Richard H. Rand
Professor of Mathematics and Mechanical and Aerospace Engineering

 

Web Site

www.tam.cornell.edu/Rand.html

Contact Information

Office:  438 Malott Hall
207 Kimball Hall
Phone:  (607) 255-4739
(607) 255-7145
Fax:  (607) 255-7149
Email:  rand@math.cornell.edu

Courses & Office Hours

Education

Sc.D. (1967) Columbia University

Research Area: Nonlinear dynamics

My research involves using perturbation methods and bifurcation theory to obtain approximate solutions to differential equations arising from nonlinear dynamics problems in engineering and biology.

Current projects involve differential delay equations, quasiperiodic forcing in Mathieu’s equation and dynamics of coupled oscillators.  Applications include MEMS (micro electrical mechanical systems), effects of biorhythms on retinal dynamics, dynamics of gene copying, and cardiac arrythmias.  These projects are conducted jointly with graduate students and with experts in the respective application area.

Selected Publications

Lecture Notes on Nonlinear Vibrations, version 52, 2005.

Analysis of frequency locking in optically driven MEMS resonators (with M. Pandey, K. Auburn, M. Zalalutdinov, R. B. Reichenbach, A. T. Zehnder, and H. G. Craighead), J. Microelectromechanical Systems 15 (2006), 1546–1554.

The damped nonlinear quasiperiodic Mathieu equation near 2:2:1 resonance (with N. Abouhazim and M. Belhaq), Nonlinear Dynamics 45 (2006), 237–247.

Dynamics of three coupled van der Pol oscillators with application to circadian rhythms (with K. Rompala and H. Howland), Communications in Nonlinear Science and Numerical Simulation 12 (2007), 794–803.

Hopf bifurcation formula for first order differential-delay equations (with A. Verdugo), Communications in Nonlinear Science and Numerical Simulation 12 (2007), 859–864.

Stability of strongly nonlinear normal modes (with G. Recktenwald), Communications in Nonlinear Science and Numerical Simulation 12 (2007), 1128–1132.

Perturbation analysis of entrainment in a micromechanical limit cycle oscillator (with M. Pandey and A. Zehnder), Communications in Nonlinear Science and Numerical Simulation 12 (2007), 1291–1301.

Synchronization in the Winfree model of coupled nonlinear oscillators (with D. D. Quinn and S. Strogatz), Physical Review E 75 (2007), 036218.

Trigonometric simplification of a class of conservative nonlinear oscillators (with G. Recktenwald), Nonlinear Dynamics 49 (2007), 193–201.

Two models for the parametric forcing of a nonlinear oscillator (with N. Abouhazim and M. Belhaq), Nonlinear Dynamics 50 (2007), 147–160.

2:1 resonance in the delayed nonlinear Mathieu equation (with T. M. Morrison), Nonlinear Dynamics 50 (2007), 341–352.

Effect of quasiperiodic gravitational modulation on the stability of a heated fluid layer (with T. Boulal, S. Aniss, and M. Belhaq) Physical Review E 76 (2007), 056320.

Hopf bifurcation in a DDE model of gene expression (with A. Verdugo), Communications in Nonlinear Science and Numerical Simulation 13 (2008), 235–242.

Dynamics of four coupled phase-only oscillators (with J. Wong), Communications in Nonlinear Science and Numerical Simulation 13 (2008), 501–507.

Center manifold analysis of a DDE model of gene expression (with A. Verdugo), Communications in Nonlinear Science and Numerical Simulation 13 (2008), 1112–1120.

Autoparametric quasiperiodic excitation (with S. M. Sah, G. Recktenwald, and M. Belhaq), International J. Nonlinear Mechanics 43 (2008), 320–327.

Dynamics of three coupled limit cycle oscillators with application to artificial intelligence (with L. Mendelowitz and A. Verdugo), Communications in Nonlinear Science and Numerical Simulation 14 (2009), 270–283.

Last modified: July 20, 2009