Specialty
A new arXiv preprint gives a positive answer to a partition question about sets of nice recurrence. The result is a theorem about abstract mathematical systems, not an experiment or a measured effect.
Scientific publication4 min read
A numerical study of a one-dimensional shallow-water model found that a dissipative run produced a dominant soliton in each direction of propagation. The modeled crest-height ratio was about 3, above the study’s reported criterion of greater than 1.25.
Scientific publication6 min read
A computational study tested ensembles of randomly constructed reservoir computers in three deterministic chaotic systems. It reported a roughly 25-step Hénon-map ensemble horizon and Lorenz 96 ensemble forecasts that remained successful for at least 2.5 Lyapunov times. Performance-weighted averaging outperformed plain averaging.
Scientific publication3 min read
A mathematical preprint gives a positive answer to a question in ergodic theory: every free ergodic probability-measure-preserving action of a free group has an orbit-equivalent representative that is totally weak mixing. The result is existential and theoretical; it does not settle whether the representative can be made mixing.
Scientific publication4 min read
A new arXiv preprint presents a mathematical framework for constructing generalized coherent states in quantum billiards. It projects a minimal-dispersion wave packet onto continued eigenstates and develops analytical and numerical routes for studying the result. The work remains a formal construction, with no independent validation of its accuracy or long-term behavior.
Scientific publication3 min read
A new arXiv preprint reports that phase-space flux calculations closely tracked average flip rates in a simulated equal-mass, equal-arm double pendulum. The result supports a statistical prediction of event rates within the tested model, while leaving questions about regular motion, broader pendulum designs and higher energies.
Scientific publication4 min read
A new arXiv preprint gives arithmetic proofs that the parabolic multiplicity at 0 is 1 for a quadratic polynomial and an entire map at primitive root-of-unity parameters. It extends the polynomial argument to unicritical maps of arbitrary degree, but some valuation patterns remain conjectural and one computer-assisted exceptional case is reported without computational details.
Scientific publication5 min read