The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipation

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dc.contributor.authorPaul, Mark R.en
dc.contributor.authorClark, M. T.en
dc.contributor.authorCross, M. C.en
dc.date.accessioned2024-10-07T19:11:37Zen
dc.date.available2024-10-07T19:11:37Zen
dc.date.issued2006-08-21en
dc.description.abstractThe stochastic dynamics of micron and nanoscale cantilevers immersed in a viscous fluid are quantified. Analytical results are presented for long slender cantilevers driven by Brownian noise. The spectral density of the noise force is not assumed to be white and the frequency dependence of the noise force is determined from the fluctuation-dissipation theorem. The analytical results are shown to be useful for the micron scale cantilevers that are commonly used in atomic force microscopy. A general thermodynamic approach is developed that is valid for cantilevers of arbitrary geometry as well as for arrays of multiple cantilevers whose stochastic motion is coupled through the fluid. It is shown that the fluctuation-dissipation theorem permits the calculation of stochastic quantities via straightforward deterministic methods. The thermodynamic approach is used with deterministic finite element numerical simulations to quantify the auto-correlation and noise spectrum of cantilever fluctuations for a single micron scale cantilever and the cross-correlations and noise spectra of fluctuations for an array of two experimentally motivated nanoscale cantilevers as a function of cantilever separation. The results are used to quantify the noise reduction possible using correlated measurements with two closely spaced nanoscale cantilevers. © IOP Publishing Ltd.en
dc.description.notesSubmitted to Nanotechnology April 26, 2006en
dc.description.versionPublished versionen
dc.format.extentPages 4502-4513en
dc.format.extent12 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1088/0957-4484/17/17/037en
dc.identifier.eissn1361-6528en
dc.identifier.issn0957-4484en
dc.identifier.issue17en
dc.identifier.orcidPaul, Mark [0000-0002-0701-1955]en
dc.identifier.other077GXen
dc.identifier.urihttps://hdl.handle.net/10919/121292en
dc.identifier.volume17en
dc.language.isoenen
dc.publisherIOP Publishingen
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000240018200037&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.relation.urihttp://dx.doi.org/10.1088/0957-4484/17/17/037en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.titleThe stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipationen
dc.title.serialNanotechnologyen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
pubs.organisational-groupVirginia Techen
pubs.organisational-groupVirginia Tech/Engineeringen
pubs.organisational-groupVirginia Tech/Engineering/Mechanical Engineeringen
pubs.organisational-groupVirginia Tech/All T&R Facultyen
pubs.organisational-groupVirginia Tech/Engineering/COE T&R Facultyen

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