The pulsar spectral index distribution

The flux density spectra of radio pulsars are known to be steep and, to first order, described by a power-law relationship of the form S_{\nu} \propto \nu^{\alpha}, where S_{\nu} is the flux density at some frequency \nu and \alpha is the spectral index. Although measurements of \alpha have been made over the years for several hundred pulsars, a study of the intrinsic distribution of pulsar spectra has not been carried out. From the result of pulsar surveys carried out at three different radio frequencies, we use population synthesis techniques and a likelihood analysis to deduce what underlying spectral index distribution is required to replicate the results of these surveys. We find that in general the results of the surveys can be modelled by a Gaussian distribution of spectral indices with a mean of -1.4 and unit standard deviation. We also consider the impact of the so-called "Gigahertz-peaked spectrum" pulsars. The fraction of peaked spectrum sources in the population with significant turn-over at low frequencies appears to be at most 10%. We demonstrate that high-frequency (>2 GHz) surveys preferentially select flatter-spectrum pulsars and the converse is true for lower-frequency (<1 GHz) surveys. This implies that any correlations between \alpha and other pulsar parameters (for example age or magnetic field) need to carefully account for selection biases in pulsar surveys. We also expect that many known pulsars which have been detected at high frequencies will have shallow, or positive, spectral indices. The majority of pulsars do not have recorded flux density measurements over a wide frequency range, making it impossible to constrain their spectral shapes. We also suggest that such measurements would allow an improved description of any populations of pulsars with 'non-standard' spectra.Comment: 8 pages, 5 figures. Accepted by MNRA

Low Dirac Eigenmodes and the Topological and Chiral Structure of the QCD Vacuum

Several lattice calculations which probe the chiral and topological structure of QCD are discussed. The results focus attention on the low-lying eigenmodes of the Dirac operator in typical gauge field configurations.Comment: Talk presented at the DPF2000 Conferenc

Adiabatic quantization of Andreev levels

We identify the time $T$ between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent $\lambda$), coupled to a superconductor by an $N$-mode point contact. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods $T_{n}$, which in turn generate a ladder of excited states $\epsilon_{nm}=(m+1/2)\pi\hbar/T_{n}$. The largest quantized period is the Ehrenfest time $T_{0}=\lambda^{-1}\ln N$. Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension $W/\sqrt{N}$, much below the width $W$ of the point contact.Comment: 4 pages, 3 figure

Laser spot welding of laser textured steel to aluminium

Laser welding of dissimilar metals (steel and aluminium) was investigated with the aim to increase the maximum tensile shear load of the Fe-Al joints. The increase was achieved by texturing the surface of steel prior to the laser spot welding process which was performed in a lap-joint configuration with the steel positioned on top of the aluminium and with a texture faced down to the aluminium surface. This configuration enabled an increase of the bonding area of the joints, because the molten aluminium filled in the gaps of the texture, without the need of increasing the process energy which typically leads to the growth of the intermetallic compounds. Different textures (containing hexagonally arranged craters, parallel lines, grid and spiral patterns) were tested with different laser welding parameters. The Fe-Al joints obtained with the textured steel were found to have up to 25% higher maximum tensile-shear load than the joints obtained with the untextured steel

(Never) Mind your p's and q's: Von Neumann versus Jordan on the Foundations of Quantum Theory

In two papers entitled "On a new foundation [Neue Begr\"undung] of quantum mechanics," Pascual Jordan (1927b,g) presented his version of what came to be known as the Dirac-Jordan statistical transformation theory. As an alternative that avoids the mathematical difficulties facing the approach of Jordan and Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert space formalism of quantum mechanics. In this paper, we focus on Jordan and von Neumann. Central to the formalisms of both are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in quantum mechanics. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identication of sets of canonically conjugate variables, i.e., p's and q's. For von Neumann, not constrained by the analogy to classical mechanics, it required only the identication of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p's and q's. Jordan and von Neumann also stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan (1927b) was the first to state those rules in full generality. Von Neumann (1927a) rephrased them and, in a subsequent paper (von Neumann, 1927b), sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics.Comment: New version. The main difference with the old version is that the introduction has been rewritten. Sec. 1 (pp. 2-12) in the old version has been replaced by Secs. 1.1-1.4 (pp. 2-31) in the new version. The paper has been accepted for publication in European Physical Journal

Triton's surface age and impactor population revisited in light of Kuiper Belt fluxes: Evidence for small Kuiper Belt objects and recent geological activity

Neptune's largest satellite, Triton, is one of the most fascinating and enigmatic bodies in the solar system. Among its numerous interesting traits, Triton appears to have far fewer craters than would be expected if its surface was primordial. Here we combine the best available crater count data for Triton with improved estimates of impact rates by including the Kuiper Belt as a source of impactors. We find that the population of impactors creating the smallest observed craters on Triton must be sub-km in scale, and that this small-impactor population can be best fit by a differential power-law size index near -3. Such results provide interesting, indirect probes of the unseen small body population of the Kuiper Belt. Based on the modern, Kuiper Belt and Oort Cloud impactor flux estimates, we also recalculate estimated ages for several regions of Triton's surface imaged by Voyager 2, and find that Triton was probably active on a time scale no greater than 0.1-0.3 Gyr ago (indicating Triton was still active after some 90% to 98% of the age of the solar system), and perhaps even more recently. The time-averaged volumetric resurfacing rate on Triton implied by these results, 0.01 km$^3$ yr$^{-1}$ or more, is likely second only to Io and Europa in the outer solar system, and is within an order of magnitude of estimates for Venus and for the Earth's intraplate zones. This finding indicates that Triton likely remains a highly geologically active world at present, some 4.5 Gyr after its formation. We briefly speculate on how such a situation might obtain.Comment: 14 pages (TeX), plus 2 postscript figures Stern & McKinnon, 2000, AJ, in pres

HST Imaging of the Globular Clusters in the Fornax Cluster: NGC 1399 and NGC 1404

The Fornax cluster galaxies NGC 1399 and NGC 1404 are ideal for studying the effects of a cluster environment on globular cluster systems. Here we present new optical imaging of these two galaxies from both the Hubble Space Telescope's Wide Field and Planetary Camera 2 and the Cerro Tololo Inter-American Observatory's 1.5m telescope. The combination of both data sets provides unique insight on the spatial and colour distribution of globular clusters. From B-I colours, we find that both galaxies have a broad globular cluster metallicity distribution that is inconsistent with a single population. Two Gaussians provide a reasonable representation of the metallicity distribution in each galaxy. The metal-rich subpopulation is more centrally concentrated than the metal-poor one. We show that the radial metallicity gradient can be explained by the changing relative mix of the two globular cluster subpopulations. We derive globular cluster surface density profiles, and find that they are flatter (i.e. more extended) than the underlying starlight. The total number of globular clusters and specific frequency are calculated to be N = 5700 +/- 500, S_N = 11.5 +/- 1.0 for NGC 1399 and N = 725 +/- 145, S_N = 2.0 +/- 0.5 for NGC 1404. Our results are compared to the expectations of globular cluster formation scenarios.Comment: 21 pages, Latex, 13 figures, submitted to MNRA

A photoelectron diffraction investigation of vanadyl phthalocyanine on Au(1 1 1)

Scanned-energy mode photoelectron diffraction using the O 1s and V 2p emission perpendicular to the surface has been used to investigate the orientation and internal conformation of vanadyl phthalocyanine (VOPc) adsorbed on Au(1 1 1). The results confirm earlier indications from scanning tunnelling microscopy that the Vdouble bond; length as m-dashO vanadyl bond points out of, and not into, the surface. The Vdouble bond; length as m-dashO bondlength is 1.60 ± 0.04 Å, not significantly different from its value in bulk crystalline VOPc. However, the V atom in the adsorbed molecule is almost coplanar with the surrounding N atoms and is thus pulled down into the approximately planar region defined by the N and C atoms by 0.52 (+0.14/−0.10) Å, relative to its location in crystalline VOPc. This change must be attributed to the bonding interaction between the molecule and the underlying metal surface

Unquenched QCD with Light Quarks

We present recent results in unquenched lattice QCD with two degenerate light sea quarks using the truncated determinant approximation (TDA). In the TDA the infrared modes contributing to the quark determinant are computed exactly up to some cutoff in quark off-shellness (typically 2$\Lambda_{QCD}$). This approach allows simulations to be performed at much lighter quark masses than possible with conventional hybrid MonteCarlo techniques. Results for the static energy and topological charge distributions are presented using a large ensemble generated on very coarse (6$^4$) but physically large lattices. Preliminary results are also reported for the static energy and meson spectrum on 10$^3$x20 lattices (lattice scale $a^{-1}$=1.15 GeV) at quark masses corresponding to pions of mass $\leq$ 200 MeV. Using multiboson simulation to compute the ultraviolet part of the quark determinant the TDA approach becomes an exact with essentially no increase in computational effort. Some preliminary results using this fully unquenched algorithm are presented.Comment: LateX, 39 pages, 16 eps figures, 1 ps figur