# Richard O. Moore

### Contact Info

Title: | Associate Professor |

Email: | richard.o.moore@njit.edu |

Office: | 603 Cullimore |

Hours: | Spring 2016: Mon Fri 2:30-4 or by appointment. |

Phone: | 973-596-5557 |

Dept: | Mathematical Sciences |

Webpage: | http://web.njit.edu/~rmoore |

**Academic Interests: **industrial mathematics, modeling, optical communications, nonlinear wave equations, dynamical systems, stochastic processes, numerical methods

### About Me

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.

### Education

- PhD, Applied Mathematics, Northwestern University
- MS, Applied Mathematics, Northwestern University
- BSc, Combined Honors Physics and Mathematics, University of British Columbia

### Website

http://web.njit.edu/~rmoore### Research Interests

- 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

### Selected Publications

- 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.
- T. Schäfer and R. O. Moore, A path integral method for coarse-graining noise in stochastic differential equations with multiple time scales, submitted to Physica D.
- R. O. Moore, G. Biondini and W. L. Kath, A method to compute statistics of large, noise-induced perturbations of nonlinear Schrödinger solitons, SIAM J. Appl. Math. (2007)
- C. J. McKinstrie, R. O. Moore, S. Radic and R. Jiang, Phase-sensitive amplification of chirped optical pulses in fibers, Opt. Exp. (2007).
- R. O. Moore, T. Schäfer, C. K. R. T. Jones, Soliton broadening under random dispersion fluctuations: Importance sampling based on low-dimensional reductions, Opt. Comm. (2005).
- R. O. Moore, K. Promislow, Renormalization group reduction of pulse dynamics in thermally loaded optical parametric oscillators, Physica D, 206 (2005) pp. 62-81.
- E. T. Spiller, W. L. Kath, R. O. Moore and C. J. McKinstrie, Computing Large Signal Distortions and Bit-Error Ratios in DPSK Transmission Systems, IEEE Phot. Tech. Lett., 17 (5) (2005) pp. 1022-1024.
- R. O. Moore, G. Biondini and W. L. Kath, Importance sampling for noise-induced amplitude and timing jitter in soliton transmission systems,Opt. Lett., 28 (1) (2003) pp. 105-107.
- T. Schäfer, R. O. Moore and C. K. R. T. Jones, Pulse propagation in media with deterministic and random dispersion variations, Opt. Comm., 214 (1-6) (2002) pp. 353-362.
- R. O. Moore, G. Biondini and W. L. Kath, Self-induced thermal effects and modal competition in continuous-wave optical parametric oscillators, J. Opt. Soc. Am. B, 19 (4) (2002) pp. 802-811.
- R. O. Moore, W. L. Kath, B. Sandstede, C. K. R. T. Jones and J. C. Alexander, Stability of multiple pulses in optical fibers with phase-sensitive amplification, Opt. Comm., 195 (1-4) (2001) pp. 127-139.