8 citations · 13 across the 8 of their papers we have counts for
9 papers
Exponential Dichotomies for Elliptic Equations on Multidimensional Domains
Margaret Beck, Ryan Goh, Alanna Haslam-Hyde
The existence of exponential dichotomies has been well-established as a powerful tool to study existence, stability, and bifurcations of coherent structures. Currently, the applica…
Numerical Continuation and Bifurcation in Nonlinear PDEs: Stability, invasion and wavetrains in the Swift-Hohenberg equation
David Lloyd, Ryan Goh, Jens D. M. Rademacher
We discuss some aspects of numerical continuation and bifurcation for partial differential equations, specifically pattern formation and coherent structures. For the sake of clarit…
Efficient numerical computation of spiral spectra with exponentially-weighted preconditioners
Stephanie Dodson, Ryan Goh, Bjorn Sandstede
The stability of nonlinear waves on spatially extended domains is commonly probed by computing the spectrum of the linearization of the underlying PDE about the wave profile. It is…
Transverse modulational dynamics of quenched patterns
Sierra Dunn, Ryan Goh, Benjamin Krewson
We study the modulational dynamics of striped patterns formed in the wake of a planar directional quench. Such quenches, which move across a medium and nucleate pattern-forming ins…
Growing patterns
Ryan Goh, Arnd Scheel
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of pattern…
Oblique and checkerboard patterns in the quenched Cahn-Hilliard model
Ryan Goh, Ben Hosek
We consider transversely modulated fronts in a directionally quenched Cahn-Hilliard equation, posed on a two-dimensional infinite channel, with both parameter and source-term type…
Asymptotic approximation of a modified compressible Navier-Stokes system
Ryan Goh, C. Eugene Wayne, Roland Welter
We study the long time asymptotics of a modified compressible Navier-Stokes system (mcNS) inspired by the previous work of Hoff and Zumbrun. We introduce a new decomposition of the…
Spectral stability of pattern-forming fronts in the complex Ginzburg-Landau equation with a quenching mechanism
Ryan Goh, Björn de Rijk
We consider pattern-forming fronts in the complex Ginzburg-Landau equation with a traveling spatial heterogeneity which destabilizes, or quenches, the trivial ground state while pr…
Vortices in stably-stratified rapidly rotating Boussinesq convection
Ryan Goh, C. Eugene Wayne
We study the Boussinesq approximation for rapidly rotating stably-stratified fluids in a three dimensional infinite layer with either stress-free or periodic boundary conditions in…