MSc in Physics & Mathematics · University of Granada, Spain
I am a physics and mathematics student with a strong interest in computational methods for physical systems. My main research areas are:
🔵 Computational Electromagnetics — integral equation methods, scattering, wave propagation
🟢 Monte Carlo Methods — stochastic simulation, diffusion MC, particle-in-cell
🔴 Numerical Methods in general — spectral methods, finite differences, integrators, FFT
I enjoy working at the intersection of mathematical rigour and physical intuition, building solvers from scratch and comparing them with theoretical predictions.
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Collisionless-Plasma-Vlasov-Maxwell Semi-Lagrangian schemes and Particle-in-Cell (PIC) Monte Carlo for the 1D Vlasov–Maxwell system. Simulates Weibel (electromagnetic) and two-stream (electrostatic) plasma instabilities. Implements Strang splitting with cubic Catmull–Rom interpolation and FFT-based Poisson solver. |
Two-stream instability: exponential growth of the electric field and electrostatic energy |
Radar cross section of a 2D PEC cylinder — MFIE vs analytical solution |
MoM-electromagnetic-scattering Method of Moments implementation of EFIE and MFIE for electromagnetic scattering by PEC bodies. Solves 2D cylinder (pulse and triangular basis) and 3D sphere (RWG basis functions). Validated against analytical Mie series. |
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Diffusion-Monte-Carlo-for-harmonic-bosons Diffusion Monte Carlo (DMC) simulation of |
Ground-state energy distribution for N=100 bosons — importance-sampling DMC |
Gaussian wave packet scattering off a rectangular barrier |
Cayley (Crank–Nicolson) integrator for the 1D time-dependent Schrödinger equation. Exact norm conservation, transmission coefficient |
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Chebyshev-Spectral-Galerkin-Helmholtz Chebyshev spectral–Galerkin discretisation of the 2D Helmholtz equation. Includes full theoretical derivation of the weak formulation, construction of basis functions satisfying Dirichlet BCs, Kronecker-product matrix assembly, and exponential convergence study. |
Exponential (spectral) convergence of the Chebyshev–Galerkin method |
Protoplanetary disk formation via inelastic collisions — N-body simulation |
Verlet-algorithm-applied-to-molecular-and-planetary-dynamics Velocity-Verlet N-body integrator (Numba-accelerated) for the Solar System, planet-formation via inelastic collisions, and 2D Lennard-Jones molecular dynamics. Tracks energy conservation, radial distribution function, and temperature equilibration. |
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Quantum-transport-nanoelectronics Quantum transport simulation in 1D nanostructures: particle-in-a-box, double-well potential, and ballistic MOSFET I–V characteristics. Solves the Schrödinger equation self-consistently with quantum confinement effects and computes conductance vs gate voltage. |
MOSFET I–V family of curves with quantum confinement |
Spacecraft escape trajectory in the Earth–Moon rotating frame |
Earth-Moon-Spacecraft-restricted-three-body Numerical integration of the circular restricted three-body problem (CR3BP) in the Earth–Moon system. Explores Lagrange points, Jacobi integral conservation, spacecraft transfer orbits, and chaotic meteorite trajectories. |
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Critical-and-Cooperative-Phenomena-Simulations Monte Carlo simulations of critical phenomena: KPZ universality class, scaling collapse, and wetting dynamics. Extracts critical exponents via finite-size scaling and validates against theoretical predictions of the KPZ universality class. |
Interface width variance vs time — KPZ universality class (RDSR model) |
Quantum harmonic oscillator ground state via imaginary-time FFT propagation |
Self-contained recursive and iterative FFT implementations validated against analytical DFTs and NumPy. Applied to the quantum harmonic oscillator via FFT-based split-operator imaginary-time propagation. Includes performance benchmarks. |
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Stochastic-Evolutionary-Game-Theory Monte Carlo simulation of evolutionary dynamics in finite populations. Computes fixation probabilities and fixation times for different game-theoretic payoff matrices, comparing stochastic results with analytical predictions from the Moran process. |
Fixation probability vs initial frequency — Monte Carlo vs analytical Moran process |
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MOSFET-1f-Noise-Characterization Experimental characterization of 1/f (flicker) noise in a MOSFET using an HP 35670A FFT spectrum analyzer. Extracts oxide trap density |
Drain current noise spectra S_Id(f) for 20 gate bias points showing 1/f behaviour |
Full FRAM operation: Write → Wait → Read — voltage, polarisation and current readout |
FRAM-Ferroelectric-Memory-Simulation Numerical simulation of a ferroelectric RAM (FRAM) cell based on HfO₂ using the Landau-Devonshire free energy and Landau-Khalatnikov polarisation dynamics. Simulates the P-E hysteresis loop, Write → Wait → Read operation, and the ferroelectric phase transition P_r(T) near the Curie temperature. |
Typical spin configurations of the 2D Ising model at six temperatures spanning the phase transition |
Monte Carlo simulation of the 2D Ising model with Metropolis and Glauber dynamics. Validates observables against exact analytical solutions (J = 0) and the Onsager exact solution (J ≠ 0). Tracks the ferromagnetic phase transition at |
FDTD 2D: PML absorbs the wave (top) vs PEC reflections (bottom) at six time steps |
FDTD-PML-Absorbing-Boundary-Conditions FDTD solvers for the 1D and 2D electromagnetic wave equations with Perfectly Matched Layer (PML) absorbing boundary conditions. Implements the Gedney polynomial conductivity profile with correct staggered-grid treatment and full 2D corner handling (σ = σ_x + σ_y). Validates reflection against theoretical |
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Three themes of dynamics on complex networks. Neural networks: McCulloch–Pitts logic gates, Hodgkin–Huxley conductance-based neuron (full 4D and reduced 2D), FitzHugh–Nagumo excitability, Tsodyks–Markram dynamic synapses, and Hopfield attractor memory with finite-temperature phase transition at T_c = 1. Social dynamics: voter model on Watts–Strogatz and Barabási–Albert networks, Abrams–Strogatz language competition. Ecological networks: niche model of food webs, trophic coherence, and May stability criterion. |
Hopfield attractor network: overlap m(T) vs temperature showing phase transition at T_c = 1 |
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Lattice Monte Carlo simulation of quantum mechanics in Euclidean (imaginary) time, following Creutz & Freedman (1981). Computes ground-state wavefunctions, energy levels, effective potentials, and instanton kink configurations in the double-well potential. Validated against Blankenbecler-DeGrand-Sugar benchmark. Numba JIT-compiled. |
Single instanton kink: Metropolis path transitioning between double-well minima vs analytical tanh solution |
ID–VD output curves for V_G = 0.3, 0.6, 0.9, 1.2 V — triode and saturation regions |
2D TCAD drift-diffusion simulation of a 180 nm n-channel MOSFET (Synopsys Sentaurus). Generates full I–V characterisation (ID–VG, ID–VD), extracts V_T, SS, g_m, I_ON/I_OFF, DIBL, and optimises the gate metal work function across four variants to maximise I_ON/I_OFF. |
University of Granada · Faculty of Sciences · Academic Year 2025/2026