6,379 research outputs found
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
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