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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
QuickTimeª and a TIFF (LZW) decompressor are needed to see this picture. QuickTimeª and a TIFF (LZW) decompressor are needed to see this picture. QuickTimeª and a TIFF (LZW) decompressor are needed to see this picture. QuickTimeª and a TIFF (LZW) decompressor are needed to see this picture. Forward substitution Backward substitution Assumes β ii
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: =1 Chapter 9: Molecular-dynamics Integrate equations of motion-- classical! Discrete form of Newtons second law Forces from interaction potential For a simple pair potential, we get F i = -r i U r r 1 , r r 2 ,..., r r N ( ) U r r 1 ,..., r r N ( ) = 1 2 u ( ij 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,...
View Full Document

Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online