Geometry of W-algebras from the affine Lie algebra point of view

To classify the classical field theories with W-symmetry one has to classify the symplectic leaves of the corresponding W-algebra, which are the intersection of the defining constraint and the coadjoint orbit of the affine Lie algebra if the W-algebra in question is obtained by reducing a WZNW model. The fields that survive the reduction will obey non-linear Poisson bracket (or commutator) relations in general. For example the Toda models are well-known theories which possess such a non-linear W-symmetry and many features of these models can only be understood if one investigates the reduction procedure. In this paper we analyze the SL(n,R) case from which the so-called W_n-algebras can be obtained. One advantage of the reduction viewpoint is that it gives a constructive way to classify the symplectic leaves of the W-algebra which we had done in the n=2 case which will correspond to the coadjoint orbits of the Virasoro algebra and for n=3 which case gives rise to the Zamolodchikov algebra. Our method in principle is capable of constructing explicit representatives on each leaf. Another attractive feature of this approach is the fact that the global nature of the W-transformations can be explicitly described. The reduction method also enables one to determine the ``classical highest weight (h. w.) states'' which are the stable minima of the energy on a W-leaf. These are important as only to those leaves can a highest weight representation space of the W-algebra be associated which contains a ``classical h. w. state''.Comment: 17 pages, LaTeX, revised 1. and 7. chapter

The ρ\rho Meson Light-Cone Distribution Amplitudes of Leading Twist Revisited

We give a complete re-analysis of the leading twist quark-antiquark light-cone distribution amplitudes of longitudinal and transverse $\rho$ mesons. We derive Wandzura-Wilczek type relations between different distributions and update the coefficients in their conformal expansion using QCD sum rules including next-to-leading order radiative corrections. We find that the distribution amplitudes of quarks inside longitudinally and transversely polarized $\rho$ mesons have a similar shape, which is in contradiction to previous analyses.Comment: 21 pages, latex2e, requires a4wide.sty and epsf.sty, 6 PS figures include

Wannier functions for quasi-periodic finite-gap potentials

In this paper we consider Wannier functions of quasi-periodic g-gap ($g\geq 1$) potentials and investigate their main properties. In particular, we discuss the problem of averaging underlying the definition of Wannier functions for both periodic and quasi-periodic potentials and express Bloch functions and quasi-momenta in terms of hyperelliptic $\sigma$ functions. Using this approach we derive a power series expansion of the Wannier function for quasi-periodic potentials valid at $|x|\simeq 0$ and an asymptotic expansion valid at large distance. These functions are important for a number of applied problems

The First Extrasolar Planet Discovered with a New Generation High Throughput Doppler Instrument

We report the detection of the first extrasolar planet, ET-1 (HD 102195b), using the Exoplanet Tracker (ET), a new generation Doppler instrument. The planet orbits HD 102195, a young star with solar metallicity that may be part of the local association. The planet imparts radial velocity variability to the star with a semiamplitude of $63.4\pm2.0$ m s$^{-1}$ and a period of 4.11 days. The planetary minimum mass ($m \sin i$) is $0.488\pm0.015$ $M_J$.Comment: 42 pages, 11 figures and 5 tables, Accepted for publication in Ap

Pattern formation on the surface of a bubble driven by an acoustic field

The final stable shape taken by a fluid–fluid interface when it experiences a growinginstability can be important in determining features as diverse as weather patterns inthe atmosphere and oceans, the growth of cell structures and viruses, and the dynamicsof planets and stars. An example which is accessible to laboratory study is that of anair bubble driven by ultrasound when it becomes shape-unstable through a parametricinstability. Above the critical driving pressure threshold for shape oscillations, which isminimal at the resonance of the breathing mode, regular patterns of surface waves areobserved on the bubble wall. The existing theoretical models, which take account only ofthe interaction between the breathing and distortion modes, cannot explain the selectionof the regular pattern on the bubble wall. This paper proposes an explanation which isbased on the consideration of a three-wave resonant interaction between the distortionmodes. Using a Hamiltonian approach to nonlinear bubble oscillation, corrections tothe dynamical equations governing the evolution of the amplitudes of interacting surfacemodes have been derived. Steady-state solutions of these equations describe the formationof a regular structure. Our predictions are confirmed by images of patterns observed onthe bubble wall