1,306 research outputs found
Parametric resonances in electrostatically interacting carbon nanotube arrays
We study, numerically and analytically, a model of a one-dimensional array of
carbon nanotube resonators in a two-terminal configuration. The system is
brought into resonance upon application of an AC-signal superimposed on a
DC-bias voltage. When the tubes in the array are close to each other,
electrostatic interactions between tubes become important for the array
dynamics. We show that both transverse and longitudinal parametric resonances
can be excited in addition to primary resonances. The intertube electrostatic
interactions couple modes in orthogonal directions and affect the mode
stability.Comment: 11 pages, 12 figures, RevTeX
On the variational homotopy perturbation method for nonlinear oscillators
In this paper we discuss a recent application of a variational homotopy
perturbation method to rather simple nonlinear oscillators . We show that the
main equations are inconsistent and for that reason the results may be of
scarce utility
Nonparallel stability of two-dimensional nonuniformly heated boundary-layer flows
An analysis is presented for the linear stability of water boundary-layer flows over nonuniformly flat plates. Included in the analysis are disturbances due to velocity, pressure, temperatures, density, and transport properties as well as variations of the liquid properties with temperature. The method of multiple scales is used to account for the nonparallelism of the mean flow. In contrast with previous analyses, the nonsimilarity of the mean flow is taken into account. No analysis agrees, even qualitatively, with the experimental data when similar profiles are used. However, both the parallel and nonparallel results qualitatively agree with the experimental results of Strazisar and Reshotko when nonsimilar profiles are used
Breakdown of Conformal Invariance at Strongly Random Critical Points
We consider the breakdown of conformal and scale invariance in random systems
with strongly random critical points. Extending previous results on
one-dimensional systems, we provide an example of a three-dimensional system
which has a strongly random critical point. The average correlation functions
of this system demonstrate a breakdown of conformal invariance, while the
typical correlation functions demonstrate a breakdown of scale invariance. The
breakdown of conformal invariance is due to the vanishing of the correlation
functions at the infinite disorder fixed point, causing the critical
correlation functions to be controlled by a dangerously irrelevant operator
describing the approach to the fixed point. We relate the computation of
average correlation functions to a problem of persistence in the RG flow.Comment: 9 page
Superconducting Nanowires as Nonlinear Inductive Elements for Qubits
We report microwave transmission measurements of superconducting Fabry-Perot
resonators (SFPR), having a superconducting nanowire placed at a supercurrent
antinode. As the plasma oscillation is excited, the supercurrent is forced to
flow through the nanowire. The microwave transmission of the resonator-nanowire
device shows a nonlinear resonance behavior, significantly dependent on the
amplitude of the supercurrent oscillation. We show that such
amplitude-dependent response is due to the nonlinearity of the current-phase
relationship (CPR) of the nanowire. The results are explained within a
nonlinear oscillator model of the Duffing oscillator, in which the nanowire
acts as a purely inductive element, in the limit of low temperatures and low
amplitudes. The low quality factor sample exhibits a "crater" at the resonance
peak at higher driving power, which is due to dissipation. We observe a
hysteretic bifurcation behavior of the transmission response to frequency sweep
in a sample with a higher quality factor. The Duffing model is used to explain
the Duffing bistability diagram. We also propose a concept of a nanowire-based
qubit that relies on the current dependence of the kinetic inductance of a
superconducting nanowire.Comment: 28 pages, 7 figure
Quasienergy description of the driven Jaynes-Cummings model
We analyze the driven resonantly coupled Jaynes-Cummings model in terms of a
quasienergy approach by switching to a frame rotating with the external
modulation frequency and by using the dressed atom picture. A quasienergy
surface in phase space emerges whose level spacing is governed by a rescaled
effective Planck constant. Moreover, the well-known multiphoton transitions can
be reinterpreted as resonant tunneling transitions from the local maximum of
the quasienergy surface. Most importantly, the driving defines a quasienergy
well which is nonperturbative in nature. The quantum mechanical quasienergy
state localized at its bottom is squeezed. In the Purcell limited regime, the
potential well is metastable and the effective local temperature close to its
minimum is uniquely determined by the squeezing factor. The activation occurs
in this case via dressed spin flip transitions rather than via quantum
activation as in other driven nonlinear quantum systems such as the quantum
Duffing oscillator. The local maximum is in general stable. However, in
presence of resonant coherent or dissipative tunneling transitions the system
can escape from it and a stationary state arises as a statistical mixture of
quasienergy states being localized in the two basins of attraction. This gives
rise to a resonant or an antiresonant nonlinear response of the cavity at
multiphoton transitions. The model finds direct application in recent
experiments with a driven superconducting circuit QED setup.Comment: 13 pages, 8 fi
Noise-enabled precision measurements of a Duffing nanomechanical resonator
We report quantitative experimental measurements of the nonlinear response of
a radiofrequency mechanical resonator, with very high quality factor, driven by
a large swept-frequency force. We directly measure the noise-free transition
dynamics between the two basins of attraction that appear in the nonlinear
regime, and find good agreement with those predicted by the one-dimensional
Duffing equation of motion. We then measure the response of the transition
rates to controlled levels of white noise, and extract the activation energy
from each basin. The measurements of the noise-induced transitions allow us to
obtain precise values for the critical frequencies, the natural resonance
frequency, and the cubic nonlinear parameter in the Duffing oscillator, with
direct applications to high sensitivity parametric sensors based on these
resonators.Comment: 5 pages, 5 figure
Geometric model and analysis of rod-like large space structures
The application of geometrical schemes to large sphere antenna reflectors was investigated. The purpose of these studies is to determine the shape and size of flat segmented surfaces which approximate general shells of revolution and in particular spherical and paraboloidal reflective surfaces. The extensive mathematical and computational geometry analyses of the reflector resulted in the development of a general purpose computer program. This program is capable of generating the complete design parameters of the dish and can meet stringent accuracy requirements. The computer program also includes a graphical self contained subroutine which graphically displays the required design
Geometric modeling and analysis of large latticed surfaces
The application of geometrical schemes, similar to geodesic domes, to large spherical antenna reflectors was investigated. The shape and size of flat segmented latticed surfaces which approximate general shells of revolution, and in particular spherical and paraboloidal reflective surfaces, were determined. The extensive mathematical and computational geometric analyses of the reflector resulted in the development of a general purpose computer program capable of generating the complete design parameters of the dish. The program also includes a graphical self contained subroutine for graphic display of the required design
Effective constitutive relations for large repetitive frame-like structures
Effective mechanical properties for large repetitive framelike structures are derived using combinations of strength of material and orthogonal transformation techniques. Symmetry considerations are used in order to identify independent property constants. The actual values of these constants are constructed according to a building block format which is carried out in the three consecutive steps: (1) all basic planar lattices are identified; (2) effective continuum properties are derived for each of these planar basic grids using matrix structural analysis methods; and (3) orthogonal transformations are used to determine the contribution of each basic set to the overall effective continuum properties of the structure
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