotakoski
 Atom, Energy, Entropy, Ion, Chemical bond, successfull atomistic simulation

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