On a nonlinear recurrent relation

We study the limiting behavior for the solutions of a nonlinear recurrent relation which arises from the study of Navier-Stokes equations. Some stability theorems are also shown concerning a related class of linear recurrent relations.Comment: to appear in Journal of Statistical Physic

The n-tangle of odd n qubits

Coffman, Kundu and Wootters presented the 3-tangle of three qubits in [Phys. Rev. A 61, 052306 (2000)]. Wong and Christensen extended the 3-tangle to even number of qubits, known as $n$-tangle [Phys. Rev. A 63, 044301 (2001)]. In this paper, we propose a generalization of the 3-tangle to any odd $n$-qubit pure states and call it the $n$-tangle of odd $n$ qubits. We show that the $n$-tangle of odd $n$ qubits is invariant under permutations of the qubits, and is an entanglement monotone. The $n$-tangle of odd $n$ qubits can be considered as a natural entanglement measure of any odd $n$-qubit pure states.Comment: 7 pages, no figure

Making Clean Energy with a Kerr Black Hole: a Tokamak Model for Gamma-Ray Bursts

In this paper we present a model for making clean energy with a Kerr black hole. Consider a Kerr black hole with a dense plasma torus spinning around it. A toroidal electric current flows on the surface of the torus, which generates a poloidal magnetic field outside the torus. On the surface of the tours the magnetic field is parallel to the surface. The closed magnetic field lines winding around the torus compress and confine the plasma in the torus, as in the case of tokamaks. Though it is unclear if such a model is stable, we look into the consequences if the model is stable. If the magnetic field is strong enough, the baryonic contamination from the plasma in the torus is greatly suppressed by the magnetic confinement and a clean magnetosphere of electron-positron pairs is built up around the black hole. Since there are no open magnetic field lines threading the torus and no accretion, the power of the torus is zero. If some magnetic field lines threading the black hole are open and connect with loads, clean energy can be extracted from the Kerr black hole by the Blandford-Znajek mechanism. The model may be relevant to gamma-ray bursts. The energy in the Poynting flux produced by the Blandford-Znajek mechanism is converted into the kinetic energy of the electron-positron pairs in the magnetosphere around the black hole, which generates two oppositely directed jets of electron-positron pairs with super-high bulk Lorentz factors. The jets collide and interact with the interstellar medium, which may produce gamma-ray bursts and the afterglows.Comment: 14 pages, 1 figure, accepted by Ap

Natural frequency prediction for laminated rectangular plates with extension-bending or extension-twisting and shearing-bending coupling

This article presents closed form natural frequency solutions for two classes of mechanically coupled laminate with: extension-bending or; extension-twisting and shearingbending. Details on the derivation of these two laminate classes are given; all of which contain combinations of standard ply angles, e.g. +45, -45, 0 and 90°. Upper and lower bounds on the non-dimensional natural frequencies are shown graphically for each class of laminate over a range of aspect ratios. Finally, differences are highlighted between these bounds and others obtained by the simplifying assumption that the two laminate classes contain only cross plies or angle plies, respectively