7,279 research outputs found
Sommerfeld's image method in the calculation of van der Waals forces
We show how the image method can be used together with a recent method
developed by C. Eberlein and R. Zietal to obtain the dispersive van der Waals
interaction between an atom and a perfectly conducting surface of arbitrary
shape. We discuss in detail the case of an atom and a semi- infinite conducting
plane. In order to employ the above procedure to this problem it is necessary
to use the ingenious image method introduced by Sommerfeld more than one
century ago, which is a generalization of the standard procedure. Finally, we
briefly discuss other interesting situations that can also be treated by the
joint use of Sommerfeld's image technique and Eberlein-Zietal method.Comment: To appear in the proceedings of Conference on Quantum Field Theory
under the Influence of External Conditions (QFEXT11
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
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
Alternative Fourier Expansions for Inverse Square Law Forces
Few-body problems involving Coulomb or gravitational interactions between
pairs of particles, whether in classical or quantum physics, are generally
handled through a standard multipole expansion of the two-body potentials. We
discuss an alternative based on a compact, cylindrical Green's function
expansion that should have wide applicability throughout physics. Two-electron
"direct" and "exchange" integrals in many-electron quantum systems are
evaluated to illustrate the procedure which is more compact than the standard
one using Wigner coefficients and Slater integrals.Comment: 10 pages, latex/Revtex4, 1 figure
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
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
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