Computational Physics Modelling
10 weeks · 0 milestones
Build a real computational physics model or simulation using numerical methods — finite difference, Monte Carlo, molecular dynamics, or numerical integration of differential equations — implemented in code (Python with NumPy/SciPy, Julia, or equivalent). The proof is the submitted code (must be runnable as-is with documented dependencies), parameters with rationale, numerical outputs, visualisation of results, and a written validation section comparing the model output to an analytical solution or published reference value where one exists. Computational physics modelling is fully accessible — all tools are free and open source. Reviewed by a physicist who runs the submitted code independently to confirm it produces the documented outputs; the reviewer also asks you to modify a specific parameter and predict the outcome, then verify it during the review session.
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3 milestones
Select a specific physical system and the numerical method appropriate for modelling it, then derive the governing equations you will implement. Computational physics modelling is the primary route — no physical laboratory is required. Choose a system with known analytical solutions or published results so that M2 validation is possible: 1D heat equation, planetary orbital mechanics, damped harmonic oscillator, 2D Ising model, Lotka-Volterra predator-prey dynamics, or similar well-characterised systems.
Proof required
Submit a written system specification (the physical system, the governing equation(s) in mathematical form, the boundary conditions, and the initial conditions), your chosen numerical method with a justification for why it is appropriate for this system, and the theoretical derivation showing how the governing equations are discretised for numerical implementation.
What gets checked
- Governing equations are written in standard mathematical notation — not described in words but expressed as differential or integral equations with defined variables and parameters
- Method justification addresses the specific properties of the system that influence the choice — not 'Runge-Kutta is good for ODEs' but why RK4 specifically is appropriate given the stiffness, time scale, and accuracy requirements of this system
- Discretisation derivation shows each step from the continuous equation to the numerical approximation — not just the final finite-difference formula