In this paper, we provide a different uniqueness results for inverse spectral problems of conformable fractional Sturm-Liouville operators of order $\alpha$ ($0 < \alpha\leq 1$), with a jump and ...eigen-parameter dependent boundary conditions. Further, we study the asymptotic form of solutions, eigenvalues and the corresponding eigenfunctions of the problem. Also, we consider three terms of the inverse problem, from the Weyl function, the spectral data and two spectra. Moreover, we can also extend Hald's theorem to the problem.
Shocks are abundant both in astrophysical and laboratory systems. While the electric fields generated at shock fronts have recently attracted great attention, the associated self-generated magnetic ...field is rarely studied, despite its ability to significantly affect the shock profile in the nonideal geometry where density and temperature gradients are not parallel. We report here the observation of a magnetic field at the front of a Mach ∼6 shock propagating in a low-density helium gas system. Proton radiography from different projection angles not only confirms the magnetic field's existence, but also provides a quantitative measurement of the field strength in the range ∼5 to 7 T. X-ray spectrometry allowed inference of the density and temperature at the shock front, constraining the plasma conditions under which the magnetic and electric fields are generated. Simulations with the particle-in-cell code lsp attribute the self-generation of the magnetic field to the Biermann battery effect (∇n_{e}×∇T_{e}).
This paper presents a finite element approach for modelling three-dimensional crack propagation in quasi-brittle materials, based on the
strain injection
and
the crack-path field
techniques. These ...numerical techniques were already tested and validated by static and dynamic simulations in 2D classical benchmarks Dias et al., in: Monograph CIMNE No-134. International Center for Numerical Methods in Engineering, Barcelona,
(2012)
; Oliver et al. in Comput Methods Appl Mech Eng 274:289–348,
(2014)
; Lloberas-Valls et al. in Comput Methods Appl Mech Eng 308:499–534,
(2016)
and, also, for modelling tensile crack propagation in real concrete structures, like concrete gravity dams Dias et al. in Eng Fract Mech 154:288–310,
(2016)
. The main advantages of the methodology are the low computational cost and the independence of the results on the size and orientation of the finite element mesh. These advantages were highlighted in previous works by the authors and motivate the present extension to 3D cases. The proposed methodology is implemented in the finite element framework using continuum constitutive models equipped with strain softening and consists, essentially, in injecting the elements candidate to capture the cracks with some goal oriented strain modes for improving the performance of the injected elements for simulating propagating displacement discontinuities. The goal-oriented strain modes are introduced by resorting to mixed formulations and to the Continuum Strong Discontinuity Approach (CSDA), while the crack position inside the finite elements is retrieved by resorting to the
crack-path field
technique. Representative numerical simulations in 3D benchmarks show that the advantages of the methodology already pointed out in 2D are kept in 3D scenarios.
Rock discontinuities are planes of separation that influence the hydraulic and mechanical behavior of rock masses because they are main conduits for fluid flow and sources of major deformations. ...Joints can be open fractures, or closed when chemical alteration or decomposition of materials heal the surfaces. Discontinuities in rock masses are significant, because they affect slope stability, underground excavations, and reservoir engineering. Here, Diaz et al characterize deep closed joint surfaces.
We present a design and synthesis procedure for a new 90 ° waveguide hybrid with ultra-low amplitude imbalance. This novel hybrid design is based on Reed's multiple branch waveguide hybrid. The ...primary feature of this quadrature hybrid design is the introduction of a controllable ripple in the operational band by, firstly changing the heights of the input and output branches and, secondly, by introducing three waveguide-height discontinuity sections placed symmetrically in the main waveguide. This layout allows ultra-low amplitude imbalance over a wide operational band. At the same time, it permits a greater input/output branch height as compared to the Reed's 5-branch waveguide hybrid, which should ease fabrication for short-mm and sub-mm wavelengths. This design concept is demonstrated through a 90 ° waveguide hybrid for the 159-216 GHz band (30% fractional bandwidth). Our simulations indicate that the amplitude imbalance of the hybrid is better than 0.2 dB over the most of the 159-216 GHz band with a phase imbalance better than ±4 ° . Experimental verification of the hybrid shows excellent agreement with the simulations.
Discontinuities in earnings distributions at zero have been widely cited as evidence of earnings management but not without controversy. Recent research suggests discontinuities may be mere artifacts ...of certain research design choices. We find that the well-known zero-earnings discontinuity disappears soon after passage of the Sarbanes–Oxley Act (SOX) and has not returned. We also find that neither the discontinuity nor its disappearance require the effects of widely cited alternative (non-earnings management) explanations for the zero-earnings discontinuity.
•Prior research reports that earnings distributions have a discontinuity at zero.•Some research interprets the discontinuity as evidence of earnings management.•Some research suggests the discontinuity is an artifact of research design choices.•We find a discontinuity in all but 1 year before 2002, but not in any year after.•Neither scaling, sample selection, income taxes, nor special items explain our results.
Time and frequency transfer through global navigation satellite system (GNSS) precise point positioning (PPP) based on carrier-phase measurements has been widely used for clock comparisons in ...national timing laboratories. However, the time jumps up to one nanosecond at the day boundary epochs of adjacent daily batches lead to discontinuities in the time transfer results. Therefore, it is a major obstacle to achieve continuous carrier phase time transfer. The day-boundary discontinuities have been studied for many years, and they are believed to be caused by the long-term pseudorange noise during estimation of the clock offset in the daily batches and are nearly in accordance with a Gaussian curve. Several methods of eliminating the day-boundary discontinuity were proposed during the past fifteen years, such as shift and overlapping, longer batch processing, clock handover, and ambiguity stacking. Some errors and new noise limit the use of such methods in the long-term clock stability comparison. One of the effective methods is phase ambiguity fixing resolution in zero-differenced PPP, which is based on the precise products of wide-lane satellite bias (WSB) provided by the new international GNSS Service (IGS) Analysis Center of Centre National d'Etudes Spatiales (CNES) and Collecte Localisation Satellites (CLS). However, it is not suitable for new GNSS, such as the Beidou Satellite System (BDS), GALILEO, and QZSS. For overcoming the drawbacks above, Multi-GNSS Experiment (MGEX) observation data of 10 whole days from MJD 58624 to 58633have been network processed by batch least square resolution. These observations come from several ground receivers located in different national timing laboratories. Code and carrier phase ionosphere-free measurements of GPS and BDS satellites are used, and the time transfer results from network processing are compared with PPP results provided by Bureau International des Poids et Mesures (BIPM) and used for international atomic time (TAI) computation (TAIPPP) and universal time coordination (UTC). It is shown that the time offsets of three different time links are almost continuous and the day-boundary discontinuities are sharply eliminated by network processing, although a little extent of day-boundary discontinuities still exist in the results of UTC(USNO)-UTC(PTB). The accuracy of time transfer has been significantly improved, and the frequency stability of UTC(NTSC)-UTC(PTB) can be up to 6.8 × 10
on average time of more than one day. Thus, it is suitable for continuous multi-GNSS time transfer, especially for long-term clock stability comparison.
ABSTRACTRock discontinuity information plays a key role in engineering activities. In severely fragmented and discontinuous samples, the identification accuracy of rock discontinuities can be ...improved with the help of geologic knowledge with identified spatial features and geoscience interaction mechanisms. Therefore, we proposed a new method – a knowledge-based intelligent recognition method for rock discontinuities that used point cloud data – to correct inaccurate identification by considering the spatial relationships of rock discontinuities. This paper integrated the geologic knowledge bases in rock discontinuity information extraction rules and combined the generative rule inference model with the region growing method for intelligent extraction. In the case study, we developed four typical rule sets as examples based on the constructed rule system to group rock discontinuities and subsume the fractured rock discontinuities. Results show that this new method is effective in identifying and classifying rock discontinuities of complex areas with a greater reduction in manual intervention.
An efficient finite-element-method-based scattering operator (FEM-SO) is proposed. Utilizing field based propagation operators as boundary conditions, arbitrary light waves including radiation and ...evanescent waves can be treated at input and output ports. In contrast to conventional scattering operator techniques, the FEM-SO is applicable to arbitrary structures by using finite element models. In addition, considering structural discontinuities at the connecting boundary of scattering operators, an interface matrix to satisfy the boundary conditions between unit structures is introduced. To verify the present approach, numerical examples are shown for propagation characteristics of high-index-contrast waveguide facet and power spectrum of a photonic-crystal Fabry-Pérot (FP) cavity filter.
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