Free Energy of a Dilute Bose Gas: Lower Bound

A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density $\rho$ and temperature $T$. In the dilute regime, i.e., when $a^3\rho \ll 1$, where $a$ denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term $4\pi a (2\rho^2 - [\rho-\rho_c]_+^2)$. Here, $\rho_c(T)$ denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and $[ ]_+$ denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., $T \sim \rho^{2/3}$ or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [arXiv:math-ph/0601051] for estimating correlations to temperatures below the critical one.Comment: LaTeX2e, 53 page

Polarimetric airborne scientific instrument, mark 2, an ice‐sounding airborne synthetic aperture radar for subglacial 3D imagery

Polarimetric Airborne Scientific INstrument, mark 2 (PASIN2) is a 150 MHz coherent pulsed radar with the purpose of deep ice sounding for bedrock, subglacial channels and ice-water interface detection in Antarctica. It is designed and operated by the British Antarctic Survey from 2014. With multiple antennas, oriented along and across-track, for transmission and reception, it enables polarimetric 3D estimation of the ice base with a single pass, reducing the gridding density of the survey paths. The off-line data processing stream consists of channel calibration; 2D synthetic aperture radar (SAR) imaging based on back-projection, for along-track and range dimensions; and finally, a direction of arrival estimation (DoA) of the remaining across-track angle, by modifying the non-linear MUSIC algorithm. Calibration flights, during the Antarctic Summer campaigns in 16/17 and 19/20 seasons, assessed and validated the instrument and processing performances. Imaging flights over ice streams and ice shelves close to grounding lines demonstrate the 3D sensing capabilities. By resolving directional ambiguities and accounting for reflector across-track location, the true ice thickness and bed elevation are obtained, thereby removing the error of the usual assumption of vertical DoA, that greatly influence the output of flow models of ice dynamics

The landscape of gifted and talented education in England and Wales: How are teachers implementing policy?

This is an Author's Accepted Manuscript of an article published in Research Papers in Education, 27(2), 167-186, 2012, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/02671522.2010.509514.This paper explores the evidence relating to how primary schools are responding to the ‘gifted and talented’ initiative in England and Wales. A questionnaire survey which invited both closed and open-ended responses was carried out with a national sample of primary schools. The survey indicated an increasing proportion of coordinators, compared with a survey carried out in 1996, were identifying their gifted and talented children as well as having associated school policies. However, the survey also highlighted a number of issues which need addressing if the initiative is to achieve its objective of providing the best possible educational opportunities for children. For example, it was found that a significant number of practitioners were not aware of the existence of the National Quality Standards for gifted and talented education, provided by the UK government in 2007, and the subject-specific criteria provided by the UK’s Curriculum Authority for identification and provision have been largely ignored. The process of identifying children to be placed on the ‘gifted and talented’ register seems haphazard and based on pragmatic reasons. Analysis of teachers’ responses also revealed a range of views and theoretical positioning held by them, which have implications for classroom practice. As the ‘gifted and talented’ initiative in the UK is entering a second decade, and yet more significant changes in policy are introduced, pertinent questions need to be raised and given consideration

Quantum spin systems at positive temperature

We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature $\beta$ and the magnitude of the quantum spins \CalS satisfy \beta\ll\sqrt\CalS. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with \CalS\gg1. The most notable examples are the quantum orbital-compass model on $\Z^2$ and the quantum 120-degree model on $\Z^3$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state.Comment: 47 pages, version to appear in CMP (style files included

YREC: The Yale Rotating Stellar Evolution Code

The stellar evolution code YREC is outlined with emphasis on its applications to helio- and asteroseismology. The procedure for calculating calibrated solar and stellar models is described. Other features of the code such as a non-local treatment of convective core overshoot, and the implementation of a parametrized description of turbulence in stellar models, are considered in some detail. The code has been extensively used for other astrophysical applications, some of which are briefly mentioned at the end of the paper.Comment: 10 pages, 2 figures, ApSS accepte

The California Current System: A multiscale overview and the development of a feature-oriented regional modeling system (FORMS)

17 USC 105 interim-entered record; under review.Over the past decade, the feature-oriented regional modeling methodology has been developed and applied in several ocean domains, including the western North Atlantic and tropical North Atlantic. This methodology is model-independent and can be utilized with or without satellite and/or in situ observations. Here we develop new feature-oriented models for the eastern North Pacific from 36◦ to 48◦N – essentially, most of the regional eastern boundary current. This is the firsttime feature-modeling has been applied to a complex eastern boundary current system. As a prerequisite to feature modeling, prevalent features that comprise the multiscale and complex circulation in the California Current system (CCS) are first overviewed. This description is based on contemporary understanding ofthe features and their dominant space and time scales of variability. A synergistic configuration of circulation features interacting with one another on multiple and sometimes overlapping space and time scales as a meander-eddy-upwelling system is presented. The second step is to define the feature-oriented regional modeling system (FORMS). The major multiscale circulation features include the mean flow and southeastward meandering jet(s) of the California Current (CC), the poleward flowing California Undercurrent (CUC), and six upwelling regions along the coastline. Next, the typical synoptic width, location, vertical extent, and core characteristics of these features and their dominant scales of variability are identified from past observational, theoretical and modeling studies. The parameterized features are then melded with the climatology, in situ and remotely sensed data, as available. The methodology is exemplified here for initialization of primitiveequation models. Dynamical simulations are run as nowcasts and short-term (4–6 weeks) forecasts using these feature models (FM) as initial fields and the Princeton Ocean Model (POM) for dynamics. The set of simulations over a 40-day period illustrate the applicability of FORMS to a transient eastern boundary current region such as the CCS. Comparisons are made with simulations initialized from climatology only. The FORMS approach increases skill in severalfactors, including the: (i) maintenance of the low-salinity pool in the core of the CC; (ii) representation of eddy activity inshore of the coastal transition zone; (iii) realistic eddy kinetic energy evolution; (iv) subsurface (intermediate depth) mesoscale feature evolution; and (v) deep poleward flow evolution.This work was funded by the Office of Naval Research grants N00014-03-1-0411 and N00014-03-1-0206 at the University of Massachusetts at Dartmouth. Leslie Rosenfeld’s participation was supported by ONR grant N00014-03-WR-20009. PFJL, PJH and WGL are grateful to ONR for support under grant N00014-08-1-1097, N00014-08-1-0680 and MURI-ASAP to the Massachusetts Institute of Technology

Cosmological Black Holes on Branes

We examined analytically a cosmological black hole domain wall system. Using the C-metric construction we derived the metric for the spacetime describing an infinitely thin domain wall intersecting a cosmological black hole. We studied the behaviour of the scalar field describing a self-interacting cosmological domain wall and find the approximated solution valid for large distances. The thin wall approximation and the back raection problem were elaborated finding that the topological kink solution smoothed out singular behaviour of the zero thickness wall using a core topological and hence thick domain wall. We also analyze the nucleation of cosmological black holes on and in the presence of a domain walls and conclude that the domain wall will nucleate small black holes on it rather than large ones inside.Comment: 13 pages, Revtex, to be published in Phys.Rev. D1

Free Energies of Dilute Bose gases: upper bound

We derive a upper bound on the free energy of a Bose gas system at density $\rho$ and temperature $T$. In combination with the lower bound derived previously by Seiringer \cite{RS1}, our result proves that in the low density limit, i.e., when $a^3\rho\ll 1$, where $a$ denotes the scattering length of the pair-interaction potential, the leading term of $\Delta f$ the free energy difference per volume between interacting and ideal Bose gases is equal to 4\pi a (2\rho^2-[\rho-\rhoc]^2_+). Here, \rhoc(T) denotes the critical density for Bose-Einstein condensation (for the ideal gas), and $[\cdot ]_+$ $=$ $\max\{\cdot, 0\}$ denotes the positive part.Comment: 56 pages, no figure

Ultrarelativistic black hole in an external electromagnetic field and gravitational waves in the Melvin universe

We investigate the ultrarelativistic boost of a Schwarzschild black hole immersed in an external electromagnetic field, described by an exact solution of the Einstein-Maxwell equations found by Ernst (the ``Schwarzschild-Melvin'' metric). Following the classical method of Aichelburg and Sexl, the gravitational field generated by a black hole moving ``with the speed of light'' and the transformed electromagnetic field are determined. The corresponding exact solution describes an impulsive gravitational wave propagating in the static, cylindrically symmetric, electrovac universe of Melvin, and for a vanishing electromagnetic field it reduces to the well known Aichelburg-Sexl pp-wave. In the boosting process, the original Petrov type I of the Schwarzschild-Melvin solution simplifies to the type II on the impulse, and to the type D elsewhere. The geometry of the wave front is studied, in particular its non-constant Gauss curvature. In addition, a more general class of impulsive waves in the Melvin universe is constructed by means of a six-dimensional embedding formalism adapted to the background. A coordinate system is also presented in which all the impulsive metrics take a continuous form. Finally, it is shown that these solutions are a limiting case of a family of exact gravitational waves with an arbitrary profile. This family is identified with a solution previously found by Garfinkle and Melvin. We thus complement their analysis, in particular demonstrating that such spacetimes are of type II and belong to the Kundt class.Comment: 11 pages, REVTeX

Libraries and open society; Popper, Soros and digital information

This paper examines the role of libraries and information services, in promoting the ‘open society’ espoused by Karl Popper and George Soros. After a brief discussion of the nature of an ‘open society’, the paper covers the role played by provision of knowledge and information, of new technology, particularly the Internet, and of critical thinking and digital literacy in the development of this form of society. Conclusions are drawn for the role of libraries and librarians, with seven general principles suggested: • provision of access to a wide variety of sources without ‘negative’ restriction or censorship • provision of ‘positive’ guidance on sources, based on open and objective criteria • a recognition that a ‘free flow of information’ though essential, is not sufficient • a recognition that provision of factual information, while valuable, is not enough • a need for a specific concern for the effect of new ICTs, and the Internet in particular • promotion of critical thinking and digital literacy • a need for explicit consideration of the ethical values of librarie