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Richard Rand
Professor, Stephen H. Weiss Presidential Fellow
Departments/Programs
 Mathematics
Graduate Fields
 Applied Mathematics
 Biological and Environmental Engineering
 Computational Biology
 Mathematics
 Mechanical Engineering
 Theoretical and Applied Mechanics
 TriInstitutional Program in Computational Biology and Medicine (CBM)
Affiliations
 Mechanical and Aerospace Engineering
Research
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 equations with delay terms and include applications to MEMS (micro electrical mechanical systems), queueing theory and synchrotron dynamics. These projects are conducted jointly with graduate students and with experts in the respective application area.
Courses
Spring 2022
Fall 2022
 MATH 2930 : Differential Equations for Engineers
 MATH 4900 : Supervised Research
 MATH 4901 : Supervised Reading
Publications
 Analysis of a remarkable singularity in a nonlinear DDE (with M. Davidow and B. Shayak), Nonlinear Dynamics 90 (2017), 317323.

Lowpower photothermal selfoscillation of bimetallic nanowires (with R. De Alba, T.S. Abhilash, H.G. Craighead and J.M. Parpia), Nano Letters 17(7) (2017), 3995.

An Asymptotic Analysis of Queues with Delayed Information and Time Varying Arrival Rates (with J. Pender and E. Wesson), Nonlinear Dynamics 91 (2018), 24112427.

Mathieu’s Equation and Its Generalizations: Overview of Stability Charts and Their Features (with I. Kovacic and S.M. Sah), Applied Mechanics Reviews vol.70 (2018), 020802.

Phase Locking of Electrostatically Coupled Thermooptically Driven MEMS Limit Cycle Oscillators (with A.T. Zehnder and S. Krylov), Int. J. of NonLinear Mechanics vol.102 (2018), 92100.

The Dynamics of One Way Coupling in a System of Nonlinear Mathieu Equations (with A. Bernstein and R. Meller) The Open Mechanical Engineering Journal 12 (2018) 108123.