The mass of unimodular lattices

The purpose of this paper is to show how to obtain the mass of a unimodular lattice from the point of view of the Bruhat-Tits theory. This is achieved by relating the local stabilizer of the lattice to a maximal parahoric subgroup of the special orthogonal group, and appealing to an explicit mass formula for parahoric subgroups developed by Gan, Hanke and Yu. Of course, the exact mass formula for positive defined unimodular lattices is well-known. Moreover, the exact formula for lattices of signature (1,n) (which give rise to hyperbolic orbifolds) was obtained by Ratcliffe and Tschantz, starting from the fundamental work of Siegel. Our approach works uniformly for the lattices of arbitrary signature (r,s) and hopefully gives a more conceptual way of deriving the above known results.Comment: 15 pages, to appear in J. Number Theor

Electron acceleration by cascading reconnection in the solar corona I Magnetic gradient and curvature effects

Aims: We investigate the electron acceleration in convective electric fields of cascading magnetic reconnection in a flaring solar corona and show the resulting hard X-ray (HXR) radiation spectra caused by Bremsstrahlung for the coronal source. Methods: We perform test particle calculation of electron motions in the framework of a guiding center approximation. The electromagnetic fields and their derivatives along electron trajectories are obtained by linearly interpolating the results of high-resolution adaptive mesh refinement (AMR) MHD simulations of cascading magnetic reconnection. Hard X-ray (HXR) spectra are calculated using an optically thin Bremsstrahlung model. Results: Magnetic gradients and curvatures in cascading reconnection current sheet accelerate electrons: trapped in magnetic islands, precipitating to the chromosphere and ejected into the interplanetary space. The final location of an electron is determined by its initial position, pitch angle and velocity. These initial conditions also influence electron acceleration efficiency. Most of electrons have enhanced perpendicular energy. Trapped electrons are considered to cause the observed bright spots along coronal mass ejection CME-trailing current sheets as well as the flare loop-top HXR emissions.Comment: submitted to A&

Protocluster Discovery in Tomographic Lyα\alpha Forest Flux Maps

We present a new method of finding protoclusters using tomographic maps of Ly$\alpha$ Forest flux. We review our method of creating tomographic flux maps and discuss our new high performance implementation, which makes large reconstructions computationally feasible. Using a large N-body simulation, we illustrate how protoclusters create large-scale flux decrements, roughly 10 $h^{-1}$Mpc across, and how we can use this signal to find them in flux maps. We test the performance of our protocluster finding method by running it on the ideal, noiseless map and tomographic reconstructions from mock surveys, and comparing to the halo catalog. Using the noiseless map, we find protocluster candidates with about 90% purity, and recover about 75% of the protoclusters that form massive clusters ($> 3 \times 10^{14} \, h^{-1} M_{\odot}$). We construct mock surveys similar to the ongoing COSMOS Lyman-Alpha Mapping And Tomography Observations (CLAMATO) survey. While the existing data has an average sightline separation of 2.3 $h^{-1}$Mpc, we test separations of 2 - 6 $h^{-1}$Mpc to see what can be tolerated for our application. Using reconstructed maps from small separation mock surveys, the protocluster candidate purity and completeness are very close what was found in the noiseless case. As the sightline separation increases, the purity and completeness decrease, although they remain much higher than we initially expected. We extended our test cases to mock surveys with an average separation of 15 $h^{-1}$Mpc, meant to reproduce high source density areas of the BOSS survey. We find that even with such a large sightline separation, the method can still be used to find some of the largest protoclusters.Comment: 18 pages, 12 figure

Frequency-sweep examination for wave mode identification in multimodal ultrasonic guided wave signal

This article has been made available through the Brunel Open Access Publishing Fund.Ultrasonic guided waves can be used to assess and monitor long elements of a structure from a single position. The greatest challenges for any guided wave system are the plethora of wave modes arising from the geometry of the structural element which propagate with a range of frequency-dependent velocities and the interpretation of these combined signals reflected by discontinuities in the structural element. In this paper, a novel signal processing technique is presented using a combination of frequency-sweep measurement, sampling rate conversion, and Fourier transform. The technique is applied to synthesized and experimental data to identify different modes in complex ultrasonic guided wave signals. It is demonstrated throughout the paper that the technique also has the capability to derive the time of flight and group velocity dispersion curve of different wave modes in field inspections. © 2014 IEEE