Explicit Central Elements of Uq(gln)U_q(gl_n)

Using Drinfeld's central element construction and Jimbo's fusion of $R$--matrices, we construct central elements of the quantum group $U_q(gl_n)$. These elements are explicitly written in terms of the generators

The onset of convection in rotating circular cylinders with experimental boundary conditions

Convective instabilities in a fluid-filled circular cylinder heated from below and rotating about its vertical axis are investigated both analytically and numerically under experimental boundary conditions. It is found that there exist two different forms of convective instabilities: convection-driven inertial waves for small and moderate Prandtl numbers and wall-localized travelling waves for large Prandtl numbers. Asymptotic solutions for both forms of convection are derived and numerical simulations for the same problem are also performed, showing a satisfactory quantitative agreement between the asymptotic and numerical analyses

Nonlinear dynamo action in rotating convection and shear

Copyright © 2005 Cambridge University Press. Published version reproduced with the permission of the publisherMagnetic field amplification by the motion of an electrically conducting fluid is studied, using a rotating plane-layer geometry. The fluid flow is driven by convection, and by a moving bottom boundary, which leads to an Ekman layer localized at the base of the system. The system thus has the structure of an interface dynamo, with convection lying over a thin layer of shear. The combination of shear in the Ekman layer and convection above leads to amplification of seed magnetic fields. In kinematic regimes the magnetic field is mostly localized in sheets in the shear layer, but thin tongues are pulled out by the convection above and folded. The nonlinear saturation of these growing fields is studied at moderately high values of magnetic Reynolds number and Taylor number. It is found that the sheets of field tend to gain fine-scale structure when the dynamo saturates, breaking up into tubes, and the fluid flow shows complex time-dependence. Although the magnetic field lies predominantly within the highly sheared Ekman layer, this flow remains remarkably unchanged despite the action of Lorentz forces. Instead, the effect of the field is to suppress or modify the convection above. A simple alpha-omega dynamo model is set up, and gives some insights into the dynamo processes occurring in the full magnetohydrodynamic simulation

A three-dimensional multilayered spherical dynamic interface dynamo using the Malkus-Proctor formulation

Copyright © 2008 IOP PublishingWe investigate a fully three-dimensional and multilayered spherical dynamic interface dynamo using a finite-element method based on the three-dimensional tetrahedralization of the whole spherical system. The dynamic interface dynamo model consists of four magnetically coupled zones: an electrically conducting and uniformly rotating core, a thin differentially rotating tachocline, a turbulent convection envelope, and a nearly insulating exterior. In the thin tachocline at the base of the convection zone, a differential rotation, similar to that of the observed solar differential rotation, is imposed. In the convection zone, the Malkus-Proctor formulation with a prescribed α-effect is employed while the fully three-dimensional dynamic feedback of Lorentz forces is taken into account. Our numerical simulations of the dynamic interface dynamo are focused on the Taylor number Ta = 105 with a unity magnetic Prandtl number. It is shown that the dynamic interface dynamo, depending on the size of the magnetic Reynolds number Rem based on the differential rotation, can be either nonaxisymmetric or axisymmetric. When Rem is small or moderate, the dynamic dynamo is characterized by quasi-periodic and nonaxisymmetric azimuthally traveling waves. When Rem is sufficiently large, the dynamo is characterized by a strong toroidal magnetic field, axisymmetric or nearly axisymmetric, that selects dipolar symmetry and propagates equatorward. Implications of our dynamic interface dynamo for the solar dynamo are also discussed

An exact solution for arbitrarily rotating gaseous polytropes with index unity

This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2015 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.Many gaseous planets and stars are rapidly rotating and can be approximately described by a polytropic equation of state with index unity.We present the first exact analytic solution, under the assumption of the oblate spheroidal shape, for an arbitrarily rotating gaseous polytrope with index unity in hydrostatic equilibrium, giving rise to its internal structure and gravitational field. The new exact solution is derived by constructing the non-spherical Green’s function in terms of the oblate spheroidal wavefunction. We then apply the exact solution to a generic object whose parameter values are guided by the observations of the rapidly rotating star α Eridani with its eccentricity Eα = 0.7454, the most oblate star known. The internal structure and gravitational field of the object are computed from its assumed rotation rate and size. We also compare the exact solution to the three-dimensional numerical solution based on a finite-element method taking full account of rotation-induced shape change and find excellent agreement between the exact solution and the finite-element solution with about 0.001 per cent discrepancy.NSFCScience & Technology Facilities Council (STFC)HKRGCNational Science Foundatio

On fluid motion in librating ellipsoids with moderate equatorial eccentricity

Copyright © 2011 Cambridge University Pres

Algorithms to calculate the most reliable maximum flow in content delivery network

Funding Information: Funding Statement: This work was partly supported by Open Research Fund from State Key Laboratory of Smart Grid Protection and Control, China (Zhang B, www.byqsc.net/com/nrjt/), Rapid Support Project (61406190120, Zhang B), the Fundamental Research Funds for the Central Universities (2242021k10011, Zhang B, www.seu.edu.cn) and the National Key R&D Program of China (2018YFC0830200, Zhang B, www.most.gov.cn).Peer reviewedPublisher PD

On the initial-value problem in a rotating circular cylinder

Copyright © 2008 Cambridge University PressThe initial-value problem in rapidly rotating circular cylinders is revisited. Four different but related analyses are carried out: (i) we derive a modified asymptotic expression for the viscous decay factors valid for the inertial modes of a broad range of frequencies that are required for an asymptotic solution of the initial value problem at an arbitrarily small but fixed Ekman number; (ii) we perform a fully numerical analysis to estimate the viscous decay factors, showing satisfactory quantitative agreement between the modified asymptotic expression and the fuller numerics; (iii) we derive a modified time-dependent asymptotic solution of the initial value problem valid for an arbitrarily small but fixed Ekman number and (iv) we perform fully numerical simulations for the initial value problem at a small Ekman number, showing satisfactory quantitative agreement between the modified time-dependent solution and the numerical simulations