5,831 research outputs found
High-frequency asymptotic compression of dense BEM matrices for general geometries without ray tracing
Wave propagation and scattering problems in acoustics are often solved with
boundary element methods. They lead to a discretization matrix that is
typically dense and large: its size and condition number grow with increasing
frequency. Yet, high frequency scattering problems are intrinsically local in
nature, which is well represented by highly localized rays bouncing around.
Asymptotic methods can be used to reduce the size of the linear system, even
making it frequency independent, by explicitly extracting the oscillatory
properties from the solution using ray tracing or analogous techniques.
However, ray tracing becomes expensive or even intractable in the presence of
(multiple) scattering obstacles with complicated geometries. In this paper, we
start from the same discretization that constructs the fully resolved large and
dense matrix, and achieve asymptotic compression by explicitly localizing the
Green's function instead. This results in a large but sparse matrix, with a
faster associated matrix-vector product and, as numerical experiments indicate,
a much improved condition number. Though an appropriate localisation of the
Green's function also depends on asymptotic information unavailable for general
geometries, we can construct it adaptively in a frequency sweep from small to
large frequencies in a way which automatically takes into account a general
incident wave. We show that the approach is robust with respect to non-convex,
multiple and even near-trapping domains, though the compression rate is clearly
lower in the latter case. Furthermore, in spite of its asymptotic nature, the
method is robust with respect to low-order discretizations such as piecewise
constants, linears or cubics, commonly used in applications. On the other hand,
we do not decrease the total number of degrees of freedom compared to a
conventional classical discretization. The combination of the ...Comment: 24 pages, 13 figure
Complex Visibilities of Cosmic Microwave Background Anisotropies
We study the complex visibilities of the cosmic microwave background
anisotropies that are observables in interferometric observations of the cosmic
microwave background, using the multipole expansion methods commonly adopted in
analyzing single-dish experiments. This allows us to recover the properties of
the visibilities that is obscured in the flat-sky approximation. Discussions of
the window function, multipole resolution, instrumental noise, pixelization,
and polarization are given.Comment: 22 pages, 1 figure include
Maximum likelihood analysis of systematic errors in interferometric observations of the cosmic microwave background
We investigate the impact of instrumental systematic errors in
interferometric measurements of the cosmic microwave background (CMB)
temperature and polarization power spectra. We simulate interferometric CMB
observations to generate mock visibilities and estimate power spectra using the
statistically optimal maximum likelihood technique. We define a quadratic error
measure to determine allowable levels of systematic error that do not induce
power spectrum errors beyond a given tolerance. As an example, in this study we
focus on differential pointing errors. The effects of other systematics can be
simulated by this pipeline in a straightforward manner. We find that, in order
to accurately recover the underlying B-modes for r=0.01 at 28<l<384,
Gaussian-distributed pointing errors must be controlled to 0.7^\circ rms for an
interferometer with an antenna configuration similar to QUBIC, in agreement
with analytical estimates. Only the statistical uncertainty for 28<l<88 would
be changed at ~10% level. With the same instrumental configuration, we find the
pointing errors would slightly bias the 2-\sigma upper limit of the
tensor-to-scalar ratio r by ~10%. We also show that the impact of pointing
errors on the TB and EB measurements is negligibly small.Comment: 10 pages, 4 figures, accepted for publication in ApJS. Includes
improvements in clarity of presentation and Fig.4 added, in response to
refere
Theory of semiconductor quantum-wire based single- and two-qubit gates
A GaAs/AlGaAs based two-qubit quantum device that allows the controlled
generation and straightforward detection of entanglement by measuring a
stationary current-voltage characteristic is proposed. We have developed a
two-particle Green's function method of open systems and calculate the
properties of three-dimensional interacting entangled systems
non-perturbatively. We present concrete device designs and detailed, charge
self-consistent predictions. One of the qubits is an all-electric Mach-Zehnder
interferometer that consists of two electrostatically defined quantum wires
with coupling windows, whereas the second qubit is an electrostatically defined
double quantum dot located in a second two-dimensional electron gas beneath the
quantum wires. We find that the entanglement of the device can be controlled
externally by tuning the tunneling coupling between the two quantum dots.Comment: 16 pages, 13 figures, RevTex4 two-column format, to appear in Phys.
Rev.
The Schwinger Model on the lattice in the Microcanonical Fermionic Average approach
The Microcanonical Fermionic Average method has been used so far in the
context of lattice models with phase transitions at finite coupling. To test
its applicability to Asymptotically Free theories, we have implemented it in
QED, \it i.e.\rm the Schwinger Model. We exploit the possibility, intrinsic
to this method, of studying the whole plane at negligible computer
cost, to follow constant physics trajectories and measure the limit
of the chiral condensate. We recover the continuum result within 3 decimal
places.Comment: TeX file, 7 pages + 3 figures in Postscrip
The influence of noise sources on cross-correlation amplitudes
We use analytical examples and asymptotic forms to examine the mathematical
structure and physical meaning of the seismic cross correlation measurement. We
show that in general, cross correlations are not Green's functions of medium,
and may be very different depending on the source distribution. The modeling of
noise sources using spatial distributions as opposed to discrete collections of
sources is emphasized. When stations are illuminated by spatially complex
source distributions, cross correlations show arrivals at a variety of time
lags, from zero to the maximum surface-wave arrival time. Here, we demonstrate
the possibility of inverting for the source distribution using the energy of
the full cross-correlation waveform. The interplay between the source
distribution and wave attenuation in determining the functional dependence of
cross correlation energies on station-pair distance is quantified. Without
question, energies contain information about wave attenuation. However, the
accurate interpretation of such measurements is tightly connected to the
knowledge of the source distribution.Comment: 19 pages, 17 figures; Geophysical Journal Internationa
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