lecture7 - =1 Chapter 9 Molecular-dynamics • Integrate...

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Tridag.f subroutine Solves the matrix equation: Au=r Here A is a tridiagonal matrix, and u and r are column vectors. We assume we can find: A=LU Here L is lower triangular and U is upper triangular. So we solve L(Uu)=r, or Ly=r where y=Uu Good description online in Numerical Recipes

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Unformatted text preview: =1 Chapter 9: Molecular-dynamics • Integrate equations of motion-- classical! • Discrete form of Newton’s second law • Forces from interaction potential • For a simple pair potential, we get ρ F i = -r Ñ i U r r 1 , r r 2 ,..., r r N ( ) U r r 1 ,..., r r N ( ) = 1 2 u ( ij å r ij ) Integrating equations of motion F i , x = m i dv i , x dt F i , y = m i dv i , y dt F i , z = m i dv i , z dt dv i , x dt = d 2 x i dt 2 » x i ( n +1) - 2 x i ( n ) + x i ( n- 1) D t 2 x i ( n +1) = 2 x i ( n ) -x i ( n- 1) + F i , x m i D t 2 This works out to give the Verlet algorithm,...
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lecture7 - =1 Chapter 9 Molecular-dynamics • Integrate...

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