Pavel Kramarenko-Byrd

Dynamics of the Lambert W Newton Iteration: Basin Geometry, Routing Transitions, and Finite-Rank Period-Three Resonance

We study the global dynamics of Newton's method for the Lambert equation. In the coordinate u = −w, Newton's method for w exp(w) = −α is Nα(u) = (u² − α exp(u))/(u − 1), and inversion u = α/z conjugates it exactly to the Newton map of Cα(z) = z − exp(−α/z). The closed form gives...

A Dynamical Bridge from Tearing-Mode Torque Balance to Forced Kuramoto Dynamics: Coherent Forcing Geometry and Mode Locking

Mode locking of tearing modes is a major precursor to tokamak disruptions. We show that the overdamped torque balance for a tearing-mode island interacting with an error field is exactly the Adler phase-locking equation and, for multiple resonant surfaces, has the form of a heter...

A Dynamical Bridge from Tearing-Mode Torque Balance to Forced Kuramoto Dynamics: Coherent Forcing Geometry and Mode Locking

Mode locking of tearing modes is a major precursor to tokamak disruptions. We show that the overdamped torque balance for a tearing-mode island interacting with an error field is exactly the Adler phase-locking equation and, for multiple resonant surfaces, has the form of a heter...

Chiral Spectral Confinement and Parity-Resolved Evans-Zero Asymptotics for Singular Sturm–Liouville Problems

We study singular non-self-adjoint Sturm–Liouville differential expressions on a bounded interval, -ψ'' + Vψ + im(Aψ' + Bψ), m a nonzero integer, with real V, A, B. Finite-energy endpoint selection annihilates the boundary flux and yields Im λ = -(m/2)⟨A' - 2B⟩_ψ for every two-si...