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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
- Tri-Institutional 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.

## Publications

- Analysis of a remarkable singularity in a nonlinear DDE (with M. Davidow and B. Shayak), Nonlinear Dynamics 90 (2017), 317-323.
Low-power photothermal self-oscillation 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), 2411-2427.

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 Thermo-optically Driven MEMS Limit Cycle Oscillators (with A.T. Zehnder and S. Krylov), Int. J. of Non-Linear Mechanics vol.102 (2018), 92-100.

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) 108-123.