Unitary Irreducible Representations of a Lie Algebra for Matrix Chain Models

There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way. Moreover, they are the only states with a finite number of non-zero quantum numbers with respect to a certain set of maximally commuting linearly independent quantum observables. Any other state is a tensor product of a multiple meson state and a state coming from a representation of a quotient algebra that extends and generalizes the Virasoro algebra. We expect the representation theory of this quotient algebra to describe physical systems at the thermodynamic limit.Comment: 46 pages, no figure; LaTeX2e, amssymb, latexsym; typos correcte

Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a q-analog of "the wave" operator (a determinant-type differential operator) and prove certain covariance property of its powers. This result is applied to the study of some quotients of the above-mentioned quantum Harish-Chandra modules. We also prove an analog of a known result by J.Faraut and A.Koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series.Comment: 26 page

Continuous dependence estimates for nonlinear fractional convection-diffusion equations

We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators that are generators of pure jump Levy processes (e.g. the fractional Laplacian). As an application, we derive continuous dependence estimates on the nonlinearities and on the Levy measure of the diffusion term. Estimates of the rates of convergence for general nonlinear nonlocal vanishing viscosity approximations of scalar conservation laws then follow as a corollary. Our results both cover, and extend to new equations, a large part of the known error estimates in the literature.Comment: In this version we have corrected Example 3.4 explaining the link with the results in [51,59

Development of scenarios for carbon capture and storage ECCO - European value chain for CO2

AbstractThis paper describes the process of scenario development under ECCO and presents six scenarios resulting from that process. The main objective of ECCO is to facilitate robust strategic decision making regarding early and future deployment of CO2 value chains. The ECCO project strategy is based on critical evaluation of several case studies that will enlighten various aspects of CCS and point out the most promising CO2 chain alternatives. Scenarios in ECCO help to define the background for the case studies. They describe the alternative future(s) in terms of political environment, public opinion, regulatory framework, technology and infrastructure development, and global economical situation

The Late-time Expansion of the Ejecta of SN 1987A

The evolution of the shape and size of the ejecta of SN 1987A is analyzed over a period of ~ 8 years based on HST images and spectra taken between 1278 and 4336 days after the supernova outburst. We combine both proprietary and archival HST data obtained with the FOC, WFPC2 and STIS. The low resolution near-UV prism FOC spectrum obtained at day 3043 has not been described previously. Although the FWHM of the ejecta grew linearly over the time span studied, the appearance of the SN envelope also changed markedly with wavelength. At visible wavelengths (lambda ~ 5000 Angstrom) the ejecta became progressively more elongated, reaching an ellipticity epsilon ~ 0.25 by day 4000. In the near-UV (lambda ~ 2500 AA), the ejecta remained closely circular (epsilon <= 0.1) and ~ 50% larger in angular extent than in the visible. The FOC prism observations show that the large extent of the SN envelope is confined to a grouping of resonance lines spanning Mg I 2852, Mg II 2795,2802 and several Fe II multiplets -- thereby confirming that the larger size of the debris in the near-UV is due to scattering in these optically thick transitions compared to the optically thin forbidden and semi-forbidden transitions that dominate the visible spectrum. The available data are not of sufficient quality to detect the slight deviation from linear expansion expected for the outermost regions of the near-UV images as predicted by Chugai et al. (1997).Comment: Accepted for publication in A&A. 8 pages with 5 figures. Latex using Springer's A&A macros v4.0

Estimating the density scaling exponent of viscous liquids from specific heat and bulk modulus data

It was recently shown by computer simulations that a large class of liquids exhibits strong correlations in their thermal fluctuations of virial and potential energy [Pedersen et al., Phys. Rev. Lett. 100, 015701 (2008)]. Among organic liquids the class of strongly correlating liquids includes van der Waals liquids, but excludes ionic and hydrogen-bonding liquids. The present note focuses on the density scaling of strongly correlating liquids, i.e., the fact their relaxation time tau at different densities rho and temperatures T collapses to a master curve according to the expression tau propto F(rho^gamma/T) [Schroder et al., arXiv:0803.2199]. We here show how to calculate the exponent gamma from bulk modulus and specific heat data, either measured as functions of frequency in the metastable liquid or extrapolated from the glass and liquid phases to a common temperature (close to the glass transition temperature). Thus an exponent defined from the response to highly nonlinear parameter changes may be determined from linear response measurements