Theoretical Principles & Computational Physics Guide
User Defined Functions: Modular Programming & Force Law Abstraction
Dr. Alorika Chatterjee & Dr. Anirban Shaw
Science & Physics Learners
Python 3 / NumPy / SciPy
1. Core Principles & Theoretical Framework
Modular Abstraction: Encapsulates physical force laws, potentials, and numerical algorithms into reusable functions.
Pure Functions: Clean functional design where outputs depend strictly on arguments prevents global variable bugs.
Higher-Order Functions: Pass physical force functions directly into general ODE solvers (Euler, RK4).
2. Mathematical Formulation & Algorithmic Pipeline
Force law function mapping state coordinates to physical acceleration:
$$ \mathbf{f}: (\mathbf{r}, \mathbf{v}, t) \mapsto \mathbf{a} = \frac{\mathbf{F}(\mathbf{r}, \mathbf{v}, t)}{m} $$
3. Numerical Mechanics & Implementation Logic
- Signature Design: Specify explicit physical arguments (e.g.
def lennard_jones(r, eps=1.0, sigma=1.0):). - Docstrings & Units: State physical units (SI, atomic units, normalized) clearly in function docstrings.
- Multiple Returns: Return composite quantities (energy, force, status) as clean tuples.
4. Relevant Computational Practice Exercises
Exercise 1
Write a function computing the Lennard-Jones interatomic force $F(r) = -dV/dr$ and another for its potential $V(r)$.
Exercise 2
Create a general numerical derivative function <code>diff(f, x, h=1e-5)</code> using the central difference stencil.
Exercise 3
Build a modular function that solves for the terminal velocity of a falling sphere in viscous fluid with Stokes drag.
- Hans Petter Langtangen, "A Primer on Scientific Programming with Python", Springer (2016).