Pressure

Pressure - Pressure in Molecular Dynamics I In order to...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Pressure in Molecular Dynamics I where r i is the position of atom i , F i Tot is the total force acting on atom i . Tot i N i i N Tot F r r r W r r v r = = 1 1 ) ,..., ( (t)dt r m (t) r τ 1 lim W i i τ 0 N 1 i i τ Tot r & & r = = Averaging over the MD trajectory and using Newton’s law, we obtain In order to introduce pressure, let us consider a system of N atoms that is developing in a finite space and let us introduce a function that is called Clausius virial function :
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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Pressure in Molecular Dynamics II Integrating by parts (t)dt r m (t) r τ 1 lim W i i τ 0 N 1 i i τ Tot r & & r = = T Nk 3 . E . K 2 dt ) t ( r m 1 lim W B 0 N 1 i 2 i i Tot = = τ = τ = τ r & dt ) t ( r m 1 lim ) 0 ( r ) 0 ( r ) ( r ) ( r m lim W 0 N 1 i 2 i i N 1 i i i i i i Tot τ = τ = τ τ τ τ τ = r & r r & r r &
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Pressure - Pressure in Molecular Dynamics I In order to...

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