Physi

Computational physics experiments — vector calculus, complex analysis, dynamical systems, and more.

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Gallery

🧲 Stokes & Divergence Theorems

Magnetic dipole field — a quiver plot of B in the xz-plane, computed from the vector potential and verified against Stokes' theorem.

Purely radial field, strongest at the poles, vanishing at the equator — classic dipolar morphology.

Wave function cross-sections — slices through 3D quantum states reveal nodal surfaces and symmetry patterns.

Left: xz-plane cut of the |n=6⟩ state. Right: 3D isosurface of the |3,2,0⟩ hydrogen orbital.

🔢 Complex Analysis

Cauchy–Riemann orthogonality — level curves of the real and imaginary parts of an analytic function intersect at right angles everywhere.

Conformal mapping — the Joukowsky transform maps circles to airfoil-like curves.

Left: sixth roots of -64 in the Argand plane. Right: images of circles under the Joukowsky map.

🎯 Double Pendulum

Chaotic trajectory — the path of the second mass never closes, a signature of deterministic chaos.

🌊 Brownian Motion

3D random walk — 10⁴ steps of a Wiener process in three dimensions.

🔗 Coupled Oscillators

Two masses, three springs — normal modes and energy sloshing between the two bodies.

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Project structure

physi/
├── images/                  # README images & GIFs
├── src/physi/
│   ├── brownian/           # Brownian motion (1D, 2D, 3D)
│   ├── coupled_mas/        # Coupled spring-mass system
│   ├── double_pendulum/    # Manim double pendulum animation
│   ├── magnetic_field/     # Magnetic field computation
│   ├── vector_fields/      # Vector field visualization
│   ├── curricular/
│   │   ├── mathematics_methods_lab_01/   # ODEs
│   │   ├── mathematics_methods_lab_03/   # Complex analysis, catenary, pendulum
│   │   └── mm_lab_04/                    # Stokes, divergence, magnetic potential
│   └── ...                 # DFT, KANs, Monte Carlo, optics, splines, wave functions
└── pyproject.toml

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_{Python · NumPy · SciPy · Matplotlib · SymPy · Manim · Typst}

Testing