Ryan Goh

Ryan Goh
Boston University | BU · Department of Mathematics and Statistics

About

21
Publications
943
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219
Citations

Publications

Publications (21)
Article
In this article, the recently discovered phenomenon of delayed Hopf bifurcations (DHB) in reaction–diffusion partial differential equations (PDEs) is analysed in the cubic Complex Ginzburg–Landau equation, as an equation in its own right, with a slowly varying parameter. We begin by using the classical asymptotic methods of stationary phase and ste...
Article
We consider pattern-forming fronts in the complex Ginzburg–Landau equation with a traveling spatial heterogeneity which destabilises, or quenches, the trivial ground state while progressing through the domain. We consider the regime where the heterogeneity propagates with speed c just below the linear invasion speed of the pattern-forming front in...
Preprint
We study stripe formation in two-dimensional systems under directional quenching in a phase-diffusion approximation including non-adiabatic boundary effects. We find stripe formation through simple traveling waves for all angles relative to the quenching line using an analytic continuation procedure. We also present comprehensive analytical asympto...
Preprint
Full-text available
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 momentum field into its irrotational and incompressible parts, and a new method for approximating solutions of the heat equation in terms of Hermite functions in which $...
Preprint
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 progressing through the domain. We consider the regime where the heterogeneity propagates with speed $c$ just below the linear invasion speed of the pattern-forming front i...
Article
Full-text available
During gastrulation, the pluripotent epiblast self-organizes into the 3 germ layers—endoderm, mesoderm and ectoderm, which eventually form the entire embryo. Decades of research in the mouse embryo have revealed that a signaling cascade involving the Bone Morphogenic Protein (BMP), WNT, and NODAL pathways is necessary for gastrulation. In vivo, WNT...
Preprint
We present results on stripe formation in the Swift-Hohenberg equation with a directional quenching term. Stripes are "grown" in the wake of a moving parameter step line, and we analyze how the orientation of stripes changes depending on the speed of the quenching line and on a lateral aspect ratio. We observe stripes perpendicular to the quenching...
Preprint
Full-text available
During gastrulation, the pluripotent epiblast is patterned into the three germ layers, which form the embryo proper. This patterning requires a signaling cascade involving the BMP, Wnt and Nodal pathways; however, how these pathways function in space and time to generate cell-fate patterns remains unknown. Using a human gastruloid model, we show th...
Article
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 the vertical direction. For initial conditions satisfying a certain quasi-geostrophic smallness condition, we use dispersive estimates and the large rotation limit to pr...
Article
We study the effect of domain growth on the orientation of striped phases in a Swift-Hohenberg equation. Domain growth is encoded in a step-like parameter dependence that allows stripe formation in a half plane, and suppresses patterns in the complement, while the boundary of the pattern-forming region is propagating with fixed normal velocity. We...
Article
Stochastic computing (SC) is a digital computation approach that operates on random bit streams to perform complex tasks with much smaller hardware footprints compared with conventional binary radix approaches. SC works based on the assumption that input bit streams are independent random sequences of 1s and 0s. Previous SC efforts have avoided imp...
Article
We study pattern-forming dissipative systems in growing domains. We characterize classes of boundary conditions that allow for defect-free growth and derive universal scaling laws for the wavenumber in the bulk of the domain. Scalings are based on a description of striped patterns in semi-bounded domains via strain-displacement relations. We compar...
Article
Pattern-forming fronts are often controlled by an external stimulus which progresses through a stable medium at a fixed speed, rendering it unstable in its wake. By controlling the speed of excitation, such stimuli, or "triggers," can mediate pattern forming fronts which freely invade an unstable equilibrium and control which pattern is selected. I...
Technical Report
In recent times, there has been a growing interest in the machining of amorphous metallic alloys, which are also called bulk metallic glasses (BMGs). These materials differ from common polycrystalline metallic alloys, because their atoms do not assemble on a crystalline lattice, and as a result, they have unique physical, mechanical, and chemical p...
Article
Full-text available
We study Hopf bifurcation from traveling-front solutions in the Cahn-Hilliard equation. The primary front is induced by a moving source term. Models of this form have been used to study a variety of physical phenomena, including pattern formation in chemical deposition and precipitation processes. Technically, we study bifurcation in the presence o...
Article
Full-text available
We study patterns that arise in the wake of an externally triggered, spatially propagating instability in the complex Ginzburg-Landau equation. We model the trigger by a spatial inhomogeneity moving with constant speed. In the comoving frame, the trivial state is unstable to the left of the trigger and stable to the right. At the trigger location,...
Article
We study invasion fronts in a class of simple, two-species reaction-diffusion systems that occur as models for recurrent precipitation and undercooled liquids. We exhibit several different modes of front propagation: the invasion of an unstable homogeneous equilibrium can create persistent periodic patterns, transient patterns, or simply a homogene...

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