The influence of self-citation corrections on Egghe's g index

The g index was introduced by Leo Egghe as an improvement of Hirsch's index h for measuring the overall citation record of a set of articles. It better takes into account the highly skewed frequency distribution of citations than the h index. I propose to sharpen this g index by excluding the self-citations. I have worked out nine practical cases in physics and compare the h and g values with and without self-citations. As expected, the g index characterizes the data set better than the h index. The influence of the self-citations appears to be more significant for the g index than for the h index.Comment: 9 pages, 2 figures, submitted to Scientometric

Optimal parallel solution of sparse triangular systems

A method for the parallel solution of triangular sets of equations is described that is appropriate when there are many right-handed sides. By preprocessing, the method can reduce the number of parallel steps required to solve Lx = b compared to parallel forward or backsolve. Applications are to iterative solvers with triangular preconditioners, to structural analysis, or to power systems applications, where there may be many right-handed sides (not all available a priori). The inverse of L is represented as a product of sparse triangular factors. The problem is to find a factored representation of this inverse of L with the smallest number of factors (or partitions), subject to the requirement that no new nonzero elements be created in the formation of these inverse factors. A method from an earlier reference is shown to solve this problem. This method is improved upon by constructing a permutation of the rows and columns of L that preserves triangularity and allow for the best possible such partition. A number of practical examples and algorithmic details are presented. The parallelism attainable is illustrated by means of elimination trees and clique trees

Higher U(1)-gerbe connections in geometric prequantization

We promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show fairly generally how there is canonically a tower of higher gauge groupoids and Courant groupoids assigned to a higher prequantization, and establish the corresponding Atiyah sequence as an integrated Kostant-Souriau infinity-group extension of higher Hamiltonian symplectomorphisms by higher quantomorphisms. We also exhibit the infinity-group cocycle which classifies this extension and discuss how its restrictions along Hamiltonian infinity-actions yield higher Heisenberg cocycles. In the special case of higher differential geometry over smooth manifolds we find the L-infinity-algebra extension of Hamiltonian vector fields -- which is the higher Poisson bracket of local observables -- and show that it is equivalent to the construction proposed by the second author in n-plectic geometry. Finally we indicate a list of examples of applications of higher prequantization in the extended geometric quantization of local quantum field theories and specifically in string geometry.Comment: Title changed. Exposition revised. 55 page

Direct measurement of diurnal polar motion by ring laser gyroscopes

We report the first direct measurements of the very small effect of forced diurnal polar motion, successfully observed on three of our large ring lasers, which now measure the instantaneous direction of Earth's rotation axis to a precision of 1 part in 10^8 when averaged over a time interval of several hours. Ring laser gyroscopes provide a new viable technique for directly and continuously measuring the position of the instantaneous rotation axis of the Earth and the amplitudes of the Oppolzer modes. In contrast, the space geodetic techniques (VLBI, SLR, GPS, etc.) contain no information about the position of the instantaneous axis of rotation of the Earth, but are sensitive to the complete transformation matrix between the Earth-fixed and inertial reference frame. Further improvements of gyroscopes will provide a powerful new tool for studying the Earth's interior.Comment: 5 pages, 4 figures, agu2001.cl

Parallel-in-Time Multi-Level Integration of the Shallow-Water Equations on the Rotating Sphere

The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps, even when the terms accounting for the propagation of fast atmospheric waves are treated implicitly. Therefore, the use of parallel-in-time integration schemes to reduce the time-to-solution is of increasing interest, particularly in the numerical weather forecasting field. We present a multi-level parallel-in-time integration method combining the Parallel Full Approximation Scheme in Space and Time (PFASST) with a spatial discretization based on Spherical Harmonics (SH). The iterative algorithm computes multiple time steps concurrently by interweaving parallel high-order fine corrections and serial corrections performed on a coarsened problem. To do that, we design a methodology relying on the spectral basis of the SH to coarsen and interpolate the problem in space. The methods are evaluated on the shallow-water equations on the sphere using a set of tests commonly used in the atmospheric flow community. We assess the convergence of PFASST-SH upon refinement in time. We also investigate the impact of the coarsening strategy on the accuracy of the scheme, and specifically on its ability to capture the high-frequency modes accumulating in the solution. Finally, we study the computational cost of PFASST-SH to demonstrate that our scheme resolves the main features of the solution multiple times faster than the serial schemes

Finite-Size Scaling of the Level Compressibility at the Anderson Transition

We compute the number level variance $\Sigma_{2}$ and the level compressibility $\chi$ from high precision data for the Anderson model of localization and show that they can be used in order to estimate the critical properties at the metal-insulator transition by means of finite-size scaling. With $N$, $W$, and $L$ denoting, respectively, system size, disorder strength, and the average number of levels in units of the mean level spacing, we find that both $\chi(N,W)$ and the integrated $\Sigma_{2}$ obey finite-size scaling. The high precision data was obtained for an anisotropic three-dimensional Anderson model with disorder given by a box distribution of width $W/2$. We compute the critical exponent as $\nu \approx 1.45 \pm 0.12$ and the critical disorder as $W_{\rm c} \approx 8.59 \pm 0.05$ in agreement with previous transfer-matrix studies in the anisotropic model. Furthermore, we find $\chi\approx 0.28 \pm 0.06$ at the metal-insulator transition in very close agreement with previous results.Comment: Revised version of paper, to be published: Eur. Phys. J. B (2002

One Way to Model the Influence of Heterogeneous Micro Stresses on Damage

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Experimental investigation of the performance of a supersonic compressor cascade

Results are presented from an experimental investigation of a linear, supersonic, compressor cascade tested in the supersonic cascade wind tunnel facility at the DFVLR in Cologne, Federal Republic of Germany. The cascade design was derived from the near-tip section of a high-through-flow axial flow compressor rotor with a design relative inlet Mach number of 1.61. Test data were obtained over a range of inlet Mach numbers from 1.23 to 1.71, and a range of static pressure ratios and axial-velocity-density ratios (AVDR) at the design inlet condition. Flow velocity measurements showing the wave pattern in the cascade entrance region were obtained using a laser transit anemometer. From these measurements, some unique-incidence conditions were determined, thus relating the supersonic inlet Mach number to the inlet flow direction. The influence of static pressure ratio and AVDR on the blade passage flow and the blade-element performance is described, and an empirical correlation is used to show the influence of these two (independent) parameters on the exit flow angle and total-pressure loss for the design inlet condition