6,947 research outputs found
Averages and moments associated to class numbers of imaginary quadratic fields
For any odd prime , let denote the -part of the
class number of the imaginary quadratic field .
Nontrivial pointwise upper bounds are known only for ; nontrivial
upper bounds for averages of have previously been known only for
. In this paper we prove nontrivial upper bounds for the average of
for all primes , as well as nontrivial upper bounds
for certain higher moments for all primes .Comment: 26 pages; minor edits to exposition and notation, to agree with
published versio
Simulation model of erosion and deposition on a barchan dune
Erosion and deposition over a barchan dune near the Salton Sea, California, are modeled by bookkeeping the quantity of sand in saltation following streamlines of transport. Field observations of near surface wind velocity and direction plus supplemental measurements of the velocity distribution over a scale model of the dune are combined as input to Bagnold type sand transport formulas corrected for slope effects. A unidirectional wind is assumed. The resulting patterns of erosion and deposition compare closely with those observed in the field and those predicted by the assumption of equilibrium (downwind translation of the dune without change in size or geometry). Discrepancies between the simulated results and the observed or predicted erosional patterns appear to be largely due to natural fluctuations in the wind direction. The shape of barchan dunes is a function of grain size, velocity, degree of saturation of the oncoming flow, and the variability in the direction of the oncoming wind. The size of the barchans may be controlled by natural atmospheric scales, by the age of the dunes, or by the upwind roughness. The upwind roughness can be controlled by fixed elements or by sand in the saltation. In the latter case, dune scale is determined by grain size and wind velocity
High-fidelity simulation of an ultrasonic standing-wave thermoacoustic engine with bulk viscosity effects
We have carried out boundary-layer-resolved, unstructured fully-compressible
Navier--Stokes simulations of an ultrasonic standing-wave thermoacoustic engine
(TAE) model. The model is constructed as a quarter-wavelength engine,
approximately 4 mm by 4 mm in size and operating at 25 kHz, and comprises a
thermoacoustic stack and a coin-shaped cavity, a design inspired by Flitcroft
and Symko (2013). Thermal and viscous boundary layers (order of 10
m) are resolved. Vibrational and rotational molecular relaxation
are modeled with an effective bulk viscosity coefficient modifying the viscous
stress tensor. The effective bulk viscosity coefficient is estimated from the
difference between theoretical and semi-empirical attenuation curves.
Contributions to the effective bulk viscosity coefficient can be identified as
from vibrational and rotational molecular relaxation. The inclusion of the
coefficient captures acoustic absorption from infrasonic (10 Hz) to
ultrasonic (100 kHz) frequencies. The value of bulk viscosity depends on
pressure, temperature, and frequency, as well as the relative humidity of the
working fluid. Simulations of the TAE are carried out to the limit cycle, with
growth rates and limit-cycle amplitudes varying non-monotonically with the
magnitude of bulk viscosity, reaching a maximum for a relative humidity level
of 5%. A corresponding linear model with minor losses was developed; the linear
model overpredicts transient growth rate but gives an accurate estimate of
limit cycle behavior. An improved understanding of thermoacoustic energy
conversion in the ultrasonic regime based on a high-fidelity computational
framework will help to further improve the power density advantages of
small-scale thermoacoustic engines.Comment: 55th AIAA Aerospace Sciences Meeting, AIAA SciTech, 201
Inversion of spinning sound fields
A method is presented for the reconstruction of rotating monopole source
distributions using acoustic pressures measured on a sideline parallel to the
source axis. The method requires no \textit{a priori} assumptions about the
source other than that its strength at the frequency of interest vary
sinusoidally in azimuth on the source disc so that the radiated acoustic field
is composed of a single circumferential mode. When multiple azimuthal modes are
present, the acoustic field can be decomposed into azimuthal modes and the
method applied to each mode in sequence.
The method proceeds in two stages, first finding an intermediate line source
derived from the source distribution and then inverting this line source to
find the radial variation of source strength. A far-field form of the radiation
integrals is derived, showing that the far field pressure is a band-limited
Fourier transform of the line source, establishing a limit on the quality of
source reconstruction which can be achieved using far-field measurements. The
method is applied to simulated data representing wind-tunnel testing of a
ducted rotor system (tip Mach number~0.74) and to control of noise from an
automotive cooling fan (tip Mach number~0.14), studies which have appeared in
the literature of source identification.Comment: Revised version of paper submitted to JASA; five more figures;
expanded content with more discussion of error behaviour and relation to
Nearfield Acoustical Holograph
Readout of solid-state charge qubits using a single-electron pump
A major difficulty in realizing a solid-state quantum computer is the
reliable measurement of the states of the quantum registers. In this paper, we
propose an efficient readout scheme making use of the resonant tunneling of a
ballistic electron produced by a single electron pump. We treat the measurement
interaction in detail by modeling the full spatial configuration, and show that
for pumped electrons with suitably chosen energy the transmission coefficient
is very sensitive to the qubit state. We further show that by using a short
sequence of pumping events, coupled with a simple feedback control procedure,
the qubit can be measured with high accuracy.Comment: 5 pages, revtex4, 4 eps figures. v2: published versio
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