PREPRINT
Minimal Winding in the Self-Similar Collapse of Point Vortices
Sharp winding bounds and computer-assisted results for collapsing vortex configurations.
INDEPENDENT SCIENCE / RESEARCH PAPERS
Papers and research notes
Research in mathematics, fluid dynamics, dynamical systems, and computational neuroscience. Each paper links to an archived preprint and its supporting code or evidence.
These papers are preprints and have not yet been peer reviewed. Their claims and computer-assisted results should be assessed within the assumptions and limits stated in each paper.
Fluid dynamics
PREPRINT
Point-Vortex Collapse Without Rotation: A Cluster Mechanism, a Phase Diagram and a Continuum Limit
Cluster mechanisms and numerical phase diagrams for vortex collapse without rotation.
PREPRINT
Stable Self-Similar Expansion of Four and Five Point Vortices and Confinement of Vortex Patches
Computer-assisted configurations, nonlinear stability, and confinement estimates.
Neuroscience
PREPRINT
A Finite Rank Window Cannot Show That a Neural Population Code Satisfies the Eigenspectrum Smoothness Bound
The limits of inferring asymptotic smoothness from finite neural eigenspectra.
PREPRINT
Hopf Bifurcations and Bistability in the Hodgkin-Huxley Equations at the 1952 Parameters: Computer-Assisted Proofs
Computer-assisted analysis of equilibrium stability and bistability in the classical model.
PREPRINT
Traveling Pulses in a Neural Field with a Smooth Firing Rate: Computer-Assisted Existence and Spectral Stability
Computer-assisted pulse existence and spectral stability in neural field models.
PREPRINT
The Propagated Action Potential of Hodgkin and Huxley at Their 1952 Constants: A Computer-Assisted Existence Proof
A computer-assisted existence proof for the propagated action potential at two temperatures.
Dynamical systems
PREPRINT
Chaos and Analytic Non-Integrability of the Classical Double Pendulum: A Computer-Assisted Proof
Interval arithmetic proofs for chaotic dynamics at specified energies.
Cardiac electrophysiology
PREPRINT
Stable Rotating Waves in Rings of a Modified Ventricular Cell Model: Computer-Assisted Proofs
Computer-assisted proofs of stable rotating waves in rings of a ventricular cell model.
Cryptography
PREPRINT
Excluding Classical Cipher Families for the 1939 D'Agapeyeff Challenge: Key-Free Counts and Searches with Demonstrated Power
Which classical cipher families the 1939 D’Agapeyeff challenge excludes, by key-free counts and by searches with demonstrated power. No reading is claimed.
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