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Nonlinear Dynamics of Transition Waves in Multi-Stable Discrete and Continuous Media


Nadkarni, Neel P. (2017) Nonlinear Dynamics of Transition Waves in Multi-Stable Discrete and Continuous Media. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9DR2SG2.


The concept of phase transitions, i.e., switching between two or more different equilibrium states of a system, is commonly encountered in many physical, chemical and biological phenomena. The exact mechanism of this switching is a highly nonlinear dynamical process that is accommodated by the propagation of a localized wave. The characteristics of the nonlinear wave such as its profile, velocity, energy, and width of transition are governed by the type and specifics of the system that it is propagating through which may be conservative, dissipative, or diffusive in nature. The goal of this thesis is to develop a fundamental understanding of the dynamics of such processes in general nonlinear systems capable of undergoing phase transitions and the application of new theories to elucidate the kinetic and energetic properties of transition waves in different scenarios. In conservative systems, we show that there are three different modes of stable wave propagation that we analytically solve for and validate computationally. In contrast, dissipative and diffusive systems allow the stable propagation of only the strongly nonlinear kink mode whose kinetic energy and propagation velocity are linked through a linear relation. We further validate our results in dissipative systems experimentally by fabricating and testing a strongly nonlinear lattice and show that transition waves are unidirectional in nature, as predicted by theory. Finally, as an application, we devise a strategy of using the physics of dissipative phase transitions to propagate stable mechanical signals in highly dissipative media such as soft polymers which effectively damp out small-amplitude linear waves.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:phase transitions; nonlinear dynamics; discrete and continuum solid mechanics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Awards:Ernest E. Sechler Memorial Award in Aeronautics, 2016
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Kochmann, Dennis M. (advisor)
  • Daraio, Chiara (advisor)
Thesis Committee:
  • Ravichandran, Guruswami (chair)
  • Kochmann, Dennis M.
  • Daraio, Chiara
  • Cross, Michael Clifford
  • Abeyaratne, Rohan
Defense Date:2 December 2016
Funding AgencyGrant Number
National Science FoundationCMMI-1200319
Coco and Foster Stanback Space Initiative FundUNSPECIFIED
Record Number:CaltechTHESIS:01132017-035026894
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for Ch. 2 adapted for Ch. 3 adapted for Ch. 4 adapted for Ch. 5
Nadkarni, Neel P.0000-0002-4311-2817
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10010
Deposited By: Neel Nadkarni
Deposited On:13 Mar 2017 22:24
Last Modified:08 Nov 2023 00:21

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