1,120 research outputs found

    Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas

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    The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning) modes in strongly nonaxisymmetric toroidal systems is difficult to analyze numerically owing to the singular nature of ideal MHD caused by lack of an inherent scale length. In this paper, ideal MHD is regularized by using a kk-space cutoff, making the ray tracing for the WKB ballooning formalism a chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier spectrum needed for resolving toroidally localized ballooning modes with a global eigenvalue code is estimated from the Weyl formula. This phase-space-volume estimation method is applied to two stellarator cases.Comment: 4 pages typeset, including 2 figures. Paper accepted for publication in Phys. Rev. Letter

    Heliac parameter study

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    Helical axis stellarators (heliacs) with zero net current are found to possess very good stability properties. Helically symmetric or straight heliacs with bean-shaped cross sections have a first region of stability that reaches to (..beta..) of 30% or more. Those with circular cross sections have second region of stability to Mercier modes. In addition we report on the stability properties of these plasma configurations as functions of pressure profile, helical aspect ratio, and helical period length

    Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

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    We construct affinization of the algebra glλgl_{\lambda} of ``complex size'' matrices, that contains the algebras gln^\hat{gl_n} for integral values of the parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra glλ^\hat{gl_{\lambda}} results in the quadratic Gelfand--Dickey structure on the Poisson--Lie group of all pseudodifferential operators of fractional order. This construction is extended to the simultaneous deformation of orthogonal and simplectic algebras that produces self-adjoint operators, and it has a counterpart for the Toda lattices with fractional number of particles.Comment: 29 pages, no figure

    W∞\bf W_\infty Gravity - a Geometric Approach

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    A brief review is given of an adaptation of the coadjoint orbit method appropriate for study of models with infinite-dimensional symmetry groups. It is illustrated on several examples, including derivation of the WZNW action of induced D=2 D=2\, (N,0) (N,0)\, supergravity. As a main application, we present the geometric action on a generic coadjoint orbit of the deformed group of area preserving diffeomorphisms. This action is precisely the anomalous effective WZNW action of D=2 D=2 \, matter fields coupled to chiral W∞W_\infty gravity background. Similar actions are given which produce the {\em KP} hierarchy as on-shell equations of motion.Comment: 13 pages, BGU-92/11/July-PH, LaTe

    Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras

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    Darboux coordinates are constructed on rational coadjoint orbits of the positive frequency part \wt{\frak{g}}^+ of loop algebras. These are given by the values of the spectral parameters at the divisors corresponding to eigenvector line bundles over the associated spectral curves, defined within a given matrix representation. A Liouville generating function is obtained in completely separated form and shown, through the Liouville-Arnold integration method, to lead to the Abel map linearization of all Hamiltonian flows induced by the spectral invariants. Serre duality is used to define a natural symplectic structure on the space of line bundles of suitable degree over a permissible class of spectral curves, and this is shown to be equivalent to the Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general construction is given for g=gl(r)\frak{g}=\frak{gl}(r) or sl(r)\frak{sl}(r), with reductions to orbits of subalgebras determined as invariant fixed point sets under involutive automorphisms. The case g=sl(2)\frak{g=sl}(2) is shown to reproduce the classical integration methods for finite dimensional systems defined on quadrics, as well as the quasi-periodic solutions of the cubically nonlinear Schr\"odinger equation. For g=sl(3)\frak{g=sl}(3), the method is applied to the computation of quasi-periodic solutions of the two component coupled nonlinear Schr\"odinger equation.Comment: 61 pg

    Privacy, Ethics, and Institutional Research

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    Despite widespread agreement that privacy in the context of education is important, it can be difficult to pin down precisely why and to what extent it is important, and it is challenging to determine how privacy is related to other important values. But that task is crucial. Absent a clear sense of what privacy is, it will be difficult to understand the scope of privacy protections in codes of ethics. Moreover, privacy will inevitably conflict with other values, and understanding the values that underwrite privacy protections is crucial for addressing conflicts between privacy and institutional efficiency, advising efficacy, vendor benefits, and student autonomy. My task in this paper is to seek a better understanding of the concept of privacy in institutional research, canvas a number of important moral values underlying privacy generally (including several that are explicit in the AIR Statement), and examine how those moral values should bear upon institutional research by considering several recent cases
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