The Hierarchical Interface-enriched Finite Element Method (HIFEM) is a technique for solving problems containing discontinuities in the field gradient using finite element meshes that do not conform ...(match) the domain morphology. The method is suitable for analyzing problems with complex geometries or when such geometry is not known a priori. Contrary to the eXtended/Generalized Finite Element Method (X/GFEM), enrichments are placed on nodes created along interfaces, and a recursive enrichment strategy is used to resolve multiple discontinuities crossing single elements. In this manuscript we rigorously study the approximating properties and stability of HIFEM. A study on the enrichments’ polynomial order shows that the formulation does not pass the patch test as long as enrichments do not replicate the approximating properties of partition of unity shape functions. Regarding stability, we show that condition numbers of system matrices grow at the same rate as those of standard FEM—and without requiring a preconditioner. This intrinsic stability is accomplished by means of a proper construction of enrichment functions that are properly scaled as interfaces approach mesh nodes. We further demonstrate that, even without scaling, using a simple preconditioner recovers stability. The method’s stability is further demonstrated on the modeling of challenging thermal and mechanical problems with complex morphologies.
•The stability of the Hierarchical Interface-enriched Finite Element Method (HIFEM) is studied in detail. We show that the condition number of the system matrix remains stable with a simple modification of enrichment functions obtained from a 1-D analytical result.•The method is also stable without scaling functions but applying a simple Jacobi-like preconditioner.•The stability of HIFEM is showcased not only with academic examples but with real engineering problems.•We look at the approximating properties of the method, and show that in order to pass a simple discontinuity patch test, care must be taken when constructing enrichment functions.
We investigate whether the presence of fiscal rules might limit the insurgence of a Political Budget Cycle (PBC) in investment spending at municipal level. Data based on the balance sheets of Italian ...municipalities are explored for the period 1999–2012. We investigate the effect of the Domestic Stability Pact (DSP) and rely on the fact that, since 2001, this tax rule has not been binding for municipalities with under 5,000 inhabitants. Our main contribution consists of exploiting this quasi-experimental setting by means of a difference-in-discontinuities estimation strategy in order to obtain unbiased estimates. In comparison with existing results, our study makes three observations. Firstly, the easing of fiscal rules generates an increase in capital expenditure only in the year immediately before elections. Secondly, this increase only arises for those investments which produce immediately-visible effects. Finally, the size of the electoral cycle shows a 136 percent increase in these investments which is more than five times larger than that reported in the literature.
In this article we define the semigroup associated to a primitive substitution. We use it to construct a minimal automaton which generates a substitution sequence u in reverse reading. We show, in ...the case where the substitution has a coincidence, that this automaton completely describes the semicocycle discontinuities of u.
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In view of the problem of identifying palaeochannels with high concealment and complex geological structures, this paper proposes an intelligent recognition method for palaeochannels based on ...Frangi filtering and deep learning. The methodology makes use of Maximum Entropy Wigner–Ville Distribution (MEWVD) method to process the original instantaneous amplitude data, which enhance the distinct features of micro palaeochannels in different sensitive frequency bands. The sample 2-D stratigraphic images generated from these data is labelled for the pre-training process of Attention R2U-Net neural network model. Subsequently, Frangi filter is used to identify and enhance the linear structures of river channels in target stratigraphic images, improving the identification effect of the neural network. Finally, RGB data fusion and 3-D visualization carving are performed on the identification data. This method not only eliminates redundant information using the Frangi filter but also proves that the Attention R2U-Net network model structure with attention mechanism and residual convolution structure can effectively improve the segmentation effect for river channels at different scales. Experimental examples show that this method achieves pixel-level feature segmentation of 3-D seismic data for palaeochannels, accurately depicting their shape, width, thickness, flow direction and other features, thus providing support for subsequent well deployment and horizontal well fracturing selection.
Apart from the lithosphere-asthenosphere boundary (LAB), mid-lithospheric discontinuities (MLDs) in thick and old continental lithospheres appear to play an important role in global plate tectonics. ...Initiation of intra-continental subduction, delamination of the lower continental lithospheric mantle and removal of cratonic roots are likely to occur along MLDs.
Here we introduce the ‘pargasosphere’ hypothesis which could account for the origin of both boundaries. The observation that pargasitic amphibole is stable even at very low bulk ‘water’ concentration (~a few hundreds ppm wt.) implies that the solidus of the shallow upper mantle (<3 GPa) is usually the pargasite dehydration solidus at ~1100 °C. In young continental and oceanic lithosphere (<70 Ma) this solidus defines the LAB. The LAB separates the deeper, partial melt bearing asthenosphere from the shallower melt barren lithosphere, explaining their contrasting rheology.
In old continents pargasite breaks down at the sub-solidus pargasite dehydration boundary at ~3 GPa and liberates ‘water’-rich fluids. This latter process may be responsible for the formation of MLDs. The occurrence of partial melts or fluids beyond the pargasite stability field can explain commonly observed geophysical anomalies associated with the LAB and MLDs.
We present forward modelled variations of shear wave velocity and resistivity at the LAB and MLDs for idealised lithospheric columns. These columns are constructed based on the ‘pargasosphere’ hypothesis and geotherms corresponding to continental lithospheres with various tectono-thermal ages. The ‘pargasosphere’ hypothesis offers a number of other empirically testable implications. For instance, cooling asthenosphere beneath young extensional continental and oceanic lithosphere settings can be the source of surface CO2 emanations even at locations distant from areas with active volcanoes. The Vrancea zone (Eastern Europe) appears to be a suitable site for testing the ‘pargasosphere’ hypothesis for elucidating the origin of intermediate-depth earthquakes (70–300 km) and to explain the delamination of the lower continental lithospheric mantle.
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•‘Pargasosphere’ refers to part of the upper mantle where pargasite is stable.•The rheology of the shallow upper mantle (<100 km) is controlled by pargasite.•The upper limit of pargasite stability defines mid-lithosphere discontinuities.•Along this horizon, the lower part of the continental lithosphere can delaminate.•In the cooling asthenosphere, formation of pargasite can lead to CO2 emission.
We present a novel electromagnetic bandgap (EBG) structure, which can be used to manufacture low-cost waveguiding structures at high frequencies. The unit cell of the proposed EBG consists of ...glide-symmetric holes in parallel plate waveguide. Using this unit cell in groove gap waveguide technology has a number of advantages over pin-type EBG at high frequencies, such as acquiring higher accuracy because of larger periodicity as well as an easier and cheaper manufacturing process. The performance of the proposed waveguiding structure is demonstrated using both a straight and a double 90° bent lines through simulation and measurement.
Geophysically detectible mid-lithospheric discontinuities (MLD) and lithosphere-asthenosphere boundaries (LAB) beneath cratons have received much attention over recent years, but a consensus on their ...origin has not yet emerged. Cratonic lithosphere composition and origin is peculiar due to its ultra-depletion during plume or accretionary tectonics, cool present-day geothermal gradients, compositional and rheological stratification and multiple metasomatic overprints. Bearing this in mind, we integrate current knowledge on the physical properties, chemical composition, mineralogy and fabric of cratonic mantle with experimental and thermodynamic constraints on the formation and migration of melts, both below and within cratonic lithosphere, in order to find petrologically viable explanations for cratonic mantle discontinuities.
LABs characterised by strong seismic velocity gradients and increased conductivity require the presence of melts, which can form beneath intact cratonic roots reaching to ~200–250km depth only in exceptionally warm and/or volatile-rich mantle, thus explaining the paucity of seismical LAB observations beneath cratons. When present, pervasive interaction of these - typically carbonated - melts with the deep lithosphere leads to densification and thermochemical erosion, which generates topography at the LAB and results in intermittent seismic LAB signals or conflicting seismic, petrologic and thermal LAB depths. In rare cases (e.g. Tanzanian craton), the tops of live melt percolation fronts may appear as MLDs and, after complete lithosphere rejuvenation, may be sites of future, shallower LABs (e.g. North China craton).
Since intact cratons are presently tectonomagmatically quiescent, and since MLDs produce both positive and negative velocity gradients, in some cases with anisotropy, most MLDs may be best explained by accumulations (metasomes) of seismically slow minerals (pyroxenes, phlogopite, amphibole, carbonates) deposited during past magmatic-metasomatic activity, or fabric inherited from cratonisation. They may accumulate as layers at, or as subvertical veins above, the depth at which melt flow transitions from pervasive to focussed flow at the mechanical boundary layer, causing azimuthal and radial anisotropy. Thermodynamic calculations investigating the depth range in which small-volume melts can be produced relative to the field of phlogopite stability and the presence of MLDs show that phlogopite precipitates at various pressures as a function of age-dependent thermal state of the cratonic mantle, thus explaining variable MLD depths. Even if not directly observed, such metasomes have been shown to be important ingredients in small-volume volatile-rich melts typically penetrating cratonic lithospheres. The apparent sparseness of evidence for phlogopite-rich assemblages in the mantle xenolith record at geophysically imaged MLD depths, if not due to preferential disaggregation in the kimberlite or alteration, may relate to vagaries of both kimberlite and human sampling.
•Review of petrologically plausible explanations for cratonic mantle discontinuities•Melt at cratonic LAB depth (≥200km) due to anomalous sublithospheric X-T, retarded drainage and/or resupply•Conflicting seismic-petrologic LAB signatures due to thermochemical-mechanical erosion•MLDs result mostly from past deposition of metasomes at mechanical boundary layers.•Omnipresent metasomes documented by alkaline melts, underestimated due to non-representative sampling
Anomalous launch of a surface wave with different handedness phase control is achieved in a terahertz metasurface based on phase discontinuities. The polarity of the phase profile of the surface ...waves is found to be strongly correlated to the polarization handedness, promising polarization‐controllable wavefront shaping, polarization sensing, and environmental refractive‐index sensing.
Surface discontinuities, such as cylindrical protrusions or dents, are commonly found on artificial aircraft or vehicle surfaces. Despite being electrically small in size, their sheer quantity can ...significantly affect the scattering characteristics of the target. Due to the large contrast between the surface discontinuity and surrounding geometry, the efficient scattering analysis of these targets is technically challenging in both mesh generation and numerical simulation. In this communication, two novel basis functions are presented based on the discontinuous Galerkin integral equation (DGIE) framework. Using the so-called extended half-RWG and modified top junction basis functions, the cylindrical surface discontinuities with different or variable height-radius ratios can be efficiently discretized without requiring mesh conformality. Extensive numerical simulations of surface discontinuities on a low-RCS testbed are performed to verify the accuracy, flexibility, and robustness of the proposed method.
Intersecting discontinuities are often encountered in rock engineering and sometimes associated with damaging geohazards. Our understanding of intersecting discontinuities instability remains vastly ...insufficient due to difficulties in comprehensively monitoring the failure process. Here we use microseismic (MS) monitoring to virtualize the MS events in the rock masses surrounding a powerhouse crown and investigate the effect of geological features on the occurrence of MS events. We subsequently build a three-dimensional numerical model and validate this model using the in-situ measurements by multipoint displacement meters. The numerical results demonstrate how the displacements of surrounding rock masses near the fault and the dyke increase and reveal possible causes, such as stress condition as well as geometry and orientation of rock discontinuities. We also discuss the correlation between the tempo-spatial distribution of MS events and the failure pattern of rock masses and confirm the weakened dyke as the main cause of the rock collapse. This study highlights that the stability of intersecting discontinuities can be controlled by both the geometrical and mechanical properties of individual discontinuities, and attentions should be paid to key properties favorable for rock instability.
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