Global Dimension of Polynomial Rings in Partially Commuting Variables

For any free partially commutative monoid $M(E,I)$, we compute the global dimension of the category of $M(E,I)$-objects in an Abelian category with exact coproducts. As a corollary, we generalize Hilbert's Syzygy Theorem to polynomial rings in partially commuting variables.Comment: 11 pages, 2 figure

The Impact of Isospin Breaking on the Distribution of Transition Probabilities

In the present paper we investigate the effect of symmetry breaking in the statistical distributions of reduced transition amplitudes and reduced transition probabilities. These quantities are easier to access experimentally than the components of the eigenvectors and were measured by Adams et al. for the electromagnetic transitions in ^{26}Al. We focus on isospin symmetry breaking described by a matrix model where both, the Hamiltonian and the electromagnetic operator, break the symmetry. The results show that for partial isospin conservation, the statistical distribution of the reduced transition probability can considerably deviate from the Porter-Thomas distribution.Comment: 16 pages, 8 figures, submitted to PR

On the Hausdorff volume in sub-Riemannian geometry

For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous function. We then prove that up to dimension 4 it is smooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4 on every smooth curve) but in general not C^5. These results answer to a question addressed by Montgomery about the relation between two intrinsic volumes that can be defined in a sub-Riemannian manifold, namely the Popp and the Hausdorff volume. If the nilpotent approximation depends on the point (that may happen starting from dimension 5), then they are not proportional, in general.Comment: Accepted on Calculus and Variations and PD

Assessment of atmospheric aerosols from two reanalysis products over Australia

Assessments of atmospheric aerosols from reanalysis are important for understanding uncertainty in model simulations, and ultimately predictions, such as for solar power or air quality forecasts and assessments. This study intercompares total aerosol optical depth (AOD) and dust AOD (DAOD) from two global reanalyses datasets, the European Centre for Medium-Range Weather Forecasts (ECMWF) Monitoring Atmospheric Composition and Climate (MACC) and the NASA Modern-Era Retrospective Analysis for Research-2 (MERRA-2). These are evaluated against AeroSpan (Aerosol characterisation via Sun photometry: Australian Network) ground observations which forms part of the Aerosol Robotic Network (AERONET) over the Australian continent for the 2002–2012 period. During dust storms, AeroSpan/AERONET AOD measurements were missing due to cloud screening. To overcome validation limitations in sun photometry for dust events, a nephelometer's scattering coefficient is qualitatively compared against reanalysis of DAOD at a key dust storm activation site, Tinga Tingana in South Australia (~200 km east of Lake Eyre). A specific extreme event that occurred in 2009 originating from the Lake Eyre basin, a major dust source covering one-sixth of Australia, was studied. The results show that MERRA-2 reanalysis overestimates monthly total AOD twice as much compared to AeroSpan/AERONET ground observations but seems better correlated against AeroSpan/AERONET than ECMWF/MACC. Mean data of MERRA-2 time series over 10 years provide lower DAOD values and lower dust aerosol estimates than ECMWF/MACC reanalysis (over the Lake Eyre basin with spatial averaging). Specifically at Tinga Tingana, the correlation from MERRA-2 (0.45 correlation) and ECMWF/MACC (0.43 correlation) against AeroSpan/AERONET's AOD were similar. Between MERRA-2 and ECMWF/MACC decade long daily gridded DAOD, the correlation coefficient was high at 0.73, again indicating similarity between the datasets. MERRA-2 total AOD correlation is significantly higher (by 0.26) against AeroSpan/AERONET than ECMWF/MACC. MERRA-2 also provides higher AOD values in extreme cases which may correspond to dust storms. During dust storms, a hybrid strategy using nephelometers and hourly reanalysis from MERRA-2 is able to identify dust storms better than AeroSpan/AERONET. Overall, this work can enable and inform better aerosol data assimilation into forecast models such as for solar energy, agriculture or air quality over Australia

Statistical Theory for Incoherent Light Propagation in Nonlinear Media

A novel statistical approach based on the Wigner transform is proposed for the description of partially incoherent optical wave dynamics in nonlinear media. An evolution equation for the Wigner transform is derived from a nonlinear Schrodinger equation with arbitrary nonlinearity. It is shown that random phase fluctuations of an incoherent plane wave lead to a Landau-like damping effect, which can stabilize the modulational instability. In the limit of the geometrical optics approximation, incoherent, localized, and stationary wave-fields are shown to exist for a wide class of nonlinear media.Comment: 4 pages, REVTeX4. Submitted to Physical Review E. Revised manuscrip

Exact soliton solutions of coupled nonlinear Schr\"odinger equations: Shape changing collisions, logic gates and partially coherent solitons

The novel dynamical features underlying soliton interactions in coupled nonlinear Schr{\"o}dinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by explicitly constructing multisoliton solutions (upto four-soliton solutions) for two coupled and arbitrary $N$-coupled nonlinear Schr{\"o}dinger equations using the Hirota bilinearization method, we bring out clearly the various features underlying the fascinating shape changing (intensity redistribution) collisions of solitons, including changes in amplitudes, phases and relative separation distances, and the very many possibilities of energy redistributions among the modes of solitons. However in this multisoliton collision process the pair-wise collision nature is shown to be preserved in spite of the changes in the amplitudes and phases of the solitons. Detailed asymptotic analysis also shows that when solitons undergo multiple collisions, there exists the exciting possibility of shape restoration of atleast one soliton during interactions of more than two solitons represented by three and higher order soliton solutions. From application point of view, we have shown from the asymptotic expressions how the amplitude (intensity) redistribution can be written as a generalized linear fractional transformation for the $N$-component case. Also we indicate how the multisolitons can be reinterpreted as various logic gates for suitable choices of the soliton parameters, leading to possible multistate logic. In addition, we point out that the various recently studied partially coherent solitons are just special cases of the bright soliton solutions exhibiting shape changing collisions, thereby explaining their variable profile and shape variation in collision process.Comment: 50 Pages, 13 .jpg figures. To appear in PR

Thermal history of the string universe

Thermal history of the string universe based on the Brandenberger and Vafa's scenario is examined. The analysis thereby provides a theoretical foundation of the string universe scenario. Especially the picture of the initial oscillating phase is shown to be natural from the thermodynamical point of view. A new tool is employed to evaluate the multi state density of the string gas. This analysis points out that the well-known functional form of the multi state density is not applicable for the important region $T \leq T_H$, and derives a correct form of it.Comment: 39 pages, no figures, use revtex.sty, aps.sty, aps10.sty & preprint.st

Stability of Spatial Optical Solitons

We present a brief overview of the basic concepts of the soliton stability theory and discuss some characteristic examples of the instability-induced soliton dynamics, in application to spatial optical solitons described by the NLS-type nonlinear models and their generalizations. In particular, we demonstrate that the soliton internal modes are responsible for the appearance of the soliton instability, and outline an analytical approach based on a multi-scale asymptotic technique that allows to analyze the soliton dynamics near the marginal stability point. We also discuss some results of the rigorous linear stability analysis of fundamental solitary waves and nonlinear impurity modes. Finally, we demonstrate that multi-hump vector solitary waves may become stable in some nonlinear models, and discuss the examples of stable (1+1)-dimensional composite solitons and (2+1)-dimensional dipole-mode solitons in a model of two incoherently interacting optical beams.Comment: 34 pages, 9 figures; to be published in: "Spatial Optical Solitons", Eds. W. Torruellas and S. Trillo (Springer, New York

Effectiveness and cost-effectiveness of daily all-over-body application of emollient during the first year of life for preventing atopic eczema in high-risk children (The BEEP trial): protocol for a randomised controlled trial.

BACKGROUND: Atopic eczema (AE) is a common skin problem that impairs quality of life and is associated with the development of other atopic diseases including asthma, food allergy and allergic rhinitis. AE treatment is a significant cost burden for health care providers. The purpose of the trial is to investigate whether daily application of emollients for the first year of life can prevent AE developing in high-risk infants (first-degree relative with asthma, AE or allergic rhinitis). METHODS: This is a protocol for a pragmatic, two-arm, randomised controlled, multicentre trial. Up to 1400 term infants at high risk of developing AE will be recruited through the community, primary and secondary care in England. Participating families will be randomised in a 1:1 ratio to receive general infant skin-care advice, or general skin-care advice plus emollients with advice to apply daily to the infant for the first year of life. Families will not be blinded to treatment allocation. The primary outcome will be a blinded assessment of AE at 24 months of age using the UK Working Party Diagnostic Criteria for Atopic Eczema. Secondary outcomes are other definitions of AE, time to AE onset, severity of AE (EASI and POEM), presence of other allergic diseases including food allergy, asthma and hay fever, allergic sensitisation, quality of life, cost-effectiveness and safety of the emollients. Subgroup analyses are planned for the primary outcome according to filaggrin genotype and the number of first-degree relatives with AE and other atopic diseases. Families will be followed up by online and postal questionnaire at 3, 6, 12 and 18 months with a face-to-face visit at 24 months. Long-term follow-up until 60 months will be via annual questionnaires. DISCUSSION: This trial will demonstrate whether skin-barrier enhancement through daily emollient for the first year of life can prevent AE from developing in high-risk infants. If effective, this simple and cheap intervention has the potential to result in significant cost savings for health care providers throughout the world by preventing AE and possibly other associated allergic diseases. TRIAL REGISTRATION: ISRCTN registry; ID: ISRCTN21528841 . Registered on 25 July 2014

Measurement of cosmic-ray low-energy antiproton spectrum with the first BESS-Polar Antarctic flight

The BESS-Polar spectrometer had its first successful balloon flight over Antarctica in December 2004. During the 8.5-day long-duration flight, almost 0.9 billion events were recorded and 1,520 antiprotons were detected in the energy range 0.1-4.2 GeV. In this paper, we report the antiproton spectrum obtained, discuss the origin of cosmic-ray antiprotons, and use antiprotons to probe the effect of charge sign dependent drift in the solar modulation.Comment: 18 pages, 1 table, 5 figures, submitted to Physics Letters