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Almost all event-triggered control (ETC) strategies were designed for discrete-time or continuous-time systems. In order to unify these existing theoretical results of ETC and develop ETC strategies for nonlinear systems, whose state variables evolve steadily at one time and change intermittently at another time, this article investigates quasisynchronization of delayed neural networks (NNs) on time scales with discontinuous activation functions via ETC approaches. First, the existence of the Filippov solutions is proved for discontinuous NNs with finite discontinuities. Second, two static event-triggered conditions and two dynamic event-triggered conditions are established to avoid continuous communication between the master-slave systems under algebraic/matrix inequality criteria. Third, under static/dynamic event-triggered conditions, a positive lower bound of event-triggered intervals is demonstrated to be greater than a positive number for each event-based controller, which shows that the Zeno behavior will not occur. Finally, two numerical simulations are carried out to show the effectiveness of the presented theoretical results in this article.

This paper develops the sliding mode control strategy for linear impulsive systems with matched disturbances. Such systems describe dynamical systems that evolve according to continuous process most of the time with matched disturbances, but instantaneously exhibit discontinuities, i.e., impulsive disturbances. A suitable sliding surface function is proposed and the resulting sliding mode dynamics are a class of linear impulsive systems. Some sufficient conditions coupled with impulse time sequences are proposed to guarantee the reachability of the predesigned sliding surface and the stability of the reduced-order impulsive systems under sliding motion, respectively. We show how restrictions on the structure of the systems and impulses should be imposed to ensure the feasibility of the proposed sliding mode control strategy in comparison with general sliding mode control in continuous space. To show the effectiveness of the proposed approach, two simulation examples are presented at the end.

The assessment of rock mass in situ permeability is challenging for large-scale projects such as reservoirs created by dams, where water tightness issues are of prime importance. The in situ permeability is strongly related to the frequency and distribution of discontinuities in the rock mass and quantified by rock quality designation (RQD). This paper analyzes the data of hydraulic conductivity and discontinuities sampled at different depths during the borehole investigations in the limestone and sandstone formations for the construction of hydraulic structures in Oman. Cores recovered from boreholes provide RQD data, and in situ Lugeon tests elucidate the permeability. A modern technique of multivariate adaptive regression splines (MARS) assisted in correlating permeability and RQD along with the depth. In situ permeability shows a declining trend with increasing RQD, and the depth of investigation is within 50 m. This type of relationship can be developed based on detailed initial investigations at the site where the hydraulic conductivity of discontinuous rocks is required to be delineated. The relationship can approximate the permeability by only measuring the RQD in later investigations on the same site, thus saving the time and cost of the site investigations. The applicability of the relationship developed in this study to another location requires a lithological similarity of the rock mass that can be verified through preliminary investigation at the site.

This paper explores the effects of technological discontinuities on the competences of incumbent firms. In contrast to Tushman and Anderson, I argue that a given technological discontinuity can be ...

In this technical correspondence, a multilayer formation (MLF) control problem is considered and solved by a unified framework. The agents in each layer present a sort of hierarchical distinction: receive information from former layers, communicate inside the current layer, and send information to subsequent layers. With an arbitrary number of layers, we extend the previous result from undirected graphs to directed ones. The proposed controller achieves MLF without using the distributed estimators and the acceleration information. This removes the induced discontinuities and alleviates the system complexity. It is then proved that the closed-loop errors are semiglobally uniformly ultimately bounded. Simulations are presented to illustrate the effectiveness of this approach.

Made available in DSpace on 2021-06-25T11:03:26Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-01-01 In this work we propose a steady-state modeling of DC-DC converters driven by multiple pulse width modulation (PWM) signals. The proposed DC-DC converter modeling uses a switched state-space framework and the switching signal discontinuities is represented by a Fourier series to obtain the average model. The advantage of the proposed modeling is that it is not dependent on the DC-DC converter topology and the dimension of the state-space model is not increased with the number of storage devices. Additionally, the duty-cycle and phase displacements among the driving PWM signals can be arbitrary and systematically modeled. The effectiveness of the proposed modeling is supported by simulation and experimental results. Engenharia Eltrica, CEFET/RJ, 74351 Rio de Janeiro, Brazil, 20271-110 (e-mail: rafael.magossi@cefet-rj.br) IFSP, 119519 Sao Paulo, Brazil, 01109-010 (e-mail: leandro.elias@usp.br) Mathematics, UNESP, 28108 Ilha Solteira, SP, Brazil, 15385-000 (e-mail: flavio.faria@unesp.br) of Electrical Engeneering, University of So Paulo - USP, So Carlos, SP, Brazil, 13566-590 (e-mail: rquadros@sc.usp.br) Engenharia Eletrica, Universidade de Sao Paulo, 28133 Sao Paulo, Brazil, 05508-900 (e-mail: vilma@sc.usp.br)

Many wave propagation problems involve discontinuous material properties. We propose to solve such problems by non-overlapping domain decomposition combined with the method of difference potentials (MDP). The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with projection on the boundary. The unknowns for the Calderon's equation are the Dirichlet and Neumann data. Coupling between neighboring subdomains is rendered by applying their respective Calderon's equations to the same data at the common interface. Solutions on individual subdomains are computed concurrently using a direct solver. Our method proves to be insensitive to large jumps in the wavenumber for transmission problems, as well as interior cross-points and mixed boundary conditions, which may be a challenge to many other domain decomposition methods.

Do hedge funds hedge? In negative states of the world, often not as much as they should. For several styles, we report larger market betas when market returns are low (i.e., “beta in the tails”). We justify this finding through a combination of negative-mean jumps in the market returns and large market jump betas: when moving to the left tail of the market return distribution jump dynamics dominate continuous dynamics and the overall systematic risk of the fund is driven by the higher systematic risk associated with return discontinuities. Methodologically, the separation of continuous and discontinuous dynamics is conducted by exploiting the informational content of the high-order infinitesimal cross-moments of hedge-fund and market returns.

Surface wave (SW) methods offer promising options for an effective and sustainable development of seismic exploration, but they still remain under-exploited in hard rock sites. We present a successful application of active and passive surface wave tomography for the characterization of the southern continuation of the Siilinjärvi phosphate deposit (Finland). A semi-automatic workflow for the extraction of the path-average dispersion curves (DCs) from ambient seismic noise data is proposed, including identification of time windows with strong coherent SW signal, azimuth analysis and two-station method for DC picking. DCs retrieved from passive data are compared with active SW tomography results recently obtained at the site. Passive data are found to carry information at longer wavelengths, thus extending the investigation depth. Active and passive DCs are consequently inverted together to retrieve a deep pseudo-3D shear-wave velocity model for the site, with improved resolution. The southern continuation of the mineralization, its contacts with the host rocks and different sets of cross-cutting diabase dikes are well imaged in the final velocity model. The seismic results are compared with the latest available geological models to both validate the proposed workflow and improve the interpretation of the geometry and extent of the mineralization. Important large-scale geological boundaries and structural discontinuities are recognized from the results, demonstrating the effectiveness and advantages of the methods for mineral exploration perspectives.

In this paper, we derive delay and fractional-order dependent sufficient conditions for fractional-order gene regulatory networks (FOGRNs) with time-varying delays to be stable with H ∞ /passivity performance. Distinct from the existing works on delayed FOGRNs, the Lyapunov-Krasovskii functional (LKF) is suitably structured so that the delay functions can be non-differentiable or even have jump type discontinuities. Further, the positive-definiteness condition is relaxed for the matrices involved in LKF. A new set of linear matrix inequality (LMI) conditions that ensure the stability of FOGRNs with certain H ∞ /passivity performance level is derived using various results on fractional derivatives/integrals and convex property of LMIs. Finally, the results obtained are verified with existing FOGRNs via numerical simulations.

Cracks, broadly defined as compliant discontinuities, are a major cause of elastic anisotropy. However, few models are available for quantifying crack properties relevant to anisotropy. We developed a rock-physics model to quantify crack angular distribution and normal-to-tangential compliance ratio from pressure-dependent acoustic velocities measured in the laboratory. Our model uses a rectangular function of variable width and amplitude to extract the maximum dip angle of cracks, which is a direct quantification of crack alignment relative to the bedding plane. We tested the model on an organic-rich shale data set and confirmed that crack alignment and compliance ratio strongly impact Thomsen anisotropy parameters, thus demonstrating the model as a useful tool for better understanding how cracks affect elastic anisotropy.

Irregular acquisition geometry causes discontinuities in the appearance of surface wave events, and a large offset causes seismic records to appear as aliased surface waves. The conventional method of sampling data affects the accuracy of the dispersion spectrum and reduces the resolution of surface waves. At the same time, “mode kissing” of the low-velocity layer and inhomogeneous scatterers requires a high-resolution method for calculating surface wave dispersion. This study tests the use of the multiple signal classification (MUSIC) algorithm in 3D multichannel and aliased wavefield separation. Azimuthal MUSIC is a useful method to estimate the phase velocity spectrum of aliased surface wave data, and it represents the dispersion spectra of low-velocity and inhomogeneous models. The results of this study demonstrate that the mode kissing affects dispersion imaging, and inhomogeneous scatterers change the direction of surface-wave propagation. Surface waves generated from the new propagation directions also are dispersive. The scattered surface wave has a new dispersion pattern different from that of the entire record. Diagonal loading is introduced to improve the robustness of azimuthal MUSIC, and numerical experiments demonstrate the resultant effectiveness of imaging aliasing surface waves. A phase-matched filter is applied to the results of azimuthal MUSIC, and phase iterations are unwrapped in a fast and stable manner. Aliased surface waves and body waves are separated during this process. Overall, field data demonstrate that the azimuthal MUSIC and the phase-matched filters can successfully separate aliased surface waves.

Impedance inversion is an effective method to estimate the properties of subsurface model from poststack seismic data. However, owing to the low quality of seismic data and other reasons, impedance inversion methods usually suffer from spatial discontinuities and low resolution. In order to overcome these problems, we have developed an impedance inversion method based on geological structure-guided total variation (GSGTV) constraint. Different from traditional TV constraint, GSGTV considers the spatial distribution of geological structures instead of imposing gradient constraints on impedance only in fixed directions (horizontal and vertical). Therefore, GSGTV not only retains the advantage of traditional TV that can preserve the edge of layer, but also overcomes the shortcomings of traditional TV that is only suitable for inverting block structures. This ensures that GSGTV can simultaneously improve the resolution and spatial continuity of the inversion result. The realization of impedance inversion method based on GSGTV constraint requires three steps. First, estimate the local structural orientation of the subsurface from seismic data. Then, construct GSGTV regularization term based on the local structural orientation. Finally, establish the inversion objective function and solve the function by the split-Bregman iterative algorithm. We compared the proposed method and the impedance inversion method based on traditional TV constraint with synthetic and real seismic data. The inversion results confirm that our method can improve the resolution and spatial continuity.

The purpose of the present study is to compare the well-posedness criteria of the free-pressure two-fluid model, single-pressure two-fluid model, and two-pressure two-fluid model in a vertical pipe. Two-fluid models were solved using the Conservative Shock Capturing Method. A water faucet case is used to compare two-fluid models. The free pressure two-fluid model can accurately predict discontinuities in the solution field if the problem's initial condition satisfies the Kelvin Helmholtz instability conditions. The single-pressure two-fluid model can accurately predict the behavior of flows in which the two phases are poorly coupled. The two-pressure two-fluid model is an unconditionally well-posed one; if in the free-pressure two-fluid model and single-pressure two-fluid model, the range of velocity difference of two phases exceeds certain limits, the models will be ill-posed. The two-pressure two-fluid model produces more numerical diffusion than the free-pressure two-fluid and single-pressure two-fluid models in the solution field. High numerical diffusion of two-pressure two-fluid models leads to failure to better comply with the problem's analytical solution. Results show that a single-pressure model is a powerful model for numerical modeling of gas-liquid two-fluid flows in the vertical pipe due to a broader range of well-posed than free-pressure models and less numerical diffusion than the two-pressure model.

This paper designs a fifth-order weighted compact nonlinear scheme (WCNS) on a five-point stencil to solve one- and two-dimensional Hamilton-Jacobi equations. The five-point WCNS is used to compute the left and right limits of first-order spatial derivatives of the HJ equations in the Lax-Friedrichs monotone numerical Hamiltonian. The WENO-Z type interpolation for cell-edge values of the solutions is used to suppress numerical oscillations which may appear near discontinuities. Five- and seven-point WENO-Z schemes for Hamilton-Jacobi equations are also designed for comparisons. The performance of the WCNS and the two WENO-Z schemes is demonstrated by several numerical examples in one-dimensional and two-dimensional cases.

Phase unwrapping is a critical step of interferometric synthetic aperture radar (InSAR) processing, and its accuracy directly determines the reliability of subsequent applications. Many phase unwrapping methods have been proposed, most of which assume that the phase has spatial continuity, while decorrelation noise and aliasing fringes invalidate the assumptions, resulting in poor performance of these methods. To obtain more reliable unwrapping results, in this paper, a deep convolutional neural network, called DENet, is proposed for predicting the probabilities of phase discontinuities in interferograms. The main advantages of DENet are: (1) using branching structure to extract detailed and high-level features separately, to retain details while making full use of contextual information; (2) using multi-channel input, including interferogram, range/azimuthal phase gradients, and residues map, to provide effective guidance for discontinuity prediction; and (3) using a single network to estimate phase discontinuities in both range and azimuth directions simultaneously. To train the network, a data set simulation strategy is proposed to generate enough training samples. The strategy considers a variety of phase components such as terrain-related phase, random deformation, atmospheric turbulence, and noise. The phase discontinuity estimated by DENet is then converted to costs in the minimum cost flow solver of SNAPHU to obtain the final unwrapped phase. Based on validations of simulated and real interferograms, the proposed method exhibits excellent performance compared to traditional and deep learning unwrapping methods. The proposed method can effectively unwrap large-scale, low-quality interferograms, which is expected to significantly improve the accuracy of InSAR applications.

Diffracted waves provide an opportunity to detect small-scale subsurface structures because they give wide illumination direction of geologic discontinuities, such as faults, pinch outs, and collapsed columns. However, separating diffracted waves is challenging because diffracted waves have greater geometric amplitude losses and are generally weaker than reflections. To retain more diffracted waves, we have developed a prestack diffraction separation method based on the local slope pattern and plane-wave destruction (PWD) method. In general, it is difficult to distinguish between hyperbolic reflections and hyperbolic diffractions using data-driven local slope estimation in the shot domain. Therefore, we transfer slope estimation in the shot domain to velocity analysis in the common-midpoint domain and ray parameter calculation in the stack domain. The connection between local slope and the normal moveout velocity and the surface-ray parameter is known, which provides a novel approach for estimating the local slope of hyperbolic reflected waves in the shot domain. The estimated slope can provide an exact slope-based operator for the PWD method, thus allowing the PWD to separate diffracted waves from reflected waves in the shot domain. Synthetic and field data tests demonstrate the feasibility and effectiveness of our prestack diffraction separation method.

Spectral decomposition is a proven tool in seismic interpretation. It helps interpreters highlight channels and map temporal bed thickness and other geologic discontinuities. In spectrally decomposed seismic data, amplitude spectra contain notch patterns. The period of these notch patterns inversely correlates to the reservoir layer’s thickness and/or its interval velocity. Additional cepstral decomposition will directly extract the bed time thickness or arrival time under simple reflectivity setups. Based on these observations, we have adopted a new workflow for reflectivity retrieval in stably phased seismic. There is no need to understand the details of the wavelet in this workflow. We find that the reflector time and its “apparent strength” can be identified in a transformed seismic resonance domain resulting from a modified cepstrum analysis. We find that linear hot spots in this domain lead to direct quantification of the reflectivity series. The timing and strength of the linear hot spots reveals reflector times and scaled reflectivity coefficients. We applied this method for thickness prediction for a target deepwater reservoir with a complex geologic setting. Because of the large reservoir thickness variations and weak impedance contrast with underlying lithology, identification of the base reservoir and therefore the reservoir thickness has been historically challenging in this field. In a blind test, the reservoir thicknesses evaluated from this method are close to the true vertical thickness found in wells.

A method for predicting losses over the area of the deposit to minimize the risks of accidents and gas and oil and water showings for the Permian-Carboniferous reservoir of the Usinskoye field was developed. In addition, the analysis of the influence of faults on the number of losses in wells during drilling was carried out. Based on the more than 250 wells drilling analysis, it was revealed that a significant problem during drilling was the loss of drilling fluid. This complication was found in 46% of drilled wells. The intensity of the studied losses was in a wide range: from insignificant losses to strong ones, with a complete loss of mud circulation. The faults identified both from well drilling data and from seismic data were characterized by a different number of wells with and without losses. Using the combination of various statistical methods, individual and complex models for predicting losses in wells depending on the distance from the fault were obtained. Using multilevel probabilistic-statistical modeling, the study of the influence of faults on losses was carried out: initially, based on the data of all wells, regardless of the methods for identifying faults - the first-level model; by the method of identifying faults (drilling / seismic exploration) - second-level models; according to the data of individual faults - the model of the third level. At the fourth level, a complex model was built, which takes into account the calculation results obtained at the previous levels of statistical modeling. The presence of direct and inverse dependences of the absorption probability from the shortest distance to the fault was established. Using linear discriminant analysis, the results of predicting the probability of absorption were checked.

This paper aims to analyze the fixed-time synchronization of a class of discontinuous fuzzy inertial neural networks with time-varying delays based on the new improved fixed-time stability lemmas. First of all, by using the generalized variable transformation and Filippov solution theory, the discontinuities of the considered neural system can be coped with and the error system is established. By relaxing the conditions of the C-regular Lyapunov function, two new fixed-time stability lemmas are proved via simple inequality techniques. The setting times are also estimated and are more accurate in comparison with the previous ones. Finally, one typical numerical example is carried out to verify the correctness and the advantages of the main results.

We study the causal effect of incarceration on reoffending using discontinuities in North Carolina’s sentencing guidelines. A regression discontinuity analysis shows that 1 year of incarceration ca...

Engineering systems continuously interact with nano-sized particles coming from natural or artificial sources. Considering nano-sized contaminants the detrimental effects are known as soiling and fouling phenomena. The objective of the present work is to gather morphological and three-dimensional quantitative information of discontinuities such as voids and pores within the nano-sized particle layer and in correspondence to the substrate/layer interface using microtomography. Deposits are obtained through impact tests using fine powder (soil and soot), and there are realized on a low-density material substrate characterized by different surface roughness values. The packing process and the discontinuities at the substrate-to-layer interfaces explain macroscopic effects as detachment and spallation but at the same time, give the possibility to understand more in detail the process related to the deposition mechanisms involved in this type of test defining general guidelines to predict the fouling phenomenon and to improve the capability of the removal process.

Remote sensing imagery and geoelectrical surveys used in this study help to evaluate the groundwater potentiality in the metamorphic formations of the North Cameroon. The methodology of the work is then mainly based on the extraction and identification of lineaments or fracture zones which acts as the passageway for groundwater. Manual and automatic extraction technics applied on the Landsat-8 images made it possible to find sixty one (61) lineaments. The main directions of these lineaments are N-S and N22°E (NNE-SSW) and the secondary directions are N10°E, NE-SW, then W-E to N100°E. According to the lineament density map, high density values are located at the centre and at the western part of the study area. The lineament density contrasts show the level of fracturing in the area. This fracturing is also evidenced by the geoelectrical survey. Indeed, results of the electrical resistivity profiling and 2D electrical imaging around or near lineaments, reveal the existence of fractures and shear zones characterized by the conductive discontinuities in the electrical current responses. Usually, the discontinuities sus-evocated above form potential groundwater targets. So, based on the combined results from remote sensing and geoelectrical method, the present study thus demonstrates the effectiveness of using this approach for assessing the availability of potential groundwater zones in the metamorphic formations. However, methods used in this study should be supported by the drill hole methods for the validity of results.

The two-dimensional shallow water equations (SWEs) are a hyperbolic system of first-order nonlinear partial differential equations which have a characteristic of strong gradient. In this study, a newly-developed numerical model, based on local radial point interpolation method (LRPIM), is adopted to simulate discontinuity in shallow water flows. In order to accurately capture the information of wave propagation, the LRPIM is combined with the split-coefficient matrix (SCM) method to transform the SWEs into a characteristic form and the selection of the direction of local support domain is introduced into the LRPIM. An improved meshless artificial viscosity (MAV) technique is developed to minimize the non-physical oscillations near the discontinuities. Then, the LRPIM and the second-order Runge–Kutta method are adopted for spatial and temporal discretization of the SWEs, respectively. The feasibility and validity of the proposed numerical model are verified by the classical dam-break problem and the mixed flow pattern problem. The comparison of the obtained results with the analytical solution and other numerical results showed that the MAV method combined with LRPIM can accurately capture the shocks and has high accuracy in dealing with discontinuous flow by adding appropriate viscosity to the equations in the discontinuous region.

In order to study the instantaneous mechanical properties of rock mass discontinuities with different 3D morphologies during the shear process, the Brazilian splitting method is used to prepare natural rock mass discontinuities, and the high-precision 3D scanning test of discontinuities is carried out. The Z 2 is selected as the evaluation parameter of the discontinuities. Based on the graded cyclic shear test results of discontinuities, the influence of the morphology characteristics on the strength and deformation characteristics is analyzed. With the increase of shear times, the 3D morphology characteristic parameters of the structural plane decrease steadily after the graded cyclic shear. Based on the test curve, the graded cyclic shear characteristics of rock mass discontinuities are analyzed from the shear deformation, and the shear process of the discontinuities is finely divided by combining with the variation characteristics of shear stiffness. Combined with the 3D morphology parameters, an empirical formula for the shear strength of discontinuities is proposed. Through verification, the effect of the new model is better than that of the classical JRC-JCS model.

We consider a prototypical nonlinear parabolic equation whose flux has three distinguished features: it is nonlinear with respect to both the unknown and its gradient, it is homogeneous, and it depends only on the direction of the gradient. For such equation, we obtain existence and uniqueness of entropy solutions to the Dirichlet problem, the homogeneous Neumann problem, and the Cauchy problem. Qualitative properties of solutions, such as finite speed of propagation and the occurrence of waiting-time phenomena, with sharp bounds, are shown. We also discuss the formation of jump discontinuities both at the boundary of the solutions’ support and in the bulk.

This work presents a methodology for the statistical validation of discontinuity surfaces obtained from point clouds using digital photogrammetry from drones. Our methodology allows you to review the quality of the data obtained with photogrammetry and decide whether these measurements are representative of the discontinuity surfaces that they analyze. It consists of three steps, the first one being a shape analysis that allows defining which statistical model should be used: Fisher for circularly symmetric clusters or Bingham fits better for axially symmetric clusters. This step also makes the most significant difference to other works since our methodology starts from the premise that not all discontinuity surfaces are flat. Therefore, Fisher parameters do not allow validating data that do not correspond to a plane. In the second step of the methodology, we calculate the consistency parameters that depend on the statistical model defined in step 1. The parameters are similar for both models; both estimate κ which indicates how much the sample is concentrated around the mean orientation and validates the existence of this and which is the value of the generating angle of a cone with a 95 % confidence limit that it contains within the mean orientation. Finally, step 3 is used when there are control measurements to compare the point cloud data and define if both samples characterize the same discontinuity surface in the rock mass. The results obtained on a rock outcrop allowed us to observe that the measurements obtained from the drone faithfully represent the discontinuity surface analyzed when these were compared with the measurements made manually with the compass. Furthermore, the dispersion parameters (

The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of genuine nonlinearity, namely the ability for shocks and rarefactions to form instead of contact discontinuities. In the context of the Whitham modulation equations, this paper demonstrate that a loss of genuine nonlinearity leads to the appearance of a dispersive set of dynamics in the form of the modified Korteweg de-Vries equation governing the evolution of the waves instead. Its form is universal in the sense that its coefficients can be written entirely using linear properties of the underlying waves such as the conservation laws and linear dispersion relation. This insight is applied to two systems of physical interest, one an optical model and the other a stratified hydrodynamics experiment, to demonstrate how it can be used to provide insight into how waves in these systems evolve when genuine nonlinearity is lost.

The main purpose of this paper is to extend the result obtained by Beirao da Veiga (2000) from the whole-space case to slip boundary cases. Denote by u two components of the velocity u. To fix ideas set ū = (u1,u2, 0) (the half-space) or $${\boldsymbol{\bar u}} = {\hat u_1}{\hat e_1} + {\hat u_2}{\hat e_2}$$ (the general boundary case (see (7.1))). We show that there exists a constant K, which enjoys very simple and significant expressions such that if at some time τ ∈ (0,T) one has $$\lim {\sup _{t \to \tau - 0}}\left\| {{\boldsymbol{\bar u}}(t)} \right\|_{{L^3}(\Omega )}^3 < \left\| {{\boldsymbol{\bar u}}(\tau )} \right\|_{{L^3}(\Omega )}^3 + K$$ , then u is continuous at τ with values in L3(Ω). Roughly speaking, the above norm-discontinuity of merely two components of the velocity cannot occur for steps’ amplitudes smaller than K. In particular, if the above condition holds at each τ ∈ (0,T), the solution is smooth in (0,T) × Ω. Note that here there is no limitation on the width of the norms $$\left\| {{\boldsymbol{\bar u}}(t)} \right\|_{{L^3}(\Omega )}^3$$ . So K is independent of these quantities. Many other related results are discussed and compared among them. This is a second main aim of this paper. New results are proved in Sections 5–7.

Most of the rock masses in the outer crust of the Earth are discontinuous. They are divided by joints, faults, fractures, etc. And those discontinuities, generally referred to as joints, greatly affect the property of the rock masses. The paper experimentally investigates the stress wave propagation crossing the jointed specimens. The tests were conducted on the split Hopkinson pressure bar (SHPB). The test specimens consist of two parts cast by cement mortar. Both parts have an irregular surface, and they were designed to match each other completely. The surfaces where two parts meet make an artificial joint. The surfaces of the joints were scanned by a three-dimensional scanner to obtain its actual topography and then to calculate the roughness of the surface, i.e., the joint roughness coefficient (JRC). A set of jointed specimens with JRC ranging from 0 to 20 were made and used in dynamic compression experiments. During the tests, signals were captured by strain gauges stuck on the incident and transmitted bars of the SHPB apparatus. The incident, reflected, and transmitted waves across the jointed specimens were obtained from the test records. We found out that more stress wave would transmit through the jointed specimen with larger JRC. Besides, collected data were processed to get the dynamic stress-strain relation of jointed specimens and the stress-closure curves of the joints. The results show that the joint increases the deformation of the specimen, and the stiffness of the jointed specimen would increase slightly when the joint is rougher.

Computer-aided manufacturing (CAM) software outputs machining data by encoding a tool-path into a series of G-codes which are composed of various lengths of line segments. The discontinuities of these line segments may cause inefficiency for computer numerical control (CNC) system. To achieve high-speed continuous motions, corner smoothing algorithms based on look-ahead methods are widely used. However, it is difficult to meet smoothing trajectories in real-time requirements. Based on machine learning method, in this paper, a support vector machine (SVM) system is presented for directly outputting classification results of the various geometric continuities at the transition corners. The feature values used for generating continuity classification model are extracted from sampling paths of the previous publication work: the machining parameters, length, fairness criteria, the root mean square (RMS) contour errors, and dominant stage type of movement of each sampling path are calculated. The acceleration/deceleration (ACC/DEC) feedrate planning scheme is used to determine the feedrate at the transition corners. Simulations and experiments show that the proposed algorithm can realize accurately and efficiently continuity classification in real-time requirements under the conditions of machining accuracy.

Advanced numerical analysis of structures forces the massive implementation of numerical algorithms, relying on certain convergence of sequences of discrete finite element and similar approximations in spaces of integrable functions, conceding non-physical discontinuities and imperfectness to all numerical results. This is demonstrated on a model example of a thick elastic beam on the 2-parametric Pasternak subsoil. A potential remedy, discussed in this paper, comes from the implementation of available knowledge of analytical solutions in standard variational formulations. The resulting sparse system of linear algebraic equations can be derived without any numerical differentiation; the numerical quadrature is limited to some integrals of explicitly known (MAPLE-generated) functions. Potential generalizations, including selected nonlinear problems, are sketched.

This letter discusses the eco-driving problem, considering both electric and conventional powertrains, and presents a pathway to solving it numerically using an indirect collocation method. Despite the low-order system dynamics, the piecewise fuel/efficiency map, gear shifting, and real-world traffic/road situations bring system discontinuities/switchings and pure state constraints into the problem formulation, which make the problem highly nonlinear and nontrivial to solve. This letter introduces smooth approximations to convert the original problem to an unconstrained (and penalized) smooth boundary-value problem. This approach eliminates the discussion of the switching structure and leads to a lightweight Newton-method-based solution procedure.

A large amount of high-quality teleseismic data is used for common conversion point (CCP) stacking of receiver functions in the Longmenshan area. The results show that a large-scale high-velocity anomaly or lithospheric delamination can completely destroy upper mantle discontinuities or erase the phase boundary of olivine, which is a very important finding and can be used to assess stagnant slabs in the mantle transition zone globally. The deepening region of the 660 km discontinuity beneath the Songpan-Ganzi terrane might indicate that the large-scale high-velocity anomaly in the mantle transition zone is a cold domain and can affect the topography of upper mantle discontinuities.

Seismic coherence is of the essence for seismic interpretation as it highlights seismic discontinuity features caused by the deposition process, reservoir boundaries, tectonic movements, etc. Since its appearance in 1995, seismic coherence has become one of the most popular and highly recognized interpretation tools. In the last 25 years, there have been different kinds of approaches to calculate seismic coherence attributes, such as cross-correlation, semblance, and eigen-structure. We have also seen different coherence enhancement techniques and modified ways for coherence calculation to address different problems in diverse field applications. In this survey, we provide a general overview of seismic coherence, which is commonly used to delineate structural and stratigraphic discontinuities. We cover the development of the seismic coherence attributes via introducing existing approaches for coherence calculation, enhancement, spectral band-limited coherence methods, and offset-/azimuth-limited coherence methods. In addition, we also discuss the possible coherence artifacts and pitfalls. To better compare different techniques, field applications are provided, where different disciplinary coherence attributes with enhancement techniques are calculated for the channel, fault, carbonate karst, and volcano interpretation.

This article considers changes in Morocco’s contentious politics, where the 2011 Arab uprisings have not broken mobilizations from their routinized course. We consider that all the characteristics ...

The shear motion in Newtonian fluids, that is, the fluid vorticity, represents an intrinsic loss mechanism governed by a diffusion equation. Its description involves the trace-free part of the fluid viscous stress tensor. This part is missing in the Biot theory of poroelasticity. As a result, the fluid vorticity is not captured and only one shear wave (S-wave) is predicted. The missing fluid vorticity has implications for the propagation of S-waves across discontinuities. This becomes most apparent in the problem of S-wave propagation across the welded contact of an elastic solid with a porous medium. At such a contact, the no-slip condition between the elastic solid and the constituent parts of the porous medium, the solid frame and the pore fluid, must hold. This requirement translates into a vanishing relative motion of the fluid with respect to the solid frame, that is, the filtration field, at the contact. Nevertheless, our analysis indicates that for the Biot theory, in the low-frequency regime, a nonzero, although insignificantly small, filtration field exists at the contact. However, more importantly, the filtration field is noticeable when the transition to the high-frequency regime occurs. This constitutes a disagreement with the requirement of a no-slip boundary condition and renders the prediction unphysical. This shortcoming is circumvented by including the fluid viscous stress tensor into the poroelastic constitutive relations, as stipulated by the de la Cruz-Spanos poroelasticity theory. Then, a second S-wave is predicted that manifests as the fluid vorticity at the macroscale. This process is distinct from the fast S-wave, the other predicted S-wave akin to the Biot S-wave. We find that the generation of this process at the contact induces a filtration field equal and opposite to that associated with the fast S-wave. Therefore, the no-slip condition is satisfied and the S-wave reflection/transmission across a discontinuity becomes physically meaningful.

In nonparametric regression with jump discontinuities, one major challenge is to determine the number of jumps in a regression curve. Most existing methods to solve that problem are based on either a sequence of hypothesis tests or model selection, by introducing some extra tuning parameters that may not be easy to determine in practice. This article aims to develop a data-driven new methodology for determining the number of jumps, using an order-preserved sample-splitting strategy together with a cross-validation-based criterion. Statistical consistency of the determined number of jumps by our proposed method is established. More interestingly, the proposed method allows us to move beyond just point estimation, and it can quantify uncertainty of the proposed estimate. The key idea behind our method is the construction of a series of statistics with marginal symmetry property and this property can be used for choosing a data-driven threshold to control the false discovery rate of our method. The proposed method is computationally efficient. Numerical experiments indicate that it has a reliable performance in finite-sample cases. An R package jra is developed to implement the proposed method.

The interface crack problems in the two-dimensional (2D) decagonal quasi-crystal (QC) coating are theoretically and numerically investigated with a displacement discontinuity method. The 2D general solution is obtained based on the potential theory. An analogy method is proposed based on the relationship between the general solutions for 2D decagonal and one-dimensional (1D) hexagonal QCs. According to the analogy method, the fundamental solutions of concentrated point phonon displacement discontinuities are obtained on the interface. By using the superposition principle, the hypersingular boundary integral-differential equations in terms of displacement discontinuities are determined for a line interface crack. Further, Green’s functions are found for uniform displacement discontinuities on a line element. The oscillatory singularity near a crack tip is eliminated by adopting the Gaussian distribution to approximate the delta function. The stress intensity factors (SIFs) with ordinary singularity and the energy release rate (ERR) are derived. Finally, a boundary element method is put forward to investigate the effects of different factors on the fracture.

An efficient approach based on the path-independent interaction-integral (I-integral) is suggested for assessing the crack tip loading in elastic structures without having to geometrically model a physical crack. Exploiting just the elastic solution of the uncracked structure, the I-integral is adapted incorporating the closed formulation of crack tip stress and displacement fields of an auxiliary crack, which in this approach is interpreted as hypothetical physical crack. Different specimens and crack configurations are investigated, sparing the expensive numerical modeling of discontinuities, and stress intensity factors are assessed according to the auxiliary crack approach. Various results are verified based on classic crack tip loading analyses.

A singular integral equation method is proposed to analyze the two-dimensional (2D) multiple cracks in anisotropic piezoelectric bimaterial. Using the Somigliana formula, a set of singular integral equations for the multiple crack problems are derived, in which the unknown functions are the derivatives of the generalized displacement discontinuities of the crack surfaces. Then, the exact analytical solution of the extended singular stresses and extended stress intensity factors near the crack tip is obtained. Singular integrals of the singular integral equations are computed by the Gauss–Chebyshev collocation method. Finally, numerical solutions of the extended stress intensity factors of some examples are presented and discussed.

In this paper, a second-order Godunov-type finite volume technique based upon the wave propagation algorithm has been defined which mainly addresses second-order, one-dimensional, macroscopic traffic flow models. Four widely used models that have fundamental differences in terms of the equations form were chosen to evaluate this formula. These models use Riemann’s solution propagating different jump discontinuity from each finite-volume cell interface. The proposed modified flux-wave formula is well-balanced and includes the related source term within the flux-differencing from each cell interface. Therefore, no additional numerical treatment is required with respect to the source terms. The numerical results obtained herein have been compared with high-order relaxations schemes including fifth-order WENO and second-order MUSCL (for three models in a straight homogeneous road) and Roe decomposition technique (for two models in a ring road). The results show that the defined approach is capable to provide stable and realistic response for the macroscopic traffic models without numerical diffusion. Additionally, a very good agreement achieved with the reference solution and also higher order schemes. It is also inferred that the plausibility and positivity conserving conditions have been maintained for the modified flux wave approach for all of the examined models.

Geological discontinuities play a significant role in the assessment of rock slope stability. Rock slope stability has been studied on the main road between Sulav and Amadiya resorts in Duhok governorate on the southern limb of Mateen anticline, to determine the expected rock slides on this road. Five (5) stations were chosen to study these rock slides that may occur on these steep slopes. All these stations within Pila Spi Formation that consists of hard dolomitic limestone and covering the areas from Sulav resort towards Amadiya district with a length of up to 2.5 Kms. The Stereographic analysis was used to study and classify the stability of these slopes. The analysis showed in all stations the possibility of plane sliding to happen on the bedding plane, and the wedge sliding between the bedding plane and planes of all joint sets, as well as the occurrence of rockfall on some stations.

How many ways can we explore the Sun? We have images in many wavelengths and squiggly lines of many parameters that we can use to characterize the Sun. We know that while the Sun is blindingly bright to the naked eye, it also has regions that are dark in some wavelengths of light. All of those classifications are based on vision. Hearing is another sense that can be used to explore solar data. Some data, such as the sunspot number or the extreme ultraviolet spectral irradiance, can be readily sonified by converting the data values to musical pitches. Images are more difficult. Using a raster scan algorithm to convert a full-disk image of the Sun to a stream of pixel values creates variations that are dominated by the pattern of moving on and off the limb of the Sun. A sonification of such a raster scan will contain discontinuities at the limbs that mask the information contained in the image. As an alternative, Hilbert curves are continuous space-filling curves that map a linear variable onto the two-dimensional coordinates of an image. We have investigated using Hilbert curves as a way to sample and analyze solar images. Reading the image along a Hilbert curve keeps most neighborhoods close together as the resolution (i.e., the order of the Hilbert curve) increases. It also removes most of the detector size periodicities and may reveal larger-scale features. We present several examples of sonified solar data, including sunspot number, extreme ultraviolet (EUV) spectral irradiances, an EUV image, and a sequence of EUV images during a filament eruption.

Staring spotlight images with a spatial resolution of up to tens of centimeters are good data sources for urban applications including displacement mapping. However, phase discontinuities, layover, and shadowing effect are also associated with staring spotlight interferograms, adding to the difficulties in height estimation and spatial phase unwrapping. The scattering mechanism of the staring spotlight images in the urban environment is complicated, thus it is difficult to simulate and remove the reference height of staring spotlight interferograms directly. In addition, global spatial phase unwrapping networks tend to smooth phase discontinuities. With the aim of implementing height estimation and phase unwrapping for TerraSAR-X Staring Spotlight interferograms, a workflow for phase unmixing of TerraSAR-X staring spotlight interferograms is proposed in this paper. The PS height is estimated in the baseline domain rather than the spatial domain. Taking into account the length and height change of each connection, the spatial phase unwrapping network is adjusted and segmented into isolated networks. The connected components of the adjusted spatial phase unwrapping network can be identified using graph theory. Spatial phase unwrapping is implemented in individual networks. The unfolded height phase is separated from the unwrapped phase, and the remaining phase is deformation dominated. Compared with the traditional global spatial phase unwrapping method, this study demonstrates the feasibility of the proposed least squares parameter search and graph partition based workflow in urban area, for phase unmixing of TerraSAR-X staring spotlight interferograms in building scale for PS height and deformation, as evidenced by external LiDAR DSM and temperature records.

Discontinuities in the products that occur during manufacture, mounting or upon operation can be missed during non-destructive testing which do not provide their complete detectability at a current level of the technology. Therefore, it is necessary to take into account that certain structural elements may have discontinuities of significant dimensions. We present the results of using the methods of probability theory in studying the residual imperfections that remains in the structure after non-destructive control and repair of the previously identified defects. We used the results of operational control of units carried out by ultrasonic and radiographic methods. We present a method for determining a multifactorial coefficient that takes into account the detectability of defects, the number of control procedures and the errors in the instrumentation and methodological support, as well as a generalized equation for the probability distribution of detecting discontinuities. The developed approach provides assessing of the level of damage to the studied objects, their classification proceeding from the quantitative data and determination of the values of postulated discontinuities for deterministic calculations. The results obtained can be used to improve the methods of monitoring NPP facilities.

This paper presents an experimental investigation about the effect of the hole on the crushing force of thin tubes with the square cross-section under axial impact with a high strain rate. To this ...

A high-resolution population dynamic model has been developed to describe the microstructure evolution in homogeneous precipitation of spherical precipitates during thermal aging. By solving the continuity equation with a high-resolution scheme based on the flux-limiter methods for hyperbolic conservation laws, this model has second-order accuracy in smooth regions and gives well-resolved, nonoscillatory discontinuities formed during the nucleation stage. The predictions of the model are in very good agreement with the reported experimental data for Al–Sc alloys, especially at early aging time. Through fitting the experimental data, a value of $$180 \pm 5{\text{ mJ m}}^{ - 2}$$ is obtained for the $${\text{Al}}/{\text{Al}}_{3} {\text{Sc}}$$ interfacial energy, which is reliable on condition that the aging time is not very long.