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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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