Application of the SSCTRK numerical simulation program to the evaluation of the SSC magnet aperture

The SSCTRK numerical simulation code has been used to estimate the benefit of increasing the SSC dipole aperture from 4 to 5 cm. The increase in maximum amplitude of stable betatron oscillations depends on the level to which systematic errors have been corrected. Two cases have been studied, a highly corrected ring and a ring with limited corrections. The maximum stable amplitude increase is approximately a factor of the ring with limited systematic corrections. The aperture comparison has been made at 10{sup 5} revolutions. Magnetic error assumptions are described in detail and a new table of errors suggested for future simulations is given. 8 figs., 6 tabs

Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations

Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation of the partition functions for particles that carry internal quantum numbers. The partition function is shown to be a sum of one or more group characters. The utility of character expansions in calculating the partition functions is explored. Several examples are given to illustrate these techniques.Comment: 16 pages of RevTe

Local Variational Principle

A generalization of the Gibbs-Bogoliubov-Feynman inequality for spinless particles is proven and then illustrated for the simple model of a symmetric double-well quartic potential. The method gives a pointwise lower bound for the finite-temperature density matrix and it can be systematically improved by the Trotter composition rule. It is also shown to produce groundstate energies better than the ones given by the Rayleigh-Ritz principle as applied to the groundstate eigenfunctions of the reference potentials. Based on this observation, it is argued that the Local Variational Principle performs better than the equivalent methods based on the centroid path idea and on the Gibbs-Bogoliubov-Feynman variational principle, especially in the range of low temperatures.Comment: 15 pages, 5 figures, one more section adde

Fitting the integrated Spectral Energy Distributions of Galaxies

Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details ofdust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (sedfitting.org), where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.Comment: 54 pages, 26 figures, Accepted for publication in Astrophysics & Space Scienc

TEST OF SQUARE LAW FOR DEUTERON FORMATION IN RELATIVISTIC NUCLEAR COLLISIONS

We analyze a large body of data on nuclear collisions between 200 MeV and 2 GeV per nucleon in order to test the relation between the deuteron and proton invariant inclusive cross sections, The empirical "square law" stating that the deuteron yield is proportional to the square of the proton yield is found to hold remarkably well although small systematic deviations are also found

Long range imaginary optical potential in elastic scattering. [Cross sections, 48 MeV]

The long range imaginary optical potential arising from quadrupole Coulomb excitation is derived in closed form. An analytical closed form for elastic scattering is obtained by inserting this potential into a weak absorption modified form of Frahn's strong absorption model

Implementation of one-turn maps in SSCTRK using ZLIB

The particle tracking code SSCTRK is currently being adapted to operational simulation and beam-beam effect studies for the Collider rings of the SSC. During beam-beam effect studies, the lattice content of the bending arcs is normally not varied, making fast truncated Taylor map tracking through the arcs an attractive option. The implementation of SSCTRK as a truncated Taylor map tracking program has been carried out using the differential algebra library ZLIB, which simplified the task to that of straightforward translation of SSCTRK kick and drift arithmetic operations to calls to the corresponding polynomial operation subroutines of ZLIB. The accuracy and speed (relative to normal SSCTRK tracking) of truncated Taylor map tracking at 2mm betatron oscillation amplitude was studied in various orders of the map. The seventh order map was found to be in agreement with the normal SSCTRK to about eight significant figures on the first turn, and to a fraction of 1% on the 100,000th turn, for a typical 5cm magnet aperture lattice, and could be made to track at ten times the speed of the normal SSCTRK kick-drift tracking on a scalar architecture (Sun) workstation. (The map tracking subroutines of ZLIB are optimized for vector and parallel architecture supercomputers, and typically achieve even faster relative performance on these, but operational simulation studies will be more conveniently carried out on dedicated workstations which have the incoming generation of superscalar'' CPUs)