Chapter 1: MD Methods Flashcards Preview

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Flashcards in Chapter 1: MD Methods Deck (11):
1

Main Uses 
(MD Methods: 2 points)

  • to obtain dynamic information about the system
  • to calculate statistical (i.e. thermodynamic) averages

2

Ergodicity Hypothesis

For significant number of particles, the time average is the same as the ensemble average

3

Ergodicity, MD, MC

4

Overview
(MD Methods)

  • approximate solutions to equation of motion using finite difference method

5

Euler Method 
(Algorithm)

Derive by Taylor expanding x(+ ∆)

6

Euler Methods 
(Failures)

  • Energy grows without bound for oscillatory phenomena
    • not symplectic - not compatible with Hamiltonian symmetries

7

Verlet Integrator 
(Algorithm)

  • derive by Taylor expanding (+ ∆) and (t - ∆) and adding together
  • velocity comes from centered finite difference method

8

Verlet Integrator 
(Failure)

Not self-starting

9

Velocity-Verlet Integrator 
(Algorithm)

  1. Initial setup
  2. Calculate new position x(t + ∆)
  3. Calculate half-step velocity v(t + 0.5∆)
  4. Calculate new force a(t + ∆)
  5. Claculate final velocity v(t + ∆)

10

Velocity-Verlet Integrator 
(Benefits)

  • equivalent to Verlet integrator
  • includes velocity explicitly
  • self-starting

11

Verlet Integrator 
(Benefits)

  • more stable than Euler method
  • preserves physical properties
  • time reversible