Discontinuous Line Research Articles

Correction to: Limit Cycles in a Class of Planar Discontinuous Piecewise Quadratic Differential Systems with a Non-regular Line of Discontinuity (II)

Correction to: Limit Cycles in a Class of Planar Discontinuous Piecewise Quadratic Differential Systems with a Non-regular Line of Discontinuity (II)

Discontinuity-enhanced icephobic surfaces for low ice adhesion

HypothesisPassive low ice-adhesion surfaces are frequently composed of soft materials; however, soft materials potentially present durability issues, which could be overcome by fabricating composite surfaces with patterned rigid and soft areas. Here we propose the innovative concept of discontinuity-enhanced icephobic surfaces, where the stress concentration at the edge between rigid and soft areas, i.e. where discontinuities in elasticity are located, facilitates ice detachment. ExperimentsComposite model surfaces were fabricated with controlled rigid-soft ratios and discontinuity line lengths. The ice adhesion values were measured while recording the ice/substrate interface, to unravel the underpinning ice detachment mechanism. The experiments were complemented by numerical simulations that provided a better understanding of the ice detachment mechanism. FindingsIt was found that when a surface contains rigid and soft areas, stress is concentrated at the edge between soft and hard areas, i.e. at the discontinuity line, rather than all over the soft or rigid areas. An unexpected non-unidirectional crack propagation was observed for the first time and elucidated. When rigid and deformable materials are present, the crack occurs on the discontinuity line and propagates first on rigid and then on soft areas. Moreover, it was demonstrated that an increase in discontinuities promotes crack initiation and leads to a reduction of ice adhesion.

Limit Cycles in a Class of Planar Discontinuous Piecewise Quadratic Differential Systems with a Non-regular Line of Discontinuity (II)

Limit Cycles in a Class of Planar Discontinuous Piecewise Quadratic Differential Systems with a Non-regular Line of Discontinuity (II)

A new species of the newt genus Hypselotriton (Amphibia, Urodela, Salamandridae) from Jiangxi Province, southeastern China.

A new newt species, Hypselotritonhuanggangensis sp. nov., is described based on nine specimens collected from Huanggangshan Mountains, Yanshan County, Jiangxi, China. Morphologically, the new species is characterized by the combination of nine external characters: (1) obvious black patches with clear boundaries on the whole body; (2) ground color of the dorsal body tan; (3) ground color of venter bright orange; (4) skin rough; (5) vertebral ridge weak; (6) fingers and toes overlapping when forelimb and hindlimb adpressed towards each other along body; (7) postocular orange spot absent; (8) small white warty glands around the eye; (9) two discontinuous longitudinal lines formed by white warty glands from neck to lateral parts of tail. Molecularly, the new species forms an independent clade with strong support in the phylogenetic trees of the genus based on the mitochondrial locus of NADH dehydrogenase subunit 2 (ND2) gene fragments. The new species distinctly differs from H.fudingensis by differences in its body measurements, vertebral ridge, dorsal black patches, and ventral black patches. Furthermore, the new species and H.fudingensis are geographically isolated by a series of high mountain ranges, including the Wuyishan and Jiufengshan Mountains. The number of Hypselotriton species is now 11.

Non-diffusive neural network method for hyperbolic conservation laws

In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately computing weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in subdomains bounded by discontinuity lines (DLs), the latter defined from the Rankine-Hugoniot jump conditions. The proposed approach allows to efficiently consider an arbitrary number of entropic shock waves, shock wave generation, as well as wave interactions. Some numerical experiments are presented to illustrate the strengths and properties of the algorithms.

Targeting Wavefront Discontinuity Lines for Scar-Related Ventricular Tachycardia Ablation: A Novel Functional Substrate Ablation Approach

BackgroundThe boundaries of critical isthmuses for re-entrant ventricular tachycardia (VT) are formed by wavefront discontinuities (fixed lines of block, slow propagation, and rotational propagation) seen during baseline rhythm. It is unknown whether wavefront discontinuities can be automatically identified and targeted for ablation using electroanatomic mapping systems. ObjectivesThe purpose of this study was to assess the electrophysiologic characteristics of automatically projected wavefront discontinuity lines (WADLs) and outcomes of an ablation strategy targeting WADLs in a mixed cohort of VT patients. MethodsLate activation substrate maps were analyzed from 1 or more baseline rhythm wavefronts. WADLs were identified using the Carto Extended Early Meets Late module. Number, total length, and distance to critical VT sites were measured. VT recurrence and VT-free survival were followed. ResultsIn total, 49 patients underwent 52 ablations with 71 unique substrate maps analyzed (18.8% epicardial; 62.0% right ventricular paced, 28.2% sinus rhythm, 9.9% left ventricular paced). A total of 28 VT critical sites were identified in 24 patients. WADLs were present in 49 of 71 (69.0%) maps. WADLs were present regardless of cardiomyopathy etiology, mapping wavefront, or surface. At a WADL threshold of 30%, 73.9% of critical VT sites were in close proximity (≤15 mm) to a WADL. VT-free survival was 62% at 1 year, with a competing risk model estimating a 1-year risk of VT recurrence of 23%. ConclusionsWADLs can be automatically projected in a majority of patients in a mixed cohort of cardiomyopathy etiology, mapped wavefronts, and myocardial surfaces mapped. Targeting WADLs results in low rate of VT recurrence at 1 year.

Flux and symmetry effects on quantum tunneling

AbstractMotivated by the analysis of the tunneling effect for the magnetic Laplacian, we introduce an abstract framework for the spectral reduction of a self-adjoint operator to a hermitian matrix. We illustrate this framework by three applications, firstly the electro-magnetic Laplacian with constant magnetic field and three equidistant potential wells, secondly a pure constant magnetic field and Neumann boundary condition in a smoothed triangle, and thirdly a magnetic step where the discontinuity line is a smoothed triangle. Flux effects are visible in the three aforementioned settings through the occurrence of eigenvalue crossings. Moreover, in the electro-magnetic Laplacian setting with double well radial potential, we rule out an artificial condition on the distance of the wells and extend the range of validity for the tunneling approximation recently established in Fefferman et al. (SIAM J Math Anal 54: 1105–1130, 2022), Helffer & Kachmar (Pure Appl Anal, 2024), thereby settling the problem of electro-magnetic tunneling under constant magnetic field and a sum of translated radial electric potentials.

Limit cycles of discontinuous piecewise differential Hamiltonian systems separated by a circle, or a parabola, or a hyperbola

Piecewise differential systems in the plane have been extensively studied in the last two decades, due to the vast application of these systems to describe natural phenomena. The knowledge of the existence or not of periodic solutions, in particular, of the limit cycles, is very important for understanding the dynamics of the differential systems. In this article we studied the maximum number of limit cycles of discontinuous piecewise differential systems, formed by two Hamiltonians systems of degree one with three distinct lines of discontinuity either a circle, or a parabola, or a hyperbola.

Bifurcation structures of a two-dimensional piecewise linear discontinuous map: analysis of a cobweb model with regime-switching expectations

We consider the bifurcations occurring in a two-dimensional piecewise-linear discontinuous map that describes the dynamics of a cobweb model in which firms rely on a regime-switching expectation rule. In three different partitions of the phase plane, separated by two discontinuity lines, the map is defined by linear functions with the same Jacobian matrix, having two real eigenvalues, one of which is negative and one equal to 0. This leads to asymptotic dynamics that can belong to two or three critical lines. We show that when the basic fixed point is attracting, it may coexist with at most three attracting cycles. We have determined their existence regions, in the two-dimensional parameter plane, bounded by border collision bifurcation curves. At parameter values for which the basic fixed point is repelling, chaotic attractors may exist - either one that is symmetric with respect to the basic fixed point, or, if not symmetric, the symmetric one also exists. The homoclinic bifurcations of repelling cycles leading to the merging of chaotic attractors are commented by using the first return map on a suitable line. Moreover, four different kinds of homoclinic bifurcations of a saddle 2-cycle, leading to divergence of the generic trajectory, are determined.

Introduction.The post-Berlusconi centre right and the challenge of governing

ABSTRACT This introduction to the ‘Politics in Italy 2024’ special issue sheds light on the main events that unfolded during the course of the last year. A central focus is on the passing of Silvio Berlusconi, discussing his legacy and the consequences of his death for the Italian party system. This introduction also discusses the extent to which Fratelli d’Italia (FdI) was able to honour its election pledges, and to act in such a way as to draw a clear line of discontinuity with previous governments. Drawing on Peter Mair’s well-known idea that parties in power are torn between responsibility and responsiveness, we explore the factors that propelled the Meloni government in the direction of the former objective. These aspects are assessed against the available empirical evidence presented in this special issue, revealing that despite notable instances of rupture, Giorgi Meloni’s government has largely followed in the footsteps of its predecessors.

Limit Cycles of Discontinuous Piecewise Differential Hamiltonian Systems Separated by a Straight Line

In this article, we study the maximum number of limit cycles of discontinuous piecewise differential systems, formed by two Hamiltonians systems separated by a straight line. We consider three cases, when both Hamiltonians systems in each side of the discontinuity line have simultaneously degree one, two or three. We obtain that in these three cases, this maximum number is zero, one and three, respectively. Moreover, we prove that there are discontinuous piecewise differential systems realizing these maximum number of limit cycles. Note that we have solved the extension of the 16th Hilbert problem about the maximum number of limit cycles that these three classes of discontinuous piecewise differential systems separated by one straight line and formed by two Hamiltonian systems with a degree either one, two, or three, which such systems can exhibit.

Flow over a single dimple recessed in a flat plate

Direct numerical simulations have been conducted to investigate a zero-pressure-gradient boundary layer flow over a single shallow dimple. Here, the dimple depth to dimple diameter ratio (d/D) as well as the Reynolds number (based on D and free-stream velocity) are fixed at 0.05 and 20 000, respectively. The effect of inlet boundary layer thickness δ on a given dimple is investigated by considering δ/D∈[0.023,0.1]. The flow within the dimple exhibits either a horseshoe vortex (a continuous core line through the two spirals within the dimple) or a tornado-like vortex pair (discontinuous core line). For the given parameter range, four different flow patterns have been identified within the single dimple: (i) a steady symmetric horseshoe vortex pattern for δ/D∈[0.053,0.1], (ii) a steady asymmetric horseshoe vortex pattern for δ/D=0.04, (iii) a quasi-periodic asymmetric horseshoe vortex pattern for δ/D=0.033, and (iv) a mixed horseshoe and tornado-like vortex pattern for δ/D=0.023. The growth of the streamwise vorticity, mainly caused by the tilting of the vertical vorticity, plays a key role in the transition between the different flow patterns. Dimple-induced velocity streaks above the single dimple have been investigated in detail for the first time, showing four different streaks: (i) a high-speed streak above the dimple, (ii) two side-low-speed streaks located outside the dimple span, (iii) two side-high-speed streaks, and (iv) a mid-low-speed streak in between them. These are mainly caused by a flow acceleration effect and a flow diffuser effect over the dimple, as well as a “lift-up” mechanism within the downstream part of the dimple, tilting the boundary layer upward.

Regular and chaotic dynamics in a 2D discontinuous financial market model with heterogeneous traders

We develop a financial market model where three types of traders operate simultaneously: fundamentalists and chartists of two types, namely, trend followers and contrarians. The dynamics of this model is described by a two-dimensional discontinuous map defined by two linear functions, where one acts in the partition between two (parallel) discontinuity lines and the other one acts outside this partition. Our analysis shows that despite the linearity of the map components, its dynamics can be quite complex, with various, possibly coexisting attracting cycles and chaotic attractors. As a first step towards the understanding how the overall bifurcation structure observed in the parameter space of the map is organized, we obtain analytically the boundaries of periodicity regions related to the simplest attracting period-n cycles, n≥3, with one point in the middle partition and n−1 points outside it. These boundaries can be related to border-collision bifurcations (when a point of the cycle collides with a discontinuity line) as well as to degenerate bifurcations (associated with eigenvalues on the unit circle). We show also some elements of period-adding and period-incrementing bifurcation structures for which the cycles mentioned above are basic. From an economic point of view, our study confirms that a fairly simple financial market model with heterogeneous agents is able to produce complicated boom-bust dynamics typical of real financial markets.

Correlative Scan Matching Position Estimation Method by Fusing Visual and Radar Line Features

Millimeter-wave radar and optical cameras are one of the primary sensing combinations for autonomous platforms such as self-driving vehicles and disaster monitoring robots. The millimeter-wave radar odometry can perform self-pose estimation and environmental mapping. However, cumulative errors can arise during extended measurement periods. In particular scenes where loop closure conditions are absent and visual geometric features are discontinuous, existing loop detection methods based on back-end optimization face challenges. To address this issue, this study introduces a correlative scan matching (CSM) pose estimation method that integrates visual and radar line features (VRL-SLAM). By making use of the pose output and the occupied grid map generated by the front end of the millimeter-wave radar’s simultaneous localization and mapping (SLAM), it compensates for accumulated errors by matching discontinuous visual line features and radar line features. Firstly, a pose estimation framework that integrates visual and radar line features was proposed to reduce the accumulated errors generated by the odometer. Secondly, an adaptive Hough transform line detection method (A-Hough) based on the projection of the prior radar grid map was introduced, eliminating interference from non-matching lines, enhancing the accuracy of line feature matching, and establishing a collection of visual line features. Furthermore, a Gaussian mixture model clustering method based on radar cross-section (RCS) was proposed, reducing the impact of radar clutter points online feature matching. Lastly, actual data from two scenes were collected to compare the algorithm proposed in this study with the CSM algorithm and RI-SLAM.. The results demonstrated a reduction in long-term accumulated errors, verifying the effectiveness of the method.

A Study of New Methods for Localizing Discontinuity Lines on Extended Correctness Classes

A Study of New Methods for Localizing Discontinuity Lines on Extended Correctness Classes

8‐way high‐power high‐efficiency power divider/combiner

AbstractIn this letter, a low insertion loss power divider/combiner with a power capacity exceeding 100 kW is presented. The discussion focuses on the simultaneous achievement of high efficiency and high‐power capacity, based on the compensation analysis of discontinuous coaxial lines. An 8‐way power divider/combiner, operating within the frequency range of 7.73–9.33 GHz, has been designed, fabricated, and subjected to experimental testing. The experimental results demonstrate that within a relative bandwidth of 18.8%, the highest efficiency surpasses 98.49% and the power capacity exceeds 100 kW. Furthermore, the return loss of the multiport is better than 22.5 dB, the single port exhibits a return loss better than 20.7 dB, and the minimum isolation among the multiport is better than 27.5 dB. By comparison with other recently reported power dividers/combiners, the proposed power divider/combiner possesses both high‐power capacity and high efficiency simultaneously.

On the localization of fractal discontinuity lines from noisy data

We consider the ill-posed problem of localizing (finding the position of) the discontinuity lines of a function of two variables: the function is smooth outside the discontinuity lines, and at each point on the line it has a discontinuity of the first kind. We construct averaging procedures and study global discrete regularizing algorithms for approximating discontinuity lines. Lipschitz conditions are imposed on the discontinuity lines. A parametric family of fractal lines is constructed, for which all conditions can be checked analytically. A fractal is indicated that has a large fractal dimension, for which the efficiency of the constructed methods can be guaranteed.

Severe dust storm/thunderstorm activity over Uttar Pradesh on 13th May, 2018 - A case study

Premonsoon season over Uttar Pradesh is characterized withthunderstorm accompanied with rain, dust storm, gale winds and hail storms etc. These storms generally develop locally in association with convection and moisture convergence and seen as single cells in Doppler Weather Radar, but sometime these thunderstorms are associated with synoptic scale systems viz. Western Disturbance as cyclonic circulation/trough, induced low/ cyclonic circulation or northwest-southeast oriented trough, thereby increasing the spatial extent and severity of these thunderstorms significantly. In the present study, Duststorm/Thunderstorm activity that occurred over the state on large scale on 13th May 2018 and which claimed more than 49 human lives and large number of livestock in Uttar Pradesh has been analyzed. The purpose of this study wasto find out probable dynamic and thermodynamic aspects of this activity. The study indicates that the environment was highly favourable thermodynamically for severe thunderstorm activity with high maximum temperatures (>40C), high CAPE(>1000), high Total Total Index(>50) and high negative Lifted Index values (<-5) over most parts of the northwest Indian plains. The moisture discontinuity line was clearly noticed over south Uttar Pradesh with high moisture contents towards its north. Also 00UTC GFS wind analysis of the day at 925hPa indicated strong southeasterlies of the order of 30-35Kts over Uttar Pradesh resulting high moisture incursion in the lower levels over this region. The Low level wind shear was also high and was about 25-30Kt as evident from Skew-T gram of Lucknow for 12UTC of the day taken from Wyoming site as well as 12UTC wind shear analysis using ERA Interim daily data of ECMWF on 13 May, 2018. These features together with synoptic conditions viz; Western Disturbance (WD) in mid and upper levels and a Cyclonic Circulation (cycir) over south Haryana & neighbourhood as well as an east-west trough extending from this cycir in the lower levels made the environment highly favourable for severe thunderstorm activity over the region.

On some rational piecewise linear rotations

We study the dynamics of the piecewise planar rotations F λ ( z ) = λ ( z − H ( z ) ) , with z ∈ C , H ( z ) = 1 if Im ( z ) ≥ 0 , H ( z ) = − 1 if Im ( z ) < 0 , and λ = e iα ∈ C , being α a rational multiple of π. Our main results establish the dynamics in the so called regular set, which is the complementary of the closure of the set formed by the preimages of the discontinuity line. We prove that any connected component of this set is open, bounded and periodic under the action of F λ , with a period ℓ, that depends on the connected component. Furthermore, F λ ℓ restricted to each component acts as a rotation with a period which also depends on the connected component. As a consequence, any point in the regular set is periodic. Among other results, we also prove that for any connected component of the regular set, its boundary is a convex polygon with certain maximum number of sides.

Study of the Failure Mechanism of Soft Rock Mining Roadways Based on Limit Analysis Theory

To study the deformation and failure mechanisms of soft rock mining roadways, the 1506 return airway of Anyang Coal Mine is taken as the engineering background. Based on limit analysis theory, a failure model based on a rigid slider system is constructed to assess the failure of the soft rock surrounding a roadway. The formulas for calculating the self-weight power of the slider in the velocity discontinuity line of the rock surrounding the roadway, the work power of the surrounding rock pressure, and the energy dissipation rate of the velocity discontinuity line are derived, and the upper limit objective function of the velocity discontinuity line height is obtained. The failure characteristics and fracture evolution process of the surrounding rock under different mining stresses are analyzed by means of physical similarity simulations. The simulation results show that shear failure occurs first on the roadway side due to stress concentration. The fissures expand along the bottom angle of the roadway to the blind support area and the low-intensity support area. The cracks weaken the support strength of the angled anchor cable and bolt in the roadway shoulder. Under the action of roof pressure, the status of the rock mass inside and outside the shear slip zone changes from static to dynamic. This causes deformation and failure of the roadway roof, side, and floor.