On Weyl modules of cyclotomic qq-Schur algebras

We study on Weyl modules of cyclotomic $q$-Schur algebras. In particular, we give the character formula of the Weyl modules by using the Kostka numbers and some numbers which are computed by a generalization of Littlewood-Richardson rule. We also study corresponding symmetric functions. Finally, we give some simple applications to modular representations of cyclotomic $q$-Schur algebras.Comment: 28 page

Thermodynamic stability conditions for nonadditive composable entropies

The thermodynamic stability conditions (TSC) of nonadditive and composable entropies are discussed. Generally the concavity of a nonadditive entropy with respect to internal energy is not necessarily equivalent to the corresponding TSC. It is shown that both the TSC of Tsallis' entropy and that of the $\kappa$-generalized Boltzmann entropy are equivalent to the positivity of the standard heat capacity.Comment: 6pages; Contribution to a topical issue of Continuum Mechanics and Thermodynamics (CMT), edited by M. Sugiyam

Radiation-driven Fountain and Origin of Torus around Active Galactic Nuclei

We propose a plausible mechanism to explain the formation of the so-called "obscuring tori" around active galactic nuclei (AGNs) based on three-dimensional hydrodynamic simulations including radiative feedback from the central source. The X-ray heating and radiation pressure on the gas are explicitly calculated using a ray-tracing method. This radiation feedback drives a "fountain", that is, a vertical circulation of gas in the central a few to tens parsecs. Interaction between the non-steady outflows and inflows causes the formation of a geometrically thick torus with internal turbulent motion. As a result, the AGN is obscured for a wide range of solid angles. In a quasi-steady state, the opening angles for the column density toward a black hole < 10^23 cm^-2 are approximately +-30 deg and +-50 deg for AGNs with 10% and 1% Eddington luminosity, respectively. Mass inflows through the torus coexist with the outflow and internal turbulent motion, and the average mass accretion rate to the central parsec region is 2x10^-4 ~ 10^-3, M_sun/yr this is about ten times smaller than accretion rate required to maintain the AGN luminosity. This implies that relatively luminous AGN activity is intrinsically intermittent or that there are other mechanisms, such as stellar energy feedback, that enhance the mass accretion to the center.Comment: 12 pages, 9 figures, accepted publication in Ap

Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry

We examine the marginal deformations of double-trace type in 3d supersymmetric U(N) model with N complex free bosons and fermions. We compute the anomalous dimensions of higher spin currents to the 1/N order but to all orders in the deformation parameters by mainly applying the conformal perturbation theory. The 3d field theory is supposed to be dual to 4d supersymmetric Vasiliev theory, and the marginal deformations are argued to correspond to modifying boundary conditions for bulk scalars and fermions. Thus the modification should break higher spin gauge symmetry and generate the masses of higher spin fields. We provide supports for the dual interpretation by relating bulk computation in terms of Witten diagrams to boundary one in conformal perturbation theory.Comment: 32 pages, 3 figures, minor changes, references added, published versio

Instabilities of Spiral Shocks I: Onset of Wiggle Instability and its Mechanism

We found that loosely wound spiral shocks in an isothermal gas disk caused by a non-axisymmetric potential are hydrodynamically unstable, if the shocks are strong enough. High resolution, global hydrodynamical simulations using three different numerical schemes, i.e. AUSM, CIP, and SPH, show similarly that trailing spiral shocks with the pitch angle of larger than ~10 deg wiggle, and clumps are developed in the shock-compressed layer. The numerical simulations also show clear wave crests that are associated with ripples of the spiral shocks. The spiral shocks tend to be more unstable in a rigidly rotating disk than in a flat rotation. This instability could be an origin of the secondary structures of spiral arms, i.e. the spurs/fins, observed in spiral galaxies. In spite of this local instability, the global spiral morphology of the gas is maintained over many rotational periods. The Kelvin-Helmholtz (K-H) instability in a shear layer behind the shock is a possible mechanism for the wiggle instability. The Richardson criterion for the K-H stability is expressed as a function of the Mach number, the pitch angle, and strength of the background spiral potential. The criterion suggests that spiral shocks with smaller pitch angles and smaller Mach numbers would be more stable, and this is consistent with the numerical results.Comment: 11 pages, 14 figures, to be published in MNRAS, high quality figures can be downloaded from http://th.nao.ac.jp/~wada/paperlist.htm