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


JPLT, M Holmes-Cerfon, Modeling the relative dynamics of DNA-coated colloids, to appear in Soft Matter. arXiv

JPLT, MI Weinstein, Y Zhu, Elliptic operators with honeycomb symmetry: Dirac points, Edge States and Applications to Photonic Graphene, Archive for Rational Mechanics and Analysis (2018): 1-63. journal | arXiv

CL Fefferman, JPLT, MI Weinstein, Honeycomb Schrödinger operators in the strong binding regime Communications on Pure and Applied Mathematics 71 (2018): 1178-1270. journal | arXiv

JPLT, AG Shtukenberg, RV Kohn, Effect of step anisotropy on crystal growth inhibition by immobile impurity stoppers, Crystal Growth & Design 17 (2017): 5474-5487. journal

CL Fefferman, JPLT, MI Weinstein, Topologically protected states in one-dimensional systems, American Mathematical Society 247 (2017). journal | arXiv

CL Fefferman, JPLT, MI Weinstein, Edge states in honeycomb structures, Annals of PDE 2 (2016). journal | arXiv

CL Fefferman, JPLT, MI Weinstein, Bifurcations of edge states -- topologically protected and non-protected -- in continuous 2D honeycomb structures, 2D Materials 3 (2016): 014008. journal | arXiv

JPLT, I Vukićević, J Yang, X Xu, CL Fefferman, CW Wong, MI Weinstein, Photonic realization of topologically protected bound states in domain-wall waveguide arrays Physical Review A 93 (2016): 033822. journal | arXiv

CL Fefferman, JPLT, MI Weinstein, Topologically protected states in one-dimensional continuous systems and Dirac points, Proceedings of the National Academy of Sciences (2014): 07391. journal | pdf


Conference Papers


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

JPLT, I Vukicevic, J Yang, X Xu, CL Fefferman, CW Wong, MI 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