Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure

We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with Kahler cone substructure on manifolds with h^{1,1}>1. Since the computation depends only on a one-dimensional ray in the Kahler moduli space, it can probe slope-stability regardless of the size of h^{1,1}. Suitably normalized error measures are introduced to quantitatively compare results for different directions in Kahler moduli space. A significantly improved numerical integration procedure based on adaptive refinements is described and implemented. Finally, an efficient numerical check is proposed for determining whether or not a vector bundle is slope-stable without computing its full connection.Comment: 38 pages, 10 figure

Real-time national GPS networks: Opportunities for atmospheric sensing

Real-time national Global Positioning System (GPS) networks are being established in a number of countries for atmospheric sensing. UCAR, in collaboration with participating universities, is developing one of these networks in the United States. The network, named "SuomiNet" to honor meteorological satellite pioneer Verner Suomi, is funded by the U.S. National Science Foundation. SuomiNet will exploit the recently-shown ability of ground-based GPS receivers to make thousands of accurate upper and lower atmospheric measurements per day. Phase delays induced in GPS signals by the ionosphere and neutral atmosphere can be measured with high precision simultaneously along up to a dozen GPS ray paths in the field of view. These delays can be converted into total electron content (TEC), and integrated water vapor (if surface pressure data or estimates are available), along each GPS ray path. The resulting continuous, accurate, all-weather, real-time upper and lower atmospheric data create a variety of opportunities for atmospheric research. In this letter we describe SuomiNet, its applications, and the opportunity to coordinate national real-time GPS networks to create, a global network with larger scientific and operational potential. Copy right© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences

Magnetic Properties of a Superconductor with no Inversion Symmetry

We study the magnetic properties of a superconductor in a crystal without $z \to -z$ symmetry, in particular how the lack of this symmetry exhibits itself. We show that, though the penetration depth itself shows no such effect, for suitable orientation of magnetic field, there is a magnetic field discontinuity at the interface which shows this absence of symmetry. The magnetic field profile of a vortex in the $x-y$ plane is shown to be identical to that of an ordinary anisotropic superconductor except for a shift in the $-z$ direction by ${\tilde \kappa} \lambda_x$ (see errata). For a vortex along $z$, there is an induced magnetization along the radial direction.Comment: J. Low Temp. Physics, 140, 67 (2005); with Errat

WESTT (Workload, Error, Situational Awareness, Time and Teamwork): An analytical prototyping system for command and control

Modern developments in the use of information technology within command and control allow unprecedented scope for flexibility in the way teams deal with tasks. These developments, together with the increased recognition of the importance of knowledge management within teams present difficulties for the analyst in terms of evaluating the impacts of changes to task composition or team membership. In this paper an approach to this problem is presented that represents team behaviour in terms of three linked networks (representing task, social network structure and knowledge) within the integrative WESTT software tool. In addition, by automating analyses of workload and error based on the same data that generate the networks, WESTT allows the user to engage in the process of rapid and iterative “analytical prototyping”. For purposes of illustration an example of the use of this technique with regard to a simple tactical vignette is presented

Classical orbital paramagnetism in non-equilibrium steady state

We report the results of our numerical simulation of classical-dissipative dynamics of a charged particle subjected to a non-markovian stochastic forcing. We find that the system develops a steady-state orbital magnetic moment in the presence of a static magnetic field. Very significantly, the sign of the orbital magnetic moment turns out to be {\it paramagnetic} for our choice of parameters, varied over a wide range. This is shown specifically for the case of classical dynamics driven by a Kubo-Anderson type non-markovian noise. Natural spatial boundary condition was imposed through (1) a soft (harmonic) confining potential, and (2) a hard potential, approximating a reflecting wall. There was no noticeable qualitative difference. What appears to be crucial to the orbital magnetic effect noticed here is the non-markovian property of the driving noise chosen. Experimental realization of this effect on the laboratory scale, and its possible implications are briefly discussed. We would like to emphasize that the above steady-state classical orbital paramagnetic moment complements, rather than contradicts the Bohr-van Leeuwen (BvL) theorem on the absence of classical orbital diamagnetism in thermodynamic equilibrium.Comment: 6 pages, 4 figures, Has appeared in Journal of Astrophysics and Astronomy special issue on 'Physics of Neutron Stars and Related Objects', celebrating the 75th birth-year of G. Srinivasa

Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories

A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.Comment: 52 pages, 15 figures. LaTex formatting of figures corrected in version 2

Correction to: Real-time national GPS networks: opportunities for atmospheric sensing (Earth, Planets and Space, (2000), 52, 11, (901-905), 10.1186/BF03352303)

Portions of this letter come from the content published in the paper by Ware et al. [1]