Convex Shape Research Articles

Analysis of the slopes of Jambour Anticline in Kirkuk and its Effect on Soil Formation using Remote Sensing (RS) Data and Geographic Information Systems (GIS)

The area slope was studied according to several classifications and the matching, as well as studying the direction of the slope, the study found the direction south-east and south is prevalent in the region, because of the origin of tectonic processes, responsible for the emergence of the Jampour Anticline and the slope receding, it appears that most of the slopes in the region correspond to the directions of the river valleys, these slopes increased the speed of efficacy of riverine operations, resulting in an increase in the movement of surface materials. The shadow of the hills was also analyzed, and medium shade areas came first, followed by many shade areas, as well as studying the degree of curvature, it was found that straight, flat shapes outnumber convex and concave shapes if they reached 42.5%.The soil of the area was also studied according to Al-Ta‘i’s classification, the area soil was cultivated according to its potential for agriculture and grazing, the soil will be good for grazing, animals and forests grow due to water and wind erosion.

Microstructure, fracture toughness and high-temperature tensile property of large size Ti–46Al–5Nb-0.18C-0.3Si alloy with oriented lamella by electromagnetic confinement directional solidification

In this paper, the microstructure, fracture toughness, and high-temperature tensile property of the directionally solidified Ti–46Al–5Nb-0.18C-0.3Si alloy are investigated. The lamellar orientation of the alloy is parallel to the growth direction under the action of the seed. Due to the convex shape of the solid-liquid interface, the core grain growth preferentially, and a large-size single crystal is formed in the steady-state region. The results show that the fracture toughness of the alloy increases with the increase of the orientation angle, and the fracture behavior changes from interlamellar to translamellar. The alloy with well-aligned lamellar microstructure possesses the excellent high-temperature tensile properties, and the ultimate tensile strength (UTS) and elongation of the alloys are 636.7 ± 24.2 MPa and 23.9 ± 5.75% at 800 °C, 630.5 ± 38.45 MPa and 20.1 ± 3.6% at 850 °C, 606.9 ± 21.3 MPa and 22.6 ± 0.1% at 900 °C, respectively. Additionally, the toughening mechanism and strengthening mechanism are discussed and concluded.

Elastic Solution of a Polygon-Shaped Inclusion With a Polynomial Eigenstrain

Abstract This paper presents the Eshelby’s tensor of a polygonal inclusion with a polynomial eigenstrain, which can provide an elastic solution to an arbitrary, convex inclusion with a continuously distributed eigenstrain by the Taylor series approximation. The Eshelby’s tensor for plane strain problem is derived from the fundamental solution of isotropic Green’s function with the Hadmard regularization, which is composed of the integrals of the derivatives of the harmonic and biharmonic potentials over the source domain. Using the Green’s theorem, they are converted to two line (contour) integrals over the polygonal cross section. This paper evaluates them by direct analytical integrals. Following Mura’s work, this paper formulates the method to derive linear, quadratic, and higher order of the Eshelby’s tensor in the polynomial form for arbitrary, convex polygonal shapes of inclusions. Numerical case studies were performed to verify the analytic results with the original Eshelby’s solution for a uniform eigenstrain in an ellipsoidal domain. It is of significance to consider higher order terms of eigenstrain for the polygon-shape inclusion problem because the eigenstrain distribution is generally non-uniform when Eshelby’s equivalent inclusion method is used. The stress disturbance due to a triangle particle in an infinite domain is demonstrated by comparison with the results of the finite element method (FEM). The present solution paves the way to accurately simulate the particle-particle, partial-boundary interactions of polygon-shape particles.

The geometry of passivity for quantum systems and a novel elementary derivation of the Gibbs state

Passivity is a fundamental concept that constitutes a necessary condition for any quantum system to attain thermodynamic equilibrium, and for a notion of temperature to emerge. While extensive work has been done that exploits this, the transition from passivity at a single-shot level to the completely passive Gibbs state is technically clear but lacks a good over-arching intuition. Here, we reformulate passivity for quantum systems in purely geometric terms. This description makes the emergence of the Gibbs state from passive states entirely transparent. Beyond clarifying existing results, it also provides novel analysis for non-equilibrium quantum systems. We show that, to every passive state, one can associate a simple convex shape in a 2-dimensional plane, and that the area of this shape measures the degree to which the system deviates from the manifold of equilibrium states. This provides a novel geometric measure of athermality with relations to both ergotropy and β--athermality.

Capillary-induced deformation of an initially stressed neoHookean solid: A sessile liquid droplet

The development in lab-on-a-chip and flexible electronics has attracted great interest to understand the fluid-structure interaction. In this work, we analyze the capillary-induced deformation of an initially stressed neoHookean solid with an axisymmetric, sessile droplet on the surface in the framework of the incremental deformation theory. The neoHookean material is subjected initially to uniformly biaxial loading (stretching or compressing). Using the incremental deformation theory and the concept of breadth, we derive an explicit solution of the normal displacement component of the surface of the initially stressed neoHookean solid, which consists of a scaling factor and a shape function. The scaling factor decreases with the increase of the biaxial stretch, leading to the decrease in the deformation induced by the sessile droplet. The initially biaxial compression of the neoHookean solid increases the scaling factor. There is a critical-initial compression loading, at which the surface deformation changes from convex shape to concave shape. Increasing the ratio of the breadth to the radius of the contact zone between the sessile droplet and the initially stressed neoHookean solid increases the maximum value of the shape function.

Calculating of dumps stability laying on weak gently dipping interface

Relevance of the research. Stable parameters of dumps are critical in mining operations ensuring their safety and economic efficiency. This problem is particularly acute for mining enterprises engaged in surface mining and for coal open pit mines, in particular. One of the main problems of this issue is related to the substantiation of rigorous methods for assessing stability and determining the limiting parameters of external and internal dumps filling an embankment on weak gently dipping interface. In the technical and regulatory literature, this issue has been considered for a long time. However, there are no specific recommendations for finding the most dangerous sliding surfaces on slopes, as well as methods for calculating shearing and restraining forces along these surfaces. All the signs are that the reason for the stability loss of operated dumps is the absence of theoretically substantiated design schemes, respectively, there are errors in the design of dumping. Purpose of the work is to develop reliable methods for calculating the limiting parameters of dumps on weak gently dipping interface. The main idea of the work is to apply a new, not previously used scheme for calculating the stability of dumps on weak gently dipping interface. Research methods. The work deals with the apparatus of flow mechanics and more specifically, the rigid-plastic model (the method of limit equilibrium), and the variational, integral and differential branches of calculus act as a mathematical apparatus. Results and conclusions. Based on the results of previous studies, a new scheme for calculating the stability of the dump during its destruction along weak interface was proposed, which implies the absence of a curved section of the sliding surface under the slope and the convex shape of the sliding surface under the berm. In contrast to the existing calculation schemes, such a calculation scheme predicts significantly lower values of the critical parameters of dumps. It means that the use of the proposed scheme will prevent the destruction of dumps by landslides along the dumpbasement interface and increase the economic efficiency of enterprises. Because a sufficiently large overestimation of the critical parameters of dumps at weak interface limited by current regulatory documents has been determined, it is recommended to revise these parameters for the designed and operated dumps using the proposed schemes for calculating their stability.

Realization of a Novel Morphing Surface Using Additive Manufacturing and Its Active Control in Friction

Abstract As the need for higher efficiency of engineering components increases, so does the demand for functional surfaces. While various tribosurfaces (e.g., texturing and coatings) have been developed, many researches are aimed at static functionality. On the other hand, due to a wide range of environmental adaptability and active control, active-morphing surfaces can be highly efficient and robust. In this paper, we demonstrate a novel morphing surface and its realization using additive manufacturing (AM). By using a diaphragm structure, morphing performance is achieved even if a hard resin material is used. When air pressure is applied to the backside of the diaphragm, it changes to a convex shape and vice versa. The concept requires a complex structure for arranging airflow and a solid morphing system. The AM is one great technique to create such complex structures. As a result of actual manufacturing, the created morphing structure realizes a large morphing of 600 μm or more. In addition, the shape changes reversibly depending on the air pressure. The surface also exhibits very interesting tribological characteristics. The surface shows a friction coefficient of about 0.3 with a concavity, and then increases to 0.5–1.7 with a convexity. A real-contact area measurement reveals that the novel property occurs due to change in the real-contact area depending on surface morphology. In conclusion, the present paper provides a new concept of a novel morphing tribosurface, which selectively performs as a low-friction or break-like surface, created using AM.

Automated Process Planning System for End-Milling Operation by CAD Model in STL Format

A method for extracting the machining region from a 3D CAD model in Standard Triangulated Language (STL) format and automatically generating a tool path is proposed. First, a method is proposed for extracting the machining region and obtaining the geometrical features such as a convex or concave shape from only the 3D CAD model in STL format. The STL format uses only triangular mesh data and drops all information, which is necessary for extracting the removal volume for the machining and geometrical characteristics. Furthermore, the triangular mesh size is non-uniform. A contour line model is proposed in which the product model is minutely divided on the plane along any one axial direction and is represented by points at intervals below the indicated resolution obtained from the contour line of the cross section of the product. Subsequently, a method is proposed to determine the machining conditions for each extracted machining region and automatically generate a tool path according to the geometrical features of the machining region obtained. A machining experiment was conducted to validate the effectiveness of the proposed method. As a result of the machining experiment, it was confirmed that the tool path automatically generated from the 3D CAD model in STL format can be machined without any problems and with a practical level of accuracy.

The Influence of Abutment Macrodesign on Facial Peri-implant Tissue Dimensions for Guided Placed and Restored Implants at Healed Sites: 1-Year CBCT Findings from a Randomized Controlled Clinical Trial.

This study aimed to evaluate facial peri-implant tissue dimensions for implants connected to either convex or concave final abutments. Patients (n = 28) were randomly allocated to receive a single implant with an abutment of either convex (Group CX) or concave (Group CV) emergence shape. Twelve months after implant placement, CBCT scans were taken and reference points were identified: first visible bone-to-implant contact, implant shoulder (IS), bone crest (BC), and marginal mucosal level (MML). Mucosal thickness was evaluated at the level of IS (MT1), above the level of BC (MT2), and at the mid-distance of BC-MML (MT3). The mean total vertical peri-implant mucosa height was 3.26 ± 0.77 mm for Group CX and 3.70 ± 0.99 mm for Group CV (P = .23). The mean vertical peri-implant mucosa height below the bone crest was 0.62 ± 0.57 mm for Group CX and 1.26 ± 0.95 mm for Group CV (P = .04). Group CV had greater mean MT2 (4.09 ± 0.72 mm vs 3.36 ± 0.81 mm; P = .02) and MT3 (2.81 ± 0.66 mm vs 2.03 ± 0.60 mm; P = .005) compared to Group CX. Abutment macrodesign may have an effect on vertical and horizontal peri-implant tissue dimensions.

Concavity as a diagnostic feature of visual scenes

Despite over two decades of research on the neural mechanisms underlying human visual scene, or place, processing, it remains unknown what exactly a “scene” is. Intuitively, we are always inside a scene, while interacting with the outside of objects. Hence, we hypothesize that one diagnostic feature of a scene may be concavity, portraying “inside”, and predict that if concavity is a scene-diagnostic feature, then: 1) images that depict concavity, even non-scene images (e.g., the “inside” of an object – or concave object), will be behaviorally categorized as scenes more often than those that depict convexity, and 2) the cortical scene-processing system will respond more to concave images than to convex images. As predicted, participants categorized concave objects as scenes more often than convex objects, and, using functional magnetic resonance imaging (fMRI), two scene-selective cortical regions (the parahippocampal place area, PPA, and the occipital place area, OPA) responded significantly more to concave than convex objects. Surprisingly, we found no behavioral or neural differences between images of concave versus convex buildings. However, in a follow-up experiment, using tightly-controlled images, we unmasked a selective sensitivity to concavity over convexity of scene boundaries (i.e., walls) in PPA and OPA. Furthermore, we found that even highly impoverished line drawings of concave shapes are behaviorally categorized as scenes more often than convex shapes. Together, these results provide converging behavioral and neural evidence that concavity is a diagnostic feature of visual scenes.

Experimental analysis of wear and multi-shape burr loading during neurosurgical bone grinding

Amid bone grinding, a part of the hard tissue (i.e. bone) is usually removed to gain clearer operative excess to the tumours present beneath the bone. The tool wear and tool loading influence the thermal as well as mechanical conditions of surgery. The rise in temperature during osteotomy may cause severe consequence like thermogenesis and damage to optic nerves, cervical, and sciatic nerves. Therefore, the present study has been carried out to investigate the burr wear with different shaped grinding burrs. The burr wear is characterized in terms of burr loading, dislodging and fracture in abrasives. The burr loading is further quantified on the amount of bone adhered over the surface of the burr. The results of surface characterization revealed that minimum wear occurred in case of convex shape burr whereas cylindrical burr caused the highest wear in terms of abrasive fragmentation, dislodging, and wear flats. The minimum percentage of weight reduction observed with the convex burr i.e., 1.68% including 0.4196 g weight of dislodged abrasive (Wab) and corresponding burr loading is observed as 0.1464 g. The maximum burr loading was seen in the case of the spherical burr (Wb) i.e. 0.5907 g.

In Search of Excellence: Convex versus Concave Noble Metal Nanostructures for Electrocatalytic Applications.

Controlling the shape of noble metal nanoparticles is a challenging but important task in electrocatalysis. Apart from hollow and nanocage structures, concave noble metal nanoparticles are considered a new class of unconventional electrocatalysts that exhibit superior electrocatalytic properties as compared with those of conventional nanoparticles (including convex and flat ones). Herein, several facile and highly reproducible routes for synthesizing nanostructured concave noble metal materials reported in the literature are discussed, together with their advantages over noble metal nanoparticles with convex shapes. In addition, possible ways of optimizing the synthesis procedure and enhancing the electrocatalytic characteristics of concave metal nanoparticles are suggested. Nanostructured noble metals with concave features are found to show better catalytic activity and stability hence improve their practical applicability in electrocatalysis.

Convexity preserving level set for left ventricle segmentation

In clinical applications of cardiac left ventricle (LV) segmentation, the segmented LV is desired to include the cavity, trabeculae, and papillary muscles, which form a convex shape. However, the intensities of trabeculae and papillary muscles are similar to myocardium. Consequently, segmentation algorithms may easily misclassify trabeculae and papillary muscles as myocardium. In this paper, we propose a level set method with a convexity preserving mechanism to ensure the convexity of the segmented LV. In the proposed level set method, the curvature of the level set contours is used to control their convexity, such that the level set contour is finally deformed as a convex shape. The experimental results and the comparison with other level set methods show the advantage of our method in terms of segmentation accuracy. Compared with the state-of-the-art methods using deep-learning, our method is able to achieve comparable segmentation accuracy without the need for training, while the deep-learning based method requires a large set of training data and high-quality manual segmentation. Therefore, our method can be conveniently used in situation where training data and their manual segmentation are not available.

Scalp and Forehead Injury: Management of Acute and Secondary Defects.

The primary challenges in scalp reconstruction are the relative inelasticity of native scalp tissue and the convex shape of the calvarium. All rungs of the reconstructive ladder can be applied to scalp reconstruction, albeit in a nuanced fashion due to the unique anatomy and vascular supply to the scalp. Important defect variables to incorporate into the reconstructive decision include site, potential hairline distortion, size, depth, concomitant infection, prior radiation therapy, planned adjuvant therapy, medical comorbidities, patient desires, and potential calvarium and dura defects.

Spin Change of Asteroid 2012 TC4 Probably by Radiation Torques

Abstract Asteroid 2012 TC4 is a small (∼10 m) near-Earth object that was observed during its Earth close approaches in 2012 and 2017. Earlier analyses of light curves revealed its excited rotation state. We collected all available photometric data from the two apparitions to reconstruct its rotation state and convex shape model. We show that light curves from 2012 and 2017 cannot be fitted with a single set of model parameters; the rotation and precession periods are significantly different for these two data sets, and they must have changed between or during the two apparitions. Nevertheless, we could fit all light curves with a dynamically self-consistent model assuming that the spin states of 2012 TC4 in 2012 and 2017 were different. To interpret our results, we developed a numerical model of its spin evolution in which we included two potentially relevant perturbations: (i) gravitational torque due to the Sun and Earth and (ii) radiation torque, known as the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect. Despite our model simplicity, we found that the role of gravitational torques is negligible. Instead, we argue that the observed change of its spin state may be plausibly explained as a result of the YORP torque. To strengthen this interpretation, we verify that (i) the internal energy dissipation due to material inelasticity and (ii) an impact with a sufficiently large interplanetary particle are both highly unlikely causes of its observed spin state change. If true, this is the first case where the YORP effect has been detected for a tumbling body.

Numerical Study of Hydrodynamics of Heavily Loaded Hard-Chine Hulls in Calm Water

Hard-chine boats are usually intended for high-speed regimes where they operate in the planing mode. These boats are often designed to be relatively light, but there are special applications that may occasionally require fast boats to be heavily loaded. In this study, steady-state hydrodynamic performance of nominal-weight and overloaded hard-chine hulls in calm water is investigated with computational fluid dynamics solver program STAR-CCM+. The resistance and attitude values of a constant-deadrise reference hull and its modifications with more pronounced bows of concave and convex shapes are obtained from numerical simulations. On average, 40% heavier hulls showed about 30% larger drag over the speed range from the displacement to planing modes. Among the studied configurations, the hull with a concave bow is found to have 5–12% lower resistance than the other hulls in the semi-displacement regime and heavy loadings and 2–10% lower drag in the displacement regime and nominal loading, while this hull is also capable of achieving fast planing speeds at the nominal weight with typical available thrust. The near-hull wave patterns and hull pressure distributions for selected conditions are presented and discussed as well.

Loading Effect of Prosthetic Feet's Anthropomorphicity on Transtibial Osseointegrated Implant.

Osseointegrated implants for direct skeletal attachment of transtibial prosthesis carry risks that are yet to be fully resolved, such as early loosening, mechanical failure of percutaneous and medullar parts of implant, periprosthetic issues, and infections. Underloading could lead to early loosening and infection. Overloading might compromise the bone-implant interface. Therefore, Goldilocks loading regimen applied by transtibial bone-anchored prostheses is critical for safe and efficient development of osseointegration around the implant during rehabilitation and beyond. We hypothesized that Goldilocks loading could be achieved when ambulating with a so-called anthropomorphic prosthetic ankle showing moment-angle relationship similar to a sound ankle. Quantitative characteristics of the moment-angle curve of the sound ankle during dorsiflexion phase of a free-pace walking were extracted for 4 able-bodied participants (experiment 1). A slope of the moment-angle curve (stiffness) was calculated twice: for the first half and for the second half of the moment-angle curve. The difference of stiffnesses (those at the second half minus at the first half) was called the index of anthropomorphicity (IA). By definition, positive IA is associated with concave shape of the moment-angle curve, and the negative IA is associated with convex shape. In experiment 2, the same recordings and calculations were performed for 3 participants fitted with transtibial osseointegrated fixation during walking with their usual feet and the Free-Flow Foot (Ohio Willow Wood). The Free-Flow Foot was selected for its anthropomorphicity demonstrated in the previous studies with amputees using traditional socket attachment. The IA was 5.88 ± 0.93 for the able-bodied participants, indicating that the stiffness during the first part of the dorsiflexion phase was substantially fewer than during the second parts, as the calf muscles resisted to angulation in ankle substantially less than during the second part of dorsiflexion phase. For amputees fitted with Free-Flow Foot, IA was 2.68 ± 1.09 and -2.97 ± 2.37 for the same amputees fitted with their usual feet. Indexes of anthropomorphicity, while of different magnitude, were positive in control able-bodied group and in the amputee group wearing Free-Flow Foot, which was qualitatively associated with concave shape of their moment-angle curves. The 3 usual feet worn by the participants were classified as nonanthropomorphic as their individual moment-angle curves were convex and the corresponding IAs were negative. Furthermore, this study showed that a foot with anthropomorphic characteristics tends to decrease maximal loads at the bone-implant interface as compared to the nonanthropomorphic feet and possibly may minimize the risks to compromise the integrity of this interface.

The action of ciliary muscle contraction on accommodation of the lens explored with a 3D model

The eye's accommodative mechanism changes optical power for near vision. In accommodation, ciliary muscle excursion relieves lens tension, allowing it to return to its more convex shape. Lens deformation alters its refractive properties, but the mechanics of ciliary muscle actions are difficult to intuit due to the complex architecture of the tissues involved. The muscle itself comprises three sections of dissimilarly oriented cells. These cells contract, transmitting forces through the zonule fibers and extralenticular structures. This study aims to create a finite element model (FEM) to predict how the action of the ciliary muscle sections leads to lens displacement. The FEM incorporates initialization of the disaccommodated lens state and ciliary muscle contraction, with three muscle sections capable of independent activation, to drive accommodative movement. Model inputs were calibrated to replicate experimentally measured disaccommodated lens and accommodated ciliary muscle shape changes. Additional imaging studies were used to validate model predictions of accommodative lens deformation. Models were analyzed to quantify mechanical actions of ciliary muscle sections in lens deformation and position modulation. Analyses revealed that ciliary muscle sections act synergistically: the circular section contributes most to increasing lens thickness, while longitudinal and radial sections can oppose this action. Conversely, longitudinal and radial sections act to translate the lens anteriorly with opposition from the circular section. This FEM demonstrates the complex interplay of the three sections of ciliary muscle in deforming and translating the lens during accommodation, providing a useful framework for future investigations of accommodative dysfunction that occurs with age in presbyopia.

The reverse Kakeya problem

Abstract We prove a generalization of Pál's conjecture from 1921: if a convex shape P can be placed in any orientation inside a convex shape Q in the plane, then P can also be turned continuously through 360° inside Q. We also prove a lower bound of Ω(m n 2) on the number of combinatorially distinct maximal placements of a convex m-gon P in a convex n-gon Q. This matches the upper bound proven by Agarwal et al.

Existence, symmetry breaking bifurcation and stability of two-dimensional optical solitons supported by fractional diffraction.

We study existence, bifurcation and stability of two-dimensional optical solitons in the framework of fractional nonlinear Schrödinger equation, characterized by its Lévy index, with self-focusing and self-defocusing saturable nonlinearities. We demonstrate that the fractional diffraction system with different Lévy indexes, combined with saturable nonlinearity, supports two-dimensional symmetric, antisymmetric and asymmetric solitons, where the asymmetric solitons emerge by way of symmetry breaking bifurcation. Different scenarios of bifurcations emerge with the change of stability: the branches of asymmetric solitons split off the branches of unstable symmetric solitons with the increase of soliton power and form a supercritical type bifurcation for self-focusing saturable nonlinearity; the branches of asymmetric solitons bifurcates from the branches of unstable antisymmetric solitons for self-defocusing saturable nonlinearity, featuring a convex shape of the bifurcation loops: an antisymmetric soliton loses its stability via a supercritical bifurcation, which is followed by a reverse bifurcation that restores the stability of the symmetric soliton. Furthermore, we found a scheme of restoration or destruction the symmetry of the antisymmetric solitons by controlling the fractional diffraction in the case of self-defocusing saturable nonlinearity.