Computer-Assisted Proofs and Coherent Shear Drift in Hasegawa-Wakatani Dynamics
Document Type
Presentation
Location
Math Conference Room: College of Arts and Sciences
Start Date
10-2-2026 12:00 PM
End Date
10-2-2026 1:00 PM
Description
Numerical simulations of nonlinear partial differential equations can produce coherent structures that are reproducible, dynamically organized, and have small numerical residuals, yet may not approximate any solution of the intended continuum problem. This talk presents a computer-assisted proof program for distinguishing verified finite-dimensional structures from continuum-relevant solutions motivated by the Hasegawa-Wakatani drift-wave model on the torus. The broader goal is to understand when a discrete plasma model contains genuine solutions of the numerical system that are nevertheless spurious from the point of view of the continuum equations, and when time-dependent coherent structures observed in simulations can be sharpened toward objects suitable for rigorous validation. As a first example, we study dynamically stable spurious solutions of a discretized steady Hasegawa-Wakatani problem. These solutions can be certified as exact solutions of the finite-dimensional system, while continuum energy estimates exclude nearby nontrivial smooth steady states. A second part investigates a time-dependent coherent vorticity drift that is better modeled by a smooth-shear finite-time recurrence, than by a global periodic or relative-periodic orbit. In this representation, upper and lower regions of the torus undergo opposite toroidal drift, with the recurrence modeled by a position-dependent shear shift.
Computer-Assisted Proofs and Coherent Shear Drift in Hasegawa-Wakatani Dynamics
Math Conference Room: College of Arts and Sciences
Numerical simulations of nonlinear partial differential equations can produce coherent structures that are reproducible, dynamically organized, and have small numerical residuals, yet may not approximate any solution of the intended continuum problem. This talk presents a computer-assisted proof program for distinguishing verified finite-dimensional structures from continuum-relevant solutions motivated by the Hasegawa-Wakatani drift-wave model on the torus. The broader goal is to understand when a discrete plasma model contains genuine solutions of the numerical system that are nevertheless spurious from the point of view of the continuum equations, and when time-dependent coherent structures observed in simulations can be sharpened toward objects suitable for rigorous validation. As a first example, we study dynamically stable spurious solutions of a discretized steady Hasegawa-Wakatani problem. These solutions can be certified as exact solutions of the finite-dimensional system, while continuum energy estimates exclude nearby nontrivial smooth steady states. A second part investigates a time-dependent coherent vorticity drift that is better modeled by a smooth-shear finite-time recurrence, than by a global periodic or relative-periodic orbit. In this representation, upper and lower regions of the torus undergo opposite toroidal drift, with the recurrence modeled by a position-dependent shear shift.