Yiping is a Vice Chancellor’s Research Fellow at Northumbria University. He is an applied mathematician primarily interested in nonlinear differential equations and their applications to the physical sciences.
I am a vice chancellor's research fellow in extreme environments at Northumbria University. My main research interests lie in the mathematical areas of nonlinear waves, pattern formation, and applied dynamical systems, and the application areas of nonlinear optics, climate dynamics, and fluid mechanics.
Previously, I held postdoctoral positions at University of Colorado at Boulder, Northwestern University, and University of Chicago, and obtained my PhD in physics at University of California at Berkeley advised by Edgar Knobloch.
My teaching interests lie primarily in mathematics, including both fundamental courses such as differential equations, linear algebra, and multivariate calculus, and advanced courses such as applied analysis, computational mathematics, and mathematical modeling.
My personal website can be found here.
My Google Scholar profile can be found here.
My Northumbria Research Link can be found here.
- PhD (Physics, UC Berkeley) 2011
- BSc (Physics and Mathematics, HKUST) 2006
Research Themes and Scholarly Interests
My research interests lie generally in applied nonlinear mathematics and physical applied mathematics. A central theme is the study of nonlinear differential equations via analytical and numerical means. My research can be roughly divided into the following three areas.
Nonlinear waves/Nonlinear optics: My research on nonlinear waves focuses on waves in higher spatial dimensions, including in particular an emerging field of nonlinear optics known as nonlinear topological photonics. My prior work has centered on traveling edge waves in photonic graphene. I have also worked on 2D dispersive shock waves, and waves in 2D granular lattices.
Pattern formation/Applied dynamical systems: My research on pattern formation focuses on spatially localized states in dissipative systems, drawing upon dynamical systems techniques such as bifurcation theory and numerical continuation. My prior work has centered on localized states in forced oscillatory systems. I have also worked on localized states in the 1D Brusselator model.
Climate dynamics/Fluid mechanics: My research on climate dynamics focuses on minimal models of climate components poorly represented in general circulation models. I have also worked on some fluid problems including convection and self-similar flows.
Y.-P. Ma and E. Knobloch. Two-dimensional localized structures in harmonically forced oscillatory systems. Physica D 337, 1-17 (2016).
M. J. Ablowitz, A. Demirci, and Y.-P. Ma. Dispersive shock waves in the Kadomtsev-Petviashvili and Two Dimensional Benjamin-Ono equations. Physica D 333, 84-98 (2016).
M. J. Ablowitz, C. W. Curtis, and Y.-P. Ma. Adiabatic dynamics of edge waves in photonic graphene. 2D Materials 2 (2), 024003 (2015).
M. J. Ablowitz, C. W. Curtis, and Y.-P. Ma. Linear and nonlinear traveling edge waves in optical honeycomb lattices. Phys. Rev. A 90, 023813 (2014).
A. R. Champneys, E. Knobloch, Y.-P. Ma and T. Wagenknecht. Homoclinic snakes bounded by a saddle-center periodic orbit. SIAM J. Appl. Dyn. Syst. 11(4), 1583-1613 (2012).
Y.-P. Ma, J. Burke and E. Knobloch. Defect-mediated snaking: A new growth mechanism for localized structures. Physica D 239, 1867-1883 (2010).