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Unformatted text preview: will start to fail. I Obviously, it’s better to err rather toward too short than too long Δ t . I Conventionally, Δ t has been a constant troughout the simulations, and has been chosen using some rulesofthumb, based on experience. Notes I For example: “ The distance traveled by the atoms should be limited to 1/20 of the interatomic distance b ( Δ x 6 b / 20 ) ”: I From equipartition theorem ± 1 2 m i v 2 i , α ² = 1 2 k B T (3) I While h v i i = q ∑ α ³ v 2 i , α ´ , this leads to h v i i = s 3 k B T m i (4) Notes I As the distribution goes much beyound the h v i i , we use 5 h v i i as the velocity for the estimation: 5 h v i i = Δ x Δ t ⇔ Δ t = Δ x 5 h v i i 6 b 5 × 20 r m i 3 k B T (5) I Note that this depends on the mass of the atom ( m i ). Notes...
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 Winter '12
 Kotakoski
 Kinetic Energy, Fundamental physics concepts, molecular dynamics simulations, Dr. Jani Kotakoski

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