lecture12 - Molecular-Dynamics Simulation E q u ilib r iu m...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Molecular-Dynamics Simulation Equilibrium Simulation Prof. Patrick Schelling Department of Physics University of Central Florida Florida Materials Simulators Meeting and Workshop, May 8-9, 2006
Background image of page 1

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

View Full Document Right Arrow Icon
Some good references… 1. “Computer Simulation of Liquids”, Allen and Tildesley 2. “The Art of Molecular Dynamics Simulation”, Rapaport
Background image of page 2
r F i = m i d 2 r r i dt 2 MD simulation Integrate to obtain ! r r i ( t )
Background image of page 3

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

View Full Document Right Arrow Icon
r F i = m i d 2 r r i dt 2 Is that all there is to it? Simulation can in some sense be regarded as intermediate between experiment and theory • Need a model for forces, interactions • Provides a test of theoretical predictions • Comparison to experiment tests models and theory
Background image of page 4
What kinds of problems? • Complex systems where theory is difficult • Many particles • Sample a large number of configurations • Statistical averaging A eq = d " P ( " ) A ( " ) # Γ represents a point in a 6N dimensional phase space (coordinates and momenta of N particles)
Background image of page 5

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

View Full Document Right Arrow Icon
• Classical dynamics result in Γ (t) • Time averages can be made instead of ensemble averages Connection to molecular dynamics A time = 1 t A ( " ( t ')) dt ' 0 t # If averaging time is long enough the system should have time to sample the phase space and then, A time " A eq
Background image of page 6
Ensembles A eq = d " P ( " ) A ( " ) # What configurations Γ does the simulation sample? In other words, what is P( Γ )? The two most common are : • Microcanonical ensemble (constant energy) • Canonical ensemble (constant temperature) P ( " ) = # ( E $ H ( " )) P ( " ) = A exp # E ( " ) k B T $ % ( )
Background image of page 7

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

View Full Document Right Arrow Icon
r F i = m i d 2 r r i dt 2 d 2 r r i dt 2 " r r i ( t + # t ) $ 2 r r i ( t ) + r r i ( t $# t ) # t 2 r r i ( t + " t ) = 2 r r i ( t ) # r r i ( t #" t ) + " t 2 m i r F i ( t ) Verlet Algorithm: numerical integration More complicated methods like the Gear predictor- corrector algorithm exist, but Verlet works pretty well
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 29

lecture12 - Molecular-Dynamics Simulation E q u ilib r iu m...

This preview shows document pages 1 - 9. Sign up to view the full document.

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