49 citations · 112 across the 15 of their papers we have counts for
16 papers
Synchronization in pairs of opto-thermally driven mechanically coupled micro-oscillators
Aditya Bhaskar, Mark Walth, Richard H. Rand +1
We study the phenomenon of synchronization in pairs of doubly clamped, mechanically coupled silicon micro-oscillators. A continuous-wave laser beam is used to drive the micro-beams…
Bistability in coupled opto-thermal micro-oscillators
Aditya Bhaskar, Mark Walth, Richard H. Rand +1
In this work, we experimentally investigate the dynamics of pairs of opto-thermally driven, mechanically coupled, doubly clamped, silicon micromechanical oscillators, and numerical…
Breaking the Symmetry in Queues with Delayed Information
Philip Doldo, Jamol Pender, Richard Rand
Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of q…
Unbounded sequences of stable limit cycles in the delayed Duffing equation: an exact analysis
Si Mohamed Sah, Bernold Fiedler, B. Shayak +1
The delayed Duffing equation is shown to possess an infinite and unbounded sequence of rapidly oscillating, asymptotically stable periodic solutions,…
Coexistence of infinitely many large, stable, rapidly oscillating periodic solutions in time-delayed Duffing oscillators
Bernold Fiedler, Alejandro López Nieto, Richard H. Rand +3
We explore stability and instability of rapidly oscillating solutions for the hard spring delayed Duffing oscillator Fix . We target…
Simplified model and analysis of a pair of coupled thermo-optical MEMS oscillators
Richard H. Rand, Alan T. Zehnder, B. Shayak +1
Motivated by the dynamics of micro-scale oscillators with thermo-optical feedback, a simplified third order model, capturing the key features of these oscillators is developed, whe…
The Mathieu Differential Equation and Generalizations to Infinite Fractafolds
Shiping Cao, Anthony Coniglio, Xueyan Niu +2
One of the well-studied equations in the theory of ODEs is the Mathieu differential equation. A common approach for obtaining solutions is to seek solutions via Fourier series by c…
Limiting the Oscillations in Queues with Delayed Information Through a Novel Type of Delay Announcement
Sophia Novitzky, Jamol Pender, Richard Rand +1
Many service systems use technology to notify customers about their expected waiting times or queue lengths via delay announcements. However, in many cases, either the information…
Dynamics of Two Coupled van der Pol Oscillators with Delay Coupling Revisited
Mark Gluzman, Richard Rand
The problem of two van der Pol oscillators coupled by velocity delay terms was studied by Wirkus and Rand in 2002. The small-epsilon analysis resulted in a slow flow which containe…
An Asymptotic Analysis of Queues with Delayed Information and Time Varying Arrival Rates
Jamol Pender, Richard H. Rand, Elizabeth Wesson
Understanding how delayed information impacts queueing systems is an important area of research. However, much of the current literature neglects one important feature of many queu…
Analysis of a remarkable singularity in a nonlinear DDE
Matthew Davidow, B. Shayak, Richard H. Rand
In this work we investigate the dynamics of the nonlinear DDE (delay-differential equation) x''(t)+x(t-T)+x(t)^3=0 where T is the delay. For T=0 this system is conservative and exh…
Low-power photothermal self-oscillation of bimetallic nanowires
Roberto De Alba, T. S. Abhilash, Richard Rand +2
We investigate the nonlinear mechanics of a bimetallic, optically absorbing SiN-Nb nanowire in the presence of incident laser light and a reflecting Si mirror. Situated in a standi…
Managing Information in Queues: The Impact of Giving Delayed Information to Customers
Jamol Pender, Richard H. Rand, Elizabeth Wesson
Delay or queue length information has the potential to influence the decision of a customer to use a service system. Thus, it is imperative for service system managers to understan…
Delay Terms in the Slow Flow
Si Mohamed Sah, Richard H. Rand
This work concerns the dynamics of nonlinear systems that are subjected to delayed self-feedback. Perturbation methods applied to such systems give rise to slow flows which charact…
Long-range Synchronization of Nanomechanical Oscillators with Light
Shreyas Y. Shah, Mian Zhang, Richard Rand +1
We experimentally demonstrate mutual synchronization of two free-running nanomechanical oscillators separated by an effective distance of 30 meters and coupled through light. Due t…
Master-Slave Locking of Optomechanical Oscillators Over A Long Distance
Shreyas Y. Shah, Mian Zhang, Richard Rand +1
Frequency-locking and other phenomena emerging from nonlinear interactions between mechanical oscillators are of scientific and technological importance. However, existing schemes…