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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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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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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
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
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
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
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
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
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
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
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