Zobrazeno 1 - 10
of 94
pro vyhledávání: '"Goh, Ryan"'
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 known that convective transport, whether driven by the nonlinear patt
Externí odkaz:
http://arxiv.org/abs/2405.05897
We investigate the slow passage through a pitchfork bifurcation in a spatially extended system, when the onset of instability is slowly varying in space. We focus here on the critical parameter scaling, when the instability locus propagates with spee
Externí odkaz:
http://arxiv.org/abs/2401.05672
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 instabilities in their wake, have been shown in numerous applications to
Externí odkaz:
http://arxiv.org/abs/2307.16711
Autor:
Goh, Ryan, Scheel, Arnd
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 patterns has long been recognized as a strong selection mechanism. We present
Externí odkaz:
http://arxiv.org/abs/2302.13486
Autor:
Goh, Ryan, Hosek, Ben
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 heterogeneities. Such quenching heterogeneities travel through the dom
Externí odkaz:
http://arxiv.org/abs/2302.04642
This work studies front formation in the Allen-Cahn equation with a parameter heterogeneity which slowly varies in space. In particular, we consider a heterogeneity which mediates the local stability of the zero state and subsequent pitchfork bifurca
Externí odkaz:
http://arxiv.org/abs/2212.09131
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 quenc
Externí odkaz:
http://arxiv.org/abs/2102.02905
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
Externí odkaz:
http://arxiv.org/abs/2012.12966
In this article, the phenomenon of delayed Hopf bifurcations (DHB) in reaction-diffusion PDEs is analyzed in the cubic Complex Ginzburg-Landau equation with a slowly-varying parameter. We use the classical asymptotic methods of stationary phase and s
Externí odkaz:
http://arxiv.org/abs/2012.10048
Autor:
Goh, Ryan, de Rijk, Björn
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 heterog
Externí odkaz:
http://arxiv.org/abs/2006.15083