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💻 Computational Statistical Mechanics

Computational Statistical Mechanics for Materials Simulation

📚 5 Chapters 💻 35 Code Examples ⏱️ 100-120 minutes 📊 Intermediate
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🎯 Series Overview

Computational statistical mechanics is a methodology for simulating thermodynamic properties and dynamic behavior of materials using Monte Carlo and molecular dynamics methods. In this series, from Metropolis method, importance sampling, replica exchange method, molecular dynamics method to free energy calculations, you will learn theory and Python implementation in pairs and apply them to materials property prediction.

Learning Path

flowchart LR A[Chapter 1
Monte Carlo Methods] B[Chapter 2
Molecular Dynamics] C[Chapter 3
Replica Exchange] D[Chapter 4
Free Energy] E[Chapter 5
Property Prediction] A --> B --> C --> D --> E style A fill:#667eea,stroke:#764ba2,stroke-width:2px,color:#fff style B fill:#667eea,stroke:#764ba2,stroke-width:2px,color:#fff style C fill:#667eea,stroke:#764ba2,stroke-width:2px,color:#fff style D fill:#667eea,stroke:#764ba2,stroke-width:2px,color:#fff style E fill:#667eea,stroke:#764ba2,stroke-width:2px,color:#fff

📋 Learning Objectives

  • Understand the principles of Metropolis Monte Carlo method and be able to implement it
  • Simulate phase transitions using importance sampling and replica exchange method
  • Understand the fundamentals of molecular dynamics method and simulate atomic systems with Lennard-Jones potential
  • Understand and implement extended ensemble methods
  • Predict materials properties using free energy calculation methods

📖 Prerequisites

Basic knowledge of classical statistical mechanics and fundamentals of numerical computation are required. It is desirable to understand basic Python usage.

Chapter 1
Fundamentals of Monte Carlo Method

Learn the Monte Carlo method, which is fundamental to statistical mechanics calculations. Understand the algorithm of the Metropolis method and the principles of importance sampling, and implement Ising model simulations in Python. Also covers acceptance ratio optimization and ergodicity verification.

Monte Carlo method Metropolis method Importance sampling Markov chain Ising model Ergodicity
💻 7 Code Examples ⏱️ 20-24 minutes
Read Chapter 1 →
Chapter 2
Advanced Sampling Methods

Learn efficient sampling techniques that overcome energy barriers. Understand the principles of Wang-Landau method, multicanonical sampling, and umbrella sampling, and implement density of states calculations and phase transition detection in Python. Also discusses the application ranges and limitations of each method.

Wang-Landau method Multicanonical method Umbrella sampling Density of states Importance sampling Phase transition detection
💻 7 Code Examples ⏱️ 20-24 minutes
Read Chapter 2 →
Chapter 3
Fundamentals of Molecular Dynamics Method

Learn classical mechanical simulations of atoms and molecules. Understand the Verlet integration method and its variants (Leap-frog method, velocity Verlet method), and implement Lennard-Jones system simulations in Python. Also master structural analysis techniques such as radial distribution functions and temperature/pressure control algorithms.

Molecular dynamics method Verlet integration Lennard-Jones Radial distribution function Temperature control Periodic boundary conditions
💻 7 Code Examples ⏱️ 20-24 minutes
Read Chapter 3 →
Chapter 4
Replica Exchange Method and Extended Ensemble Methods

Learn advanced sampling techniques to solve multiple minimum problems. Understand the principles of parallel tempering (replica exchange method), replica exchange MD, and simulated annealing, and implement energy landscape exploration in Python. Also covers applications to materials structure optimization.

Replica exchange method Parallel tempering Simulated annealing Extended ensemble Energy landscape Structure optimization
💻 7 Code Examples ⏱️ 20-24 minutes
Read Chapter 4 →
Chapter 5
Free Energy Calculations and Materials Property Prediction

Learn free energy calculation methods for evaluating thermodynamic stability of materials. Understand thermodynamic integration, Bennett acceptance ratio (BAR method), and free energy perturbation, and calculate materials phase stability and interfacial energy in Python. Also introduces application examples to real materials.

Free energy calculation TI method Bennett method Phase stability Interfacial energy Materials property prediction
💻 7 Code Examples ⏱️ 20-24 minutes
Read Chapter 5 →

📚 Recommended Learning Paths

Pattern 1: Beginner - Theory and Practice Balanced (5-7 days)

Pattern 2: Intermediate - Fast Track (3 days)

Pattern 3: Topic-Focused - Computational Skills (1 day)

🎯 Overall Learning Outcomes

Upon completing this series, you will achieve:

Knowledge Level

Practical Skills

Application Ability

🛠️ Technologies and Tools Used

Main Libraries

Development Environment

Recommended Tools

🚀 Next Steps

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