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A new canonical reduction of three-vortex motion and its application to vortex-dipole scattering
We use Jacobi coordinates and Nambu brackets to derive a new representation of the motion of three vortices which, unlinke all previous reductions, introduces no singularities into the system. We use this to study the scattering of dipoles by stationary vortices.
Atul Anurag
,
Roy Goodman
,
Ellison O'Grady
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DOI
arXiv
Supplement
An English Translation of Gröbli's Ph.D. Dissertation: "Specielle Probleme über die Bewegung geradliniger paralleler Wirbelfäden"
A complete English translation of Walter Gröbli’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 of exact solutions in the cases of three, four and $2n$ vortices with certain restriction on the vortices’ circulation and the symmetry of the initial configuration.
Roy Goodman
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arXiv
SIAM New York – New Jersey – Pennsylvania Section Holds Inaugural Conference
SIAM NNP held its first conference!
Kathleen Kavanaght
,
Roy Goodman
PDF
Web
QGLAB: A MATLAB Package for Computations on Quantum Graphs
We describe QGLAB, a new MATLAB package for analyzing partial differential equations on quantum graphs.
Roy Goodman
,
Gracie Conte
,
Jeremy Marzuola
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arXiv
GitHub
Apodizer Design to Efficiently Couple Light into a Fiber Bragg Grating
We use an optimal control framework to efficiently couple light into a fiber Bragg grating, improving a previously-reported 66 percent transmission to 88 percent.
Jimmie Adriazola
,
Roy Goodman
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DOI
Transition to instability of the leapfrogging vortex quartet
We show via analytical perturbation theory that the leapfrogging vortex quartet becomes unstable exactly at the critical ratio $\alpha= \phi^{-2}.$
Roy Goodman
,
Brandon Behring
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Journal
arXiv
Efficient Manipulation of Bose-Einstein Condensates in a Double-Well Potential
We use optimal control based on a Galerkin-truncated model to transfer a BEC from one well of a two-well potential to the other.
Jimmie Adriazola
,
Roy Goodman
,
Panos Kevrekidis
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Journal
arXiv
A Reduction-Based Strategy for Optimal Control of Bose-Einstein Condensates
Applications of Bose-Einstein Condensates (BEC) often require that the condensate be prepared in a specific complex state. Optimal …
Jimmie Adriazola
,
Roy Goodman
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Journal
arXiv
An Optimal Control Approach to Gradient-Index Design for Beam Reshaping
We address the problem of reshaping light in the Schrödinger optics regime from the perspective of optimal control theory. In …
Jimmie Adriazola
,
Roy Goodman
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Journal
arXiV
Solitary Waves in Mass-in-Mass Lattices
We consider the existence of spatially localized traveling wave solutions of the mass-in-mass lattice. Under an anti-resonance …
Timothy Faver
,
Roy Goodman
,
Doug Wright
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Journal
arXiv
Markdown: A Writing Tool for Every Applied Mathematician's Toolbox
Hey, applied mathematicians. You should be using Markdown.
Roy Goodman
PDF
Web
Loss of Physical Reversibility in Reversible Systems
A dynamical system is said to be reversible if, given an output, the input can always be recovered in a well-posed manner. …
Amir Sagiv
,
Adi Ditkowski
,
Roy Goodman
,
Gadi Fibich
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Journal
arXiv
In Memoriam: Richard Haberman
On December 31, 2018, my friend and colleauge Rich Haberman passed away. Alejandro Aceves, Peter Miller, and I wrote a short tribute.
Alejandro Aceves
,
Roy Goodman
,
Peter Miller
PDF
Stability of Leapfrogging Vortex Pairs: A Semi-analytic Approach
We investigate the stability of a one-parameter family of periodic solutions of the four-vortex problem known as
leapfrogging
orbits. …
Brandon Behring
,
Roy Goodman
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Journal
arXiv
Topological features determining the error in the inference of networks using transfer entropy
The problem of inferring interactions from observations of individual behavior in networked dynamical systems is ubiquitous in science …
Roy Goodman
,
Maurizio Porfiri
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Journal
Drift of spectrally stable shifted states on star graphs
When the coefficients of the cubic terms match the coefficients in the boundary conditions at a vertex of a star graph and satisfy a …
Adilbek Kairzhan
,
Dmitry Pelinovsky
,
Roy Goodman
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Journal
arXiv
Four Decades of Kink Interactions in Nonlinear Klein-Gordon Models: A Crucial Typo, Recent Developments and the Challenges Ahead
Article on DSweb with Panos Kevrekidis.
Panos Kevrekidis
,
Roy Goodman
PDF
NLS bifurcations on the bowtie combinatorial graph and the dumbbell metric graph
We consider the bifurcations of standing wave solutions to the nonlinear Schrödinger equation (NLS) posed on a quantum graph consisting …
Roy Goodman
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Journal
Mathematical Analysis of Fractal Kink-Antikink Collisions in the $\varphi^4$ Model
We analyze the fractal structure seen in kink-antikink collisions of the $\varphi^4$ equation. The analysis is based on qualitative …
Roy Goodman
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arXiv
Book
Book Review, Methods of Mathematical Modeling by Witelski and Bowen
From SIAM Review. Emoji Review: 👍
Roy Goodman
PDF
Journal
Bifurcations of relative periodic orbits in NLS/GP with a triple-well potential
The nonlinear Schrödinger/Gross–Pitaevskii (NLS/GP) equation is considered in the presence of three equally-spaced potentials. …
Roy Goodman
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Journal
arXiv
Self-trapping and Josephson tunneling solutions to the nonlinear Schrödinger / Gross-Pitaevskii Equation
We study the long-time behavior of solutions to the nonlinear Schrödinger / Gross-Pitaevskii equation (NLS/GP) with a symmetric …
Roy Goodman
,
Jeremy Marzuola
,
Michael Weinstein
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Journal
Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates
We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary …
Roy Goodman
,
Panos Kevrekidis
,
Ricardo Carretero Gónzalez
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Journal
A Mechanical Analog of the Two-Bounce Resonance of Solitary Waves: Modeling and Experiment
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known …
Roy Goodman
,
Amin Rahman
,
Michael Bellanich
,
Catherine Morrison
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Journal
arXiv
High-order Adaptive Method for Computing Two-dimensional Invariant Manifolds of Maps
An efficient and accurate numerical method is presented for computing invariant manifolds of maps which arise in the study of dynamical …
Jacek Wróbel
,
Roy Goodman
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Journal
High-Order Bisection Method for Computing Invariant Manifolds of Two-Dimensional Maps
We describe an efficient and accurate numerical method for computing smooth approximations to invariant manifolds of planar maps, based …
Roy Goodman
,
Jacek Wróbel
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Journal
Hamiltonian Hopf bifurcations and dynamics of NLS/GP standing-wave modes
We examine the dynamics of solutions to nonlinear Schrödinger/Gross– Pitaevskii equations that arise due to semisimple indefinite …
Roy Goodman
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Journal
arXiv
Nonlinear hydrodynamic phenomena in Stokes flow regime
We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a …
Jerzy Bławzdziewicz
,
Roy Goodman
,
N. Khurana
,
E. Wajnryb
,
Yuan-Nan Young
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Journal
Special Issue
Stability and instability of nonlinear defect states in the coupled mode equations---analytical and numerical study
Coupled backward and forward wave amplitudes of an electromagnetic field propagating in a periodic and nonlinear medium at Bragg …
Roy Goodman
,
Michael Weinstein
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Journal
arXiv
Hysteretic and chaotic dynamics of viscous drops in creeping flows with rotation
We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a …
Yuan-Nan Young
,
Jerzy Bławzdziewicz
,
Vittorio Cristini
,
Roy Goodman
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Journal
Chaotic scattering in solitary wave interactions: A singular iterated-map description
We derive a family of singular iterated maps—closely related to Poincaré maps—that describe chaotic interactions between …
Roy Goodman
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Journal
arXiv
Chaotic Scattering and the $n$-bounce Resonance in Solitary Wave Interactions
We present a new and complete analysis of the n-bounce resonance and chaotic scattering in solitary wave collisions. In these …
Roy Goodman
,
Richard Haberman
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Journal
arXiv
Vector soliton interactions in birefringent optical fibers
We consider the interactions of two identical, orthogonally polarized vector solitons in a nonlinear optical fiber with two …
Roy Goodman
,
Richard Haberman
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Journal
arXiv
Trapping light with grating defects
Gap solitons are localized traveling waves that exist in Bragg grating optical fibers. We demonstrate a family of grating defects that …
Roy Goodman
,
Richart Slusher
,
Michael Weinstein
,
Martin Klaus
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Book
Kink-antikink collisions in the $\phi^4$ equation: The $n$-bounce resonance and the separatrix map
We provide a detailed mathematical explanation of a phenomenon known as the two-bounce resonance observed in collisions between kink …
Roy Goodman
,
Richard Haberman
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Journal
Strong NLS soliton--defect interactions
We consider the interaction of a nonlinear Schrödinger soliton with a spatially localized (point) defect in the medium through which it …
Roy Goodman
,
Philip Holmes
,
Michael Weinstein
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Journal
arXiv
Interaction of sine-Gordon kinks with defects: The two-bounce resonance
A model of soliton–defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov …
Roy Goodman
,
Richard Haberman
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Journal
arXiv
Trapping of kinks and solitons by defects: phase space transport in finite-dimensional models
We study models of Fei et al. and of Forinash et al of kinks in the sine-Gordon equation, and solitons in the nonlinear Schrodinger …
Philip Holmes
,
Roy Goodman
,
Michael Weinstein
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Collection
Stopping Light on a Defect
Gap solitons are localized nonlinear coherent states that have been shown both theoretically and experimentally to propagate in …
Roy Goodman
,
Richart Slusher
,
Michael Weinstein
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Journal
arXiv
Interaction of sine-Gordon kinks with defects: phase space transport in a two-mode model
We study a model derived by Fei et al. [Phys. Rev. A 45 (1992) 6019] of a kink solution to the sine-Gordon equation interacting with an …
Roy Goodman
,
Philip Holmes
,
Michael Weinstein
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Nonlinear propagation of light in one-dimensional periodic structures
We consider the nonlinear propagation of light in an optical fiber waveguide as modeled by the anharmonic Maxwell-Lorentz equations …
Roy Goodman
,
Michael Weinstein
,
Philip Holmes
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Journal
arXiv
Modulations in the leading edges of midlatitude storm tracks
Downstream development is a term encompassinga variety of effects relating to the propagation of storm systems at midlatitude. We …
Roy Goodman
,
Andrew Majda
,
David McLaughlin
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Journal
Trigger Waves in a Model for Catalysis
We consider the model of catalysis due to Ziff, Gulari, and Barshad [Phys Rev. Lett. 56, 2553 (1986)] as a pattern formation problem. …
Roy Goodman
,
David Graff
,
Leonard Sander
,
Patrick Leroux-Hugon
,
Eric Clement
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