md2011-01-note 6

md2011-01-note 6 - It is worth noting that we assumed here...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
I It is worth noting that we assumed here that after a long enough time ρ i ( d ) is independent of the initial state ( r N ( 0 ) , p N ( 0 ) ) I If this is true, we can improve on our statistics by running several MD simulations in parallel (f.ex. in a PC cluster) and average over the individual results: ρ i ( d ) = initial conditions ± lim t 1 t R t 0 d t 0 ρ i ( r ; r N ( 0 ) , p N ( 0 ) , t 0 ) ² number of initial conditions . (6) I As a limiting case, we consider averaging over all possible initial conditions for constant N , V and E . I In that case, we can introduce an integral: initial conditions f ( r N ( 0 ) , p N ( 0 )) number of initial conditions R E d r N d p N f ( r N ( 0 ) , p N ( 0 )) Ω ( N , V , E ) , (7) where f is an arbitraty function of the initial coordinates and Ω ( N , V , E ) = R E d r N d p N . Notes
Background image of page 1

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

View Full DocumentRight Arrow Icon
I This now corresponds to the classical “ensemble average”, which we denote by h . . . i
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

md2011-01-note 6 - It is worth noting that we assumed here...

This preview shows document pages 1 - 3. Sign up to view the full document.

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