On the evolution and gravitational collapse of a toroidal vortex

The evolution and collapse of a gaseous toroidal vortex under the action of self-gravitation are considered using the Hamiltonian mechanics approach. It is shown that evolution occurs in three main stages separated by characteristic time scales. First, a compression along the small radius to a quasi-equilibrium state takes place, followed by a slower compression along the large radius to a more stable compact vortex object. In the latter stage, the possibility of effective scattering and ejection of particles along the vortex axis (jet formation) is detected.As a result, mass, energy, and momentum losses take place, and the vortex collapses.     

Self-reversal phenomena of toroidal current by reversing the external toroidal field in helicity-driven toroidal plasmas

In order to understand self-organization in helicity-driven systems, we have investigated the dynamics of low-aspect-ratio toroidal plasmas by decreasing the external toroidal field and reversing its sign in time. Consequently, we have discovered that the helicity-driven toroidal plasma relaxes towards the flipped state. Surprisingly, it has been observed that not only toroidal flux but also poloidal flux reverses sign spontaneously during the relaxation process. The self-reversal of the magnetic fields is attributed to the nonlinear growth of the n=1 kink instability of the central open flux.     

On the appearance of a convective toroidal vortex in Lake Baikal

Warm natural gas floating up from the bottom of Lake Baikal causes convection in the water column in the form of a toroidal body of revolution—toroidal vortex. The giant convection, several kilometers in size, arises once the Rayleigh number achieves a critical value (1000–2000). A linear relationship is found between the depth of a water pond and the size of the toroidal body.     

On Lorentz invariant distributions

n-point Lorentz invariant tempered distributions with the supports for one-point only in are described.     

On the velocity distributions of granular gases

We present a new approach to determine velocity distributions in granular gases to improve the Sonine polynomial expansion of the velocity distribution function, at higher inelasticities, for the homogeneous cooling regime of inelastic hard spheres. The perturbative consistency is recovered using a new set of dynamical variables based on the characteristic function and we illustrate our approach by computing the first four Sonine coefficients for moderate and high inelasticities. The analytical coefficients are compared with molecular dynamics simulations results and with a previous approach by Huthmann et al.     

On the consistent inference of probability distributions

We respond to criticism (Karbelkar 1986) concerning our approach to consistent inference of probabilities for reproducible experiments (Tikochinskyet al 1984).     

On generalized distributions and pathways

The scalar version of the pathway model of Mathai [A.M. Mathai, Linear Alg. Appl. 396 (2005) 317] is shown to be associated with a large number of probability models used in physics. Different families of densities are listed here, which are all connected through the pathway parameter α, generating a distributional pathway. The idea is to switch from one functional form to another through this parameter and it is shown that one can proceed from the generalized type-1 beta family to generalized type-2 beta family to generalized gamma family. It is also shown that the pathway model is available by maximizing a generalized measure of entropy, leading to an entropic pathway, covering the particularly interesting cases of Tsallis statistics [C. Tsallis, J. Stat. Phys. 52 (1988) 479] and superstatistics [C. Beck, E.G.D. Cohen, Physica A 322 (2003) 267].     

Schur duality in the toroidal setting

The classical Frobenius-Schur duality gives a correspondence between finite dimensional representations of the symmetric and the linear groups. The goal of the present paper is to extend this construction to the quantum toroidal setup with only elementary (algebraic) methods. This work can be seen as a continuation of [J, D1 and C2] (see also [C-P and G-R-V]) where the cases of the quantum groups U _q (sl(n)), Y(sl(n)) (the Yangian) and U _q (sl(n)) are given. In the toroidal setting the two algebras involved are deformations of Cherednik's double affine Hecke algebra introduced in [C1] and of the quantum toroidal group as given in [G-K-V]. Indeed, one should keep in mind the geometrical construction in [G-R-V] and [G-K-V] in terms of equivariant K-theory of some flag manifolds. A similar K-theoretic construction of Cherednik's algebra has motivated the present work. At last, we would like to lay emphasis on the fact that, contrary to [J, D1 and C2], the representations involved in our duality are infinite dimensional. Of course, in the classical case, i.e.,q=1, a similar duality holds between the toroidal Lie algebra and the toroidal version of the symmetric group. The authors would like to thank V. Ginzburg for a useful remark on a preceding version of this paper. Communicated by M. Jimbo     

On the particle multiplicity distributions at high energy

An experiment has been performed to study the inclusive photoproduction of π⁰ mesons. Photoproduced π⁰'s were detected in a hodoscope consisting of 14 lead glass Cerenkov counters. To obtain the cross sections at a photon energy of 6 GeV we used the photon-difference method. Data are presented in terms of the Feynman variable $\text{x = q}{}_6{}^1\text{(√s/2)}$ and the trnasverse momentum q⊥. We have measured four q⊥ distributions at x = 0.2, 0.4, 0.6 and 0.8. The results dhow that the π⁰ rate at small values of q⊥ is smaller than the π± rate. The data can be fitted smoothly by a form A exp (?Bq_⊥²) with a value about 3.5 GeV^?2 for the slope parameter B.     

On the internal temperature distributions in radiation-heated bodies

An approximate but fairly accurate method of finding the temperature field in a multi-dimensional, radiation-heated body is proposed. A relationship law is derived which, in the opinion of the authors, makes it possible to sound the entire temperature field inside a heated (or cooled) body.     

Effects of edge-localized mode-induced neoclassical toroidal viscosity torque on the toroidal intrinsic rotation in the EAST tokamak

Intrinsic rotation has been observed in lower hybrid current-driven (LHCD) H-mode plasmas with type-III edge-localized modes (ELMs) on Experimental Advanced Superconducting Tokamak (EAST), and it is found that the edge toroidal rotation accelerated before the onset of the ELM burst. Magnetic perturbation analysis shows there is a perturbation amplitude growth below 30 kHz corresponding to the edge rotation acceleration. Using the filament model, the neoclassical toroidal viscosity (NTV) code shows there is a co-current NTV torque at the edge, which may be responsible for the edge rotation acceleration. For maximum displacement ～1 cm and toroidal mode number n=15, the calculated torque density is ～0.44 N/m², comparable with the average edge toroidal angular momentum change rate ～1.24 N/m². Here, the 1 cm maximum magnetic surface displacement estimated from the experimental observation corresponds to a maximum magnetic perturbation ～ 10^?3–10^?2 T, in accordance with magnetic perturbation measurements during ELMs. By varying n from 10 to 20, the magnitude of the edge NTV torque density is mainly ～0.1–1 N/m². This significant co-current torque indicates that the NTV theory may be important in rotation problems during ELMs in H-mode plasmas. To better illuminate the problem, magnetic surface deformation obtained from other codes is desired for a more accurate calculation.     

Quasi-helically symmetric toroidal stellarators

It is computationally shown that there are toroidal stellarators whose magnetic field strength is helically symmetric in magnetic coordinates. Accordingly, these stellarators, without collisions, strictly confine guiding centre orbits.     

On the physical relevance of max- and log-max-selfsimilar distributions

This work emphasizes the special role played by max-semistable and log-max-semistable distributions as relevant statistical models of various observable and “internal” variables in Physics. Some of their remarkable properties (chiefly self-similarity) are displayed in some detail. One of their characteristic features is a log-periodic variation of the scale parameter which appears in the stable extreme value distributions. Received 29 November 1999 and Received in final form 24 March 2000     

On the probability distributions of relaxation times in glasses

The scale of relaxation times in glasses has led to generalizations of the Drude model of the dielectric function in terms of an integral, containing a Drude kernel and a probability distribution. This integral equation is solved by a Mellin or a Stieltjes transform. Beyond known results, we obtain the probability distribution of the Havriliak-Negami dielectric function. Even more general classes of dielectric models can be dealt with, using Mellin's transform. They may serve as checks for numerical procedures applied to the underlying ill-posed problem, if experimental data for the dielectric function are used. Received: 2 February 1998 / Accepted: 17 March 1998     

On the semileptonic decay distributions from the next heavy quark

Motivated by the discovery of λ(9.4), we study the semileptonic decay correlations of the next heavy quark, and their consequences for thee ⁺ e ^? colliding beam and neutrino experiments. A detailed comparison is made with the corresponding correlations from the production and decay of charm and heavy leptons, τ^±. Some tests of the \({\rm B}^0 - \bar {\rm B}^0 \) mixing ( \(B = b\bar q\) withbaQ=?1/3 heavy quark) are suggested fore ⁺ e ^? colliding beam experiments.     

Transport-driven toroidal rotation in the tokamak edge

The interaction of passing-ion drift orbits with spatially inhomogeneous but purely diffusive radial transport is demonstrated to cause spontaneous toroidal spin-up in a simple model of the tokamak edge. Physically, major-radial orbit shifts cause orbit-averaged diffusivities to depend on v(∥), including its sign, leading to residual stress. The resulting pedestal-top intrinsic rotation scales with T(i)/B(θ), resembling typical experimental scalings. Additionally, an inboard (outboard) X point enhances co- (counter)current rotation.     

On the determination of the polarized sea distributions of the nucleon

The possibilities to determine the flavor structure of the polarized sea (antiquark) distributions of the nucleon via vector boson production at high energy polarized hadron–hadron colliders, such as the Relativistic Heavy–Ion Collider (RHIC), are studied in detail. In particular the perturbative stability of the expected asymmetries in two representative models for the (un)broken flavor structure are investigated by confronting perturbative QCD leading order predictions of the expected asymmetries with their next–to–leading order counterparts. Received: 28 November 2000 / Published online: 5 February 2001