Trigonometric sl(2) Gaudin model with boundary terms

We review the derivation of the Gaudin model with integrable boundaries. Starting from the non-symmetric R-matrix of the inhomogeneous spin-1/2 XXZ chain and generic solutions of the reflection equation and the dual reflection equation, the corresponding Gaudin Hamiltonians with boundary terms are calculated. An alternative derivation based on the so-called classical reflection equation is discussed.Comment: 16 page

Acoustic metafluids made from three acoustic fluids

Significant reduction in target strength and radiation signature can be achieved by surrounding an object with multiple concentric layers comprised of three acoustic fluids. The idea is to make a finely layered shell with the thickness of each layer defined by a unique transformation rule. The shell has the effect of steering incident acoustic energy around the structure, and conversely, reducing the radiation strength. The overall effectiveness and the precise form of the layering depends upon the densities and compressibilities of the three fluids. Nearly optimal results are obtained if one fluid has density equal to the background fluid, while the other two densities are much greater and much less than the background values. Optimal choices for the compressibilities are also found. Simulations in 2D and 3D illustrate effectiveness of the three fluid shell. The limited range of acoustic metafluids that are possible using only two fluid constituents is also discussed.Comment: 12 pages, 11 figure

Francoprovençal: Documenting contact varieties in Europe and North America

This special issue of the International Journal of the Sociology of Language brings together articles from an international set of authors that situate the family of Francoprovençal (FP) dialects in terms of formal structures, contexts of contact, practice and policy. FP has been the subject of little scholarly attention. This dearth of research is largely the result of its ambiguous status. Ever since it was introduced by Ascoli (1878 [1874]), the notion of FP has been questioned. There has long been disagreement over its linguistic borders and the linguistic criteria used for demarcation. As late as 2007, scholars have asked: le francoprovençal existe-t-il ? [does FP exist?] (Tuaillon 2007: 9). This is the first collection describing FP across its entire geographical distribution and assembling varied sociolinguistic approaches. Previous collections include a dialectology volume focusing on the status and structure of FP (Marzys (1971); a posthumous volume focusing on Lyonnais (Gardette 1983); and Fréchet (2009), consisting of descriptions of both FP and Occitan. These works – though important contributions to FP linguistics – provide little quantitative substance. Moreover, little work on FP has been produced in English, which limits access to researchers worldwide who might be interested in the sociolinguistic context of FP or comparison with other minority-language contexts. To begin to fill this void, we introduce FP, then outline the key themes of this issue and the range of sociolinguistic traditions covered

Spontaneous Breaking of Chiral Symmetry as a Consequence of Confinement

We show that at the leading order in the large-$N$ expansion a lattice QCD motivated linear rising confinement potential at large distances leads to a non-local four-quark interaction that realizes spontaneous breaking of chiral symmetry (SBCS) in the same way the Nambu-Jona-Lasinio model does. The dynamical quark mass $m$, which represents the solution of the gap-equation, is proportional to the square root of the string tension $\sigma$ and takes the form at the leading order in the large-$N$ expansion $m=2 \sqrt{\sigma}/\pi$ with $\sigma=0.27$ GeV$^2$. The Nambu-Jona-Lasinio phenomenological constant $G_1$, which is responsible for SBCS, is expressed in terms of the string tension and the confinement radius.Comment: 10 pages, 0 figures, latex, IK-TUW-Preprint 930540

Critical Phenomena in DIS

Saturation in deep inelastic scattering (DIS) and deeply virtual Compton scattering (DVCS) is associated with a phase transition between the partonic gas, typical of moderate $x$ and $Q^2$, and partonic fluid appearing at increasing $Q^2$ and decreasing Bjorken $x$. In the statistical interpretation of DIS, the large-$x,(1-x)^n$ factor in the SF is associated with a statistical distribution (perfect gas), while the low-$x$, Regge behaved factor $x^{b(Q^2)}$ produces deviations from the perfect gas and ultimately leads to a gas-liquid phase transition. In this paper we do not intend to propose another parametrization of the structure function; instead we suggest a new insight into the internal structure of the nucleon, as seen in DIS, and its connection with that revealed in high-energy nucleons and heavy-ion collisions.Comment: 20 pages, 8 figures, reported at the CPOD Conference, Dubna, 2010, to be published in the International Journal of Modern Physics

Four-jet angular distributions and color charge measurements: leading order versus next-to-leading order

We present the next-to-leading order perturbative QCD prediction to the four-jet angular distributions used by experimental collaborations at LEP for measuring the QCD color charge factors. We compare our results to ALEPH data corrected to parton level. We perform a leading order ``measurement'' of the QCD color factor ratios by fitting the leading order perturbative predictions to the next-to-leading order result. Our result shows that in an experimental analysis for measuring the color charge factors the use of the O($\alpha_s^3$) QCD predictions instead of the O($\alpha_s^2$) results may shift the center of the fit by a relative factor of 1+2\as in the $T_R/C_F$ direction.Comment: 14 pages, 10 tables, 5 figures, revtex, eps style