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The paper presents a modification of the asymptotic averaging method for solving the homogenization problem of elastic properties for composite materials. The elasticity of the phase interface is taken into account. The conditions of a soft imperfect interface are considered, which account for a displacement jump on the phase boundary. A review of the interface-modeling methods in composite materials is presented. The finite element method is used for the numerical implementation of the averaging method. A model of a interface finite element is proposed. Elastic properties averaging is adapted to the presence of a discontinuity in the displacement field. Application limits of the soft imperfect interface are estimated in terms of interphase layer properties. The identification of the interface parameters using experimental data is considered. Computational experiments are conducted for dispersed-reinforced and unidirectional composite with isotropic inclusion.

In this paper, we have considered a very general van der Waals equation of state to study the one-dimensional motion of magnetogasdynamic (MGD) equations. Transport equations for the discontinuity waves are obtained and studied in detail. The effect of van der Waals excluded volume and the intermolecular force of attraction on the evolution of these waves is studied. Explicit expressions for the jump in the mass density and the magnetic pressure are obtained and analyzed in detail. Finally, the interaction of the weak discontinuity with the characteristic shock is studied and the amplitudes of the reflected and the transmitted waves are obtained.

This paper proposes a numerical approach using the Rayleigh-Ritz method for the free vibration analysis of three-dimensional flexible rectangular fluid tanks with a surface crack. A hypothetical boundary along the crack is assumed, such that it divides the steel wall of the tank into two regions. The total potential energy is obtained from the summation of the potential energy of two regions and the crack. The discontinuity in the wall is created with the local line-springs along the crack, reducing the flexural strength of the steel wall at the crack location. A set of static beam differential equations is used for the shape function of the tank-wall vibration, where the cracks are modeled along the transverse direction of these beams. The velocity potential of the liquid is estimated through the separation of variables and the superposition method. A numerical study was then conducted based on the proposed method. The results indicate that the crack reduces the natural frequencies of the steel tank. It is also worth mentioning that the calculations are performed with acceptable accuracy and low computational costs.

Beam-in-beam large sliding contact exists in simulations of drillstring-riser systems, offshore pipe-in-pipe systems, medical catheter-guidewire-stent systems, among others. Large sliding between the pipes may lead to discontinuity of contact force and non-sparsity of system Jacobian in numeric simulations, which then may result in non-physical disturbances and low efficiency. To overcome this phenomenon, a consistent-contact-force algorithm and a highly efficient implicit-integration scheme are proposed in this paper. Geometric treatments are applied in gap and overlap areas to obtain continuous contact force, in addition to contact-history-based fast detection. The contact force Jacobian is ignored as the flexible multibody system is solved with an inexact Newton iteration and an empirical formula is used to estimate the convergence conditions. Four numeric examples are computed to verify the presented method, including a buckling benchmark and a riser-recoil industrial application. The numeric results show that the proposed method is accurate and highly efficient.

Based on embedded analysis, an accurate pin power reconstruction (PPR) method is proposed for conventional nodal analysis. Unlike the common form function (FF) method, the new PPR method, named the...

We present a new numerical algorithm to solve the recently derived equations of two-moment cosmic ray hydrodynamics (CRHD). The algorithm is implemented as a module in the moving mesh Arepo code. Therein, the anisotropic transport of cosmic rays (CRs) along magnetic field lines is discretised using a path-conservative finite volume method on the unstructured time-dependent Voronoi mesh of Arepo. The interaction of CRs and gyroresonant Alfv\'en waves is described by short-timescale source terms in the CRHD equations. We employ a custom-made semi-implicit adaptive time stepping source term integrator to accurately integrate this interaction on the small light-crossing time of the anisotropic transport step. Both the transport and the source term integration step are separated from the evolution of the magneto-hydrodynamical equations using an operator split approach. The new algorithm is tested with a variety of test problems, including shock tubes, a perpendicular magnetised discontinuity, the hydrodynamic response to a CR overpressure, CR acceleration of a warm cloud, and a CR blast wave, which demonstrate that the coupling between CR and magneto-hydrodynamics is robust and accurate. We demonstrate the numerical convergence of the presented scheme using new linear and non-linear analytic solutions., Comment: 24 pages, 15 figures, submitted to MNRAS, comments are welcome!

In order to investigate the energy transfer mechanism and the nonequilibrium effect during water evaporation in its own pure vapor at low pressures, a series of precise measurements are conducted to obtain the temperature profile near the liquid-vapor interface and the evaporation rates in an annular pool in a closed chamber. The results show that the interface temperature of the vapor side is higher than that of the liquid side when water evaporates in its own pure vapor at low pressures (ranging from 394 to 1467 Pa), the temperature discontinuity across the interface exists in all experimental conditions. The magnitude of the temperature discontinuity is strongly affected by the vapor pressure. A uniform temperature layer with a thickness of about 2 mm is found below the evaporating interface because of the coupling effect of evaporation cooling and thermocapillary convection. The energy required for evaporation is mainly transferred by thermocapillary convection in the uniform temperature layer. Furthermore, the numerical simulation results confirm that the evaporation flux near the cylinders is much larger than that at the middle region, which implies that most of the latent heat required for evaporation is transferred to the interface near the cylinders.

In this study, a computational framework is proposed for thermomechanical contact and debonding problems with proper thermal resistance at the interface. Using the Variational Multiscale (VMS) framework, we present a fully coupled thermomechanical formulation with an explicit expression of the pressure at the contact interface. The formulation considers the quasi-static balance of the momentum and the transient heat transfer problem in a fully coupled fashion. At the interface, two different contact constitutive models are utilized for tension and compression. For tensile problems, in the mechanical phase, a tensile debonding model is employed, whereas in the thermal phase, the displacement-dependent model is employed. For compressive problems, in the mechanical phase, a Coulomb frictional model is employed while in the thermal phase, a pressure-dependent model is embedded. Because of the naturally derived interface stability terms that possess area- and stress-weighting, the proposed VMS formulation accommodates contact/debonding and contact/frictional sliding at the interface due to both thermal and mechanical loading without losing numerical stability. The proposed method is applied to a class of numerical test problems with discontinuity at the interfaces, and good agreement with analytical and numerical data is achieved.

An inverse problem is considered for a system of semilinear elliptic equations that simulate radiative heat transfer with Fresnel matching conditions on the surfaces of discontinuity of the refractive index. The problem consists in finding the right-hand side of the heat equation, which is a linear combination of given functionals from their specified values on the solution. The solvability of the inverse problem is proved without restrictions on smallness. A sufficient condition for the uniqueness of the solution is presented.

The discontinuities in historical Chinese radiosonde datasets are attributed to artificial errors. In order to reflect more realistically basic conditions of the atmosphere over China and provide more reasonable radiosonde data as input to climate change analysis and to atmospheric reanalysis data assimilation systems, this paper proposes a scheme to identify breakpoints and adjust biases in daily radiosonde observations. The ongoing ECMWF ReAnalysis-Interim (ERA-Interim) 12-h forecasts are used as reference series in the scheme, complemented by the ECMWF Twentieth Century Reanalysis (ERA-20C). A series of breakpoint identification schemes are developed and combined with metadata to detect breakpoints. The Quantile-Matching (QM) method is applied to test and adjust daily radiosonde data on 12 mandatory pressure levels collected at 80 sounding stations during 1979–2013. The adjusted temperatures on mandatory levels are interpolated to significant levels for temperature adjustment on these levels. The adjustment scheme not only solves the data discontinuity problem caused by changes in observational instruments and bias correction methods, but also solves the discontinuity problem in the 1200 minus 0000 UTC temperature time series on mandatory levels at individual sounding stations. Before the adjustment, obvious discontinuities can be found in the deviation field between the raw radiosonde data and ERA-Interim reanalysis with relatively large deviations before 2001. The deviation discontinuity is mainly attributed to the nationwide upgrade of the radiosonde system in China around 2001. After the adjustment, the time series of deviations becomes more continuous. In addition, compared with the adjusted temperature data on mandatory levels over 80 radiosonde stations in China contained in the Radiosonde Observation Correction Using Reanalyses (RAOBCORE) 1.5, the dataset adjusted by the method proposed in the present study exhibits higher quality than RAOBCORE 1.5, while discontinuities still exist in the time series of temperature at 0000, 1200, and 1200 minus 0000 UTC in RAOBCORE 1.5.

There are some special phenomena like longitudinal end effect, saturation effect, skin effect, edge effect, and half-filled slots which make the single-sided linear induction motor (SSLIM) analysis more complicated compared to its rotary counterparts. Finite element method (FEM) can be the best choice for complete modeling of SSLIM considering all phenomena. But it is not possible to include the non-linear magnetization curve of iron into the time-harmonic FEM analysis. Thus, this article proposes a 2-D time-harmonic FEM considering all phenomena as well as the non-linear magnetization characteristics of iron using appropriate approximation. In order to overcome the Lorentz method calculation error of vertical force caused by inherent discontinuity of magnetic field intensity at the boundaries of elements, a combined Lorentz–Maxwell method is presented. Validity of the methods and final results is proved by comparing the results with analytical results and experimental measurements.

The discharging process is ubiquitous in the production of food and pharmaceuticals. Usually, discharging devices have relatively simple structures. But unlike the outflow of liquids, due to the transitions in granular flow it is considered a discontinuous process and there is not yet a complete theoretical framework that describes granular outflow from an orifice. In this work, the transition of granular kinematic states near to the outlet is examined experimentally. The transition boundary of a kinematic discontinuity was not found in the study, but there was a transition boundary of velocity profile including velocity gradient transition and motion direction transition near to the outlet. Furthermore, two methods to determinate the transition boundary of velocity profile were developed. This work further clarifies the mechanism and position of flow transition near the outlet during the discharge of grains. This can not only help to solve problems in the discharging process, but also help to enhance our understanding of complex flow properties of granular solids confined by a bottleneck.

In soft and conformal contacts, the assumptions made in the Hertz theory are violated to some extent, leading to inaccurate outcomes. An alternative contact approach is the Kelvin-Voigt model that suffers from a discontinuity existing in its constitutive law. The finite element method is also expensive computationally to be used for contact simulation. The present study introduces a concept to simulate either soft or conformal contacts and develops mathematically closed-form contact models, which are nonlinear, promising, and easy-to-implement while resolving the discontinuity issue with the Kelvin-Voigt model. Two demonstrative applications, i.e. a ball-on-plate contact and a spherical joint, are considered. The developed approaches are integrated into forward dynamics algorithms to be assessed and compared against available contact approaches in the literature. Moreover, a finite element analysis is constructed for comparison purposes. It can be concluded that the proposed contact models are robust and easy-to-implement for non-Hertzian soft and conformal contacts.

The sliding motion along the boundaries of discontinuous regions has been actively studied in B-spline free-form deformation framework. This study focusses on the sliding motion for a velocity field-based 3D+t registration. The discontinuity of the tangent direction guides the deformation of the object region, and a separate control of two regions provides a better registration accuracy. The sliding motion under the velocity field-based transformation is conducted under the [Formula: see text] -Rényi entropy estimator using a minimum spanning tree (MST) topology. Moreover, a new topology changing method of the MST is proposed. The topology change is performed as follows: inserting random noise, constructing the MST, and removing random noise while preserving a local connection consistency of the MST. This random noise process (RNP) prevents the [Formula: see text] -Rényi entropy-based registration from degrading in sliding motion, because the RNP creates a small disturbance around special locations. Experiments were performed using two publicly available datasets: the DIR-Lab dataset, which consists of 4D pulmonary computed tomography (CT) images, and a benchmarking framework dataset for cardiac 3D ultrasound. For the 4D pulmonary CT images, RNP produced a significantly improved result for the original MST with sliding motion (p

This paper presents a flexible and adaptive fourth-order diffusion model for image noise removal. A flexible fourth-order diffusion equation is first presented. Then, an efficient and robust contextual discontinuity indicator based on the bilateral kernel is constructed and combined with the local discontinuity indicator (local spatial gradient) to get the desired adaptive fourth-order diffusion model. The proposed model degenerates to an anisotropic equation which performs the tangent smoothing for sharpening the inter-object boundaries and reduces to an isotropic equation which implements the fast smoothing in the homogenous regions for noise removal. Moreover, it is able to overcome the staircase artifacts arisen by most of second-order diffusion models. Experimental results are provided to validate the effectiveness of the proposed model with regard to objective evaluation metrics and visual performance which outperform those of some benchmark models.

In engineering structures, such as large fluid-filled pipelines, continuous monitoring for damage detection is needed. To address this issue, we study the generation of guided waves in pipes by using a circumferential strip of macro fiber composite transducer to generate and detect torsional and flexural lower modes. The propagated elastic waves and their resulting reflected and mode-converted signals at the interaction wave discontinuity are post-processed with basis pursuit denoising using a Gabor dictionary to improve signal identification. Numerical results are obtained and experimentally tested on a stainless-steel pipe A-36 (43.6 and 48.2 mm in inner and outer diameter). It was found that the proposed method makes it possible to identify an artificial discontinuity by detecting the scattered wave and converted modes of a propagated torsional wave.

In this paper, a new non-gradient-based topology optimization (TO) method proposed. Simulated annealing (SA) with crystallization factor used to generate new solutions. During this process, the newly generated solutions evaluated based on the SA concept. A density filter also applied to remove the discontinuity of shapes. The innovation of this method is applying the history of accepted or rejected solutions by the crystallization factor. Results of compliance minimization of cantilever and MBB-beams from the proposed method compared with the results of gradient-based methods. The main advantage of the proposed method is the improvement of convergence of the results as well as no need for the derivative of the objective function.

This paper discusses the well posedness of an initial value problem describing the motion of a Bingham fluid in a basin with a degenerate bottom topography. A physical interpretation of such motion is discussed. The system governing such motion is obtained from the Shallow Water-Bingham models in the regime where the Froude number degenerates, i.e taking the limit of such equations as the Froude number tends to zero. Since we are considering equations with degenerate coefficients, then we shall work with weighted Sobolev spaces in order to establish the existence of a weak solution. In order to overcome the difficulty of the discontinuity in Bingham's constitutive law, we follow a similar approach to that introduced in [G. DUVAUT and J.-L. LIONS, Springer-Verlag, 1976]. We study also the behavior of this solution when the yield limit vanishes. Finally, a numerical scheme for the system in 1D is furnished.

The detection of event GW170817 and its electromagnetic counterpart started the era of multi‐messenger astronomy with gravitational waves. The observational constraints from this event and the estimation of mass and radius of PSR J0030 + 0451 is being used to get insights related to the nature of matter inside these compact objects. In this work, we construct hybrid equations of state using modern parametrizations of the relativistic mean field model for the outer core and a generalization of the Constant Speed of Sound parametrization that allow to study sharp sequential phase transitions in the inner core. Moreover, we study non‐radial perturbations of these stellar configurations using the relativistic Cowling approximation. We focus our attention on the g‐modes that arise due to the sharp phase transitions and show that, due to the second phase transition, a new g‐mode appears, g2‐mode, with frequencies smaller that ∼0.5 kHz.

HighlightsSolved the problem of optimal design, in the sense of minimal film usage, of round bale diameter and height.Necessary and sufficient optimality conditions derived in the form of easy-to-solve cubic equations.Bales of a maximum volume achievable with an actual wrapper and of optimal dimensions ensure minimal film usage.Up to 10% savings in film usage if bale dimensions are optimally designed and wrapping parameters properly selected.Abstract. The combined 3D method is used for wrapping cylindrical bales of agricultural materials based on biaxial rotation of the film applicators. The demand for minimization of plastic film consumption keeps increasing, with the goal to save the environment, reduce plastic costs, and minimize wrapping time. Consequently, methods have been reported to solve the problem of optimal wrapping parameters for the conventional wrapping method. In this article, a model-based problem of such a design based on round bale dimensions (diameter and height) that minimizes film consumption for the combined 3D method is mathematically formulated and analyzed. The film consumption per unit of bale volume is used as a measure of film usage. Generally, it is difficult to find the optimal bale dimensions that minimize the original film usage index, due to the discontinuity of the index. Thus, near-optimal parameters, being as important as optimal parameters for engineering applications, are looked for. The problem of selecting near-optimal bale dimensions was constructed by minimizing the continuous lower bound of the original film usage index. The necessary and sufficient optimality conditions for near-optimal bale dimensions were established in the form of standard cubic equations, which can easily be solved using both analytical and numerical methods. Based on the optimality conditions, analytical and numerical analyses were performed of the influence of film width, pre-assumed bale volume, and numbers of bottom and upper film layers on the near-optimal bale dimensions and film usage. The results indicated that the near-optimal bale diameter and height, hereinafter called optimal, monotonically increase, while the optimal film consumption monotonically decreases, with increasing pre-assumed bale volume. Therefore, it is recommended to use bales of a maximum volume achievable with an actual wrapper and of optimal dimensions, i.e., diameter and height. The film width also influences the optimal bale dimensions and film usage: the wider the film, the smaller the minimal film usage. To confirm the effect of near-optimal bale design on film usage, the errors of the near-optimality were examined for four to sixteen film layers. The results of the numerical experiments demonstrated that for four to sixteen layers of film, there are compositions of the bottom and upper film layers for which the relative near-optimality errors do not exceed 0.01% whenever the optimal bale dimensions are used. Simultaneously, inappropriate selection of wrapping parameters may result in increased film usage, measured by mean relative errors of 1% to 9.5%, which means up to 10% film cost savings when the bale dimensions are optimally designed according to the proposed approach, and the wrapping parameters are appropriately selected. Keywords: 3D bale wrapping, Mathematical model, Minimal film consumption, Round bales, Stretch film usage.

The article solves the problem of surface gravitational waves using the theory of tangential discontinuity between media: air-water. Using the improved equation of mass continuity and taking into account the atmosphere inhomogeneity in the gravitational field of the Earth, it is shown that during wave processes, these two media mutually influence each other, which explains the reason for the formation of a stormy condition over the ocean and the drop in atmospheric pressure before the storm. The mechanism of the formation of the “killer wave” has been established and thus the “greatest mystery of nature” has been solved. The scale of wind and tsunami wavelengths has been established.

This brief proposes a proportional-type angle filter with the variable feedback gain mechanism for motor drives using the encoder for angle feedback. In this case, the angle measurement suffers from discontinuity that has to be made continuous through low-pass filters and observers. There are three features. The first designs a real-time feedback gain update rule to improve the closed-loop filtering performance by magnifying the feedback gain in transient periods. The second introduces the disturbance observer (DOB) in the resultant proportional-type feedback filter for enhanced disturbance attenuation against the speed variations. The third proves the useful properties of the filtering error convergence and performance recovery by investigating the filtering error dynamics. A prototype 500-W permanent-magnet synchronous motor (PMSM) drive system validates the practical advantages of the proposed technique.

The phase discontinuity caused by the geometric mutation has always been a challenging problem in phase unwrapping. To solve this problem, a fast discontinuous phase unwrapping algorithm based on orientation and transformation was proposed. In the proposed algorithm, the structure tensor of the image was used to estimate the orientation of the wrapped phase diagram. The reliable weight coefficient diagram obtained from transformation and difference calculation of the orientation diagram was taken as the weight of the weighted least square method, and used the preprocessed conjugate gradient method to solve iteratively. This algorithm could quickly find the discontinuous regions, and performed a separate phase unwrapping in the discontinuous regions, which had good recognition and unwrapping effect. The principle and implementation steps of the algorithm were described in detail, and the algorithm was verified by simulation and experimental data. The experimental results show that the root mean square error of phase unwrapping is 0.36, which proves that this algorithm can quickly and accurately unwrap the discontinuous wrapped phase.

This paper is devoted to the study of the inflow problem governed by the radiative Euler equations in the one-dimensional half space. We establish the unique global-in-time existence and the asymptotic stability of the viscous contact discontinuity solution. It is different from the case involved with the rarefaction wave for the inflow problem in our previous work [ 6 ], since the rarefaction wave is a nonlinear expansive wave, while the contact discontinuity wave is a linearly degenerate diffusive wave. So we need to take good advantage of properties of the viscous contact discontinuity wave instead. Moreover, series of tricky argument on the boundary is done carefully based on the construction and the properties of the viscous contact discontinuity wave for the radiative Euler equations. Our result shows that radiation contributes to the stabilization effect for the supersonic inflow problem.

Aiming to address the problems of arbitrary orientations, large aspect ratios, and dense arrangements in ship detection, an arbitrary-oriented ship detection method based on RetinaNet is proposed. Our proposed method includes a rotated RetinaNet, a refined network, a feature alignment module, and an improved loss function. First, the rotated RetinaNet achieves rotation detection by using a feature pyramid network, rotated anchors, the skew intersection-over-union (IoU), and skew nonmaximum suppression. Then, the refined network and feature alignment module are introduced to achieve better detection accuracy. Finally, to address the boundary discontinuity, the loss function is improved by introducing the IoU constant factor. Considering the problems with the HRSC2016 dataset, we establish a new dataset with more accurate labels and more images and object samples. Through an ablation study, we thoroughly analyze the validity of the proposed rotated RetinaNet, feature alignment module, and improved loss function. The experimental results show that our method is superior to other state-of-the-art methods.

In this paper, we are concerned with nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler fluids. We focus on the case when the vorticity function has a simple discontinuity, which corresponding to a jump in vorticity at the boundary of the cross-section of the vortex ring. Using the vorticity method, we construct a family of steady vortex rings which constitute a desingularization of the classical circular vortex filament in several kinds of domains. The precise localization of the asymptotic singular vortex filament is proved to depend on the circulation and the velocity at far fields of the vortex ring, and the geometry of the domains. Some qualitative and asymptotic properties are also established.

In this work we consider differential equations of the type $$\pm\, u^{(k)} = f(u), $$ and study the extinction profile of their solutions. Emphasis is placed on the special case $-u^{(4)} = sgn(u)$, which is related to the Kuramoto-Sivashinsky equation. In this case we describe in more detail the extinction phenomenon and prove a conjecture by Galaktionov and Svirshchevskii.

Recent studies have shown that the melting of two-dimensional crystals can be either continuous or discontinuous, relying on multiple parameters such as particle stiffness, density, and particle size dispersity. However, what determines the continuity or discontinuity of the two-dimensional melting remains elusive. Here we study the two-dimensional melting of binary mixtures of soft-core particles. The two particle species are different in either particle size or particle stiffness. Starting with the mono-component systems which exhibit discontinuous hexatic-liquid transition, we gradually increase the particle size or stiffness dispersity and find that the hexatic-liquid coexistent region shrinks and eventually vanishes above a critical dispersity. Therefore, the growth of disorder caused by the particle size or stiffness dispersity leads to the discontinuous-continuous transition of the two-dimensional melting. We further find that as long as the melting is continuous the defect concentrations on the boundary between hexatic and liquid phases remain almost constant, accompanied by an almost constant correlation length. These characteristic defect concentrations and correlation length are universal and independent of particle interactions, temperature, and type of particle dispersity, which act as signatures of the continuous two-dimensional melting.

Metasurface technology has become one of the promising structures for controlling and manipulating of the phase and amplitude characteristics of the electromagnetic waves in recent years. For this reason, the determination of the exact diffracted fields is also crucial especially in the edge or discontinuity points of these types of materials. In the paper, the discontinuity problem by the junction between the layers of an anomalously reflecting metasurface and an impedance half-screen is taken into consideration. These two planar layers have a common edge discontinuity where the diffracted waves occur. The scattered waves from the structure are obtained by the novel technique of the method of transition boundary, which especially offers the relation between the diffracted and scattered geometrical optical waves at the transition boundaries. The diffracted wave expressions are derived by the technique of the method of transition boundary and the uniform wave expressions are obtained by the method of uniform geometrical theory of diffraction. The diffracted and total wave results of the method of transition boundary are also compared and verified by the well-known theory of physical optics. The behaviors of the total wave and its components are analyzed numerically.

An automatic recognition of discontinuities in borehole images is a desirable way to overcome the inefficiency and inconsistency inherent in the conventional method of manual annotation. The rough borehole walls and prominent noise failed the application of existing recognition methods to borehole images taken in the coal-measure strata. This paper presents a novel approach to automatically convert coal-measure strata borehole images into identified discontinuity maps. The developed procedure formed an integrated feature representation for the borehole image through combining the color information of image and the textural features generated from multi-channel filtering. Image regions containing discontinuities are then separated from other regions by implementing fuzzy c-means clustering on the acquired feature representation. The identification of discontinuities is finally accomplished by searching for four predefined patterns (named topographic model) on the intensity transection of image regions. The proposed method is proven to be superior in the respects of noise suppression, discontinuity positioning, and recognition completeness.

Altres ajuts: Universidad Politécnica de Madrid Young Researchers (Grant Number: VJIDOCUPM18MGB) i ICREA This article presents an exhaustive study of the sensitivity in reflective-mode phase-variation sensors based on an open-ended transmission line with a step-impedance discontinuity. Such discontinuity delimits the sensing region (which extends up to the open end of the so-called sensing line), from the transmission line section connected to the input port (design line), which is used to enhance the sensitivity. The theoretical analysis provides the design guidelines to achieve a sensor with high sensitivity compared with the one based on an ordinary (uniform) line with a similar length. In particular, it is shown that for sensitivity optimization, the electrical length of the design line must be set to 90° (or an odd multiple), whereas either a 90° (or an odd multiple) or a 180° (or an even or odd multiple) sensing line can be alternatively used in order to maximize the sensitivity. It is shown that the impedance contrast, defined as the ratio between the characteristic impedances of the design and sensing line, is a key parameter for sensitivity enhancement, and it must be as low or as high as possible for the 90° or 180° sensing lines, respectively. For validation purposes, two prototype devices (one with a 90° and the other one with a 180° sensing line) have been designed and fabricated following the design guidelines. Such devices have been tested by loading the sensing region with several materials with different dielectric constants. Compared with the ordinary line-based sensors, it is found that the maximum sensitivity is enhanced by a factor of 19.7 and 11.4 in the phase-variation sensor based on a 90° and 180° sensing line, respectively. Finally, the sensor concept is generalized to a multisection step-impedance transmission line as a means of further increasing the sensitivity, and a prototype device exhibiting 528.7° maximum sensitivity is implemented.

When interpolating data with certain regularity, spline functions are useful. They are defined as piecewise polynomials that satisfy certain regularity conditions at the joints. In the literature about splines it is possible to find several references that study the apparition of Gibbs phenomenon close to jump discontinuities in the results obtained by spline interpolation. This work is devoted to the construction and analysis of a new nonlinear technique that allows to improve the accuracy of splines near jump discontinuities eliminating the Gibbs phenomenon. The adaption is easily attained through a nonlinear modification of the right hand side of the system of equations of the spline, that contains divided differences. The modification is based on the use of a new limiter specifically designed to attain adaption close to jumps in the function. The new limiter can be seen as a nonlinear weighted mean that has better adaption properties than the linear weighted mean. We will prove that the nonlinear modification introduced in the spline keeps the maximum theoretical accuracy in all the domain except at the intervals that contain a jump discontinuity, where Gibbs oscillations are eliminated. Diffusion is introduced, but this is fine if the discontinuity appears due to a discretization of a high gradient with not enough accuracy. The new technique is introduced for cubic splines, but the theory presented allows to generalize the results very easily to splines of any order. The experiments presented satisfy the theoretical aspects analyzed in the paper. We would like to thank the anonymous referees for their valuable comments, which have helped to significantly improve this work. This work was funded by project 20928/PI/18 (Proyecto financiado por la Comunidad Autónoma de la Región de Murcia a través de la convocatoria de Ayudas a proyectos para el desarrollo de investigación científica y técnica por grupos competitivos, incluida en el Programa Regional de Fomento de la Investigación Científica y Técnica (Plan de Actuación 2018) de la Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia), by the national research project MTM2015- 64382-P (MINECO/FEDER) and by NSF grant DMS-1719410.

This paper deals with hyperbolic conservation laws exhibiting a flux discontinuity at the origin and which does not admit a weak solution satisfying the Rankine–Hugoniot jump condition. We therefore seek unbounded solutions in the form of shadow waves supported by at the origin. The shadow waves are defined as nets of piecewise constant functions approximating a shock wave to which we add a delta function and possibly another unbounded part.

The Stefan two-phase problem with an internal source, as well as the heat conduction problem for rectangular and curvilinear regions, has been solved by the method of rapid sine-expansion, which involves the Fourier series. The problem of heat conduction in a body of rectangular form was solved in a general form with the Dirichlet conditions and an internal heat source by the method of rapid expansion, and thereafter the problem for a body of curvilinear shape. The solutions obtained were used in considering the Stefan problem with unknown curvilinear interface. Expressions are presented for matching the input data of the problem, on satisfaction of which the solution will be universally continuous everywhere in the region of the rectangle together with derivatives up to the sixth order inclusive. The nonfulfillment of these conditions leads to the discontinuity of the solution at the corner points. The algorithms of the solution of problems in rectangular and curvilinear regions, as well as of the Stefan twophase problem, are written. The solution for the rectangular region is represented in an explicit form, whereas the solution for the curvilinear region and the solution of the Stefan problem are reduced to a closed algebraic system of equations of small volume.

A common defect found when reproducing old vinyl and gramophone recordings with mechanical devices are the long pulses with significant low-frequency content caused by the interaction of the arm-needle system with deep scratches or even breakages on the media surface. Previous approaches to their suppression on digital counterparts of the recordings depend on a prior estimation of the pulse location, usually performed via heuristic methods. This paper proposes a novel Bayesian approach capable of jointly estimating the pulse location; interpolating the almost annihilated signal underlying the strong discontinuity that initiates the pulse; and also estimating the long pulse tail by a simple Gaussian Process, allowing its suppression from the corrupted signal. The posterior distribution for the model parameters as well for the pulse is explored via Markov-Chain Monte Carlo (MCMC) algorithms. Controlled experiments indicate that the proposed method, while requiring significantly less user intervention, achieves perceptual results similar to those of previous approaches and performs well when dealing with naturally degraded signals.

In the present work, damage produced by a crack in a statically loaded beam is first evaluated. Subsequently, an attempt is made to repair the effect of the crack by attaching a piezoelectric patch to the beam as an actuator. Static analysis of PZT patched cracked beam along with rotational spring is performed using Ritz method. Subsequently, a finite element analysis is performed by using ABAQUS 6.12 to collate the analytical results. It is shown in the study that when PZT patch is subjected to external electric field, it yields a local reactive moment, which counters the crack effects. An equation is procured in order to compute the required actuation voltage for repairing of cracks. A parametric study is performed for various boundary conditions and loading patterns. It is distinctly noticed that the technique nullifies the discontinuity in slope curve which develops due to a crack.

This paper investigates fundamental properties of a new class of dynamical systems, which are everywhere smooth except for a codimension-$n$ discontinuity manifold with an arbitrary positive intege...

Regression discontinuity (RD) designs are increasingly common in political science. They have many advantages, including a known and observable treatment assignment mechanism. The literature has emphasized the need for “falsification tests” and ways to assess the validity of the design. When implementing RD designs, researchers typically rely on two falsification tests, based on empirically testable implications of the identifying assumptions, to argue the design is credible. These tests, one for continuity in the regression function for a pretreatment covariate, and one for continuity in the density of the forcing variable, use a null of no difference in the parameter of interest at the discontinuity. Common practice can, incorrectly, conflate a failure to reject evidence of a flawed design with evidence that the design is credible. The well-known equivalence testing approach addresses these problems, but how to implement equivalence tests in the RD framework is not straightforward. This paper develops two equivalence tests tailored for RD designs that allow researchers to provide statistical evidence that the design is credible. Simulation studies show the superior performance of equivalence-based tests over tests-of-difference, as used in current practice. The tests are applied to the close elections RD data presented in Eggers et al. (2015b).

In this paper we propose an explicit predictor-corrector finite difference scheme to numerically solve one-dimensional conservation laws with discontinuous flux function appearing in various physical model problems, such as traffic flow and two-phase flow in porous media. The proposed method is based on the second-order MacCormack finite difference scheme and the solution is obtained by correcting first-order schemes. It is shown that the order of convergence is quadratic in the grid spacing for uniform grids when applied to problems with discontinuity. To illustrate some properties of the proposed scheme, numerical results applied to linear as well as non-linear problems are presented.

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

Method of successive approximations for the solution of the Wiener---Hopf functional equations system is offered. The method uses the presentation of matrix coefficient of the system as a sum of two matrices, where the first matrix assumes the exact factorization, and the second matrix --- matrix-perturbation --- is much smaller than the first matrix in the domain of system definition. Solution of the system is sought in the form of expansions in powers of the matrix-perturbation. At each step of the approximation the solution of the system is carried out by means of the Wiener---Hopf method using factorization of the main component of the matrix coefficient. The example of the use of method is considered for the solution of the problem about the calculation of the pre-fracture zone parameters in connecting material near the tip of the interfacial crack outcoming from the angular point of the broken interface of two different materials. The zone is modeled by the discontinuity line of displacement, on which the stresses meet the Mises---Hill failure criterion. It is shown that under certain conditions, already in the first approximation, the method allows to obtain solutions with permissible accuracy.

We consider Sturm-Liouville problems with a discontinuity in an interior point, which are motivated by the inverse problems for the torsional modes of the Earth. We assume that the potential on the right half-interval and the coefficient in the right boundary condition are given. Half-inverse problems are studied, that consist in recovering the potential on the left half-interval and the left boundary condition from the eigenvalues. If the discontinuity belongs to the left half-interval, the position and the parameters of the discontinuity also can be reconstructed. In this paper, we provide reconstructing algorithms and prove existence of solutions for the considered inverse problems. Our approach is based on interpolation of entire functions.

Purpose. The purpose of the work is to determine and analyze the technical parameters of the bench for railway wheels complex tests, providing for the combination of fatigue and contact strength tests, their simultaneous performing on same test-bench. Methodology. Determination of the technical parameters of the test-bench was carried out based on comparing the characteristics of fatigue and contact strength tests of railway wheels. Requirements for fatigue tests and related equipment are determined based on an analysis of the current regulations and patent review. A model of the contact strength test-bench with the introduction of necessary changes in terms of ensuring the cyclicity of the working effort application was adopted as the basic model for the development of a complex test-bench. The criterion for the possibility of complex tests, involving the simultaneous testing of railway wheels for fatigue and contact strength, was the dependence of the test-bench roller diameter on the parameters of the tested wheel, the wheelset axle load, which includes the tested wheel and the wheel material endurance limit. Findings. The analysis of the obtained dependence showed that the roller diameter as a function of the load in the contact zone of the “wheel – roller” pair has second order discontinuity in the section where this load changes from the minimum to the maximum value. Analytical dependence is also presented and analyzed in graphical form. The generalization of the results obtained made it possible to conclude that it is impossible to carry out complex tests of railway wheels, which provide for the combination of fatigue strength tests with contact strength tests, subject to their simultaneous holding at the same test-bench. Originality. For the proposed scheme of the bench for complex tests of railway wheels, for the first time, we obtained the dependence linking the parameters of the test wheel, the parameters of the bench, the wheel pair axle load and the wheel material endurance limit. Practical value. The results obtained can be used as a basis for the development of new test-benches for railway wheels.

Periodic motions in a discontinuous dynamical system are studied. The discontinuous dynamical system consists of three distinct linear dynamical systems with two different circular boundaries. Analytical conditions for switching and sliding motions at the two circular boundaries are developed. From such analytical conditions, periodic motions in discontinuous dynamical systems can be determined through specific mapping structures. Illustrations give periodic motions in discontinuous dynamical systems, which are different from the continuous dynamical systems. In different domains, the motions are different, and the discontinuity of the periodic motions at the boundaries is observed, and the sliding motion on the boundaries is also a portion of periodic motion. Such periodic motions in discontinuous dynamical systems do not have any Fourier series. The methodology presented in this paper can be applied to other discontinuous dynamical systems. The circular boundaries can be treated different energy levels as control conditions in engineering systems.

Carbon Nanotubes (CNTs) are considered a promising reinforcement for engineering advanced structures, such as aerospace applications. It became inevitable to tailor structures not only by conventional geometric but also by mechanical properties tailoring, to acquire the maximum load-carrying capacity. Therefore, this research presented a novel Finite Element (FE) modeling of Axially Functionally Graded CNT Reinforced Composite (AFG-CNTRC) beams, based on Timoshenko beam theory. However, an obstacle is raised due to properties discontinuity produced between consecutive elements in axial gradation. A solution is proposed based on the ladder-pattern concept. It defined a locally specific value at each element, satisfying the overall required distribution. It followed by a convergence test, static, and dynamic analysis with comprehensive parametric studies. The obtained results showed that the model is convergent, accurate, free of shear-locking, and suitable for axial gradation. Moreover, this study introduced an advanced technique for axial properties tailoring, utilizing privileges of CNT and aggregation. The longitudinal tailoring depends on both the CNT orientation angle and gradation index, which played a crucial role in response control and adjusting beam stiffness together with strength. This approach could solve enormous engineering problems, especially at critical cross-sections design and constraint response, without affecting the total weight.

Permanental sequences with non-symmetric kernels that are generalization of the potentials of a Markov chain with state space { 0 , 1 ∕ 2 , … , 1 ∕ n , … } and a single instantaneous state that was introduced by Kolmogorov, are studied. Depending on a parameter in the kernels we obtain an exact rate of divergence of the sequence at 0, an exact local modulus of continuity of the sequence at 0, or a precise bounded discontinuity for the sequence at 0.

This article proposes a novel decomposition technique to address the challenges of electromagnetic (EM) parametric modeling, where the values of geometrical parameters change in a large range. In this method, a systematic and automated algorithm based on second-order derivative information is proposed to decompose the overall geometrical range into a set of subranges. Using the proposed technique, a smooth region is decomposed into a few large subregions, while a highly nonlinear region is decomposed into many small subregions. The proposed technique provides an efficient mathematical methodology to perform the decomposition in a systematic and automated process. An artificial neural network (ANN) model with a simple structure, hereby referred to as a submodel, is developed with geometrical parameters as variables in each subregion. When the values of geometrical parameters change from the region of one submodel to another submodel, the discontinuity of the EM responses is observed at the boundary between the adjacent submodels. There are many submodel boundaries in the overall model resulting in the complex multidimensional discontinuity problem. A submodel modification process is proposed to solve this multidimensional discontinuity problem to obtain a continuous model over the entire region. Parallel data generation, parallel submodel training, and parallel submodel modification are proposed to speed up the modeling development process. Compared with standard modeling methods using a single model to cover the entire wide geometrical range, the proposed method can obtain better model accuracy with short model-development time. Two microwave filter examples are used to illustrate the validity of the proposed technique.

We consider an inhomogeneous boundary value problem for a system of semilinear elliptic equations modeling radiative heat transfer with Fresnel matching conditions on the surfaces of discontinuity of the refractive index. The unique solvability of the boundary value problem is proved without requiring the initial data to be small.

This paper investigates the variational finite element formulation and its numerical implementation of the damage evolution in solids, using a new discrete embedded discontinuity approach. For this purpose, the kinematically optimal symmetric (KOS) formulation, which guarantees kinematics, is consistently derived. In this formulation, rigid body motion of the parts in which the element is divided is obtained. To guarantee equilibrium at the discontinuity surfaces, the length of the discontinuity is introduced in the numerical implementation at elemental level. To illustrate and validate this approach, two examples, involving mode-I failure, are presented. Numerical results are compared with those reported from experimental tests. The presented discontinuity formulation shows a robust finite element method to simulate the damage evolution processes in quasi-brittle materials, without modifying the mesh topology when cohesive cracks propagate.

In beginning textbooks, bounded real valued functions with domain R and one point of discontinuity are usually defined piecewise with each piece being given by a formula. When I first took calculus...