Computational Physics

1. Applications
   1. Quantum Mechanics
      1. Schrödinger Equation Simulations
         1. Time-Dependent Schrödinger Equation Solutions
         2. Time-Independent Schrödinger Equation Solutions
         3. Potential Well and Barrier Simulations
         4. Quantum Harmonic Oscillator
      2. Density Functional Theory (DFT)
         1. Local Density Approximation (LDA)
         2. Generalized Gradient Approximation (GGA)
         3. Hybrid Functionals
         4. Time-dependent DFT
      3. Quantum Monte Carlo Methods
         1. Variational Monte Carlo
         2. Diffusion Monte Carlo
         3. Path Integral Monte Carlo
      4. Quantum Field Theory and Lattice Gauge Theory
         1. Lattice Quantum Chromodynamics (QCD)
         2. Non-Abelian Gauge Theories
         3. Quantum Electrodynamics on a Lattice
         4. Renormalization Group Approaches
   2. Solid State Physics
      1. Electronic Band Structure Calculations
         1. Tight Binding Model
         2. k·p Perturbation Theory
         3. Ab Initio Approaches
         4. Green’s Function Methods
         5. Wannier Functions
      2. Phonon Calculations
         1. Lattice Dynamics
         2. Anharmonic Effects
         3. Phonon Dispersion Curves
         4. Thermal Conductivity Modeling
      3. Molecular Dynamics of Solids
         1. Force Field Development
         2. Atomic Scale Modelling of Crystals
         3. Grain Boundary Dynamics
      4. Spin Dynamics
         1. Micromagnetic Simulations
         2. Spin Wave Theory
         3. Quantum Spin Models
   3. Statistical Mechanics
      1. Microcanonical, Canonical, and Grand Canonical Ensembles
         1. Partition Function Calculations
         2. Thermodynamic Properties Derivation
         3. Fluctuation-Dissipation Theorems
      2. Monte Carlo Simulations
         1. Metropolis Algorithm
         2. Cluster Algorithms
         3. Determining Phase Diagrams
      3. Molecular Dynamics in Soft Matter
         1. Polymer Chain Dynamics
         2. Colloidal Particle Systems
         3. Liquid Crystal Modeling
   4. Fluid Dynamics
      1. Navier-Stokes Equation Simulations
         1. Direct Numerical Simulations (DNS)
         2. Large Eddy Simulations (LES)
         3. Reynolds-Averaged Navier-Stokes (RANS) Simulations
      2. Computational Fluid Dynamics (CFD)
         1. Discretization Techniques
         2. Boundary Layer Analysis
         3. Mesh Generation and Adaptation
      3. Turbulence Modeling
         1. Statistical Theories of Turbulence
         2. LES vs. RANS in Turbulence
         3. Turbulent Jet and Wake Flows
      4. Multiphase Flow Simulations
         1. Volume of Fluid (VOF) Method
         2. Level Set Method
         3. Lattice Boltzmann Methods for Multiphase
   5. Astrophysics
      1. N-body Simulations
         1. Dark Matter Halos Simulation
         2. Galactic Dynamics
         3. Star Cluster Formation
      2. Stellar Evolution Models
         1. Hertzsprung-Russell Diagram Simulations
         2. Nuclear Fusion Processes
         3. Supernova Explosion Modeling
      3. Galaxy Formation and Evolution
         1. Morphological Classification of Galaxies
         2. Merger Histories of Galaxies
         3. Star Formation Rates in Galaxies
      4. Cosmic Microwave Background Analysis
         1. Anisotropy Measurements
         2. Cosmic Inflation Models
         3. CMB Spectrum and Polarization
   6. High Energy Physics
      1. Particle Detector Simulations
         1. Calorimetry Techniques
         2. Tracking and Vertexing
         3. Simulation of Detector Response
      2. Simulation of Particle Collision Events
         1. Event Generators
         2. Parton Distribution Functions
         3. Hadronization Models
      3. Lattice Quantum Chromodynamics (LQCD)
         1. Confinement Phenomena
         2. Meson and Baryon Spectroscopy
         3. Chiral Symmetry Breaking
   7. Plasma Physics
      1. Magnetohydrodynamic Simulations
         1. Stability of Confinement Configurations
         2. Magnetized Plasma Turbulence
         3. Magnetic Reconnection Processes
      2. Particle-in-Cell Simulations
         1. Laser-Plasma Interactions
         2. Space Plasma Environment
         3. High-Frequency Plasma Waves
      3. Fusion Reactions Modeling
         1. Tokamak Plasma Simulation
         2. Inertial Confinement Fusion
         3. Cross-section Calculations in Fusion Reactions