Molecular Dynamics Method: Theory and Implementation

About this document

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

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

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。