What's Decidable About Sequences?

We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the quantifier-free fragment, based on an encoding into the first-order theory of concatenation; the procedure has PSPACE complexity. The quantifier-free fragment of the theory of sequences can express properties such as sortedness and injectivity, as well as Boolean combinations of periodic and arithmetic facts relating the elements of the sequence and their positions (e.g., "for all even i's, the element at position i has value i+3 or 2i"). The resulting expressive power is orthogonal to that of the most expressive decidable logics for arrays. Some examples demonstrate that the fragment is also suitable to reason about sequence-manipulating programs within the standard framework of axiomatic semantics.Comment: Fixed a few lapses in the Mergesort exampl

Bosons in anisotropic traps: ground state and vortices

We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic trap, modeled by an anisotropic harmonic potential. We evaluate the wave function and the energy of the Bose Einstein condensate as a function of the particle number, both for positive and negative scattering length. The results for the transverse and vertical size of the cloud of atoms, as well as for the kinetic and potential energy per particle, are compared with the predictions of approximated models. We also compare the aspect ratio of the velocity distribution with first experimental estimates available for $^{87}$Rb. Vortex states are considered and the critical angular velocity for production of vortices is calculated. We show that the presence of vortices significantly increases the stability of the condensate in the case of attractive interactions.Comment: 22 pages, REVTEX, 8 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

Towards manufacture of ultralow loss hollow core photonic bandgap fiber

Hollow core photonic bandgap fibers (HC-PBGFs) are a class of optical fibers which guide light in a low index core region surrounded by a triangular lattice of air holes separated by a delicate silica web. The precise nature of this cladding structure requires extremely fine control of the fabrication parameters. While HC-PBGFs have found wide range of exciting research applications the initially anticipated potential for ultralow loss below that of single mode fiber (SMF) has yet to be realized. To date loss figures as low as 1.7 dB/km have been reported, however surface roughness at the core cladding interface limited further loss reduction. The loss of HC-PBGFs can potentially be decreased further by increasing the core dimensions and through optimisation of the fabrication process. To date, the manufacture of HC-PBGFs is reliant upon the two stage stack and draw process. To target ultralow loss below what has been reported to date it has become necessary to ensure repeatability and uniformity in the labor intensive stack and draw process. Repeatability is ensured through rigorous cleanliness throughout preform preparation and by precise fabrication control at each stage of manufacture. Figure 1. a) Scanning electron micrograph of a 19 cell core defect HC-PBGF, b) Attenuation scaling of the photonic bandgap (PBG) versus central guidance wavelength of 19 cell core defect HC-PBGF.Greater than 1 km lengths of HC-PBGF (Fig. 1a) can now be drawn with typical attenuations of the order of 2-3 dB/km and with significantly improved optical bandwidth (~ 100 nm) compared with previously reported. These developments open up HC-PBGF for a range of applications such as telecommunications, laser power delivery, gas sensing and strong light matter interactions, for which they have a clear advantage over conventional fibers. The attenuation scaling of the photonic bandgap (PBG) (solid curves) with central operating wavelength has been investigated in 19 cell core defect fibres (Fig. 1b). The expected attenuation proportional to lambda[-3] relationship (dashed red curve) is observed until the infrared absorption edge of silica (black dot dash curve) is breached and the attenuation increases (green curve). Through strategic fabrication improvements we have achieved repeatable low loss manufacture of HC-PBGFs. Future developments in fabrication control and fiber design will allow the realization of ultralow loss HC-PBGF

Dynamics of evaporative cooling in magnetically trapped atomic hydrogen

We study the evaporative cooling of magnetically trapped atomic hydrogen on the basis of the kinetic theory of a Bose gas. The dynamics of trapped atoms is described by the coupled differential equations, considering both the evaporation and dipolar spin relaxation processes. The numerical time-evolution calculations quantitatively agree with the recent experiment of Bose-Einstein condensation with atomic hydrogen. It is demonstrated that the balance between evaporative cooling and heating due to dipolar relaxation limits the number of condensates to 9x10^8 and the corresponding condensate fraction to a small value of 4% as observed experimentally.Comment: 5 pages, REVTeX, 3 eps figures, Phys. Rev. A in pres

In-situ velocity imaging of ultracold atoms using slow--light

The optical response of a moving medium suitably driven into a slow-light propagation regime strongly depends on its velocity. This effect can be used to devise a novel scheme for imaging ultraslow velocity fields. The scheme turns out to be particularly amenable to study in-situ the dynamics of collective and topological excitations of a trapped Bose-Einstein condensate. We illustrate the advantages of using slow-light imaging specifically for sloshing oscillations and bent vortices in a stirred condensate

Celtic FC’s 1967 Lisbon Lions:Why the European Cup victory of the first club from Britain was a defining moment for the Irish diaspora in Scotland

In 1967, in Lisbon, Celtic Football Club, won the European Cup becoming the first club outside of Portugal, Spain and Italy to win it. The win was and is totemic for the Irish Catholic immigrant community in Scotland that has historically supported Celtic. We suggest the significance of the win reveals intersections of ethnicity, religion, nationalism, and the politics of ‘sectarianism’ in Scotland. During a period of discriminatory practices and attitudes towards Irish descended Catholics in Scotland, this iconic win for a Scottish based club born of Irish Catholics personified for this diaspora that (on one level) their day had arrived. This article explores the socio-cultural significance and legacy of ‘Lisbon 67ʹ for insider and outsider groups in Scotland. We reveal that soccer remains a central component of group memory connecting the past, present and future. We suggest Celtic’s win offered confidence and hope to a marginalized group within Scotland

Persistent currents in a circular array of Bose-Einstein condensates

A ring-shaped array of Bose-Einstein condensed atomic gases can display circular currents if the relative phase of neighboring condensates becomes locked to certain values. It is shown that, irrespective of the mechanism responsible for generating these states, only a restricted set of currents are stable, depending on the number of condensates, on the interaction and tunneling energies, and on the total number of particles. Different instabilities due to quasiparticle excitations are characterized and possible experimental setups for testing the stability prediction are also discussed.Comment: 7 pages, REVTex

Inspection of defect-induced mode coupling in hollow-core photonic bandgap fibers using time-of-flight

We analyze defect-induced mode coupling in a hollow-core photonic bandgap fiber using time-of-flight, and show its utility in complementing optical time-domain reflectometry

High value of ecological information for river connectivity restoration

Context: Efficient restoration of longitudinal river connectivity relies on barrier mitigation prioritization tools that incorporate stream network spatial structure to maximize ecological benefits given limited resources. Typically, ecological bene 5 fits of barrier mitigation are measured using proxies such as the amount of accessible riverine habitat. Objectives We developed an optimization approach for barrier mitigation planning which directly incorporates the ecology of managed taxa, and applied it to an urbanizing salmonbearing watershed in Alaska. Methods: A novel river connectivity metric that exploits information on the distribution and movement of managed taxon was embedded into a barrier prioritization framework to identify optimal mitigation actions given limited restoration budgets. The value of ecological information on managed taxa was estimated by comparing costs to achieve restoration targets across alternative barrier prioritization approaches. Results: Barrier mitigation solutions informed by life history information outperformed those using only river connectivity proxies, demonstrating high value of ecological information for watershed restoration. In our study area, information on salmon ecology was typically valued at 0.8-1.2M USD in costs savings to achieve a given benefit level relative to solutions derived only from stream network information, equating to 16-28% of the restoration budget. Conclusions Investing in ecological studies may achieve win-win outcomes of improved understanding of aquatic ecology and greater watershed restoration efficiency

Higher-order mutual coherence of optical and matter waves

We use an operational approach to discuss ways to measure the higher-order cross-correlations between optical and matter-wave fields. We pay particular attention to the fact that atomic fields actually consist of composite particles that can easily be separated into their basic constituents by a detection process such as photoionization. In the case of bosonic fields, that we specifically consider here, this leads to the appearance in the detection signal of exchange contributions due to both the composite bosonic field and its individual fermionic constituents. We also show how time-gated counting schemes allow to isolate specific contributions to the signal, in particular involving different orderings of the Schr\"odinger and Maxwell fields.Comment: 11 pages, 2 figure