1,354 research outputs found
A wave-envelope of sound propagation in nonuniform circular ducts with compressible mean flows
An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave, thereby reducing the computation time and the round-off error encountered in purely numerical techniques. The solution recovers the solution based on the method of multiple scales for slowly varying duct geometry. A computer program was developed based on the wave-envelope analysis for general mean flows. Results are presented for the reflection and transmission coefficients as well as the acoustic pressure distributions for a number of conditions: both straight and variable area ducts with and without liners and mean flows from very low to high subsonic speeds are considered
Transmission of sound through nonuniform circular ducts with compressible mean flows
An acoustic theory is developed to determine the sound transmission and attenuation through an infinite, hard-walled or lined, circular duct carrying compressible, sheared, mean flows and having a variable cross section. The theory is applicable to large as well as small axial variations, as long as the mean flow does not separate. Although the theory is described for circular ducts, it is applicable to other duct configurations - annular, two dimensional, and rectangular. The theory is described for the linear problem, but the technique is general and has the advantage of being applicable to the nonlinear case as well as the linear case. The technique is based on solving for the envelopes of the quasi-parallel acoustic modes that exist in the duct instead of solving for the actual wave. A computer program was developed. The mean flow model consists of a one dimensional flow in the core and a quarter-sine profile in the boundary layer. Results are presented for the reflection and transmission coefficients in ducts with varying slopes and carrying different mean flows
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
High intermodulation gain in a micromechanical Duffing resonator
In this work we use a micromechanical resonator to experimentally study small
signal amplification near the onset of Duffing bistability. The device consists
of a PdAu beam serving as a micromechanical resonator excited by an adjacent
gate electrode. A large pump signal drives the resonator near the onset of
bistability, enabling amplification of small signals in a narrow bandwidth. To
first order, the amplification is inversely proportional to the frequency
difference between the pump and signal. We estimate the gain to be about 15dB
for our device
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
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
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
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
Mean shear flows generated by nonlinear resonant Alfven waves
In the context of resonant absorption, nonlinearity has two different
manifestations. The first is the reduction in amplitude of perturbations around
the resonant point (wave energy absorption). The second is the generation of
mean shear flows outside the dissipative layer surrounding the resonant point.
Ruderman et al. [Phys. Plasmas 4, 75 (1997)] studied both these effects at the
slow resonance in isotropic plasmas. Clack et al. [Astron. Astrophys. 494}, 317
(2009)] investigated nonlinearity at the Alfven resonance, however, they did
not include the generation of mean shear flow. In this present paper, we
investigate the mean shear flow, analytically, and study its properties. We
find that the flow generated is parallel to the magnetic surfaces and has a
characteristic velocity proportional to , where is
the dimensionless amplitude of perturbations far away from the resonance. This
is, qualitatively, similar to the flow generated at the slow resonance. The
jumps in the derivatives of the parallel and perpendicular components of mean
shear flow across the dissipative layer are derived. We estimate the generated
mean shear flow to be of the order of in both the solar
upper chromosphere and solar corona, however, this value strongly depends on
the choice of boundary conditions. It is proposed that the generated mean shear
flow can produce a Kelvin--Helmholtz instability at the dissipative layer which
can create turbulent motions. This instability would be an additional effect,
as a Kelvin--Helmholtz instability may already exist due to the velocity field
of the resonant Alfven waves. This flow can also be superimposed onto existing
large scale motions in the solar upper atmosphere.Comment: 11 page
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