Interacting Electrons on a Fluctuating String

We consider the problem of interacting electrons constrained to move on a fluctuating one-dimensional string. An effective low-energy theory for the electrons is derived by integrating out the string degrees of freedom to lowest order in the inverse of the string tension and mass density, which are assumed to be large. We obtain expressions for the tunneling density of states, the spectral function and the optical conductivity of the system. Possible connections with the phenomenology of the cuprate high temperature superconductors are discussed.Comment: 14 pages, 1 figur

On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree

In our recent works [R. Szmytkowski, J. Phys. A 39 (2006) 15147; corrigendum: 40 (2007) 7819; addendum: 40 (2007) 14887], we have investigated the derivative of the Legendre function of the first kind, $P_{\nu}(z)$, with respect to its degree $\nu$. In the present work, we extend these studies and construct several representations of the derivative of the associated Legendre function of the first kind, $P_{\nu}^{\pm m}(z)$, with respect to the degree $\nu$, for $m\in\mathbb{N}$. At first, we establish several contour-integral representations of $\partial P_{\nu}^{\pm m}(z)/\partial\nu$. They are then used to derive Rodrigues-type formulas for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ with $n\in\mathbb{N}$. Next, some closed-form expressions for $[\partial P_{\nu}^{\pm m}(z)/\partial\nu]_{\nu=n}$ are obtained. These results are applied to find several representations, both explicit and of the Rodrigues type, for the associated Legendre function of the second kind of integer degree and order, $Q_{n}^{\pm m}(z)$; the explicit representations are suitable for use for numerical purposes in various regions of the complex $z$-plane. Finally, the derivatives $[\partial^{2}P_{\nu}^{m}(z)/\partial\nu^{2}]_{\nu=n}$, $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=n}$ and $[\partial Q_{\nu}^{m}(z)/\partial\nu]_{\nu=-n-1}$, all with $m>n$, are evaluated in terms of $[\partial P_{\nu}^{-m}(\pm z)/\partial\nu]_{\nu=n}$.Comment: LateX, 40 pages, 1 figure, extensive referencin

Connecting Numerical Relativity and Data Analysis of Gravitational Wave Detectors

Gravitational waves deliver information in exquisite detail about astrophysical phenomena, among them the collision of two black holes, a system completely invisible to the eyes of electromagnetic telescopes. Models that predict gravitational wave signals from likely sources are crucial for the success of this endeavor. Modeling binary black hole sources of gravitational radiation requires solving the Eintein equations of General Relativity using powerful computer hardware and sophisticated numerical algorithms. This proceeding presents where we are in understanding ground-based gravitational waves resulting from the merger of black holes and the implications of these sources for the advent of gravitational-wave astronomy.Comment: Appeared in the Proceedings of 2014 Sant Cugat Forum on Astrophysics. Astrophysics and Space Science Proceedings, ed. C.Sopuerta (Berlin: Springer-Verlag

Search for the decay K+→π+ννˉK^+\to \pi^+ \nu \bar\nu in the momentum region Pπ<195 MeV/cP_\pi < 195 {\rm ~MeV/c}

We have searched for the decay $K^+ \to \pi^+ \nu \bar\nu$ in the kinematic region with pion momentum below the $K^+ \to \pi^+ \pi^0$ peak. One event was observed, consistent with the background estimate of $0.73\pm 0.18$. This implies an upper limit on $B(K^+ \to \pi^+ \nu \bar\nu)< 4.2\times 10^{-9}$ (90% C.L.), consistent with the recently measured branching ratio of $(1.57^{+1.75}_{-0.82}) \times 10^{-10}$, obtained using the standard model spectrum and the kinematic region above the $K^+ \to \pi^+ \pi^0$ peak. The same data were used to search for $K^+ \to \pi^+ X^0$, where $X^0$ is a weakly interacting neutral particle or system of particles with $150 < M_{X^0} < 250 {\rm ~MeV/c^2}$.Comment: 4 pages, 2 figure

Search for the decay K+ to pi+ gamma gamma in the pi+ momentum region P>213 MeV/c

We have searched for the K+ to pi+ gamma gamma decay in the kinematic region with pi+ momentum close to the end point. No events were observed, and the 90% confidence-level upper limit on the partial branching ratio was obtained, B(K+ to pi+ gamma gamma, P>213 MeV/c) < 8.3 x 10-9 under the assumption of chiral perturbation theory including next-to-leading order ``unitarity'' corrections. The same data were used to determine an upper limit on the K+ to pi+ gamma branching ratio of 2.3 x 10-9 at the 90% confidence level.Comment: 15 pages, 3 figures; no change in the results, accepted for publication in Physics Letters

Highly deformed 40^{40}Ca configurations in 28^{28}Si + 12^{12}C

The possible occurrence of highly deformed configurations in the $^{40}$Ca di-nuclear system formed in the $^{28}$Si + $^{12}$C reaction is investigated by analyzing the spectra of emitted light charged particles. Both inclusive and exclusive measurements of the heavy fragments (A $\geq$ 10) and their associated light charged particles (protons and $\alpha$ particles) have been made at the IReS Strasbourg {\sc VIVITRON} Tandem facility at bombarding energies of $E_{lab} (^{28}$Si) = 112 MeV and 180 MeV by using the {\sc ICARE} charged particle multidetector array. The energy spectra, velocity distributions, and both in-plane and out-of-plane angular correlations of light charged particles are compared to statistical-model calculations using a consistent set of parameters with spin-dependent level densities. The analysis suggests the onset of large nuclear deformation in $^{40}$Ca at high spin.Comment: 33 pages, 11 figure

Levels and equivalence in credit and qualifications frameworks: Contrasting the prescribed and enacted curriculum in school and college

Drawing on data from an empirical study of three matched subjects in upper secondary school and further education college in Scotland, this article explores some of the factors that result in differences emerging from the translation of the prescribed curriculum into the enacted curriculum. We argue that these differences raise important questions about equivalences which are being promoted through the development of credit and qualifications frameworks. The article suggests that the standardisation associated with the development of a rational credit and qualifications framework and an outcomes-based prescribed curriculum cannot be achieved precisely because of the multiplicity that emerges from the practices of translation

Further search for the decay K+→π+ννˉK^+ \to \pi^+ \nu \bar \nu in the momentum region P < 195 MeV/c

We report the results of a search for the decay $K^+ \to \pi^+ \nu \bar \nu$ in the kinematic region with $\pi^+$ momentum $140 < P < 195$ MeV/c using the data collected by the E787 experiment at BNL. No events were observed. When combined with our previous search in this region, one candidate event with an expected background of $1.22 \pm 0.24$ events results in a 90% C.L. upper limit of $2.2 \times 10^{-9}$ on the branching ratio of $K^+ \to \pi^+ \nu \bar \nu$. We also report improved limits on the rates of $K^+ \to \pi^+ X^0$ and $K^+ \to \pi^+ X^1 X^2$ where $X^0, X^1, X^2$ are hypothetical, massless, long-lived neutral particles.Comment: 5 pages, 3 figures, Accepted for publication in Phys. Rev.

The origins and development of Zuwīla, Libyan Sahara: an archaeological and historical overview of an ancient oasis town and caravan centre

Zuwīla in southwestern Libya (Fazzān) was one of the most important early Islamic centres in the Central Sahara, but the archaeological correlates of the written sources for it have been little explored. This paper brings together for the first time a detailed consideration of the relevant historical and archaeological data, together with new AMS radiocarbon dates from several key monuments. The origins of the settlement at Zuwīla were pre-Islamic, but the town gained greater prominence in the early centuries of Arab rule of the Maghrib, culminating with the establishment of an Ibāḍī state ruled by the dynasty of the Banū Khaṭṭāb, with Zuwīla its capital. The historical sources and the accounts of early European travellers are discussed and archaeological work at Zuwīla is described (including the new radiocarbon dates). A short gazetteer of archaeological monuments is provided as an appendix. Comparisons and contrasts are also drawn between Zuwīla and other oases of the ash-Sharqiyāt region of Fazzān. The final section of the paper presents a series of models based on the available evidence, tracing the evolution and decline of this remarkable site