51 research outputs found
Arbitrary distribution and nonlinear modal interaction in coupled nanomechanical resonators
We propose a general one-dimensional {\em continuous} formulation to analyze
the vibrational modes of antenna-like nanomechanical resonators consisting of
two symmetric arrays of cantilevers affixed to a central nano-beam. The
cantilever arrays can have arbitrary density and length profile along the beam.
We obtain the secular equation that allows for the determination of their
frequency spectrum and illustrate the results on the particular examples of
structures with constant or alternating cantilever length profiles. We show
that our analytical results capture the vibration spectrum of such resonators
and elucidate key relationships that could prove advantageous for experimental
device performance. Furthermore, using a perturbative approach to treat the
nonlinear and dissipative dynamics of driven structures, we analyze the
anharmonic coupling between two specific widely spaced modes of the
coupled-element device, with direct application to experiments.Comment: 8 pages, 5 figures, additional info can be found at
http://nano.bu.ed
Nonlinear supratransmission in multicomponent systems
A method is proposed to solve the challenging problem of determining the
supratransmission threshold (onset of instability of harmonic boundary driving
inside a band gap) in multicomponent nonintegrable nonlinear systems. It is
successfully applied to the degenerate three-wave resonant interaction in a
birefringent quadratic medium where the process generates spatial gap solitons.
No analytic expression is known for this model showing the broad applicability
of the method to nonlinear systems.Comment: 4 pages, 3 figure
Aharonov-Bohm effect for an exciton in a finite width nano-ring
We study the Aharonov-Bohm effect for an exciton on a nano-ring using a 2D attractive fermionic Hubbard model. We extend previous results obtained for a 1D ring in which only azimuthal motion is considered, to a more general case of 2D annular lattices. In general, we show that the
existence of the localization effect, increased by the nonlinearity, makes the phenomenon in the 2D system similar to the 1D case. However, the introduction of radial motion introduces extra frequencies, different from the original isolated frequency corresponding to the excitonic Aharonov-
Bohm oscillations. If the circumference of the system becomes large enough, the Aharonov-Bohm effect is suppressed
Transfer of BECs through discrete breathers in an optical lattice
We study the stability of a stationary discrete breather (DB) on a nonlinear
trimer in the framework of the discrete nonlinear Schr\"odinger equation
(DNLS). In previous theoretical investigations of the dynamics of Bose-Einstein
condensates in leaking optical lattices, collisions between a DB and a lattice
excitation, e.g. a moving breather (MB) or phonon, were studied. These
collisions lead to the transmission of a fraction of the incident (atomic) norm
of the MB through the DB, while the DB can be shifted in the direction of the
incident lattice excitation. Here we show that there exists a total energy
threshold of the trimer, above which the lattice excitation can trigger the
destabilization of the DB and that this is the mechanism leading to the
movement of the DB. Furthermore, we give an analytic estimate of upper bound to
the norm that is transmitted through the DB. Our analysis explains the results
of the earlier numerical studies and may help to clarify functional operations
with BECs in optical lattices such as blocking and filtering coherent (atomic)
beams.Comment: 8 pages, 5 figure
Dynamical Response of Nanomechanical Oscillators in Immiscible Viscous Fluid for in vitro Biomolecular Recognition
Dynamical response of nanomechanical cantilever structures immersed in a
viscous fluid is important to in vitro single-molecule force spectroscopy,
biomolecular recognition of disease-specific proteins, and the detection of
microscopic dynamics of proteins. Here we study the stochastic response of
biofunctionalized nanomechanical cantilevers beam in a viscous fluid. Using the
fluctuation-dissipation theorem we derive an exact expression for the spectral
density of the displacement and a linear approximation for the resonance
frequency shift. We find that in a viscous solution the frequency shift of the
nanoscale cantilever is determined by surface stress generated by biomolecular
interaction with negligible contributions from mass loading.Comment: 4 pages, 2 figures, RevTex4. See http://nano.bu.edu/ for related
paper
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