Branching: the Essence of Constraint Solving

This paper focuses on the branching process for solving any constraint satisfaction problem (CSP). A parametrised schema is proposed that (with suitable instantiations of the parameters) can solve CSP's on both finite and infinite domains. The paper presents a formal specification of the schema and a statement of a number of interesting properties that, subject to certain conditions, are satisfied by any instances of the schema. It is also shown that the operational procedures of many constraint systems including cooperative systems) satisfy these conditions. Moreover, the schema is also used to solve the same CSP in different ways by means of different instantiations of its parameters.Comment: 18 pages, 2 figures, Proceedings ERCIM Workshop on Constraints (Prague, June 2001

Knots with distinct primitive/primitive and primitive/Seifert representatives

Berge introduced knots that are primitive/primitive with respect to the genus 2 Heegaard surface, $F$, in $S^3$; surgery on such knots at the surface slope yields a lens space. Later Dean described a similar class of knots that are primitive/Seifert with respect to $F$; surgery on these knots at the surface slope yields a Seifert fibered space. Here we construct a two-parameter family of knots that have distinct primitive/Seifert embeddings in $F$ with the same surface slope, as well as a family of torus knots that have a primitive/primitive representative and a primitive/Seifert representative with the same surface slope.Comment: 12 pages, 8 figures; 2 figures update

Converging shocks in elastic-plastic solids

We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e = e_(s)(I_1)+e_(h)(ρ,ς), where e_(s) accounts for shear through the first invariant of the Cauchy–Green tensor, and e_(h) represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., e_(h) = e_(h)(ρ), with a power-law dependence e_(h) ∝ ρ_(α), shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M ∝ [log(1/R)]^α, independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M ∝ R^(−(s−1)) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part eh is that of an ideal gas, is also tested, recovering the strong-shock limit M∝R^(−(s−1)/n(γ)) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ−1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the hydrostatic part of the energy essentially commands the strong-shock behavior, the shear modulus and yield stress modify the compression ratio and velocity of the shock far from the axis or origin. A characterization of the elastic-plastic transition in converging shocks, which involves an elastic precursor and a plastic compression region, is finally exposed

Investigation of refractory composites for liquid rocket engines Final report, 1 Oct. 1969 - 31 Oct. 1970

Oxidation resistance and high temperature tests of rhenium, tungsten, hafnium, and tantalum matrix composites with iridium in oxygen, fluorine, and boron atmospheres for liquid propellant engine

Instrumentation for Millimeter-wave Magnetoelectrodynamic Investigations of Low-Dimensional Conductors and Superconductors

We describe instrumentation for conducting high sensitivity millimeter-wave cavity perturbation measurements over a broad frequency range (40-200 GHz) and in the presence of strong magnetic fields (up to 33 tesla). A Millimeter-wave Vector Network Analyzer (MVNA) acts as a continuously tunable microwave source and phase sensitive detector (8-350 GHz), enabling simultaneous measurements of the complex cavity parameters (resonance frequency and Q-value) at a rapid repetition rate (approx. 10 kHz). We discuss the principal of operation of the MVNA and the construction of a probe for coupling the MVNA to various cylindrical resonator configurations which can easily be inserted into a high field magnet cryostat. We also present several experimental results which demonstrate the potential of the instrument for studies of low-dimensional conducting systems.Comment: 20 pages including fig

An economic model of the manufacturers' aircraft production and airline earnings potential, volume 3

A behavioral explanation of the process of technological change in the U. S. aircraft manufacturing and airline industries is presented. The model indicates the principal factors which influence the aircraft (airframe) manufacturers in researching, developing, constructing and promoting new aircraft technology; and the financial requirements which determine the delivery of new aircraft to the domestic trunk airlines. Following specification and calibration of the model, the types and numbers of new aircraft were estimated historically for each airline's fleet. Examples of possible applications of the model to forecasting an individual airline's future fleet also are provided. The functional form of the model is a composite which was derived from several preceding econometric models developed on the foundations of the economics of innovation, acquisition, and technological change and represents an important contribution to the improved understanding of the economic and financial requirements for aircraft selection and production. The model's primary application will be to forecast the future types and numbers of new aircraft required for each domestic airline's fleet

A New Z=0 Metagalactic Ultraviolet Background Limit

We present new integral-field spectroscopy in the outskirts of two nearby, edge-on, late-type galaxies to search for the H alpha emission that is expected from the exposure of their hydrogen gas to the metagalactic ultraviolet background (UVB). Despite the sensitivity of the VIRUS-P spectrograph on the McDonald 2.7 m telescope to low surface brightness emission and the large field of view, we do not detect H alpha to 5 sigma upper limits of 6.4 x 10(-19) erg s(-1) cm(-2) arcsec(-2) in UGC 7321 and of 25 x 10(-19) erg s(-1) cm(-2) arcsec(-2) in UGC 1281 in each of the hundreds of independent spatial elements (fibers). We fit gas distribution models from overlapping 21 cm data of HI, extrapolate one scale length beyond the HI data, and estimate predicted H alpha surface brightness maps. We analyze three types of limits from the data with stacks formed from increasingly large spatial regions and compare to the model predictions: (1) single fibers, (2) convolution of the fiber grid with a Gaussian, circular kernel (10('') full width at half-maximum), and (3) the co-added spectra from a few hundred fibers over the brightest model regions. None of these methods produce a significant detection (>5 sigma) with the most stringent constraints on the Hi photoionization rate of Gamma(z = 0) < 1.7 x 10(-14) s(-1) in UGC 7321 and Gamma(z = 0) < 14 x 10(-14) s(-1) in UGC 1281. The UGC 7321 limit is below previous measurement limits and also below current theoretical models. Restricting the analysis to the fibers bound by the HI data leads to a comparable limit; the limit is Gamma(z = 0) < 2.3 x 10(-14) s(-1) in UGC 7321. We discuss how a low Lyman limit escape fraction in z similar to 0 redshift star-forming galaxies might explain this lower than predicted UVB strength and the prospects of deeper data to make a direct detection.U.S. Government NAG W-2166National Science FoundationUT David BrutonTexas Norman Hackerman Advanced Research Program 003658-0295-2007Cynthia and George Mitchell FoundationMcDonald Observator

The optical counterpart of SAX J1808.4-3658, the transient bursting millisecond X-ray pulsar

A set of CCD images have been obtained during the decline of the X-ray transient SAX J1808.4-3658 during April-June 1998. The optical counterpart has been confirmed by several pieces of evidence. The optical flux shows a modulation on several nights which is consistent with the established X-ray binary orbit period of 2 hours. This optical variability is roughly in antiphase with the weak X-ray modulation. The source mean magnitude of V=16.7 on April 18 declined rapidly after April 22. From May 2 onwards the magnitude was more constant at around V=18.45 but by June 27 was below our sensitivity limit. The optical decline precedes the rapid second phase of the X-ray decrease by 3 +/- 1 days. The source has been identified on a 1974 UK Schmidt plate at an estimated magnitude of ~20. The nature of the optical companion is discussed.Comment: 5 pages, 3 figures; published in MNRAS, March 15th 199