Discontinuous Research Articles

A TWO-POINT COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF ONE-DIMENSIONAL HYPERSINGULAR INTEGRAL EQUATIONS ON NONUNIFORM PARTITIONS

A quadrature formula has been constructed for calculating the hypersingular integral over a segment, which uses the ends of the segment partition intervals as nodes of piecewise constant interpolation of the integral density, as well as specially selected collocation points. A distinctive feature of the proposed quadrature formula is the ability to calculate the integral of functions that suffer a finite number of discontinuities of the first kind on the integration interval. On the basis of quadrature formula constructed, a numerical scheme for solving the characteristic hypersingular integral equation on non-regular grid is developed. Estimate of the rate of convergence of approximate solutions to exact ones is proved in the class of piecewise Ho¨lder functions.

Comprehensive study on microwave inspection of internal pipe wall thinning: Discontinuities, reflections and signals

Microwave inspection of internal pipe wall thinning (PWT) relies on reflections occurring at locations where inner radius changes. Reflections also occur at other discontinuities, such as air gaps and the pipe end, which seriously contaminate the measurement signals for PWT and pose challenges to PWT characterization. This study clarified the mechanism of reflections from different types of discontinuities using theoretical, analytical, and numerical solutions. By establishing a formula to calculate the characteristic impedance of a circular waveguide, we were able to analytically compute the scattering parameter S11 for a waveguide with a full-circumferential PWT, providing insights for PWT characterization. Furthermore, we defined the number of repetitions per unit of frequency as Ω and represented the measured S11 signals in the Ω− domain. The correspondence between Ω and traveling distance enables localization of discontinuities without considering frequency-dependent propagation velocity. The Ω domain representations primarily associated with PWT were isolated by band and converted back to the frequency domain, allowing for more effective PWT characterization.

Reexamining developmental continuity and discontinuity in the 21st century: Better aligning behaviors, functions, and mechanisms.

Developmental science aims to explain development across the lifespan. Jerome Kagan observed that the same behavior can occur for different reasons, and differing behaviors can occur for the same reason. To help account for persistence, desistence, and transformation of behavior across development, Kagan introduced various types of continuity and discontinuity of forms and functions of behavior. This framework provides opportunities for identifying explanatory mechanisms in behavior development. However, misconceptions remain in applying the concepts that Kagan introduced. Much of the literature assumes developmental continuity in constructs without examining whether assumptions are supported, leading to faulty developmental inferences. For instance, the use of the same measure across time to assess development assumes that the behavior occurs for the same reason across time (homotypic continuity). In addition, just because one behavior predicts a different behavior at a later time does not necessarily indicate that age-differing behaviors occur for the same reason (heterotypic continuity). This review aims to advance conceptualizations of continuity and discontinuity from a contemporary perspective with aims to improve mechanistic understanding of behavior development across the lifespan. To better align behaviors, functions, and mechanisms, research should (a) examine (dis)continuity of individual behaviors rather than merely syndromes, (b) identify the function(s) of the given behavior(s), and (c) identify the cognitive and biological processes that underlie the behavior-function pairs. Incorporating examples from research on development of humans and nonhuman animals, I discuss challenges from work that has followed Kagan's ideas and ways to advance understanding of continuity and discontinuity across development. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Magnetic resonance classification proposal for medial gastrocnemius muscle injuries.

Calf muscle injuries are common among athletes and occupational populations, with highly variable recovery times that are challenging to be predicted at the initial clinical evaluation. Specifically, in distal gastrocnemius muscle injuries, an ultrasound-based severity classification has shown to be useful for estimating the recovery time. According to the location of lesions and the recognition of some US signs, four types of injuries of the distal gastrocnemius muscle were described. Since magnetic resonance imaging (MRI) has proven to be useful in diagnosing and prognosticating muscle injuries by assessing the extent of affected connective tissue, a specific MRI protocol involving T1-weighted and fluid-sensitive static and dynamic acquisitions has been developed aimed to characterize the four types of injuries. We here describe the characteristics of this new MRI protocol and the interpretation of images, which will be useful to improve the recognition of acute and delayed distal gastrocnemius muscle injuries. The proposed classification includes: myoaponeurotic muscle injury without aponeurotic discontinuities (type 1), myoaponeurotic muscle injury with aponeurotic discontinuities (type 2), isolated free aponeurosis discontinuity (type 3), and a mixed myoaponeurotic-aponeurotic injury pattern (type 4). A comprehensive understanding of the MRI features associated with each injury type, in conjunction with multidisciplinary team collaboration, is essential for optimizing the athlete's recovery and return to play.

Whitham modulation theory and the classification of solutions to the Riemann problem of the Fokas–Lenells equation

AbstractIn this work, we explore the Riemann problem of the Fokas–Lenells (FL) equation given initial data in the form of a step discontinuity by employing the Whitham modulation theory. The periodic wave solutions of the FL equation are characterized by elliptic functions along with the Whitham modulation equations. Moreover, we find that the signs for the velocities of the periodic wave solutions remain unchanged during propagation. Thus, when analyzing the propagation behavior of solutions, it is necessary to separately consider the clockwise (negative velocity) and counterclockwise (positive velocity) cases. In this regard, we present the classification of the solutions to the Riemann problem of the FL equation in both clockwise and counterclockwise cases for the first time.

Hybrid Mobile Robot Path Planning Using Safe JBS-A*B Algorithm and Improved DWA Based on Monocular Camera

This paper addresses the formidable challenge of enabling autonomous navigation in Mobile Robots (MRs), focusing on the development of advanced path planning strategies. Despite their pivotal role in diverse applications, they face challenges in dynamic settings due to limitation in existing Global Path Planning (GPP) and Local Path Planning (LPP) techniques. In response to this, we propose an innovative hybrid path planning approach that enhances the A* algorithm with a risk-aware heuristic function and integrates the Jump Point Search (JPS) technique for route optimization. Additionally, B-spline smoothing is employed for perceptually global trajectory refinement. Our approach also includes an innovative improvement to the Dynamic Window Approach (DWA) to align with the proposed enhanced A* algorithm for effective local navigation. Acknowledging the importance of high-quality input in path planning, we present substantial improvements to the IRDC-Net, a monocular-image semantic-segmentation model that we studied previously. Novel improvements include the integration of quantization and the Adam optimizer, along with the implementation of the Balanced Cross-Entropy loss function. These enhancements not only elevate the output quality of IRDC-Net but also reduce the model’s training parameters. The experimental results demonstrate the performance and viability of the proposed algorithm. Ultimately, the hybrid MR’s path planning algorithm exhibits proficiency across various tasks, particularly in addressing the challenge of evading moving obstacles to ensure the robot’s safety while adhering to the global path.

Specific Characteristics of Numerical Simulation of Mechatronic Systems with PWM-Controlled Drives

This paper explores the features of numerical simulation used to analyze the dynamic behaviour of drives controlled by pulse-width modulators. Modern motor control systems commonly employ pulse-width modulation. Effective numerical modelling of such systems presents unique challenges because the models employed are continuous-event and have hybrid behaviour due to the presence of nonlinear links with discontinuities of the first kind. Therefore, it is essential to have special integration methods with variable steps, which should be factored in when developing the model. This paper shows how these problems are solved when modelling an electric drive with a DC motor using the SimInTech software.

Large eddy simulation of turbulent wake from dual-step cylinders

Numerical computations of the three-dimensional flow past dual-step cylinders using large eddy simulations are performed. The Reynolds number based on the diameter of the large cylinder, ReD, is fixed at 2000. The diameter ratio between the two cylinders is kept constant in all computations, i.e., D/d=2, where d is the diameter of the small cylinder. Investigations are carried out at different aspect ratios (ARs), defined as the ratio between the length of the large cylinder and its diameter L/D=0.2,0.5,1.0,1.5. Vortex dislocation phenomenon is observed in all the cases near the step discontinuity. The higher AR cases, L/D=1.0,1.5, exhibit similar trends with regard to wake dynamics, while they are quite different in the lower AR cases, L/D=0.2,0.5. Kelvin–Helmholtz instability is present in the wake of the dual-step cylinder with higher AR. Stable in-phase shedding and downwash characterize the wake of higher AR configurations, while oblique shedding (and flipping) is the key feature in the lower AR counterparts. Unique features are observed in the L/D=1.0 configuration that marks the transition between shedding modes.

MIMO Super-Twisting Controller using a passivity-based design

A novel MIMO Super-Twisting Algorithm is proposed in this paper for nonlinear systems with relative degree one, having a time and state-varying uncertain control matrix. The uncertainty is represented by a time and state-varying but unknown left matrix factor. Sufficient conditions for stability with full-matrix control gains are established, in contrast to the usual scalar gains. For this a smooth Lyapunov function, based on a passivity interpretation, is used. Moreover, continuous and homogeneous approximations of the classical discontinuous Super-Twisting algorithm are obtained, using a unified analysis method. Moreover, the proposed Super-Twisting algorithm is of the discontinuous type, in contrast to the usual unitary type.

Discontinuities in and Perceptions of Mental Health Service Path of Violent Young Offenders: A Qualitative Descriptive Study.

Studies on mental health service use among juvenile violent offenders prior to their acts of violence are sparse. Mostly, their service use seems to be short-term, although there may have been several service periods. Little is known about how they have perceived those services. Using a qualitative content analysis on data from forensic psychiatric examination statements, we studied discontinuities in the use of mental health services of 15-22-year-old violent Finnish offenders and descriptions of their perceptions of those services. There were several types of discontinuities: limited youth engagement and subsequent dropping out from services, or partial or total refusal of the proposed examinations or treatments. Most discontinuations were instigated by the youth themselves, followed by the parents and the service system. The subjects had perceived mental health services to be not beneficial for the most part, although some experienced benefits from medication. When treating children and adolescents with behavioral symptoms clinicians should identify the early signs of the process of disengagement from treatment and pay attention to the perceptions of the treatment of both the youth and their parents. Also, more research is needed on the user experience of mental health services among violent offenders, as well as factors relating to discontinuities along their mental health service path.

Nodal discontinuous Galerkin methods for Maxwell's equations in Lorentz-Kerr-Raman medium without nonlinear algebraic solver

The propagation of electromagnetic waves is modeled by time-dependent Maxwell's equations coupled with constitutive laws that describe the responses of the media. In this work, we consider a nonlinear model that describes the electromagnetic wave in an optical medium with the linear Lorentz effect and the cubic nonlinear instantaneous Kerr and delayed Raman effects. Mathematically this model obeys an energy conservative/dissipative law. Though there have been active efforts in designing numerical methods (e.g. of finite difference / finite element /discontinuous Galerkin type) to simulate this model, the methods proposed here are distinctive in that they are free of any nonlinear algebraic solvers. Moreover, in the absence of the Raman effect, our methods also enjoy a provable discrete energy law, and optimal a priori error estimates are further established when the exact solutions are sufficiently smooth. The key ingredients of the new methods include some novel treatment in time discretizations and nodal discontinuous Galerkin spatial discretization for the specific nonlinearities, and they also render a local nature of the methods and hence their suitability for parallel implementation with great efficiency. Numerical experiments are performed to illustrate the accuracy, stability, computational efficiency and parallel scalability of the proposed methods. We further apply the methods to simulate some physically relevant problems in one, two, and three dimensions.

Fuel-optimal powered descent guidance for lunar pinpoint landing using neural networks

This paper presents a Neural Networks (NNs) based approach to generate the fuel-optimal powered descent guidance for lunar pinpoint landing. According to Pontryagin’s Minimum Principle, the optimality conditions are first derived. To generate the dataset of optimal trajectories for training NNs, we formulate a parameterized system, which allows for generating each optimal trajectory by a simple propagation without using any optimization method. Then, a dataset containing the optimal state-thrust vector pairs can be readily collected. Since it is challenging for NNs to approximate a bang-bang (or discontinuous) type of optimal thrust magnitude, we introduce a regularisation function to the switching function so that the regularized switching function approximated by a simple NN can be used to represent the optimal thrust magnitude. Meanwhile, another two well-trained NNs are used to predict the thrust steering angle and the time of flight given a flight state. Finally, numerical simulations show that the proposed method is capable of generating the optimal guidance that steers the lunar lander to the desired landing site with acceptable landing errors.

Classical solution to mixed problems from the theory of longitudinal impact on an elastic semi-infinite rod in the case of separation of the impacting body after the collision

In this work, we consider two coupled initial-boundary value problems, which, based on the Saint-Venant theory, model the longitudinal impact phenomena in a semi-infinite rod. The mathematical formulation of the problem is two mixed problems for the one-dimensional wave equation with conjugation conditions. The Cauchy conditions are specified on the spatial half-line. The initial condition for the partial derivative with respect to the time variable has a discontinuity of the first kind at one point. The boundary condition, which includes the unknown function and its first- and second-order partial derivatives, is specified on the time half-line. The solution is constructed by the method of characteristics in an explicit analytical form. The uniqueness of the solution is proved, and the conditions under which a piecewise-smooth solution exists are established. The classical solution to a mixed problem with matching conditions is considered.

The regressive surface of marine erosion generated by tides: A case study from a Pleistocene tidal sand ridge sequence, Calabria, Southern Italy

AbstractThe regressive surface of marine erosion is a key stratigraphic discontinuity used to identify episodes of forced regression in marine strata. Typically, it marks the base of shallow‐marine (e.g. shoreface and deltaic) deposits eroding over relatively deeper‐water (e.g. shelf and prodelta) lithofacies. While well‐documented in marginal‐marine areas, its occurrence in offshore or strait settings dominated by tidal currents is less understood. This study investigates lower Pleistocene outcrops in the Plio‐Quaternary Siderno Basin, Calabria, southern Italy, where tidal sand ridges developed in a Mediterranean strait. High‐resolution drone images reveal a basinward‐dipping basal surface marking the onset of tidally dominated sedimentation. This discontinuity separates underlying shelf fines from overlying cross‐stratified, tidal bioclastic/siliciclastic arenites, indicating a prolonged period of marine regression in a strait setting. The stratal architecture of the ridges shows cross‐strata aggradation in up‐dip sections, transitioning down‐dip into balanced aggrading/prograding strata, and further basinward into markedly prograding deposits. These features are interpreted to reflect an initial phase of normal regression, evolving into forced regression. This latter stage is characterised by a progressive deepening of the basal discontinuity, causing more erosional effects on the underlying beds, with a vertical basinward fall of about 60 m over 2 km. Internal foreset geometry (two‐dimensional vs. three‐dimensional cross strata) and their vertical and lateral repetition indicate stages of equilibrium and disequilibrium for tidal bedforms, reflecting varying current speeds and water depth changes. The regressive surface of marine erosion here is formed by tidal currents, rather than waves, suggesting a new type of sequence stratigraphic discontinuity associated with tide‐dominated settings.

A highly efficient, eco‐friendly method for antireflection nanostructures on poly (ethylene terephthalate)

AbstractAntireflection surfaces are widely used in optical devices (such as vehicle display, solar cells, and architectural glass) to reduce the reflection and increase transmittance. Plasma etching shows great potential in making subwavelength antireflection structures for its advantage of scalable, low‐cost, and applicable in flexible substrates. Here, we demonstrate an antireflection nanostructure by O2 plasma etching on poly (ethylene terephthalate) (PET) substrate without additional corrosive gas species or antireflective coatings. Nanopores on the surface were formed due to the different etching rates of the organic region and silica region of the surface. The solar weighted average transmittance was improved from 91.6% to 94.8% for single‐side treated PET with silica antiblocking layer. The transmission increment was attributed to the gradient refractive index of the nanostructured surface due to the elimination of step discontinuity in refractive index. The result shows a highly efficient, eco‐friendly, solvent‐free, economical, and sputtering target‐free method for reducing the reflection and increasing the transmittance of the substrates.

Assessment of a tiling energy budget approach in a land surface model, ORCHIDEE-MICT (r8205)

Abstract. The surface energy budget plays a critical role in terrestrial hydrological and biogeochemical cycles. Nevertheless, its highly spatial heterogeneity across different vegetation types is still missing in the ORCHIDEE-MICT (ORganizing Carbon and Hydrology in Dynamic EcosystEms–aMeliorated Interactions between Carbon and Temperature) land surface model. In this study, we describe the representation of a tiling energy budget in ORCHIDEE-MICT and assess its short-term and long-term impacts on energy, hydrology, and carbon processes. With the specific values of surface properties for each vegetation type, the new version presents warmer surface and soil temperatures (∼ 0.5 °C, +3 %), wetter soil moisture (∼ 10 kg m−2, +2 %), and increased soil organic carbon storage (∼ 170 Pg C, +9 %) across the Northern Hemisphere. Despite reproducing the absolute values and spatial gradients of surface and soil temperatures from satellite and in situ observations, the considerable uncertainties in simulated soil organic carbon and hydrological processes prevent an obvious improvement in the temperature bias existing in the original ORCHIDEE-MICT model. However, the separation of sub-grid energy budgets in the new version improves permafrost simulation greatly by accounting for the presence of discontinuous permafrost types (∼ 3×106 km2), which will facilitate various permafrost-related studies in the future.

A fuel-efficient pathfinding algorithm for next-generation WIG crafts

ABSTRACT Wing-In-Ground (WIG) crafts have the advantage of being fuel-efficient by utilising the ground effect. Next-generation WIG crafts can choose flight paths that navigate over obstacles while flying at specific altitudes. However, current route computation algorithms for ships fail to account for paths that allow ships to navigate over obstacles. Leveraging fundamental path-finding approaches such as A* and Jump Point Search (JPS), our algorithms are designed to forecast routes that significantly improve operational efficiency. Validation was performed using real topographic data from Indonesia, focusing on fuel consumption metrics to evaluate the algorithms’ effectiveness. The results evaluate the superiority of our methods in optimising route selection for WIG crafts, marking a advancement in autonomous marine navigation technology.

Localised wavenumber estimation and its application to waveguide discontinuities

Wave propagation methods have been widely investigated for the potential application to the detection and localisation of discontinuities in structural waveguides. In the low-mid frequency ranges, previous preliminary works that used the analytic signal theory have considered local wavenumber estimations based on the time domain for the purpose of localisation in mechanical structures. However, these have not fully exploited the potential of this approach. This is accomplished herein for a one-dimensional infinite-like waveguide by means of two methods applied in the spatial domain; namely the Hilbert transform via the wavenumber domain estimator and the Direct Quadrature method. Modifications are proposed to make these methods more suitable to the space-wavenumber application and for the purpose of localisation. A three-dimensional plot is proposed, where local divergences of the wavenumbers indicate the positions of the discontinuities for otherwise uniform waveguides. Numerical simulations and experiments show an accurate estimation of the local wavenumbers and validate the methods with the proposed modifications for the localisation of different types of discontinuities.

Prospective secondary teachers’ noticing of students’ thinking about the limit concept: pathways of development

Research has shown that there is a need to examine prospective teachers’ development trajectories related to noticing expertise. An important content in the Spanish high school curriculum (16–18 years old) is the limit concept. Given the importance of this concept in the curriculum and the difficulties some prospective teachers have, developing their noticing of students’ mathematical thinking of this concept in teacher education programs is crucial to achieve high school student mathematics achievement. This study examines how prospective secondary school mathematics teachers (PTs) notice students’ mathematical thinking about the limit concept as they participated in a teaching module. PTs had to anticipate and interpret students’ mathematical understanding and make instructional decisions to support students’ conceptual progression using information about high school students’ understanding of the limit concept. We examined PTs changes related to how they anticipated, interpreted and made instructional decisions during the teaching module. We identified a change in how PTs conceived the understanding of the dynamic limit concept: from all-or-nothing dichotomy to progression; and a change in the instructional decisions they made: from decisions focused on changing the type of discontinuity to conceptual decisions. These changes allow us to characterise development noticing pathways. Our findings also help to identify the teaching module characteristics that support the development of PTs noticing.

Efficient and robust phase unwrapping method based on SFNet

Phase unwrapping is a crucial step in obtaining the final physical information in the field of optical metrology. Although good at dealing with phase with discontinuity and noise, most deep learning-based spatial phase unwrapping methods suffer from the complex model and unsatisfactory performance, partially due to simple noise type for training datasets and limited interpretability. This paper proposes a highly efficient and robust spatial phase unwrapping method based on an improved SegFormer network, SFNet. The SFNet structure uses a hierarchical encoder without positional encoding and a decoder based on a lightweight fully connected multilayer perceptron. The proposed method utilizes the self-attention mechanism of the Transformer to better capture the global relationship of phase changes and reduce errors in the phase unwrapping process. It has a lower parameter count, speeding up the phase unwrapping. The network is trained on a simulated dataset containing various types of noise and phase discontinuity. This paper compares the proposed method with several state-of-the-art deep learning-based and traditional methods in terms of important evaluation indices, such as RMSE and PFS, highlighting its structural stability, robustness to noise, and generalization.