James P. Lee-Thorp
Interests: PDE & Numerical Analysis
Mathematical Modeling of Materials Science Problems

Research


Here at the Courant Institute of Mathematical Sciences, my postdoctoral research centers around:
(1) numerical modeling of anisotropic crystal step motion in the presence of impurities (with Robert V. Kohn), and
(2) modeling of kinetic effects in simple colloidal DNA systems (with Miranda C. Holmes-Cerfon).

Work building off my graduate research at Columbia University (with Michael I. Weinstein), focuses on a novel bifurcation analysis of "edge states" in electronic (Schrödinger) and photonic (Maxwell) models. .

Publications


JPL-T, A. G. Shtukenberg and R. V. Kohn, Effect of step anisotropy on crystal growth inhibition by immobile impurity stoppers, Crystal Growth & Design, to appear.

C. L. Fefferman, JPL-T and M. I. Weinstein, Honeycomb Schroedinger operators in the strong binding regime, Comm. Pure Appl. Math., to appear. arXiv

C. L. Fefferman, JPL-T and M. I. Weinstein, Edge states in honeycomb structures, Annals of PDE, to appear. arXiv

C. L. Fefferman, JPL-T and M. I. Weinstein, Topologically protected states in one-dimensional systems, Memoirs of AMS 247 (2017). journal | arXiv

JPL-T, I. Vukicevic, J. Yang, X. Xu, C. L. Fefferman, C. W. Wong and M. I. Weinstein, Photonic realization of topologically protected bound states in waveguide arrays, Phys. Rev. A 93 (2016): 033822. journal | arXiv

C. L. Fefferman, JPL-T and M. I. Weinstein, Bifurcations of edge states -- topologically protected and non-protected -- in continuous 2D honeycomb structures, 2D Materials 3 (2016): 014008. journal | arXiv

C. L. Fefferman, JPL-T and M. I. Weinstein, Topologically protected states in one-dimensional continuous systems and Dirac points, Proc. Natl. Acad. Sci. (2014): 07391. journal | pdf


Conference Papers


Y. Poo, JPL-T, Y. Tan, R. Wu, M. I. Weinstein and Z. Yu, Observation of highly robust phase-defect induced photonic states, Conference on Lasers and Electro-Optics (CLEO) (2016). technical digest

JPL-T, I. Vukicevic, J. Yang, X. Xu, C. L. Fefferman, C. W. Wong and M. I. Weinstein, Photonic realization of topologically protected bound states in domain-wall waveguide arrays, Conference on Lasers and Electro-Optics (CLEO) (2016). technical digest

PhD Dissertation


Bifurcation perspective on topologically protected and non-protected states in continuous systems, Columbia University Academic Commons (2016). library | pdf