Rand, Richard Herbert

research

research and scholarship focus

Current research work 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:

Quasiperiodic forcing in Mathieu's equation
Dynamics of coupled oscillators
Coexistence phenomenon in autoparametric excitation

Applications include:

NEMS (nano electrical mechanical systems)
Effects of biorhythms on retinal dynamics
Cardiac arrythmias
Ecology of plant communities

These projects are typically conducted jointly with graduate students and with experts in the respective application area.

co investigator of

NON-LINEAR DYNAMICS OF COUPLED MEMS OSCILLATORS | Research Grant

research areas

applied and bio mathematics | research concentration area (TAM)
biorobotics and biomechanics | research concentration area (TAM)
differential equations and dynamical systems | research concentration area (Mathematics)
dynamics and nonlinear systems | research concentration area (TAM)
interdisciplinary mathematics | research concentration area (Mathematics)
microelectromechanical systems | research concentration area (TAM)

affiliations

teaching

teaches

MAE 4291 - Supervised Senior Design Experience (TBA -) | fall 2009 class
MAE 4900 - Special Investigations in Mechanical and Aerospace Engineering (TBA -) | fall 2009 class
MAE 6900 - Special Investigations in Mechanical and Aerospace Engineering (TBA -) | fall 2009 class
MAE 8900 - Research in Mechanical and Aerospace Engineering (TBA -) | fall 2009 class
MAE 9900 - Research in Mechanical and Aerospace Engineering (TBA -) | fall 2009 class
MATH 7900 - Supervised Reading & Research (TBA -) | fall 2009 class
TAM 5700 - Intermdiate Dynamics (TR 11:40:AM-12:55:PM) | fall 2008 class

service

current professional activities

Fellow, American Society of Mechanical Engineers
Member, Society for Industrial and Applied Mathematics
Editorial Boards, Journal of Vibration and Control and Communications in Nonlinear Science and Numerical Simulation

background

educational background

B.E., Cooper Union, 1964
M.S., Columbia, 1965
Sc.D., Columbia, 1967

professional background

Visiting professor at the University of California at Berkeley in 1981 and at the University of California at Los Angeles in 1989
Faculty, Cornell University, 1967-present

awards and distinctions

Received the Best Paper Award of the American Society of Agricultural Engineering, 1982
Received teaching awards from the Engineering College at Cornell in 1986,1993,1995 and 2005

featured in

Four professors named 2008 Weiss Presidential fellows | Cornell Chronicle feature

publications

selected publications (listing in progress)

Rand, R. H. 1984. Computer algebra in applied mathematics: An introduction to MACSYMA. Research Notes in Mathematics, no. 94. Boston: Pitman.

· Rand, R. H., and D. Armbruster. 1987. Perturbation methods, bifurcation theory, and computer algebra. Applied Mathematical Sciences, no. 65. New York: Springer-Verlag.

· Rand, R. H. 1994. Topics in nonlinear dynamics with computer algebra. Computation in Education, vol. 1. Langhorne, PA: Gordon and Breach Science Publishers.

· Lecture Notes on Nonlinear Vibrations, version 52, 2005
( http://audiophile.tam.cornell.edu/randdocs/nlvibe52.pdf ).

· Parametric Resonance of Hopf Bifurcation R.Rand, A.Barcilon and T.Morrison Nonlinear Dynamics 39:411-421 (2005)

· 2:1:1 Resonance in the Quasiperiodic Mathieu Equation R.Rand and T.Morrison, Nonlinear Dynamics 40:195-203 (2005)

· Coexistence Phenomenon in Autoparametric Excitation of Two Degree of Freedom Systems G.Recktenwald and R.Rand International J. Nonlinear Mechanics 40:1160-1170 (2005)

· Self-thinning and Community Persistence in a Simple Size-structured Dynamical Model of Plant Growth F.Dercole, K.Niklas and R.Rand J.Math.Biology 51:333-354 (2005)

· Third-Order Intermodulation in a MicromechanicalThermal Mixer R.B.Reichenbach, M.Zalalutdinov, K.L.Aubin, R.Rand, B.H.Houston, J.M.Parpia and H.G.Craighead J.Microelectromechanical Systems 14:1244-1252 (2005)

· Analysis of Frequency Locking in Optically Driven MEMS Resonators M. Pandey, K. Auburn, M. Zalalutdinov, R.B. Reichenbach, A.T. Zehnder, R.H. Rand and H.G. Craighead J. Microelectromechanical Systems 15:1546-1554 (2006)

· The Damped Nonlinear Quasiperiodic Mathieu Equation Near 2:2:1 Resonance N. Abouhazim, R.H. Rand and M. Belhaq Nonlinear Dynamics 45:237-247 (2006)

· Hopf Bifurcation Formula for First Order Differential-Delay Equations R.Rand and A.Verdugo Communications in Nonlinear Science and Numerical Simulation 12:859-864 (2007)

· Synchronization in the Winfree Model of Coupled Nonlinear Oscillators D.D.Quinn, R.H.Rand and S.Strogatz Physical Review E 75:036218 (2007)

· Dynamics of Three Coupled van der Pol Oscillators with Application to Circadian Rhythms K.Rompala, R.Rand and H.Howland Communications in Nonlinear Science and Numerical Simulation 12:794-803 (2007)

· Stability of Strongly Nonlinear Normal Modes G. Recktenwald and R. Rand Communications in Nonlinear Science and Numerical Simulation 12:1128-1132 (2007)

· Trigonometric Simplification of a Class of Conservative Nonlinear Oscillators G. Recktenwald and R. Rand Nonlinear Dynamics 49:193-201 (2007)

· Two Models for the Parametric Forcing of a Nonlinear Oscillator N. Abouhazim, M. Belhaq and R.H. Rand Nonlinear Dynamics 50:147-160 (2007)

· 2:1 Resonance in the Delayed Nonlinear Mathieu Equation T.M. Morrison and R.H. Rand Nonlinear Dynamics 50:341-352 (2007)

· Effect of Quasiperiodic Gravitational Modulation on the Stability of a Heated Fluid Layer T. Boulal, S. Aniss, M. Belhaq and R. Rand Physical Review E 76:056320 (2007)

· Hopf Bifurcation in a DDE Model of Gene Expression A. Verdugo and R. Rand Communications in Nonlinear Science and Numerical Simulation 13:235-242 (2008)

· Dynamics of Four Coupled Phase-Only Oscillators R. Rand and J. Wong Communications in Nonlinear Science and Numerical Simulation 13:501-507 (2008)

· Center Manifold Analysis of a DDE Model of Gene Expression A. Verdugo and R. Rand Communications in Nonlinear Science and Numerical Simulation 13:1112-1120 (2008)