Unconstrained and inequality constrained sparse polynomial optimization problems (POPs) are considered. A correlative sparsity pattern graph is defined to find a certain sparse structure in the objective and constraint polynomials of a POP. Based on this graph, sets of the supports for sums of squares (SOS) polynomials that lead to efficient SOS and semidefinite program (SDP) relaxations are obtained. Numerical results from various test problems are included to show the improved performance of the SOS and SDP relaxations.

A critical disadvantage of primal-dual interior-point methods compared to dual interior-point methods for large scale semidefinite programs (SDPs) has been that the primal positive semidefinite matrix variable becomes fully dense in general even when all data matrices are sparse. Based on some fundamental results about positive semidefinite matrix completion, this article proposes a general method of exploiting the aggregate sparsity pattern over all data matrices to overcome this disadvantage. Our method is used in two ways. One is a conversion of a sparse SDP having a large scale positive semidefinite matrix variable into an SDP having multiple but smaller positive semidefinite matrix variables to which we can effectively apply any interior-point method for SDPs employing a standard block-diagonal matrix data structure. The other way is an incorporation of our method into primal-dual interior-point methods which we can apply directly to a given SDP. In Part II of this article, we will investigate an implementation of such a primal-dual interior-point method based on positive definite matrix completion, and report some numerical results.

No abstract

No abstract

This Letter presents experimental confirmation of the presence of zonal flows in magnetically confined toroidal plasma using an advanced diagnostic system -dual heavy ion beam probes. The simultaneous observation of an electric field at two distant toroidal locations ( 1:5 m apart) in the high temperature ( 1 keV) plasma provides a fluctuation spectrum of electric field (or flow), a spatiotemporal structure of the zonal flows (characteristic radial length of 1:5 cm and lifetime of 1:5 ms), their long-range correlation with toroidal symmetry n 0 , and the difference in the zonal flow amplitude with and without a transport barrier. These constitute essential elements of turbulence-zonal flow systems, and illustrate one of the fundamental processes of structure formation in nature. Zonal flows-azimuthally symmetric bandlike shear flows-are ubiquitous phenomena in the Universe [1][2][3]; examples include Jovian belts and zones, the terrestrial atmospheric jet stream, the super-rotation of the Venusian atmosphere, and the rotation profile of the solar tachocline. Zonal flows have been expected to be present in magnetically confined toroidal plasmas [4] since the characteristics of drift wave turbulence in the plasmas are analogous to Rossby wave turbulence to cause the phenomena in the rotating planets. Recently, their crucial role in determining the turbulent level and resultant transport has been widely recognized, and the identification of the zonal flows becomes an urgent issue in the fusion research to enhance the prospect of plasma burning in the International Thermonuclear Experimental Reactor [5][6][7].In toroidal plasmas, the zonal flows emerge in electric field fluctuation symmetric m n 0 on magnetic flux surface with finite radial wave numbers (see for review, e.g., [8,9]). Two major branches of zonal flows are expected in magnetic confined toroidal plasmas, i.e., a residual flow of nearly zero frequency, and an oscillatory flow termed geodesic acoustic modes (GAMs) [10,11]. These zonal flows are driven exclusively by nonlinear interactions (or inverse cascade) through energy transfer from the microscopic drift waves. Inversely, the zonal flows regulate the drift wave turbulence and resultant transports. The time-varying E B shearing of zonal flows, similar to the mean flows [12], has a significant effect on plasma turbulence and transport.Direct nonlinear simulations have, in fact, confirmed the appearance of and generation processes for zonal flows [13][14][15][16][17][18][19][20], and their essential role in turbulence and transport of toroidal plasmas. In experiments, however, only indirect signs have been obtained for zonal flows and their role in confinement. Coherent oscillations presumed to be GAMs were detected in measurements with a heavy ion beam probe (HIBP) [21,22], with traditional probes [23,24], and with beam emission spectroscopy using a modified time-delayed-estimation analysis technique [25]. Bicoherence analysis showed an increase in nonlinear interaction between zonal flows and turbule...

Abstract. We have assembled and tested, in real time, a space weather modeling system that starts at the Sun and extends to the Earth through a set of coupled, modular components. We describe recent efforts to improve the Hakamada-Akasofu-Fry (HAF) solar wind model that is presently used in our geomagnetic storm prediction system. We also present some results of these improvement efforts. In a related paper, Akasofu

No abstract

No abstract