| Broadly, I am interested in using techniques from dynamical systems and functional analysis to the study of partial differential equations. In particular, my research focuses on the nonlinear dynamics of coherent structures and patterns in nature. These interests have so far lead me down two avenues of research, the study of how growth processes and inhomogeneities can be used to control and influence pattern forming systems, and the study of how strongly nonlinear coherent states arise in geophysical fluid systems. I aim to take a unified approach to these problems, using rigorous techniques to more deeply understand and predict new behaviors, while employing numerics and formal asymptotics to explore phenomenon, gain intuition, and numerically continue solutions. Having worked on collaborative projects in areas such as chemical vapor deposition, embryo gastrulation, and stochastic computing, I am always looking to incorporate interdisciplinary projects into my research program. |
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M. Beck, R. Goh, A. Haslam-Hyde Exponential Dichotomies in Higher-Dimensional Spatial Dynamics for Elliptic Partial Differential Equations Preprint; ( Preprint )
L. Forbes, J. Grossman, M. Avery, R. Goh, G. K. Ocker. Coherent dynamics in networks of soft-threshold integrate and fire neurons on the ring submitted; ( Preprint )
S. Dodson, R. Goh, B. Sandstede. Efficient numerical computation of spiral spectra with exponentially-weighted preconditioners
IMA J. Numer. Anal.; ( Preprint )
M. Avery, R. Goh, O. Garcia-Lopez, B. Hosek, E. Shade Fronts and patterns with a dynamic parameter ramp
Physica D 483, 134972, 2025; ( Preprint )
R. Goh, T. Kaper, T. Vo. Delayed Hopf bifurcations in reaction-diffusion systems in two space dimensions
The ANZIAM Journal, 67 (19), 2025; . ( Preprint )
S. Dunn, R. Goh, B. Krewson. Transverse modulational dynamics of quenched patterns
Chaos 34, 063104 2024; ( Preprint )
R. Goh, T.J. Kaper, A. Scheel. Pitchfork bifurcation along a slow parameter ramp: coherent structures in the critical scaling
Stud. Appl. Math 12 (2). 2024 ; ( Preprint )
R. Goh, A. Scheel. Growing patterns
Nonlinearity 36 R1, 2023. ; ( Preprint )
R. Goh, T.J. Kaper, A. Scheel, T. Vo. Fronts in the wake of a parameter ramp: slow passage through pitchfork and fold bifurcations
SIAM J. Appl. Dyn. Sys. 22 (3), 2023, 2312-2356 ; ( Preprint )
R. Goh, B. Hosek. Oblique and checkerboard patterns in the quenched Cahn-Hilliard model
J. Dyn. Diff. Eq., 1-27; 2023 ; ( Preprint )
R. Goh, C.E. Wayne, R. Welter. Asymptotic approximation of a modified compressible Navier Stokes system
Indiana Univ. Math. J., 72 (3), 2023, 1175-1237; ( Preprint )
R. Goh, T. J. Kaper, T. Vo. Delayed Hopf bifurcation and space-time buffer curves in the Complex Ginzburg-Landau equation
IMA J. of Appl. Math.,87 (2), (2022), 131–186 ; ( Preprint )
R. Goh, B. de Rijk. Spectral stability of pattern-forming fronts in the complex Ginzburg-Landau equation with a quenching mechanism
Nonlinearity, 35 (1), 170, (2021); ( Preprint )[ Code Repository ]
K. Chen, Z. Deiman, R. Goh, S. Jankovic, and A. Scheel Strain and defects in oblique stripe growth
Multiscale Model. Simul., 19(3), (2021) 1236–1260. . ( Preprint )
S. Chhabra, L. Liu, R. Goh, A. Warmflash. Dissecting the dynamics of signaling events in the BMP, WNT, and NODAL cascade during self-organized fate patterning in human gastruloids.
PLOS Biology 17(10): e3000498 (2021). ( Preprint )
M. Avery, R. Goh, O. Goodloe, A. Milewski, A. Scheel. Growing stripes, with and without wrinkles
SIAM J. Appl. Dyn. Sys., 18 (2019), 1078 – 1117 . ( Preprint )
[ Supplementary Materials], [ Movie of the moduli space with delicate arch! ], [ Code Repository ]
R. Goh, C. E. Wayne. Vortices in stably-stratified rapidly rotating Boussinesq convection,
Nonlinearity, 32 R1 (2019). (Preprint )
R. Goh, A. Scheel. Pattern-forming fronts in a Swift-Hohenberg equation with directional quenching - parallel and oblique stripes,
J. London Math. Soc., 98 (2018), 104-128. (Preprint )
Z. Wang, R. Goh, K. Bazargan, A. Scheel, N. Saraf. Stochastic Implementation and Analysis of Dynamical System Similar to the Logistic Map,
IEEE Transactions on Very Large Scale Integration Systems, (2016), 99, 1-13.
R. Goh, R. Beekie, D. Matthias, J. Nunley, A. Scheel. Universal wavenumber selection laws in apical growth,
Phys. Rev. E 94 (2016), 022219. (Preprint )
R. Goh, A. Scheel. Pattern formation in the wake of triggered pushed fronts,
Nonlinearity 29 (2016), 2196. (Preprint )
R. Goh, A. Scheel. Hopf bifurcation from fronts in the Cahn-Hilliard equation
Arch. Ration. Mech. An. 217 (2015), 1219-1263. (Preprint )
R. Goh, A. Scheel. Triggered Fronts in the Complex Ginzburg Landau Equation
J. Nonlinear Science 24 (2014), 117-144. (Preprint )
R. Goh, S. Mesuro, A. Scheel. Spatial Wavenumber Selection in Reccurrent Precipitation
SIAM J. Appl. Dyn. Sys. 10 (2011), 360-402 (Preprint )
David Lloyd, Ryan Goh, Jens D.M. Rademacher. Numerical Continuation and Bifurcation in Nonlinear PDEs: Stability, invasion and wavetrains in the Swift-Hohenberg equation
Handbook on Nonlinear Dynamics: Volume 2 Numerical Methods.; World Scientific, in preparation (Preprint)
R. Goh, S. Mesuro, A. Scheel Coherent structures in reaction-diffusion models for precipitation
Special volume on "Precipitation patterns in reaction-diffusion systems", Research Signpost (2010), 73-93. (Preprint)