A small constellation of standalone sites — each hosted at its own subdomain, each its own self-contained piece of work. Physics landscapes, atmospheric data, n-body algebra, and the occasional infrastructure dashboard.
*.briansheppard.com · static / S3 + CloudFront · updated 2026-04-25
Personal landscape exploration of whether the Alcubierre warp-drive metric can be realised with classical matter inside a Fuchs-style positive-energy shell. Includes the κβ/C scaling result, six adjacent slices, Fell–Heisenberg multi-mode shift, and an independent Warp Factory MATLAB reproduction.
A universal dimension sequence for the n-body Poisson algebra: symbolic rank sweeps, composite-potential exponent scans, helium atlas comparisons, and Bell / contextuality test results across N = 3…10 configurations.
Live regional health board for the personal AWS estate. Region cards, canary status, and rolled-up infrastructure ground-truth across deployed services. Auto-refreshing terminal-style dashboard.
Exact symbolic computation of the Lie algebra generated by the three pairwise interaction Hamiltonians of the planar Newtonian three-body problem under the Poisson bracket. Proves the dimension sequence 3, 6, 17, 116 for the first four bracket levels and a numerical lower bound d(4) ≥ 4,501, establishing super-exponential (infinite Gelfand–Kirillov) growth. The sequence is invariant under mass-ratio changes and identical for the Newtonian (1/r) and Calogero–Moser (1/r²) potentials, while the integrable harmonic potential stabilises at dimension 15 — exposing a sharp structural dichotomy driven by the singularity class of the potential rather than integrability.
A topological-complexity approach to coordinating two robots on a figure-eight track without collisions. Configuration-space invariants relate motion-planning instabilities to the topology of the workspace; we show the topological complexity of the problem is 3 and construct an explicit algorithm with three continuous instructions. Published in the PUMP Journal of Undergraduate Research, vol. 6, 224–249.