Note on a Conjecture of Wegner

The optimal packings of n unit discs in the plane are known for those natural numbers n, which satisfy certain number theoretic conditions. Their geometric realizations are the extremal Groemer packings (or Wegner packings). But an extremal Groemer packing of n unit discs does not exist for all natural numbers n and in this case, the number n is called exceptional. We are interested in number theoretic characterizations of the exceptional numbers. A counterexample is given to a conjecture of Wegner concerning such a characterization. We further give a characterization of the exceptional numbers, whose shape is closely related to that of Wegner's conjecture.Comment: 5 pages; Contributions to Algebra and Geometry, Vol.52 No1 April 201

Origins of the Ambient Solar Wind: Implications for Space Weather

The Sun's outer atmosphere is heated to temperatures of millions of degrees, and solar plasma flows out into interplanetary space at supersonic speeds. This paper reviews our current understanding of these interrelated problems: coronal heating and the acceleration of the ambient solar wind. We also discuss where the community stands in its ability to forecast how variations in the solar wind (i.e., fast and slow wind streams) impact the Earth. Although the last few decades have seen significant progress in observations and modeling, we still do not have a complete understanding of the relevant physical processes, nor do we have a quantitatively precise census of which coronal structures contribute to specific types of solar wind. Fast streams are known to be connected to the central regions of large coronal holes. Slow streams, however, appear to come from a wide range of sources, including streamers, pseudostreamers, coronal loops, active regions, and coronal hole boundaries. Complicating our understanding even more is the fact that processes such as turbulence, stream-stream interactions, and Coulomb collisions can make it difficult to unambiguously map a parcel measured at 1 AU back down to its coronal source. We also review recent progress -- in theoretical modeling, observational data analysis, and forecasting techniques that sit at the interface between data and theory -- that gives us hope that the above problems are indeed solvable.Comment: Accepted for publication in Space Science Reviews. Special issue connected with a 2016 ISSI workshop on "The Scientific Foundations of Space Weather." 44 pages, 9 figure

The Physical Processes of CME/ICME Evolution

As observed in Thomson-scattered white light, coronal mass ejections (CMEs) are manifest as large-scale expulsions of plasma magnetically driven from the corona in the most energetic eruptions from the Sun. It remains a tantalizing mystery as to how these erupting magnetic fields evolve to form the complex structures we observe in the solar wind at Earth. Here, we strive to provide a fresh perspective on the post-eruption and interplanetary evolution of CMEs, focusing on the physical processes that define the many complex interactions of the ejected plasma with its surroundings as it departs the corona and propagates through the heliosphere. We summarize the ways CMEs and their interplanetary CMEs (ICMEs) are rotated, reconfigured, deformed, deflected, decelerated and disguised during their journey through the solar wind. This study then leads to consideration of how structures originating in coronal eruptions can be connected to their far removed interplanetary counterparts. Given that ICMEs are the drivers of most geomagnetic storms (and the sole driver of extreme storms), this work provides a guide to the processes that must be considered in making space weather forecasts from remote observations of the corona.Peer reviewe

Analysis of the magnetoresistance contributions in a nanocrystallized Cr-doped FINEMET alloy

The magnetoresistance (MR) was measured at 200, 250 and 300 K in magnetic fields up to B=12 T for a nanocrystallized Fe63.5Cr 10Nb3Cu1Si13.5B9 alloy. Both the longitudinal (LMR) and transverse (TMR) component of the magnetoresistance decreased from B=0 to about 0.1 T. This could be ascribed to a giant MR (GMR) effect due to spin-dependent scattering of conduction electrons along their path between two FeSi nanograins via the non-magnetic matrix. Such a scattering may occur if the nanograin moments are not or only weakly coupled in the absence of a strong exchange coupling (due to the high Cr content in the matrix) and/or only weak dipoledipole coupling is present (due to sufficiently large separations between the nanograins). For larger fields, the GMR saturated and a slightly nonlinear increase in MR with B was observed due to a contribution by the residual amorphous matrix. The anisotropic MR effect (AMR≡LMR-TMR) was negative for all fields and temperatures investigated. By measuring the MR of melt-quenched Fe100-xSix solid solutions with x=15, 18, 20, 25 and 28, the observed AMR could be identified as originating from the FeSi nanograins having a D03 structure. © 2010 Elsevier B.V. All rights reserved.This work was supported by the Hungarian Scientific Research Fund (OTKA) through Grant T 038383 as well as by the Hungarian–Spanish Bilateral Cooperation through Grant TéT E-21/04, moreover by the Spanish Government and EU FEDER (Project MAT 2007-65227) and the PAI of the Regional Government of Andalucía (Project P06-FQM-01823). The authors thank Dr. A. Rodriguez Pierna (E.U.I.T.I. of San Sebastian, University of the Basque Country, Spain) for kindly providing the original amorphous Fe63.5Cr10Nb3Cu1Si13.5B9 alloy ribbon. M.C. is grateful to the European Commission for financial support under a Marie Curie Intra-European Fellowship for Career Development.Peer Reviewe