8,107 research outputs found
Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory
We present two open-source (BSD) implementations of ellipsoidal harmonic
expansions for solving problems of potential theory using separation of
variables. Ellipsoidal harmonics are used surprisingly infrequently,
considering their substantial value for problems ranging in scale from
molecules to the entire solar system. In this article, we suggest two possible
reasons for the paucity relative to spherical harmonics. The first is
essentially historical---ellipsoidal harmonics developed during the late 19th
century and early 20th, when it was found that only the lowest-order harmonics
are expressible in closed form. Each higher-order term requires the solution of
an eigenvalue problem, and tedious manual computation seems to have discouraged
applications and theoretical studies. The second explanation is practical: even
with modern computers and accurate eigenvalue algorithms, expansions in
ellipsoidal harmonics are significantly more challenging to compute than those
in Cartesian or spherical coordinates. The present implementations reduce the
"barrier to entry" by providing an easy and free way for the community to begin
using ellipsoidal harmonics in actual research. We demonstrate our
implementation using the specific and physiologically crucial problem of how
charged proteins interact with their environment, and ask: what other
analytical tools await re-discovery in an era of inexpensive computation?Comment: 25 pages, 3 figure
Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector
Terahertz (THz) imaging has the ability to see through otherwise opaque
materials. However, due to the long wavelengths of THz radiation
({\lambda}=300{\mu}m at 1THz), far-field THz imaging techniques are heavily
outperformed by optical imaging in regards to the obtained resolution. In this
work we demonstrate near-field THz imaging with a single-pixel detector. We
project a time-varying optical mask onto a silicon wafer which is used to
spatially modulate a pulse of THz radiation. The far-field transmission
corresponding to each mask is recorded by a single element detector and this
data is used to reconstruct the image of an object placed on the far side of
the silicon wafer. We demonstrate a proof of principal application where we
image a printed circuit board on the underside of a 115{\mu}m thick silicon
wafer with ~100{\mu}m ({\lambda}/4) resolution. With subwavelength resolution
and the inherent sensitivity to local conductivity provided by the THz probe
frequencies, we show that it is possible to detect fissures in the circuitry
wiring of a few microns in size. Imaging systems of this type could have other
uses where non-invasive measurement or imaging of concealed structures with
high resolution is necessary, such as in semiconductor manufacturing or in
bio-imaging
The Ursinus Weekly, February 27, 1903
A view of athletics in our schools and colleges • Monday Night Club • God\u27s hand in history • Freshman declamation contest • Society notes • Alumni notes • Ursinus Publication, No. 2https://digitalcommons.ursinus.edu/weekly/3076/thumbnail.jp
Efficient computation of hashes
The sequential computation of hashes at the core of many distributed storage systems and found, for example, in grid services can hinder efficiency in service quality and even pose security challenges that can only be addressed by the use of parallel hash tree modes. The main contributions of this paper are, first, the identification of several efficiency and security challenges posed by the use of sequential hash computation based on the Merkle-Damgard engine. In addition, alternatives for the parallel computation of hash trees are discussed, and a prototype for a new parallel implementation of the Keccak function, the SHA-3 winner, is introduced
Limits on Arcminute Scale Cosmic Microwave Background Anisotropy with the BIMA Array
We have used the Berkeley-Illinois-Maryland-Association (BIMA) millimeter
array outfitted with sensitive cm-wave receivers to search for Cosmic Microwave
Background (CMB) anisotropies on arcminute scales. The interferometer was
placed in a compact configuration which produces high brightness sensitivity,
while providing discrimination against point sources. Operating at a frequency
of 28.5 GHz, the FWHM primary beam of the instrument is 6.6 arcminutes. We have
made sensitive images of seven fields, five of which where chosen specifically
to have low IR dust contrast and be free of bright radio sources. Additional
observations with the Owens Valley Radio Observatory (OVRO) millimeter array
were used to assist in the location and removal of radio point sources.
Applying a Bayesian analysis to the raw visibility data, we place limits on CMB
anisotropy flat-band power Q_flat = 5.6 (+3.0 -5.6) uK and Q_flat < 14.1 uK at
68% and 95% confidence. The sensitivity of this experiment to flat band power
peaks at a multipole of l = 5470, which corresponds to an angular scale of
approximately 2 arcminutes. The most likely value of Q_flat is similar to the
level of the expected secondary anisotropies.Comment: 15 pages, 5 figures, LaTex, aas2pp4.sty, ApJ submitte
Detection of Cosmic Microwave Background Structure in a Second Field with the Cosmic Anisotropy Telescope
We describe observations at frequencies near 15 GHz of the second 2x2 degree
field imaged with the Cambridge Cosmic Anisotropy Telescope (CAT). After the
removal of discrete radio sources, structure is detected in the images on
characteristic scales of about half a degree, corresponding to spherical
harmonic multipoles in the approximate range l= 330--680. A Bayesian analysis
confirms that the signal arises predominantly from the cosmic microwave
background (CMB) radiation for multipoles in the lower half of this range; the
average broad-band power in a bin with centroid l=422 (theta = 51') is
estimated to be Delta_T/T=2.1^{+0.4}_{-0.5} x 10^{-5}. For multipoles centred
on l=615 (theta =35'), we find contamination from Galactic emission is
significant, and constrain the CMB contribution to the measured power in this
bin to be Delta_T/T <2.0 x 10^{-5} (1-sigma upper limit). These new results are
consistent with the first detection made by CAT in a completely different area
of sky. Together with data from other experiments, this new CAT detection adds
weight to earlier evidence from CAT for a downturn in the CMB power spectrum on
scales smaller than 1 degree. Improved limits on the values of H_0 and Omega
are determined using the new CAT data.Comment: 5 pages, 5 figures (gif), submitted to MNRA
Foundation of Statistical Mechanics under experimentally realistic conditions
We demonstrate the equilibration of isolated macroscopic quantum systems,
prepared in non-equilibrium mixed states with significant population of many
energy levels, and observed by instruments with a reasonably bound working
range compared to the resolution limit. Both properties are fulfilled under
many, if not all, experimentally realistic conditions. At equilibrium, the
predictions and limitations of Statistical Mechanics are recovered.Comment: Accepted in Phys. Rev. Let
Large-Scale Sunyaev-Zel'dovich Effect: Measuring Statistical Properties with Multifrequency Maps
We study the prospects for extracting detailed statistical properties of the
Sunyaev-Zel'dovich (SZ) effect associated with large scale structure using
upcoming multifrequency CMB experiments. The greatest obstacle to detecting the
large-angle signal is the confusion noise provided by the primary anisotropies
themselves, and to a lesser degree galactic and extragalactic foregrounds. We
employ multifrequency subtraction techniques and the latest foregrounds models
to determine the detection threshold for the Boomerang, MAP (several microK)
and Planck CMB (sub microK) experiments. Calibrating a simplified biased-tracer
model of the gas pressure off recent hydrodynamic simulations, we estimate the
SZ power spectrum, skewness and bispectrum through analytic scalings and N-body
simulations of the dark matter. We show that the Planck satellite should be
able to measure the SZ effect with sufficient precision to determine its power
spectrum and higher order correlations, e.g. the skewness and bispectrum.
Planck should also be able to detect the cross correlation between the SZ and
gravitational lensing effect in the CMB. Detection of these effects will help
determine the properties of the as yet undetected gas, including the manner in
which the gas pressure traces the dark matter.Comment: 13 ApJ pages, 11 figures; typos and figure 5 revised; submitted to
Ap
Two-Center Integrals for r_{ij}^{n} Polynomial Correlated Wave Functions
All integrals needed to evaluate the correlated wave functions with
polynomial terms of inter-electronic distance are included. For this form of
the wave function, the integrals needed can be expressed as a product of
integrals involving at most four electrons
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