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

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

Morphological evolution of a 3D CME cloud reconstructed from three viewpoints

The propagation properties of coronal mass ejections (CMEs) are crucial to predict its geomagnetic effect. A newly developed three dimensional (3D) mask fitting reconstruction method using coronagraph images from three viewpoints has been described and applied to the CME ejected on August 7, 2010. The CME's 3D localisation, real shape and morphological evolution are presented. Due to its interaction with the ambient solar wind, the morphology of this CME changed significantly in the early phase of evolution. Two hours after its initiation, it was expanding almost self-similarly. CME's 3D localisation is quite helpful to link remote sensing observations to in situ measurements. The investigated CME was propagating to Venus with its flank just touching STEREO B. Its corresponding ICME in the interplanetary space shows a possible signature of a magnetic cloud with a preceding shock in VEX observations, while from STEREO B only a shock is observed. We have calculated three principle axes for the reconstructed 3D CME cloud. The orientation of the major axis is in general consistent with the orientation of a filament (polarity inversion line) observed by SDO/AIA and SDO/HMI. The flux rope axis derived by the MVA analysis from VEX indicates a radial-directed axis orientation. It might be that locally only the leg of the flux rope passed through VEX. The height and speed profiles from the Sun to Venus are obtained. We find that the CME speed possibly had been adjusted to the speed of the ambient solar wind flow after leaving COR2 field of view and before arriving Venus. A southward deflection of the CME from the source region is found from the trajectory of the CME geometric center. We attribute it to the influence of the coronal hole where the fast solar wind emanated from.Comment: ApJ, accepte

Superconducting Pairing Symmetries in Anisotropic Triangular Quantum Antiferromagnets

Motivated by the recent discovery of a low temperature spin liquid phase in layered organic compound $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$ which becomes a superconductor under pressure, we examine the phase transition of Mott insulating and superconducting (SC) states in a Hubbard-Heisenberg model on an anisotropic triangular lattice. We use a renormalized mean field theory to study the Gutzwiller projected BCS wavefucntions. The half filled electron system is a Mott insulator at large on-site repulsion $U$, and is a superconductor at a moderate $U$. The symmetry of the SC state depends on the anisotropy, and is gapful with $d_{x^2-y^2}+id_{xy}$ symmetry near the isotropic limit and is gapless with $d_{x^2-y^2}$ symmetry at small anisotropy ratio.Comment: 6 pages, 5 figure

WH/ZHW_H/Z_H production associated with a T-odd (anti)quark at the LHC in NLO QCD

In the framework of the littlest Higgs model with T parity, we study the $W_H/Z_H$ production in association with a T-odd (anti)quark of the first two generations at the CERN Large Hadron Collider up to the QCD next-to-leading order. The kinematic distributions of final decay products and the theoretical dependence of the cross section on the factorization/renormalization scale are discussed. We apply three schemes in considering the QCD NLO contributions and find that the QCD NLO corrections by adopting the (II) and (III) subtraction schemes can keep the convergence of the perturbative QCD description and reduce the scale uncertainty of the leading order cross section. By using these two subtraction schemes, the QCD NLO corrections to the $W_H(Z_H) q_-$ production process enhance the leading order cross section with a K-factor in the range of $1.00 \sim 1.43$.Comment: 31 pages, 12 figures, accepted by Phys. Rev.

SUSY QCD impact on top-pair production associated with a Z0Z^0-boson at a photon-photon collider

The top-pair production in association with a $Z^0$-boson at a photon-photon collider is an important process in probing the coupling between top-quarks and vector boson and discovering the signature of possible new physics. We describe the impact of the complete supersymmetric QCD(SQCD) next-to-leading order(NLO) radiative corrections on this process at a polarized or unpolarized photon collider, and make a comparison between the effects of the SQCD and the standard model(SM) QCD. We investigate the dependence of the lowest-order(LO) and QCD NLO corrected cross sections in both the SM and minimal supersymmetric standard model(MSSM) on colliding energy $\sqrt{s}$ in different polarized photon collision modes. The LO, SM NLO and SQCD NLO corrected distributions of the invariant mass of $t\bar t$-pair and the transverse momenta of final $Z^0$-boson are presented. Our numerical results show that the pure SQCD effects in \ggttz process can be more significant in the $+ +$ polarized photon collision mode than in other collision modes, and the relative SQCD radiative correction in unpolarized photon collision mode varies from 32.09% to $-1.89$ when $\sqrt{s}$ goes up from $500 GeV$ to $1.5 TeV$.Comment: 22 pages and 13 figure

Gossamer Superconductivity near Antiferromagnetic Mott Insulator in Layered Organic Conductors

Layered organic superconductors are on the verge of the Mott insulator. We use Gutzwiller variational method to study a Hubbard model including a spin exchange coupling term. The ground state is found to be a Gossamer superconductor at small on-site Coulomb repulsion U and an antiferromagnetic Mott insulator at large U, separated by a first order phase transition. Our theory is qualitatively consistent with major experiments reported in organic superconductors.Comment: 5 pages, 3 figure