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My research belongs to nonlinear dynamics, statistical physics, and related fields, focusing on the following three areas.

Nonlinear waves; Metamaterials; Nonlinear optics: 

I am interested in nonlinear waves in optical and mechanical metamaterials. A central theme is nonlinear edge waves in optical and mechanical topological insulators, and the overall goal is to elevate the functionalities of optical and mechanical devices using various combinations between topological science and nonlinear science. I am also interested in other types of nonlinear waves including domain walls, vector solitons, self-similar solutions, and dispersive shock waves, which arise in diverse settings including the coupled nonlinear Schrödinger equation, the hyperbolic nonlinear Schrödinger equation, the Kadomtsev-Petviashvili equation, and the 2D Benjamin-Ono equation.

Climate dynamics; Statistical physics; Fluid mechanics: 

I am interested in meltwater patterns in cold environments, e.g., the polar regions. The overall goal is to construct efficient parametrization schemes for such ice-water mixtures using various models in the statistical physics of phase transitions, a prime example being an Ising model that explains the geometric characteristics of Arctic melt ponds. I am also interested in some branches of fluid mechanics including Rayleigh-Bénard convection. I have also worked on other applications of statistical physics including minority game and other problems in fluid mechanics including Homann stagnation-point flow.

Pattern formation; Dynamical systems: 

I am interested in spatially localized states in driven dissipative systems, e.g., localized Turing patterns in forced oscillatory systems and Turing-Hopf localized states in the Brusselator model. The overall goal is to understand the interplay between the interface dynamics between two patterns and the intrinsic dynamics within each pattern. The prototypical solutions can be understood using spatial dynamics, i.e., dynamical systems methods in space rather than in time. I have also worked on other applications of dynamical systems including cooperation and free-riding in social science.

• Domain walls and vector solitons in the coupled nonlinear Schrödinger equation, Snee, D., Ma, Y. 19 Jan 2024, In: Journal of Physics A: Mathematical and Theoretical
• Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model, Ma, Y., Susanto, H. Nov 2021, In: Physical Review E
• Edge Solitons in a Nonlinear Mechanical Topological Insulator, Snee, D., Ma, Y. 1 Jul 2019, In: Extreme Mechanics Letters
• Ising model for melt ponds on Arctic sea ice, Ma, Y., Sudakov, I., Strong, C., Golden, K. 21 Jun 2019, In: New Journal of Physics
• A universal asymptotic regime in the hyperbolic nonlinear Schrodinger equation, Ablowitz, M., Ma, Y., Rumanov, I. 17 Aug 2017, In: SIAM Journal on Applied Mathematics
• Conical wave propagation and diffraction in two-dimensional hexagonally packed granular lattices, Chong, C., Kevrekidis, P., Ablowitz, M., Ma, Y. 25 Jan 2016, In: Physical Review E
• Dispersive shock waves in the Kadomtsev–Petviashvili and two dimensional Benjamin–Ono equations, Ablowitz, M., Demirci, A., Ma, Y. 15 Oct 2016, In: Physica D: Nonlinear Phenomena
• The competing effects of wall transpiration and stretching on Homann stagnation-point flow, Weidman, P., Ma, Y. 1 Nov 2016, In: European Journal of Mechanics - B/Fluids
• Two-dimensional localized structures in harmonically forced oscillatory systems, Ma, Y., Knobloch, E. 15 Dec 2016, In: Physica D: Nonlinear Phenomena
• Adiabatic dynamics of edge waves in photonic graphene, Ablowitz, M., Curtis, C., Ma, Y. 13 Apr 2015, In: 2D Materials

David Snee Nonlinear Edge Waves in Mechanical Topological Insulators Start Date: 01/10/2017 End Date: 29/06/2021

Physics PhD December 01 2011