Instabilities in the two-dimensional cubic nonlinear Schrodinger equation

The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional traveling wave solution of NLS with trivial phase is unstable with respect to some infinitesimal perturbation with two-dimensional structure. If the coefficients of the linear dispersion terms have the same sign then the only unstable perturbations have transverse wavelength longer than a well-defined cut-off. If the coefficients of the linear dispersion terms have opposite signs, then there is no such cut-off and as the wavelength decreases, the maximum growth rate approaches a well-defined limit.Comment: 4 pages, 4 figure

On the invariance under area preserving diffeomorphisms of noncommutative Yang-Mills theory in two dimensions

We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.Comment: LaTeX JHEP style, 16 pages, 2 figure

Two-dimensional non-commutative Yang-Mills theory: coherent effects in open Wilson line correlators

A perturbative calculation of the correlator of three parallel open Wilson lines is performed for the U(N) theory in two non-commutative space-time dimensions. In the large-N planar limit, the perturbative series is fully resummed and asymptotically leads to an exponential increase of the correlator with the lengths of the lines, in spite of an interference effect between lines with the same orientation. This result generalizes a similar increase occurring in the two-line correlator and is likely to persist when more lines are considered provided they share the same direction.Comment: 22 pages, 1 figure, typeset in JHEP styl

Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4

We define U(n) gauge theory on fuzzy S^2_N x S^2_N as a multi-matrix model, which reduces to ordinary Yang-Mills theory on S^2 x S^2 in the commutative limit N -> infinity. The model can be used as a regularization of gauge theory on noncommutative R^4_\theta in a particular scaling limit, which is studied in detail. We also find topologically non-trivial U(1) solutions, which reduce to the known "fluxon" solutions in the limit of R^4_\theta, reproducing their full moduli space. Other solutions which can be interpreted as 2-dimensional branes are also found. The quantization of the model is defined non-perturbatively in terms of a path integral which is finite. A gauge-fixed BRST-invariant action is given as well. Fermions in the fundamental representation of the gauge group are included using a formulation based on SO(6), by defining a fuzzy Dirac operator which reduces to the standard Dirac operator on S^2 x S^2 in the commutative limit. The chirality operator and Weyl spinors are also introduced.Comment: 39 pages. V2-4: References added, typos fixe

Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies

We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic behavior of the multi-soliton solutions and found that the asymptotic configurations in soliton scattering process can be all the same as commutative ones, that is, the configuration of N-soliton solution has N isolated localized energy densities and the each solitary wave-packet preserves its shape and velocity in the scattering process. The phase shifts are also the same as commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy is introduced and the exact multi-soliton solutions are given.Comment: 18 pages, v3: references added, version to appear in JHE

Chapter 9 - Buildings

This chapter aims to update the knowledge on the building sector since the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) from a mitigation perspective. Buildings and activities in buildings are responsible for a significant share of GHG emissions, but they are also the key to mitigation strategies. In 2010, the building sector accounted for approximately 117 Exajoules (EJ) or 32% of global final energy consumption and 19% of energy-related CO2 emissions; and 51% of global electricity consumption. Buildings contribute to a significant amount of F-gas emissions, with large differences in reported figures due to differing accounting conventions, ranging from around an eighth to a third of all such emissions. The chapter argues that beyond a large emission role, mitigation opportunities in this sector are also significant, often very cost-effective, and are in many times associated with significant co-benefits that can exceed the direct benefits by orders of magnitude. The sector has significant mitigation potentials at low or even negative costs. Nevertheless, without strong actions emissions are likely to grow considerably - and they may even double by mid-century - due to several drivers. The chapter points out that certain policies have proven to be very effective and several new ones are emerging. As a result, building energy use trends have been reversed to stagnation or even reduction in some jurisdictions in recent years, despite the increases in affluence and population. The chapter uses a novel conceptual framework, in line with the general analytical framework of the contribution of Working Group III (WGIII) to the IPCC Fifth Assessment Report (AR5), which focuses on identities as an organizing principle

Probability distribution of the index in gauge theory on 2d non-commutative geometry

We investigate the effects of non-commutative geometry on the topological aspects of gauge theory using a non-perturbative formulation based on the twisted reduced model. The configuration space is decomposed into topological sectors labeled by the index nu of the overlap Dirac operator satisfying the Ginsparg-Wilson relation. We study the probability distribution of nu by Monte Carlo simulation of the U(1) gauge theory on 2d non-commutative space with periodic boundary conditions. In general the distribution is asymmetric under nu -> -nu, reflecting the parity violation due to non-commutative geometry. In the continuum and infinite-volume limits, however, the distribution turns out to be dominated by the topologically trivial sector. This conclusion is consistent with the instanton calculus in the continuum theory. However, it is in striking contrast to the known results in the commutative case obtained from lattice simulation, where the distribution is Gaussian in a finite volume, but the width diverges in the infinite-volume limit. We also calculate the average action in each topological sector, and provide deeper understanding of the observed phenomenon.Comment: 16 pages,10 figures, version appeared in JHE

Recent sarcopenia definitions—prevalence, agreement and mortality associations among men: findings from population‐based cohorts

Background The 2019 European Working Group on Sarcopenia in Older People (EWGSOP2) and the Sarcopenia Definitions and Outcomes Consortium (SDOC) have recently proposed sarcopenia definitions. However, comparisons of the performance of these approaches in terms of thresholds employed, concordance in individuals and prediction of important health-related outcomes such as death are limited. We addressed this in a large multinational assembly of cohort studies that included information on lean mass, muscle strength, physical performance and health outcomes. Methods White men from the Health Aging and Body Composition (Health ABC) Study, Osteoporotic Fractures in Men (MrOS) Study cohorts (Sweden, USA), the Hertfordshire Cohort Study (HCS) and the Sarcopenia and Physical impairment with advancing Age (SarcoPhAge) Study were analysed. Appendicular lean mass (ALM) was ascertained using DXA; muscle strength by grip dynamometry; and usual gait speed over courses of 2.4–6 m. Deaths were recorded and verified. Definitions of sarcopenia were as follows: EWGSOP2 (grip strength <27 kg and ALM index <7.0 kg/m2), SDOC (grip strength <35.5 kg and gait speed <0.8 m/s) and Modified SDOC (grip strength <35.5 kg and gait speed <1.0 m/s). Cohen's kappa statistic was used to assess agreement between original definitions (EWGSOP2 and SDOC). Presence versus absence of sarcopenia according to each definition in relation to mortality risk was examined using Cox regression with adjustment for age and weight; estimates were combined across cohorts using random-effects meta-analysis. Results Mean (SD) age of participants (n = 9170) was 74.3 (4.9) years; 5929 participants died during a mean (SD) follow-up of 12.1 (5.5) years. The proportion with sarcopenia according to each definition was EWGSOP2 (1.1%), SDOC (1.7%) and Modified SDOC (5.3%). Agreement was weak between EWGSOP2 and SDOC (κ = 0.17). Pooled hazard ratios (95% CI) for mortality for presence versus absence of each definition were EWGSOP2 [1.76 (1.42, 2.18), I2: 0.0%]; SDOC [2.75 (2.28, 3.31), I2: 0.0%]; and Modified SDOC [1.93 (1.54, 2.41), I2: 58.3%]. Conclusions There was low prevalence and poor agreement among recent sarcopenia definitions in community-dwelling cohorts of older white men. All indices of sarcopenia were associated with mortality. The strong relationship between sarcopenia and mortality, regardless of the definition, illustrates that identification of appropriate management and lifecourse intervention strategies for this condition is of paramount importance