Analysis as a source of geometry: a non-geometric representation of the Dirac equation

Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it implicitly contains a Lorentzian metric, Pauli matrices, connection coefficients for spinor fields and an electromagnetic covector potential. This observation allows us to give a simple representation of the massive Dirac equation as a system of four scalar equations involving an arbitrary two-by-two matrix operator as above and its adjugate. The point of the paper is that in order to write down the Dirac equation in the physically meaningful 4-dimensional hyperbolic setting one does not need any geometric constructs. All the geometry required is contained in a single analytic object - an abstract formally self-adjoint first order linear differential operator acting on pairs of complex-valued scalar fields.Comment: Edited in accordance with referees' recommendation

Stochastic gravitational-wave background from spin loss of black holes

Although spinning black holes are shown to be stable in vacuum in general relativity, there exists exotic mechanisms that can convert the spin energy of black holes into gravitational waves. Such waves may be very weak in amplitude, since the spin-down could take a long time, and a direct search may not be feasible. We propose to search for the stochastic background associated with the spin-down, and we relate the level of this background to the formation rate of spinning black holes from the merger of binary black holes, as well as the energy spectrum of waves emitted by the spin-down process. We argue that current LIGO-Virgo observations are not inconsistent with the existence of a spin-down process, as long as it is slow enough. On the other hand, the background may still exist as long as a moderate fraction of spin energy is emitted within Hubble time. This stochastic background could be one interesting target of next generation GW detector network, such as LIGO Voyager, and could be extracted from total stochastic background

Throughput and Robustness Guaranteed Beam Tracking for mmWave Wireless Networks

With the increasing demand of ultra-high-speed wireless communications and the existing low frequency band (e.g., sub-6GHz) becomes more and more crowded, millimeter-wave (mmWave) with large spectra available is considered as the most promising frequency band for future wireless communications. Since the mmWave suffers a serious path-loss, beamforming techniques shall be adopted to concentrate the transmit power and receive region on a narrow beam for achieving long distance communications. However, the mobility of users will bring frequent beam handoff, which will decrease the quality of experience (QoE). Therefore, efficient beam tracking mechanism should be carefully researched. However, the existing beam tracking mechanisms concentrate on system throughput maximization without considering beam handoff and link robustness. This paper proposes a throughput and robustness guaranteed beam tracking mechanism for mobile mmWave communication systems which takes account of both system throughput and handoff probability. Simulation results show that the proposed throughput and robustness guaranteed beam tracking mechanism can provide better performance than the other beam tracking mechanisms.Comment: Accepted by IEEE/CIC ICCC 201

Meso-scale modelling of 3D woven composite T-joints with weave variations

A meso-scale modelling framework is proposed to simulate the 3D woven fibre architectures and the mechanical performance of the composite T-joints, subjected to quasi-static tensile pull-off loading. The proposed method starts with building the realistic reinforcement geometries of the 3D woven T-joints at the mesoscale, of which the modelling strategy is applicable for other types of geometries with weave variations at the T-joint junction. Damage modelling incorporates both interface and constituent material damage, in conjunction with a continuum damage mechanics approach to account for the progressive failure behaviour. With a voxel based cohesive zone model, the proposed method is able to model mode I delamination based on the voxel mesh technique, which has advantages in meshing. Predicted results are in good agreement with experimental data beyond initial failure, in terms of load-displacement responses, failure events, damage initiation and propagation. The significant effect of fibre architecture variations on mechanical behaviour is successfully predicted through this modelling method without any further correlation of input parameters in damage model. This predictive method will facilitate the design and optimisation of 3D woven T-joint preforms

Experimental assessment of the mechanical behaviour of 3D woven composite T-joints

To understand the influence of the fibre architecture of 3D woven composite T-joints on mechanical performance, as well as the benefits that 3D woven T-joints can offer over the equivalent 2D laminates, experimental testing is performed on two types of 3D woven T-joint with only weave variation at the junction, and one type of 2D woven laminate T-joint. A quasi-static tensile pull-off loading is selected in this work as this out-of-plane load case is one of the typical loading conditions for such T-joint structures. The significant advantages of 3D woven composite T-joints in terms of ultimate strength and damage tolerance over the 2D alternative were identified in the testing. More importantly, this work showed that variation in the fibre architecture can considerably enhance properties such as delamination resistance and total energy absorption to failure, as well as increasing slightly the stiffness and initial failure load. This experimental assessment has demonstrated that using 3D woven reinforcements is an effective way to improve the load-bearing capability of composite T-joints over laminates, and also that this improvement could be optimised with regard to fibre architecture

Spectral asymptotics for first order systems

This is a review paper outlining recent progress in the spectral analysis of first order systems. We work on a closed manifold and study an elliptic self-adjoint first order system of linear partial differential equations. The aim is to examine the spectrum and derive asymptotic formulae for the two counting functions. Here the two counting functions are those for the positive and the negative eigenvalues. One has to deal with positive and negative eigenvalues separately because the spectrum is, generically, asymmetric.Comment: Edited in accordance with referee's recommendation