Unit 2976: Computational Physics

1. Introduction to Computational Physics

• Definition and scope of computational physics
• Historical development and milestones
• Importance of computational methods in modern physics
• Applications across various scientific fields (astrophysics, condensed matter, biophysics, etc.)

2. Numerical Methods in Computational Physics

2.1 Finite Difference Methods

• Concept and derivation
• Stability and convergence considerations
• Applications in solving partial differential equations

2.2 Numerical Integration

• Techniques: trapezoidal rule, Simpson's rule, Gaussian quadrature
• Error analysis and adaptive integration

2.3 Root Finding Algorithms

• Bisection method, Newton-Raphson method, Secant method
• Convergence criteria and practical considerations

2.4 Numerical Solutions of Differential Equations

• Euler’s method, Runge-Kutta methods
• Boundary value problems and shooting methods

3. Monte Carlo Methods

• Fundamentals of Monte Carlo simulations
• Random number generation and statistical sampling
• Applications in statistical physics (e.g., Ising model)
• Use in quantum mechanics and other physics domains

4. Molecular Dynamics Simulations

• Principles of molecular dynamics
• Algorithms: Verlet integration, velocity Verlet, leapfrog
• Force fields and interatomic potentials
• Applications in materials science and biophysics

5. Quantum Monte Carlo Methods

• Overview of quantum Monte Carlo techniques
• Solving the Schrödinger equation using stochastic methods
• Variational and diffusion Monte Carlo
• Applications in condensed matter physics and quantum chemistry

6. Computational Fluid Dynamics (CFD)

• Introduction to CFD and governing equations (Navier-Stokes)
• Numerical methods: finite volume, finite element, finite difference
• Simulation of fluid flow, heat transfer, and turbulence
• Applications in aerodynamics, meteorology, and engineering

7. High-Performance Computing in Physics

• Role of supercomputers in simulations
• Parallel computing paradigms (MPI, OpenMP)
• Optimization strategies for computational efficiency
• Case studies: large-scale simulations and modeling complex systems

8. Data Analysis and Visualization in Computational Physics

• Techniques for statistical analysis of simulation data
• Data processing pipelines and error estimation
• Visualization tools and libraries (e.g., Matplotlib, ParaView)
• Effective presentation and interpretation of computational results