Projects

The hydrogen atom

From L1–L2 exercises, Python

The radial Schrödinger equation solved with finite differences as a tridiagonal eigenvalue problem: the levels depend on $n$ only, as the Coulomb potential predicts, and match Bohr's $E_n = -\frac{13.6\,\mathrm{eV}}{n^2}$ within $0.6\,\mathrm{meV}$. The s, p and d orbitals are drawn from the exact wave functions, whose radial parts agree with the numerical ones.

The H₂ molecule: bond and vibrations

From L2–L3 exercises, Python

The bond of $\mathrm{H}_2^+$ with LCAO orbitals (bonding $\sigma_g$, antibonding $\sigma_u$), and the vibrational levels of $\mathrm{H}_2$ in a Morse potential: all 18 bound levels match the exact Morse spectrum within $0.21\,\mathrm{meV}$, and crowd together towards dissociation where the harmonic picture fails.

Quantum tunnelling of a wave packet

Personal project, Python

A Gaussian wave packet hits a square barrier. The 1D time-dependent Schrödinger equation is solved with the split-step Fourier method, which conserves the norm to machine precision, and the transmitted probability is checked against the exact plane-wave result averaged over the packet's momentum distribution: they agree within $4\,\%$ from $\frac{E}{V_0}$ = 0.1 to 1.5.

The 2D Ising model

Bachelor's lab (L3), rewritten in Python

The ferromagnetic transition with the Metropolis algorithm on a $48\times48$ lattice, updated as a checkerboard with numpy. Below $T = 2.1$ the magnetisation matches Onsager's exact solution to better than 0.01; near $T_c = 2.269$ the finite lattice rounds the transition.

Molecular dynamics of liquid argon in C++

Master's project (M1), numerical modelling in C++

$N$ argon atoms in a periodic box interacting through a Lennard-Jones potential, with four integrators to compare (Euler, Verlet, leapfrog, Runge–Kutta 4), a thermostat and simulated annealing. Verlet keeps the total energy within $4\times10^{-4}\,\%$ over $10\,\mathrm{ps}$, the speeds follow Maxwell–Boltzmann, and $g(r)$ shows the first-neighbour shell of a liquid at $3.7\,\mathrm{Å}$.

The solar system as an N-body problem

Personal project, Python

The Sun and the eight planets integrated with velocity Verlet over one orbit of Neptune, in astronomical units ($G = 4\pi^2$). The periods follow Kepler's third law within $0.2\,\%$, the gap being the planets' pull on each other, and the energy stays within $7\times10^{-7}$ over 170 years where explicit Euler loses $2\,\%$ in 10.

The nonlinear pendulum

From an L2 Python exercise

The pendulum without the small-angle approximation, integrated at a relative tolerance of $10^{-11}$: the period matches the elliptic-integral formula to six digits and diverges as the amplitude reaches 180°. The phase portrait separates oscillations from full rotations, and a damped trajectory crosses the separatrix.

The magnetic field of a solenoid

From an L2 Python exercise

The field of a finite solenoid everywhere in space, as a sum of 40 loops whose Biot–Savart field is written with elliptic integrals. On the axis it matches the current-sheet formula within $0.2\,\%$; at the centre it is $7\,\%$ below the infinite-solenoid value, since a coil six radii long leaks field at its ends.

Attenuation of gamma rays

Bachelor's lab (L3), nuclear physics

$^{137}\mathrm{Cs}$ and $^{22}\mathrm{Na}$ gammas through aluminium and copper plates, measured with a NaI scintillator. Beer–Lambert fits of the photopeak give attenuation coefficients within $6\,\%$ of the NIST XCOM values, falling with energy as Compton scattering takes over from the photoelectric effect.

Machine learning to sample the pMSSM

From my M1 internship, Python and numpy

Most random points of the 19-parameter pMSSM give no physical spectrum: only $32\,\%$ pass SOFTSUSY. A neural network written in plain numpy (backpropagation by hand, Adam) learns which ones survive, with a ROC AUC of 0.90: keeping the best-scored half doubles the valid fraction and loses fewer than one valid point in ten. Of the valid points, $11\,\%$ have a lightest Higgs boson within $3\,\mathrm{GeV}$ of the measured $125.1\,\mathrm{GeV}$.

Finding GW150914 with a matched filter

Personal project, Python, LIGO open data

The first binary black-hole merger recovered from the public LIGO strain with numpy only: noise spectrum estimated from the data, whitening, and a matched filter over a bank of inspiral chirps. The network SNR peaks at 9.9, Livingston sees it $6.3\,\mathrm{ms}$ before Hanford, and the best chirp mass, 32 $M_\odot$, is close to the catalogue's 31 $M_\odot$ in the detector frame.

Neutrino oscillations

From my L3 internship, Python

Three-flavour oscillations from the PMNS matrix, checked against unitarity and the closed-form reactor survival to $10^{-12}$, up to the spectrum a reactor experiment like JUNO measures at $52.5\,\mathrm{km}$: the fast wiggles shift between the normal and inverted mass orderings.

2048 as a Python package

Personal project

The 2048 game as an installable Python package: a D2048 class for a board of any size, move prediction and end-of-game detection, tests with pytest, a jeu2048 command, and a documentation site.

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