Science
Interactive browser demonstrations of key computational methods from my doctoral, master's, and engineering theses: spectral wave–vortex decomposition in ocean models, Lorentz trajectory integration in a Penning trap, and spectral clustering on non-linear manifolds.
Ph.D. / CICESE · Ensenada, Mexico · 2018 – 2023
On the interaction between balanced motions and internal gravity
waves in Eastern Boundary Currents.
The ocean's kinetic energy is carried by two populations with completely different
dynamics — slow, nearly-geostrophic balanced motions (eddies and
jets) and fast internal gravity waves. They occupy the same water,
so no map can separate them. The wavelength–frequency plane can.
A mode-1 internal wave has to satisfy its dispersion relation, which puts a hard floor under the wave band at the inertial frequency f:
Nothing below that curve can be a freely propagating gravity wave, so everything below it is balanced motion. Because f scales with sin φ, the boundary moves with latitude — which is exactly why a global simulation needs the filter re-derived rather than applied once.
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RELATED — production applications of similar techniques: a ~20k-simulation coastal digital twin and an operational forecast pipeline.
Applied / Numerical ocean modelling
Profiling model performance, maintaining physical and numerical validity, and building automated execution pipelines for operational forecasting.
REFERENCE — re-engineered particle core in Fortran/OpenMP
REFERENCE — ~20k simulations scheduled and reduced
REFERENCE — daily operational forecast products
REFERENCE — CI-guarded numerics in IH-TESEO
M.Sc. / CINVESTAV-IPN · Mexico City · 2011 – 2013
Penning trap in a rotating magnetic field and its coherent
states.
A quantum-mechanical study of a charged particle in an ideal Penning trap with an
additional rotating field: I derived its coherent states, ladder operators and
eigenvalues, then validated the time evolution of position and momentum
numerically. The simulation below is that validation step — the classical trajectory,
integrated live with RK4.
The trap's electrostatic quadrupole confines along z but pushes the particle outwards radially. Only the axial magnetic field holds it in — so the trap works exactly when the cyclotron frequency beats the axial one:
Raising ωz beyond this threshold destabilises the radial confinement, demonstrating the operational boundary of the trap.
Integrated with classical RK4 at Δt = 0.005, eight substeps per frame, in non-dimensional units. The radial trace is the familiar epitrochoid: a slow magnetron drift carrying a fast cyclotron gyration, modulated here by the rotating field.
B.Eng. / UPIITA-IPN · Mexico City · 2006 – 2011
A quantum data clustering algorithm based on spectral
theory.
I designed a quantum variant of spectral clustering with theoretically
constant runtime — a unitary operator built from the image's symmetric
Laplacian matrix — and demonstrated it on image segmentation with classical k-means
as post-processing. Below is the classical core of that method, computed here, with
plain k-means run on the same points for comparison.
Because the two interleaved crescents are not linearly separable, standard k-means fails to separate them and cuts through both moons. Spectral clustering builds a similarity graph and partitions the data using the graph Laplacian's eigenvectors.
The second eigenvector is the whole trick — and it is exactly the step my thesis replaced with a unitary operator. Everything around it stays the same.
When affinity scale σ exceeds ≈ 0.25, edges between the two crescents increase, reducing community separability and demonstrating the parameter sensitivity of spectral graph methods.
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Case studies covering scientific model re-engineering, automated forecasting pipelines, peak event credential verification, and open-source SDK development.