Molecular Dynamics Method: Theory and Implementation

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About this document

This is a lecture note for an intensive lecture at Kanazawa University (from Dec. 18 to 20, 2019).

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PDF (Written in Japanese)

Table of Contents

All notes are written in Japanese and slides are written in English.

• 0. Introduction [Slides]
  • What is MD?
  • Questions about MD
  • Purpose of this lecture
• 1. Classical Mechanics
  • 1.1 Euler-Lagrange equation
  • 1.2 Hamiltonian's equation
  • 1.3 Liouville Operator
  • 1.4 Variables and Observables
• 2. Pressure
  • 2.1 Global Pressure
  • 2.2 Local Stress
• 3. Temperature
  • 3.1 Maxwell Distribution
  • 3.2 Canonical Ditribution
  • 3.3 Generarized Virial Theorem
• 4. Numerical Integration
  • 4.1 Integration of ODE
  • 4.2 Integration of Equations of Motion
  • 4.3 Symplectic Integrator
• 5. Nose-Hoover Method
  • 5.1 Temperature Controll
  • 5.2 Nose-Hoover Method
  • 5.3 Problems on Nose-Hoover method
• 6. Langevin Thermostat
  • 6.1 Langevin Equation
  • 6.2 Euler-Maruyama Method
  • 6.3 H Theorem
• 7. Integration scheme for non-Hamliton systems
  • 7.1 Non-Hermiticity of Liouville Operator
  • 7.2 RESPA
  • 7.3 7.3 Time Reversibility
• 8. Generalized Liouville's Theorem of non-Hamiltonian systems
  • 8.1 Jacobi's Formula
  • 8.2 Dynamics of Jacobian
  • 8.3 Generalized Liouvllie's Theorem
• 9. Implementations and Optimization [Slides]
  • 9.1 Architecture of Computer
  • 9.2 Memory Optimization
  • 9.3 Architecture Dependent Optimization
• 10. Programming Design [Slides]
  • 10.1 Module Coupling
  • 10.2 Design for Parallelization

謝辞

中村壮伸さんにIrving-Kirkwoodによる微視的圧力定義、およびEuler-Maruyamaの方法を教えていただきました。

参考文献

• 大学演習「熱学・統計力学」 久保亮五編 裳華房
• Tuckerman教授(NYU)の講義ノート