| title | Analytical Physics Models |
|---|---|
| emoji | ⚛️ |
| colorFrom | blue |
| colorTo | purple |
| sdk | docker |
| app_port | 7860 |
| pinned | false |
Python and Julia simulations of analytical physics models combining rigorous mathematical derivations with computational visualizations of classical and modern systems.
This repository is a collection of physics models implemented from first principles. Each model is derived mathematically and then simulated computationally, with the goal of bridging theoretical understanding and numerical experimentation.
Tools used across simulations: NumPy, Matplotlib,Gaussian ,Psi4 ,Julia,etc.
| Model | Description | Key Concepts |
|---|---|---|
| Particles in a Box | Quantum mechanical simulation of a particle in a 1D infinite square well. The Hamiltonian is discretized on a grid and diagonalized to yield energy eigenvalues and wavefunctions numerically. | Schrödinger equation, matrix diagonalization, energy quantization, wavefunctions |
| Ideal Electron | Simulation of electron transport using the Drude model. Electrons are accelerated by an external field and scattered with mean free time τ, reproducing drift velocity, conductivity, and the Einstein relation. | Drift-diffusion, Maxwell-Boltzmann distribution, conductivity, Einstein relation |
| MD Simulations | Molecular dynamics of N particles interacting via the Lennard-Jones potential, integrated with the velocity Verlet algorithm inside a reflective box. | Velocity Verlet integrator, Lennard-Jones potential, energy conservation, reflective boundary conditions |
| Ising Model | 2D Ising model evolved using the Metropolis algorithm. Tracks magnetization and specific heat across temperatures to locate the phase transition at T_c ≈ 2.27 J/k. | Metropolis algorithm, spin systems, phase transitions, statistical mechanics |
| Monte Carlo Methods | Several Monte Carlo techniques: standard MC, Metropolis-Hastings (MHMC), importance sampling, and inverse transform sampling — demonstrated on π estimation and distribution fitting. | MHMC, importance sampling, inverse transform sampling, variance reduction |
| Hamiltonian Chaos | Julia simulation of the Hénon-Heiles system using the Störmer-Verlet symplectic integrator. Poincaré sections reveal the transition from ordered KAM tori to chaotic trajectories as energy increases. | Symplectic integration, Poincaré sections, KAM theorem, Hamiltonian chaos |
| Fourier Analysis | Brute-force discrete Fourier transform and FFT applied to a Gaussian, verifying that the FT of a Gaussian is a Gaussian and comparing computational cost of both approaches. | DFT, FFT, spectral analysis, Gaussian transform |
| Electrodynamics | Interactive 3D visualization of equipotential surfaces generated by two point charges. A matplotlib slider sweeps the potential value, updating the surface in real time. | Coulomb potential, equipotential surfaces, superposition |
| Discrete Dynamics | Logistic map bifurcation diagram revealing the period-doubling route to chaos as the growth parameter r varies from 2.5 to 4.0. | Logistic map, bifurcation, period-doubling, deterministic chaos |
| Calculating Activation and Reaction Energy | Activation and reaction energy calculations for an SN2 reaction using Hartree-Fock and DFT methods in Gaussian. Log files and analysis scripts included. | Potential energy surfaces, transition state theory, HF, DFT |
| Modelling Using VMD | Visualization of molecular orbitals and water cluster geometries using VMD and PyMOL. Includes cube files for HOMO/LUMO of water and a 108-molecule water simulation. | Molecular orbitals, HOMO/LUMO, VMD, PyMOL |
Ideal_Electron/3dhist.py
|
Calculating_Activation.../report.pdf
|
Monte_Carlo_Methods/estimate_Gaussian.py
|
Modelling_using_VMD/Water_Orbitals/Cube_Files
|
MIT — see LICENSE