Richard Moore´s research focuses on wave phenomena in optical communication systems and optical devices. He is particularly interested in how such systems and devices are disturbed by a variety of influences relevant to their operating environments. Current projects include using a combination of perturbation methods and importance sampling to simulate rare events in optical communication lines, and using dynamical systems techniques and rigorous reduction methods to analyze the impact of heating due to optical field absorption in devices that convert optical frequencies using parametric gain media.
PhD, Applied Mathematics, Northwestern University
MS, Applied Mathematics, Northwestern University
BSc, Combined Honors Physics and Mathematics, University of British Columbia
Investigating the robustness of optical bits (e.g., optical solitons) to deterministic and random perturbations
Developing hybrid analytical/computational methods (e.g., using biased sampling techniques) to compute statistics of low-probability events, such as bit errors in optical communication lines
Exploring the validity of finite-dimensional reductions of dispersive PDEs
Analysing patterns/localised objects and their dynamics in damped-dispersive systems
Exploring the effect of heating on dispersive systems such as optical parametric gain devices
Devising multi-scale computational techniques to exploit the disparity of time scales in physically relevant coupled hyperbolic-parabolic systems
R. O. Moore, K. Promislow, "Mean-field limit of optical parametric oscillators with self-heating", in preparation.
R. O. Moore, G. Biondini and W. L. Kath, "A method to compute statistics of large, noise-induced perturbations of nonlinear Schrödinger solitons", revised version selected for publication in SIGEST section of SIAM Review, to appear in 2008.
R. O. Moore and K. Promislow, The semi-strong limit of multipulse interaction in a thermally driven optical system, submitted to J. Diff. Eq.