20,728 research outputs found
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
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