Introduction to Scientific Computing II

1
Introduction to Scientific Computing II

• Molecular Dynamics Discretisation

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Properties of the Model

• reversibilty in time
• H-theorem
• Loschmidt objection
• Lyapunov instability

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Lyapunov Instability Example
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Lyapunov Instability Example
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Time Discretisation Euler

• position implicit Euler
• velocity explicit Euler
• combination

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Time Discretisation Störmer Verlet

• Taylor series
• forward and backward direction
• velocity-free formula

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Time Disc. Velocity Störmer Verlet

• position Taylor series (2nd order)
• velocities Crank Nicolson

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Time Discretisation Leapfrog

• position Taylor series (2nd order)
• velocities Crank Nicolson

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Evaluation

• accuracy
• stability
• costs
• conservation
• reversibility of time