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Research

The following projects are currently under development at Villanova's Nonlinear Stochastic Systems Laboratory:

Energy Localization in MEMS Arrays

Discrete breathers (also known as Intrinsic Localized Modes) are localizations of energy observed in the response of perfectly periodic Hamiltonian lattices to external forcing. Observed recently also in micro-scale oscillator (MEMS) arrays, we study using analytical and computational techniques, the influences of stochastic forces on the emergence and control of localizations in such arrays.

Representative Publications
  • 'Energy localization and white noise induced enhancement of response in a micro-scale oscillator array', Ramakrishnan S. and Balachandran B., Nonlinear Dynamics (62) 1-16, (2010).
  • 'The Influence of White Noise on Discrete Breathers in Nonlinearly Coupled Microcantilever Arrays', Ramakrishnan S. and Balachandran B., In: G. Stepan  et al. (eds.) Proceedings of IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments, Budapest, Hungary, IUTAM Book Series, Vol. 30,  pp. 247-254, Springer, 2011.
  • 'Effects of Noise on Energy Localization in Microelectromechanical Resonator Arrays', Ramakrishnan S. and Balachandran B., In: B. Dattaguru et al. (eds.), IUTAM Symposium on Multifunctional Material Structures and Systems, Bangalore, India, IUTAM Book Series, Vol. 19,  pp. 325- 334, Springer, 2010.
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Dynamics of Robotic Swarms Inspired by Complex (Biological) Systems

Complex systems are often characterized by emergent behavior as a collective that cannot be extrapolated from the analysis of individual behavior.  The realization of engineered complex systems such as robotic swarms inspired by biological systems is currently an area of intense research. We study the dynamics of robotic swarm systems with a focus on control of emergent behavior. In particular, our recent efforts have resulted in a novel analytical model for ant foraging.

Representative Publications
  • "Robot swarming over the Internet", Gilles J., Sharma B.R., Ferenc W, Kastein H, Lieu L, Wilson R, Huang Y R,  Bertozzi A,  HomChaudhuri B, Ramakrishnan S and Kumar M. American Control Conference, Montreal, 2012, (accepted).
  • "Synthesis and analysis of control laws for swarm of mobile robots emulating ant foraging behavior", Ramakrishnan S. and Kumar M., ASME 2010 Dynamic Systems and Control Conference, Boston, Massachusetts, September 2010 (invited session).
  • "A new analytical model for ant foraging", Ramakrishnan S., Laurent T., Kumar M. and Bertozzi A. (submitted).
  • "Analysis of a new PDE based model for ant foraging", Kumar M., Ramakrishnan S., Laurent T. and Bertozzi A., 9th American Institute of Mathematical Sciences (AIMS) Conference on Dynamical Systems, Orlando, Florida, July 2012 (invited session).
  • "Control laws for a swarm of mobile robots emulating ant foraging behavior: Theory and Experiments", Ramakrishnan S., Sharma B.R., Homchaudhari B. and Kumar M., (submitted).
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Vibration Energy Harvesting

In the quest for novel sustainable energy sources, energy harvesting using micro-scale piezoelectric systems that convert ambient kinetic energy to electrical power is a promising concept. Our research focuses on the analysis of the interplay between stochastic and nonlinear effects in such systems with a view towards enhancing harvesting efficiency.

Representative Publications
  • 'Nonlinear energy harvesting using coupled micro-scale oscillator arrays', Ramakrishnan S. and Kumar M., ASME 2011 5th International Conference on Energy Sustainability, Washington D.C., August 2011.
  • 'Stochastic analysis of nonlinear oscillators for vibration energy harvesting', Ramakrishnan S. and Kumar M. (submitted).
 
 

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Dynamics and Control of NanoElectroMechanical Systems

NEMS refers to micro to nano scale mechanical oscillators coupled to electronic devices of comparable dimensions. NEMS have shown immense promise for fundamental advances in applications such as sensing as well as for futuristic ideas such as quantum enabled technologies. Our research is focused on the nonlinear dynamics of NEMS.

Representative Publications
  • 'Dynamics of a Duffing nanomechanical resonator coupled to a single-electron transistor: A master equation approach', Ramakrishnan S., Gulak Y., Benaroya H. Physical Review B (78) 174304 (2008). This paper was selected for publication in Virtual Journal of Nanoscale Sci. and Tech. (18) 21 (2008).
  • 'Nonlinear Dynamics of Nanomechanical Resonators', Ramakrishnan S. et al., (Session S22:7) American Physical Society, March Meeting, Denver CO, March 2007.
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