XMM-Newton Observations of Radio Pulsars B0834+06 and B0826-34 and Implications for Pulsar Inner Accelerator

We report the X-ray observations of two radio pulsars with drifting subpulses: B0834 + 06 and B0826 - 34 using \xmm\. PSR B0834 + 06 was detected with a total of 70 counts from the three EPIC instruments over 50 ks exposure time. Its spectrum was best described as that of a blackbody (BB) with temperature $T_s=(2.0^{+2.0}_{-0.9}) \times 10^6$ K and bolometric luminosity of $L_b=(8.6^{+14.2}_{-4.4}) \times 10^{28}$ erg s$^{-1}$. As it is typical in pulsars with BB thermal components in their X-ray spectra, the hot spot surface area is much smaller than that of the canonical polar cap, implying a non-dipolar surface magnetic field much stronger than the dipolar component derived from the pulsar spin-down (in this case about 50 times smaller and stronger, respectively). The second pulsar PSR B0826 - 34 was not detected over 50 ks exposure time, giving an upper limit for the bolometric luminosity $L_b \leq 1.4 \times 10^{29}$ erg s$^{-1}$. We use these data as well as the radio emission data concerned with drifting subpulses to test the Partially Screened Gap (PSG) model of the inner accelerator in pulsars.Comment: Accepted for publication by The Astrophysical Journa

Properties of dense partially random graphs

We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small World Graphs (SWGs). But we consider the case where the average degree of each node is of order of the size of the graph (unlike SWGs, which are sparse). This allows us to calculate the mean distance and clustering, that are qualitatively similar (although not in such a dramatic scale range) to the case of SWGs. We also obtain analytically the distribution of eigenvalues of the corresponding adjacency matrices. This distribution is discrete for large eigenvalues and continuous for small eigenvalues. The continuous part of the distribution follows a semicircle law, whose width is proportional to the "disorder" of the graph, whereas the discrete part is simply a rescaling of the spectrum of the substrate. We apply our results to the calculation of the mixing rate and the synchronizability threshold.Comment: 14 pages. To be published in Physical Review

A study of the gravitational wave form from pulsars II

We present analytical and numerical studies of the Fourier transform (FT) of the gravitational wave (GW) signal from a pulsar, taking into account the rotation and orbital motion of the Earth. We also briefly discuss the Zak-Gelfand Integral Transform. The Zak-Gelfand Integral Transform that arises in our analytic approach has also been useful for Schrodinger operators in periodic potentials in condensed matter physics (Bloch wave functions).Comment: 6 pages, Sparkler talk given at the Amaldi Conference on Gravitational waves, July 10th, 2001. Submitted to Classical and Quantum Gravit

Families of Graphs with W_r({G},q) Functions That Are Nonanalytic at 1/q=0

Denoting $P(G,q)$ as the chromatic polynomial for coloring an $n$-vertex graph $G$ with $q$ colors, and considering the limiting function $W(\{G\},q) = \lim_{n \to \infty}P(G,q)^{1/n}$, a fundamental question in graph theory is the following: is $W_r(\{G\},q) = q^{-1}W(\{G\},q)$ analytic or not at the origin of the $1/q$ plane? (where the complex generalization of $q$ is assumed). This question is also relevant in statistical mechanics because $W(\{G\},q)=\exp(S_0/k_B)$, where $S_0$ is the ground state entropy of the $q$-state Potts antiferromagnet on the lattice graph $\{G\}$, and the analyticity of $W_r(\{G\},q)$ at $1/q=0$ is necessary for the large-$q$ series expansions of $W_r(\{G\},q)$. Although $W_r$ is analytic at $1/q=0$ for many $\{G\}$, there are some $\{G\}$ for which it is not; for these, $W_r$ has no large-$q$ series expansion. It is important to understand the reason for this nonanalyticity. Here we give a general condition that determines whether or not a particular $W_r(\{G\},q)$ is analytic at $1/q=0$ and explains the nonanalyticity where it occurs. We also construct infinite families of graphs with $W_r$ functions that are non-analytic at $1/q=0$ and investigate the properties of these functions. Our results are consistent with the conjecture that a sufficient condition for $W_r(\{G\},q)$ to be analytic at $1/q=0$ is that $\{G\}$ is a regular lattice graph $\Lambda$. (This is known not to be a necessary condition).Comment: 22 pages, Revtex, 4 encapsulated postscript figures, to appear in Phys. Rev.

Education and older adults at the University of the Third Age

This article reports a critical analysis of older adult education in Malta. In educational gerontology, a critical perspective demands the exposure of how relations of power and inequality, in their myriad forms, combinations, and complexities, are manifest in late-life learning initiatives. Fieldwork conducted at the University of the Third Age (UTA) in Malta uncovered the political nature of elder-learning, especially with respect to three intersecting lines of inequality - namely, positive aging, elitism, and gender. A cautionary note is, therefore, warranted at the dominant positive interpretations of UTAs since late-life learning, as any other education activity, is not politically neutral.peer-reviewe

Ground State Entropy of Potts Antiferromagnets: Bounds, Series, and Monte Carlo Measurements

We report several results concerning $W(\Lambda,q)=\exp(S_0/k_B)$, the exponent of the ground state entropy of the Potts antiferromagnet on a lattice $\Lambda$. First, we improve our previous rigorous lower bound on $W(hc,q)$ for the honeycomb (hc) lattice and find that it is extremely accurate; it agrees to the first eleven terms with the large-$q$ series for $W(hc,q)$. Second, we investigate the heteropolygonal Archimedean $4 \cdot 8^2$ lattice, derive a rigorous lower bound, on $W(4 \cdot 8^2,q)$, and calculate the large-$q$ series for this function to $O(y^{12})$ where $y=1/(q-1)$. Remarkably, these agree exactly to all thirteen terms calculated. We also report Monte Carlo measurements, and find that these are very close to our lower bound and series. Third, we study the effect of non-nearest-neighbor couplings, focusing on the square lattice with next-nearest-neighbor bonds.Comment: 13 pages, Latex, to appear in Phys. Rev.

Spanning Trees on Lattices and Integration Identities

For a lattice $\Lambda$ with $n$ vertices and dimension $d$ equal or higher than two, the number of spanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant $z_\Lambda$ for spanning trees on several lattices. By taking different unit cells in the calculation, many integration identities can be obtained. We also give $z_{\Lambda (p)}$ on the homeomorphic expansion of $k$-regular lattices with $p$ vertices inserted on each edge.Comment: 15 pages, 3 figures, 1 tabl

On the Symmetries of Integrability

We show that the Yang-Baxter equations for two dimensional models admit as a group of symmetry the infinite discrete group $A_2^{(1)}$. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. We show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. We mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. Our results also yield the generalization of the condition $q^n=1$ so often mentioned in the theory of quantum groups, when no $q$ parameter is available.Comment: 23 page

Scattering theory on graphs

We consider the scattering theory for the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.Comment: 21 pages, LaTeX, 10 eps figure

Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals

We prove a general rigorous lower bound for $W(\Lambda,q)=\exp(S_0(\Lambda,q)/k_B)$, the exponent of the ground state entropy of the $q$-state Potts antiferromagnet, on an arbitrary Archimedean lattice $\Lambda$. We calculate large-$q$ series expansions for the exact $W_r(\Lambda,q)=q^{-1}W(\Lambda,q)$ and compare these with our lower bounds on this function on the various Archimedean lattices. It is shown that the lower bounds coincide with a number of terms in the large-$q$ expansions and hence serve not just as bounds but also as very good approximations to the respective exact functions $W_r(\Lambda,q)$ for large $q$ on the various lattices $\Lambda$. Plots of $W_r(\Lambda,q)$ are given, and the general dependence on lattice coordination number is noted. Lower bounds and series are also presented for the duals of Archimedean lattices. As part of the study, the chromatic number is determined for all Archimedean lattices and their duals. Finally, we report calculations of chromatic zeros for several lattices; these provide further support for our earlier conjecture that a sufficient condition for $W_r(\Lambda,q)$ to be analytic at $1/q=0$ is that $\Lambda$ is a regular lattice.Comment: 39 pages, Revtex, 9 encapsulated postscript figures, to appear in Phys. Rev.