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pro vyhledávání: '"Goodman, Roy H."'
We introduce a new reduction of the motion of three point vortices in a two-dimensional ideal fluid. This proceeds in two stages: a change of variables to Jacobi coordinates and then a Nambu reduction. The new coordinates demonstrate that the dynamic
Externí odkaz:
http://arxiv.org/abs/2403.10383
Autor:
Goodman, Roy H.
Here we provide a complete English translation of Walter Gr\"obli's 1877 Ph.D. Thesis, together with some notes on the process. The work considers the dynamics of point vortices in a two-dimensional inviscid incompressible fluid and derives a number
Externí odkaz:
http://arxiv.org/abs/2404.01305
We describe QGLAB, a new MATLAB package for analyzing partial differential equations on quantum graphs. The software is built on the existing, object-oriented MATLAB directed-graph class, inheriting its structure and adding additional easy-to-use fea
Externí odkaz:
http://arxiv.org/abs/2401.00561
Autor:
Goodman, Roy H., Behring, Brandon M.
The point vortex system is a system of longstanding interest in nonlinear dynamics, describing the motion of a two-dimensional inviscid fluid that is irrotational except at a discrete set of moving point vortices, at which the vorticity diverges. The
Externí odkaz:
http://arxiv.org/abs/2210.16464
Autor:
Adriazola, Jimmie, Goodman, Roy H.
We address the problem of reshaping light in the Schr\"odinger optics regime from the perspective of optimal control theory. In technological applications, Schr\"odinger optics is often used to model a slowly-varying amplitude of a para-axially propa
Externí odkaz:
http://arxiv.org/abs/2112.00728
Autor:
Adriazola, Jimmie, Goodman, Roy H.
Applications of Bose-Einstein Condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal control is a reliable framework to prepare such a state while avoiding undesirable excitations, and, when applied to th
Externí odkaz:
http://arxiv.org/abs/2111.14266
We consider the existence of spatially localized traveling wave solutions of the mass-in-mass lattice. Under an anti-resonance condition first discovered by Kevrekidis, Stefanov and Xu, we prove that such solutions exist in two distinguished limits,
Externí odkaz:
http://arxiv.org/abs/2002.05573
The study of kink interactions in nonlinear Klein-Gordon models in $1+1$-dimensions has a time-honored history. Until a few years ago, it was arguably considered a fairly mature field whose main phenomenology was well understood both qualitatively an
Externí odkaz:
http://arxiv.org/abs/1909.03128
Autor:
Behring, Brandon M., Goodman, Roy H.
Publikováno v:
Phys. Rev. Fluids 4, 124703 (2019)
We investigate the stability of a one-parameter family of periodic solutions of the four-vortex problem known as `leapfrogging' orbits. These solutions, which consist of two pairs of identical yet oppositely-signed vortices, were known to W.\ Gr\"obl
Externí odkaz:
http://arxiv.org/abs/1908.08618
A dynamical system is said to be reversible if, given an output, the input can always be recovered in a well-posed manner. Nevertheless, we argue that reversible systems that have a time-reversal symmetry, such as the Nonlinear Schr{\"o}dinger equati
Externí odkaz:
http://arxiv.org/abs/1905.11291