Matches in SemOpenAlex for { <https://semopenalex.org/work/W2952865764> ?p ?o ?g. }
- W2952865764 endingPage "274" @default.
- W2952865764 startingPage "239" @default.
- W2952865764 abstract "In this paper we formulate an initial-boundary-value-problem describing the three-dimensional motion of a cantilever in a Magnetic Resonance Force Microscopy setup. The equations of motion are then reduced to a modal dynamical system using a Galerkin ansatz and the respective nonlinear forces are expanded to cubic order. The direct application of the asymptotic multiple scales method to the truncated quadratic modal system near a 2:1 internal resonance revealed conditions for periodic and quasiperiodic energy transfer between the transverse in-plane and out-of-plane modes of the MRFM cantilever. However, several discrepancies are found when comparing the asymptotic results to numerical simulations of the full nonlinear system. Therefore, we employ the reconstitution multiple scales method to a modal system incorporating both quadratic and cubic terms and derive an internal resonance bifurcation structure that includes multiple coexisting in-plane and out-of-plane solutions. This structure is verified and reveals a strong dependency on initial conditions in which orbital instabilities and complex out-of-plane non-stationary motions are found. The latter are investigated via numerical integration of the corresponding slowly-varying evolution equations which reveal that breakdown of quasiperiodic tori is associated with symmetry-breaking and emergence of irregular solutions with a dense spectral content." @default.
- W2952865764 created "2019-06-27" @default.
- W2952865764 creator A5010028754 @default.
- W2952865764 date "2004-12-01" @default.
- W2952865764 modified "2023-09-26" @default.
- W2952865764 title "The magnetic resonance force microscope" @default.
- W2952865764 cites W1499169484 @default.
- W2952865764 cites W1549365206 @default.
- W2952865764 cites W1629080377 @default.
- W2952865764 cites W1963582214 @default.
- W2952865764 cites W1964678990 @default.
- W2952865764 cites W1965245884 @default.
- W2952865764 cites W1967393072 @default.
- W2952865764 cites W1967799293 @default.
- W2952865764 cites W1968031729 @default.
- W2952865764 cites W1968041430 @default.
- W2952865764 cites W1968743074 @default.
- W2952865764 cites W1969049512 @default.
- W2952865764 cites W1969845231 @default.
- W2952865764 cites W1970665015 @default.
- W2952865764 cites W1971855778 @default.
- W2952865764 cites W1973639807 @default.
- W2952865764 cites W1974472269 @default.
- W2952865764 cites W1978547412 @default.
- W2952865764 cites W1980745639 @default.
- W2952865764 cites W1981231706 @default.
- W2952865764 cites W1981999046 @default.
- W2952865764 cites W1983718136 @default.
- W2952865764 cites W1983771928 @default.
- W2952865764 cites W1984843055 @default.
- W2952865764 cites W1988931510 @default.
- W2952865764 cites W1992336297 @default.
- W2952865764 cites W1993120286 @default.
- W2952865764 cites W1993499966 @default.
- W2952865764 cites W1993664353 @default.
- W2952865764 cites W1994933392 @default.
- W2952865764 cites W1995571561 @default.
- W2952865764 cites W2000268757 @default.
- W2952865764 cites W2001154356 @default.
- W2952865764 cites W2002765969 @default.
- W2952865764 cites W2004628543 @default.
- W2952865764 cites W2008317504 @default.
- W2952865764 cites W2008607197 @default.
- W2952865764 cites W2009445786 @default.
- W2952865764 cites W2010584380 @default.
- W2952865764 cites W2011109350 @default.
- W2952865764 cites W2014592750 @default.
- W2952865764 cites W2015552098 @default.
- W2952865764 cites W2016627128 @default.
- W2952865764 cites W2020137105 @default.
- W2952865764 cites W2022361921 @default.
- W2952865764 cites W2024347200 @default.
- W2952865764 cites W2024847743 @default.
- W2952865764 cites W2025004897 @default.
- W2952865764 cites W2029368235 @default.
- W2952865764 cites W2030033660 @default.
- W2952865764 cites W2033571651 @default.
- W2952865764 cites W2034759794 @default.
- W2952865764 cites W2035324608 @default.
- W2952865764 cites W2039690075 @default.
- W2952865764 cites W2042273419 @default.
- W2952865764 cites W2043072234 @default.
- W2952865764 cites W2043293864 @default.
- W2952865764 cites W2043609312 @default.
- W2952865764 cites W2048519790 @default.
- W2952865764 cites W2049203171 @default.
- W2952865764 cites W2051001465 @default.
- W2952865764 cites W2051007954 @default.
- W2952865764 cites W2058261705 @default.
- W2952865764 cites W2058287710 @default.
- W2952865764 cites W2059647391 @default.
- W2952865764 cites W2060133815 @default.
- W2952865764 cites W2061209688 @default.
- W2952865764 cites W2061834409 @default.
- W2952865764 cites W2066595970 @default.
- W2952865764 cites W2067852949 @default.
- W2952865764 cites W2072481443 @default.
- W2952865764 cites W2073336084 @default.
- W2952865764 cites W2073621369 @default.
- W2952865764 cites W2074221987 @default.
- W2952865764 cites W2076111440 @default.
- W2952865764 cites W2076649086 @default.
- W2952865764 cites W2077830450 @default.
- W2952865764 cites W2079806014 @default.
- W2952865764 cites W2080667709 @default.
- W2952865764 cites W2080696558 @default.
- W2952865764 cites W2082929626 @default.
- W2952865764 cites W2083444202 @default.
- W2952865764 cites W2083980223 @default.
- W2952865764 cites W2085104654 @default.
- W2952865764 cites W2088131027 @default.
- W2952865764 cites W2088657130 @default.
- W2952865764 cites W2089179315 @default.
- W2952865764 cites W2089650090 @default.
- W2952865764 cites W2089748447 @default.
- W2952865764 cites W2091250642 @default.
- W2952865764 cites W2094837872 @default.
- W2952865764 cites W2095033021 @default.