Scientific Computing

5.

Modeling and Simulation in Physics

5.1.

Classical Mechanics

5.1.1.

Newtonian Mechanics

5.1.2.

Lagrangian Mechanics

5.1.3.

Hamiltonian Mechanics

5.1.4.

N-Body Simulations

5.1.4.1.

Gravitational Systems

5.1.4.2.

Planetary Motion

5.1.4.3.

Galaxy Dynamics

5.1.4.4.

Molecular Dynamics

5.1.4.5.

Interatomic Potentials

5.1.4.6.

Lennard-Jones Potential

5.1.4.7.

Coulomb Interactions

5.1.4.8.

Time Integration Algorithms

5.1.4.9.

Verlet Algorithm

5.1.4.10.

Velocity-Verlet Algorithm

5.1.4.11.

Leapfrog Algorithm

5.1.5.

Simulating Oscillators and Chaotic Systems

5.1.5.1.

Simple Harmonic Oscillator

5.1.5.2.

Damped Oscillator

5.1.5.3.

Driven Oscillator

5.1.5.4.

Double Pendulum

5.1.5.5.

5.1.5.6.

Sensitivity to Initial Conditions

5.1.5.7.

Lyapunov Exponents

5.2.

Electromagnetism

5.2.1.

Maxwell's Equations

5.2.2.

5.2.3.

5.2.4.

Electromagnetic Waves

5.2.5.

Solving Maxwell's Equations

5.2.5.1.

Discretization Techniques

5.2.5.2.

Boundary Conditions

5.2.6.

Finite-Difference Time-Domain Method

5.2.6.1.

Grid Construction

5.2.6.2.

Time-Stepping Algorithms

5.2.6.3.

Absorbing Boundary Conditions

5.2.7.

Particle-in-Cell Simulations

5.2.7.1.

Particle Motion

5.2.7.2.

5.2.7.3.

Plasma Physics Applications

5.3.

Quantum Mechanics

5.3.1.

Schrödinger Equation

5.3.2.

Wave Functions and Observables

5.3.3.

Solving the Schrödinger Equation

5.3.3.1.

Time-Independent Equation

5.3.3.2.

Eigenvalue Problems

5.3.3.3.

Time-Dependent Equation

5.3.3.4.

Time Evolution Algorithms

5.3.3.5.

Split-Operator Method

5.3.4.

Variational Methods

5.3.4.1.

Trial Wavefunctions

5.3.4.2.

Energy Minimization

5.3.4.3.

Rayleigh-Ritz Method

5.3.5.

Perturbation Theory

5.3.6.

Hartree-Fock Method

5.3.6.1.

Self-Consistent Field Iterations

5.3.6.2.

5.3.7.

Density Functional Theory

5.3.7.1.

Exchange-Correlation Functionals

5.3.7.2.

Kohn-Sham Equations

5.3.7.3.

Plane Wave Basis

5.3.8.

Quantum Monte Carlo Methods

5.4.

Statistical Mechanics and Thermodynamics

5.4.1.

Thermodynamic Ensembles

5.4.2.

Partition Functions

5.4.3.

Phase Transitions

5.4.4.

Monte Carlo Methods

5.4.4.1.

Metropolis Algorithm

5.4.4.2.

5.4.4.3.

Acceptance Criteria

5.4.4.4.

Detailed Balance

5.4.4.5.

Simulating the Ising Model

5.4.4.6.

Lattice Construction

5.4.4.7.

Phase Transitions

5.4.4.8.

Critical Phenomena

5.4.4.9.

Wang-Landau Algorithm

5.4.5.

Molecular Dynamics

5.4.5.1.

5.4.5.2.

Integration Algorithms

5.4.5.3.

Thermostats and Barostats

5.4.5.4.

Calculating Thermodynamic Properties

5.4.5.5.

Temperature and Pressure

5.4.5.6.

Radial Distribution Function

5.4.5.7.

Transport Properties

5.5.

Computational Fluid Dynamics

5.5.1.

Fluid Mechanics Fundamentals

5.5.2.

The Navier-Stokes Equations

5.5.2.1.

Incompressible Flow

5.5.2.2.

Compressible Flow

5.5.2.3.

Boundary and Initial Conditions

5.5.3.

Grid Generation and Meshing

5.5.3.1.

Structured Grids

5.5.3.2.

Unstructured Grids

5.5.3.3.

5.5.3.4.

Adaptive Mesh Refinement

5.5.4.

Discretization Schemes

5.5.5.

Turbulence Modeling

5.5.5.1.

Reynolds-Averaged Navier-Stokes

5.5.5.2.

Large Eddy Simulation

5.5.5.3.

Direct Numerical Simulation

5.5.6.

Boundary Layer Theory

5.5.7.

Heat and Mass Transfer

5.6.

Solid Mechanics

5.6.1.

Elasticity Theory

5.6.2.

Finite Element Analysis

5.6.3.

Stress and Strain Analysis

5.6.4.

Fracture Mechanics

5.6.5.

5.7.

Astrophysics and Cosmology

5.7.1.

Stellar Structure and Evolution

5.7.1.1.

Hydrostatic Equilibrium

5.7.1.2.

Nuclear Fusion Processes

5.7.1.3.

Stellar Atmospheres

5.7.2.

Hydrodynamic and Magnetohydrodynamic Simulations

5.7.2.1.

Governing Equations

5.7.2.2.

Numerical Methods

5.7.2.3.

5.7.3.

Large-Scale Structure Formation

5.7.3.1.

Cosmological Simulations

5.7.3.2.

Dark Matter and Dark Energy Models

5.7.3.3.

N-Body Simulations

5.7.4.

Radiative Transfer

5.7.5.

Gravitational Wave Simulations

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