Two-soliton collisions in a near-integrable lattice system

We examine collisions between identical solitons in a weakly perturbed Ablowitz-Ladik (AL) model, augmented by either onsite cubic nonlinearity (which corresponds to the Salerno model, and may be realized as an array of strongly overlapping nonlinear optical waveguides), or a quintic perturbation, or both. Complex dependences of the outcomes of the collisions on the initial phase difference between the solitons and location of the collision point are observed. Large changes of amplitudes and velocities of the colliding solitons are generated by weak perturbations, showing that the elasticity of soliton collisions in the AL model is fragile (for instance, the Salerno's perturbation with the relative strength of 0.08 can give rise to a change of the solitons' amplitudes by a factor exceeding 2). Exact and approximate conservation laws in the perturbed system are examined, with a conclusion that the small perturbations very weakly affect the norm and energy conservation, but completely destroy the conservation of the lattice momentum, which is explained by the absence of the translational symmetry in generic nonintegrable lattice models. Data collected for a very large number of collisions correlate with this conclusion. Asymmetry of the collisions (which is explained by the dependence on the location of the central point of the collision relative to the lattice, and on the phase difference between the solitons) is investigated too, showing that the nonintegrability-induced effects grow almost linearly with the perturbation strength. Different perturbations (cubic and quintic ones) produce virtually identical collision-induced effects, which makes it possible to compensate them, thus finding a special perturbed system with almost elastic soliton collisions.Comment: Phys. Rev. E, in pres

Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases

We use the nonperturbative linear \delta expansion method to evaluate analytically the coefficients c_1 and c_2^{\prime \prime} which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by T_c= T_0 \{1 + c_1 a n^{1/3} + [ c_2^{\prime} \ln(a n^{1/3}) +c_2^{\prime \prime} ] a^2 n^{2/3} + {\cal O} (a^3 n)\}, where T_0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c_1 to order-\delta^2 with the result c_1= 3.06. Here, we push the calculation to the next two orders obtaining c_1=2.45 at order-\delta^3 and c_1=1.48 at order-\delta^4. Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c_2^{\prime\prime}=101.4, c_2^{\prime \prime}=98.2 and c_2^{\prime \prime}=82.9. Our analytical results seem to support the recent Monte Carlo estimates c_1=1.32 \pm 0.02 and c_2^{\prime \prime}= 75.7 \pm 0.4.Comment: 29 pages, 3 eps figures. Minor changes, one reference added. Version in press Physical Review A (2002

Embodied learning: Responding to AIDS in Lesotho's education sector

This is an Author's Accepted Manuscript of an article published in Children's Geographies, 7(1), 2009. Copyright @ 2009 Taylor & Francis, available online at: http://www.tandfonline.com/doi/abs/10.1080/14733280802630981.In contrast to pre-colonial practices, education in Lesotho's formal school system has historically assumed a Cartesian separation of mind and body, the disciplining of students' bodies serving principally to facilitate cognitive learning. Lesotho has among the highest HIV-prevalence rates worldwide, and AIDS has both direct and indirect impacts on the bodies of many children. Thus, students' bodies can no longer be taken for granted but present a challenge for education. Schools are increasingly seen as a key point of intervention to reduce young people's risk of contracting the disease and also to assist them to cope with its consequences: there is growing recognition that such goals require more than cognitive learning. The approaches adopted, however, range from those that posit a linear and causal relationship between knowledge, attitudes and practices (so-called ‘KAP’ approaches, in which the role of schools is principally to inculcate the pre-requisite knowledge) to ‘life skills programmes’ that advocate a more embodied learning practice in schools. Based on interviews with policy-makers and practitioners and a variety of documentary sources, this paper examines a series of school-based AIDS interventions, arguing that they represent a less radical departure from ‘education for the mind’ than might appear to be the case. The paper concludes that most interventions serve to cast on children responsibility for averting a social risk, and to ‘normalise’ aberrant children's bodies to ensure they conform to what the cognitively-oriented education system expects

Two-loop HTL Thermodynamics with Quarks

We calculate the quark contribution to the free energy of a hot quark-gluon plasma to two-loop order using hard-thermal-loop (HTL) perturbation theory. All ultraviolet divergences can be absorbed into renormalizations of the vacuum energy and the HTL quark and gluon mass parameters. The quark and gluon HTL mass parameters are determined self-consistently by a variational prescription. Combining the quark contribution with the two-loop HTL perturbation theory free energy for pure-glue we obtain the total two-loop QCD free energy. Comparisons are made with lattice estimates of the free energy for N_f=2 and with exact numerical results obtained in the large-N_f limit.Comment: 33 pages, 6 figure

The first multi-wavelength campaign of AXP 4U 0142+61 from radio to hard X-rays

For the first time a quasi-simultaneous multi-wavelength campaign has been performed on an Anomalous X-ray Pulsar from the radio to the hard X-ray band. 4U 0142+61 was an INTEGRAL target for 1 Ms in July 2005. During these observations it was also observed in the X-ray band with Swift and RXTE, in the optical and NIR with Gemini North and in the radio with the WSRT. In this paper we present the source-energy distribution. The spectral results obtained in the individual wave bands do not connect smoothly; apparently components of different origin contribute to the total spectrum. Remarkable is that the INTEGRAL hard X-ray spectrum (power-law index 0.79 +/- 0.10) is now measured up to an energy of ~230 keV with no indication of a spectral break. Extrapolation of the INTEGRAL power-law spectrum to lower energies passes orders of magnitude underneath the NIR and optical fluxes, as well as the low ~30 microJy (2 sigma) upper limit in the radio band.Comment: 6 pages, 1 figure. To be published in the proceedings of the conference "Isolated Neutron Stars: from the Interior to the Surface" (April 24-28, 2006, London, UK), eds. S. Zane, R. Turolla and D. Pag

Testing the Gaussian expansion method in exactly solvable matrix models

The Gaussian expansion has been developed since early 80s as a powerful analytical method, which enables nonperturbative studies of various systems using `perturbative' calculations. Recently the method has been used to suggest that 4d space-time is generated dynamically in a matrix model formulation of superstring theory. Here we clarify the nature of the method by applying it to exactly solvable one-matrix models with various kinds of potential including the ones unbounded from below and of the double-well type. We also formulate a prescription to include a linear term in the Gaussian action in a way consistent with the loop expansion, and test it in some concrete examples. We discuss a case where we obtain two distinct plateaus in the parameter space of the Gaussian action, corresponding to different large-N solutions. This clarifies the situation encountered in the dynamical determination of the space-time dimensionality in the previous works.Comment: 30 pages, 15 figures, LaTeX; added references for section

Unveiling Soft Gamma-Ray Repeaters with INTEGRAL

Thanks to INTEGRAL's long exposures of the Galactic Plane, the two brightest Soft Gamma-Ray Repeaters, SGR 1806-20 and SGR 1900+14, have been monitored and studied in detail for the first time at hard-X/soft gamma rays. This has produced a wealth of new scientific results, which we will review here. Since SGR 1806-20 was particularly active during the last two years, more than 300 short bursts have been observed with INTEGRAL. and their characteristics have been studied with unprecedented sensitivity in the 15-200 keV range. A hardness-intensity anticorrelation within the bursts has been discovered and the overall Number-Intensity distribution of the bursts has been determined. In addition, a particularly active state, during which ~100 bursts were emitted in ~10 minutes, has been observed on October 5 2004, indicating that the source activity was rapidly increasing. This eventually led to the Giant Flare of December 27th 2004, for which a possible soft gamma-ray (>80 keV) early afterglow has been detected. The deep observations allowed us to discover the persistent emission in hard X-rays (20-150 keV) from 1806-20 and 1900+14, the latter being in a quiescent state, and to directly compare the spectral characteristics of all Magnetars (two SGRs and three Anomalous X-ray Pulsars) detected with INTEGRAL.Comment: 8 pages, 7 figures, Presented at the conference "Isolated Neutron Stars: from the Surface to the Interior", London, UK, 24-28 April 200

(Borel) convergence of the variationally improved mass expansion and the O(N) Gross-Neveu model mass gap

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass dependence) are transmuted into expansions in 1/F, where $F \sim 1/g(m)$ for $m \gg \Lambda$ while $F \sim (m/\Lambda)^\alpha$ for m \lsim \Lambda, $\Lambda$ being the basic scale and $\alpha$ given by renormalization group coefficients. (Borel) convergence holds in a range of $F$ which corresponds to reach unambiguously the strong coupling infrared regime near $m\to 0$, which can define certain "non-perturbative" quantities, such as the mass gap, from a resummation of this alternative expansion. Convergence properties can be further improved, when combined with $\delta$ expansion (variationally improved perturbation) methods. We illustrate these results by re-evaluating, from purely perturbative informations, the O(N) Gross-Neveu model mass gap, known for arbitrary $N$ from exact S matrix results. Comparing different levels of approximations that can be defined within our framework, we find reasonable agreement with the exact result.Comment: 33 pp., RevTeX4, 6 eps figures. Minor typos, notation and wording corrections, 2 references added. To appear in Phys. Rev.

Fertility, Living Arrangements, Care and Mobility

There are four main interconnecting themes around which the contributions in this book are based. This introductory chapter aims to establish the broad context for the chapters that follow by discussing each of the themes. It does so by setting these themes within the overarching demographic challenge of the twenty-first century – demographic ageing. Each chapter is introduced in the context of the specific theme to which it primarily relates and there is a summary of the data sets used by the contributors to illustrate the wide range of cross-sectional and longitudinal data analysed

Finite Theories and the SUSY Flavor Problem

We study a finite SU(5) grand unified model based on the non-Abelian discrete symmetry A_4. This model leads to the democratic structure of the mass matrices for the quarks and leptons. In the soft supersymmetry breaking sector, the scalar trilinear couplings are aligned and the soft scalar masses are degenerate, thus solving the SUSY flavor problem.Comment: 17 pages, LaTeX, 1 figur