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Nonlinear stochastic dynamics of a nanomechanical resonator coupled to a single electron transistor

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Text
TitleInfo (ID = T-1); (type = )
Title
Nonlinear stochastic dynamics of a nanomechanical resonator coupled to a single electron transistor
Identifier (type = hdl)
http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16761
Identifier
ETD_497
Language
LanguageTerm
English
Genre (authority = marcgt)
theses
Subject (ID = SBJ-1); (authority = RUETD)
Topic
Mechanical and Aerospace Engineering
Subject (ID = SBJ-1); (authority = ETD-LCSH)
Topic
Nanoelectromechanical systems
Subject (ID = SBJ-1); (authority = ETD-LCSH)
Topic
Nanoelectronics
Abstract
Nanoelectromechanical systems (NEMS) comprise nanometer to micrometer scale mechanical oscillators coupled to electronic devices of comparable dimensions. NEMS have great potential for sensor applications as well as for exploring fundamental physics. The dynamics of a nanomechanical resonator coupled to a single electron transistor (SET) is considered in the Duffing regime using a master equation approach and a Langevin approach. In the first approach, the master equations are derived and solved using a finite element method as well as a moment approximation method for both the single-well and the (inverted) double-well Duffing potentials. It is observed that the SET damps the resonator motion much more effectively in the single-well Duffing case in comparison with the linear case. In the double-well case we observe the existence of a limit cycle wherein the SET and the resonator exist in a state of dynamic equilibrium. This is followed by the onset of instability in the numerical solutions. The results from the master equation approach are used in a numerical fitting procedure to characterize the damping term in the averaged equations of motion of the system. It is observed that a linear damping term provides the best fit in all cases except for the strongly nonlinear regime. Based on this result, a Langevin equation is written down from which a Fokker-Planck equation is derived for the system. The Fokker-Planck equation is solved analytically, in closed form, for the steady state. In the time dependent case, the equation is solved using a finite element method and the results are shown to be in qualitative agreement with those obtained using the master equation approach. Therefore it is established that the SET-resonator system attains a steady state much more rapidly in the single-well Duffing regime. Finally, the steady state analytical solution to the Fokker-Planck equation is utilized to show that the steady state effective temperature is lower in the presence of the single-well Duffing nonlinearity.
PhysicalDescription
Extent
xiv, 148 pages
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application/pdf
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Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 144-147).
Name (ID = NAME-1); (type = personal)
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Ramakrishnan
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Subramanian
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Subramanian Ramakrishnan
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Benaroya
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Haym
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Haym Benaroya
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Baruh
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Haim
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Advisory Committee
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Haim Baruh
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NamePart (type = family)
Norris
NamePart (type = given)
Andrew
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RoleTerm (authority = RULIB); (type = )
internal member
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Advisory Committee
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Andrew Norris
Name (ID = NAME-5); (type = personal)
NamePart (type = family)
Gajic
NamePart (type = given)
Zoran
Role
RoleTerm (authority = RULIB); (type = )
outside member
Affiliation
Advisory Committee
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Zoran Gajic
Name (ID = NAME-1); (type = corporate)
NamePart
Rutgers University
Role
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degree grantor
Name (ID = NAME-2); (type = corporate)
NamePart
Graduate School - New Brunswick
Role
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school
OriginInfo
DateCreated (point = ); (qualifier = exact)
2007
DateOther (qualifier = exact); (type = degree)
2007
Location
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NjNbRU
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TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Identifier (type = doi)
doi:10.7282/T37D2VJP
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The author owns the copyright to this work.
Copyright
Status
Copyright protected
Availability
Status
Open
AssociatedEntity (AUTHORITY = rulib); (ID = 1)
Name
SUBRAMANIAN RAMAKRISHNAN
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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Detail
Non-exclusive ETD license
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License
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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