Convex Angle Research Articles

The association between arterial blood supply to the anterior chest and juxta-apical thorax-asymmetry-associated right thoracic female adolescent idiopathic scoliosis

This cross-sectional study was carried out to investigate the role of arterial blood supply to the anterior chest wall in the pathogenesis of idiopathic scoliosis in adolescent females. Previous investigations have postulated that there is some asymmetry of the breasts in female adolescents with thoracic scoliosis that may be linked with anatomic and functional asymmetry of the internal mammary (IMA) artery that is the main supplier to the mammary gland. For this reason the present study investigated several anatomic and hemodynamic flow parameters of the IMA with color Doppler ultrasonography (CDU). Twenty female adolescents with right convex thoracic scoliosis were examined with roentgenograms to measure scoliosis curve, vertebral rotation, and concave and convex rib-vertebra angle at three vertebrae (apical, and one level above and one below the apical vertebra). Sixteen comparable nonscoliotic females were used as controls. CDU measured the IMA lumen diameter, its cross-sectional area, time average mean flow, and flow volume per minute. In scoliotics the obtained roentgenographic and ultrasonographic parameters were compared with each other to disclose any relationship. The reliability of CDU was high and the intraobserver variability low (ANOVA, P=0.92–0.94). There was no statistically significant difference in the ultrasonographic parameters of the IMA between right and left side in each individual or between scoliotics and controls. In scoliotics significant (P<0.05–0.01) correlations were shown between anatomic and hemodynamic parameters of internal mammary artery and juxta-apical convex and concave rib-vertebra angle. This study showed that the blood supply to the anterior chest wall in female adolescent scoliotics suffering from right-convex thoracic scoliosis is significantly correlated with juxta-apical convex and concave rib-vertebra angles. Thus, although this study found no correlation between scoliosis characteristics and anterior wall blood supply, it theoretically supports the hypothesis of a possible correlation between juxta-apical thorax asymmetry and anterior chest-wall blood supply in idiopathic scoliosis.

Effect of Processing on Precision of Composite Panels

As the demand for precision composite parts increases, understanding the effects of processing parameters on composite precision is needed. This study is devoted to observing the warping tendency of angles and investigating the effects of the part thickness, tool material, and stacking orientation on the precision of angled composite parts. Composite parts with both concave and convex angles were fabricated with various thickness, tool material, and stacking orientation. It was found that composite angled parts always warped inward. As the part angle decreased, the warp angle decreased. The resin volume fraction gradient induced a further inward warping tendency at convex angles. Rigidity improvement achieved by increasing the thickness overcame this resin gradient effect. The precision at convex angles was, thus, improved. However, the precision at concave angles worsened with increasing part thickness. The tool material was found to significantly affect the part precision at both concave and convex angles. Angled parts fabricated in molds made of advanced composite tools yielded much better angle precision than that fabricated in mold made of aluminum tools. As far as the stacking orientation was concerned, the best precision at a 135° convex angle was achieved with a stacking orientation of [0/90/0/90/0/90/90/0], whereas at a 90° concave angle the best precision was achieved with [90/0]4Tfor a laminate of 8 plies. A stacking sequence with a [0/90] orientation was found to cause upward warping. This could be used to counterbalance other inherent warping tendencies.

Stationary Simple Waves on a Barotropic Liquid Shear Flow

Stationary three‐dimensional flows of a barotropic liquid in a gravity field are considered. In the shallow‐water approximation, the Euler equations are transformed into a system of integrodifferential equations by the Euler‐Lagrange change of coordinates. A system of simple‐wave equations is obtained, for which the theorem of existence of a solution attached to a given shear flow is proved. As an example, a particular solution analogous to the solution of the problem of a gas flow around a convex angle is given.

Shape representation in area V4: position-specific tuning for boundary conformation.

Visual shape recognition in primates depends on a multi-stage pathway running from primary visual cortex (V1) to inferotemporal cortex (IT). The mechanisms by which local shape signals from V1 are transformed into selectivity for abstract object categories in IT are unknown. One approach to this issue is to investigate shape representation at intermediate stages in the pathway, such as area V4. We studied 109 V4 cells that appeared sensitive to complex shape in preliminary tests. To achieve a more complete picture of shape representation in V4, we tested each cell with a set of 366 stimuli, constructed by systematically combining convex and concave boundary elements into closed shapes. Using this large, diverse stimulus set, we found that all the cells in our sample responded to a wide variety of shapes and did not appear to encode any single type of global shape. However, for most cells the shapes evoking strongest responses were characterized by a consistent type of boundary conformation at a specific position within the stimulus. For example, a given cell might be tuned for shapes containing concave curvature at the right, with other parts of the shape having little or no effect on responses. Many cells were tuned for more complex boundary configurations (e.g., a convex angle adjacent to a concave curve). We quantified this kind of shape tuning with Gaussian functions on a curvature x position domain. These tuning functions fit the neural responses much better than tuning functions based on edge or axis orientation. Thus individual V4 cells appear to encode moderately complex boundary information at specific locations within larger shapes. This finding suggests that, at intermediate stages in the V1-IT transformation, complex objects are represented at least partly in terms of the configurations and positions of their contour components.

Multiple tool path planning for NC machining of convex pockets without islands

This work focuses on machining of pockets with convex angles and containing no islands. The approach is a hybrid contouring – staircasing one. Contouring aims at clearing enough space around the boundary to allow efficient staircasing in the interior. Three tools are foreseen: two for contouring and one for staircasing. The algorithm for contouring is based on creating offsets of the pocket boundary and checking them for self-crossing. Staircasing is based on parametrisation of the tool path with respect to its orientation to the pocket, so as to minimise the tool path length. Machining strategy is complemented by choosing the best combination of diameters of the three tools used. This is simply done by first enumerating all available combinations and then excluding the non-feasible ones, in order to compare the rest according to tool path length (or to machining time when individual feed values are known). The output of the program, which was implemented in Fortran, is the tool path, the CNC part program, which is created automatically, and a numerical comparison of all the tool-angle combinations tried out. A machining simulation based on the CNC program output is conducted on commercial CAM software to demonstrate validity of the result.

Effects of thoracolumbosacral orthosis on spinal deformities, trunk asymmetry, and frontal lower rib cage in adolescent idiopathic scoliosis.

Prospective study. To document immediate and late changes in shape and balance of the thoracic and lumbar spine and lower rib cage on the frontal plane induced by treatment with a thoracolumbosacral orthosis (TLSO). The effect of TLSO on lateral plane of spinal deformity, frontal lower rib cage, trunk balance, and natural history are poorly understood. Twenty-four female adolescents with major thoracic and/or lumbar scoliosis, averaging 30 degrees and 26 degrees, respectively, were treated with a full-time TLSO program. Scoliosis, kyphosis, convex, and concave rib-vertebral angles T7 to T12, frontal trunk balance, frontal vertebral inclination, rotation and translation from T7 to L4-vertebrae were measured before bracing, 1 month after bracing, and biannually thereafter in brace and without brace for a 4-year period and reevaluated at the age of 20 years, at an average of 3.5 years after termination of bracing to measure any permanent changes. Thoracolumbosacral orthosis treatment corrected both thoracic and lumbar scoliosis and reduced lateral trunk shift at the expense of significant, although temporary reduced physiological thoracic kyphosis, increased lateral displacement of T7 to T10, increased frontal inclination of L2 to L4, and elevation of the apical concave rib in favor of reduction of lateral displacement of T11 to L4; decreased frontal inclination of T7, T9, and T11; and derotated L1 and L2 and thoracic apical vertebra without affecting drooping of the 7th to 12th ribs. In this series, there was marked inconsistency in the obtained changes in several of the roentgenographic parameters in the different evaluations, which is probably because of the empiric application of the TLSO during different periods of treatment. 3.5 years after termination of TLSO-wearing, all roentgenographic parameters remained to the prebrace values. Thoracolumbosacral orthosis program maintained the measured roentgenographic parameters at the prebrace levels in progressive adolescent idiopathic scoliosis, but it had no effect on the droop of the seven lower ribs. The TLSO treatment stopped progression of scoliosis and reduced the number of patients requiring surgery. Thus, it changed the natural history of scoliosis.

A geometrical method for computing the distribution of boundary shear stress across irregular straight open channels

A method called Merged Perpendicular Method (M.P.M.)has been developed to compute the distribution of boundary shear stress across irregular straight channels. In a concave angle of a cross section, computed shear stress is lower than in a convex angle. Comparison with experimental data has shown that the new method calculates more accurate shear stress than other geometrical methods.

Improvement of Impact Energy for Copper/Aluminium Friction Welded Joint due to the Shape of Interface Edge.

The friction welding for copper and aluminium is useful to minimize the diffusion thickness at the interface between copper and aluminium. The minimization of diffusion thickness is required for maintaining the joint strength, because brittle intermetallic compounds are formed at the friction weld interface between copper and aluminium. However, the improvement techniques on joint strength characteristics have not fully been clarified. In this study, stress singularities at the intersection of free surfaces and the interface between copper and aluminium are investigated using finite element analysis. It was confirmed that the no free-edge stress singularities existed in case of convex angle. In this experiment, copper and aluminium friction welded joints with convex apex angle were fabricated as to minimize the diffusion thickness, such ad > 1 μm at the interface between copper and aluminium. It was confirmed that the good tensile strength could be observed in any cases. The Charpy impact energy became comparatively low values in case of 90 degree of apex angle, and revealed a remarkable good impact energy can be obtained in case of the convex angle that showed no free-edge stress singularities.

Experimental study on the accuracy of advanced composite tools for slanted shapes

AbstractHigh quality advanced composite tools (ACTs) have been introduced to the growing tooling market. Since ACTs are used for high precision composite parts, even minor warpage in a tool might render the parts useless. Trial and error in making or remaking an accurate ACT are time‐consuming and expensive. This paper is devoted to investigating the effects of processing on the accuracy of ACTs for slanted shapes. An experimental design based on the Taguchi Method is employed. The experimental parameters investigated are postcure, mold material, laminate thickness, cure temperature, preheat, bleeder, pressure, and caul sheet. Warpage is used to verify the accuracy of ACTs. Optimum processing conditions and critical parameters have been found. The warpage that results under optimum processing conditions decreased significantly. Based on the findings in fiber volume fraction gradients, the observed convex and concave angle differences in warpage can be explained. To overcome the tendency to warpage, by means of an asymmetric doubler or insert in angle corners, a proper amount of asymmetry is implemented, which successfully improves the accuracy of the ACT shape.

Effects of the Combined VDS-Zielke and Harrington Operation on the Frontal Rib Cage Deformity of Double Major Curves in Idiopathic Scoliosis

This study analyzed the changes in the frontal plane of the deformed lower rib cage and the scoliosis-related alterations on the spine in patients with double major curve-pattern idiopathic scoliosis. The results obtained preoperatively, after the Zielke operation, postoperatively after the Harrington instrumentation, and at the follow-up evaluation were compared to investigate which changes of the elements of the rib cage deformity are caused by each of the two instrumentations. Previously, Wojcik reported on the effects of a Zielke operation on the lower rib in mild S-shaped idiopathic scoliosis. No previous data exist regarding the lower rib cage deformities in severe idiopathic double major-pattern scoliosis and their changes after combined VDS-Zielke and Harrington instrumentation. Fifteen patients who underwent the staged Zielke operation followed by Harrington rod instrumentation were followed-up for an average period of 31.1 months. The methods used in our study included Cobb angle and a segmental analysis (T7-T12) of each of convex and concave rib-vertebra angles, rib-vertebra angle differences, vertebral rotation, and vertebral tilt. In this series, the apical convex ribs showed an increased droop preoperatively compared with the concave apical ribs. The VDS-Zielke operation corrected the lumbar scoliosis in an average of 63% of patients, whereas the thoracic scoliosis showed an immediate spontaneous correction of 30%. The VDS-Zielke operation also produced a significant correlation of the scoliosis-related vertebral tilt (T10-T12), derotated the lumbar vertebrae and the T12 vertebra significantly, elevated the "mobile" concave ribs, and increased the droop of the lower (T11, T12) "mobile" convex ribs. The Harrington instrumentation did not change the vertebral rotation, the vertebral tilt, the convex rib-vertebra angle, or the L4 obliquity, but significantly changed the apical concave rib-vertebra angle. The combined Zielke-Harrington instrumentation reduced the thoracic kyphosis and the thoracolumbar junction-kyphosis significantly, whereas the lumbar lordosis remained practically unchanged. Only the anterior VDS-Zielke instrumentation significantly corrects severe spinal deformities, elevates the three lower ribs on the concavity, and increases the droop of the two lower ribs on the convexity in the severe idiopathic double major curve-pattern scoliosis combined operated (Zielke-Harrington). Therefore, the Harrington instrumentation should have only limited use in cosmetic scoliosis surgery and should be replaced with posterior multi-hook instrumentation with a derotation effect.

Some solutions of karman's equation describing the transonic flow past a corner point on a profile with a curvilinear generatrix

Transonic flows in the neighbourhood of a corner point on a profile are investigated in a class of self-similar solutions of Karman's equation. The corner point is formed by the intersection of two smooth curves, the tangents to which make a convex angle. The generatrix, which lies in the subsonic part of the flow is assumed to be curvilinear and to vary according to a power law. Values of the self-similarity index are found for which transonic flows are possible either with a free streamline or with a rarefaction wave.

Plane initiation of a detonation

The conditions for exciting a plane detonation wave were experimentally observed to be independent of the initial [gas] pressure. The explanation is based on the concept that impacts of transverse waves play a leading role in initiating and propagating the detonation. The dimension of the effective zone which is responsible for initiating the detonation is close to the dimension of the chemical [energy] peak. Formulas are presented for estimating the energy equivalent of the initiator, based on the concept of transforming the plane detonation wave into a spherical, cylindrical, or plane detonation by diffracting the initial wave by convex angle. The basic analytical conclusions of the concept are confirmed by experiment.

Harrington-Luque and Cotrel-Dubousset Instrumentation for Idiopathic Thoracic Scoliosis

This article reports a comparison of the Cotrel-Dubousset (CD) operation with the Harrington-Luque (HL) procedure for the treatment of adolescent idiopathic thoracic scoliosis. Thirty-nine patients were studied preoperatively and postoperatively using segmental radiologic measurements including Cobb angle, end-vertebra angles (EVAs), surgical flexibility index, vertebral rotation, displacement and tilt, convex and concave rib-vertebra angles (RVAs), and kyphosis and lordosis. Cotrel-Dubousset is not significantly different from HL with respect to Cobb angle (%), surgical flexibility index, apical vertebral displacement, apical vertebral rotation, apical rib-vertebra angles, kyphosis, and lordosis. It is significantly better than the HL with respect to the correction of vertebral displacement at T10-11; lower EVA of the thoracic curve; vertebral rotation mainly above the apex; convex RVAs above the apex; and concave RVAs at T10. The surgical correction of vertebral tilt above and below the apex of the thoracic curve is significantly related to the correction of convex and concave RVAs. The view that persistent deformity of ribs is a factor needing surgical correction in some patients with adolescent idiopathic thoracic scoliosis having posterior instrumentation and fusion needs further evaluation.

An Analysis of the Effect of the Zielke Operation on the Rib Cage of S-Shaped Curves in Idiopathic Scoliosis

This report evaluates the rib cage in 16 patients with S-shaped idiopathic scoliosis having the Zielke operation and followed-up for an average period of 30 months. Methods used include Cobb angle and a segmental evaluation (T7-T12) of each of convex and concave rib-vertebra angles (RVAs), rib-vertebra angle differences (RVADs), vertebral rotation, tilt and displacement. Preoperatively, the apical convex ribs droop more than the concave ribs, but the most striking difference is an asymmetry of RVAs, with increasing droop of the concave RVAs from T7-T12. The effect of the Zielke operation (on the lower curve) is: (a) to correct the Cobb angle, vertebral tilt, and displacement of the upper (thoracic) curve; (b) to derotate the spine; (c) to elevate the mobile concave ribs; (d) to have little or no effect on the stiff apical convex ribs; and (e) to increase the droop of the mobile lower convex ribs. During follow-up, six of the upper (thoracic) curves progressed. The apical RVAD and apical convex RVA are not prognostic. The concave RVAs maintain their position while convex RVAs elevate relative to the concave ribs.

On subsonic laminar separation from the discontinuity edge of a profile

Asymptotic methods are used to study a steady subsonic flow of a perfect gas past a convex angle at high Reynolds' numbers. The solution /1/ describing a potential flow past a corner with a free streamline is taken as the limit solution. The pressure gradient in this solution tends to infinity on approaching the corner point from the direction of incoming flow. Its effect on the boundary layer is to form a domain of free interaction, first studied in /2–4/. The Navier-Stokes equations were solved outside the domain of free interaction in the complete neighborhood of the corner in /1/. The flow in the domain of free interaction was studied under the assumption that the surface of the corner is thermally insulated. The problem describing this flow in the first approximation is reduced by means of affine transformations to a problem of laminar separation of an incompressible fluid /5/. This makes it possible to establish a similarity law for subsonic gas flows in the neighborhood of a corner point.

On the elastic-plastic torsion problem

It is shown that solving the elastic-plastic torsion problem is equivalent to solving a nonlinear boundary value problem. The equivalence is valid for a strictly convex cross-section and angles of twist large enough that the plastic region encloses the elastic region. The advantage of this formulation is that no free boundaries are present.

Diffraction of solitary waves

Whitham's extension of geometrical optics to nonlinear diffraction is applied to solitary waves of reference amplitudea 0 in water of uniform depthd 0 on the hypotheses thata 0≪d 0 and that the angle through which a diffracted wave is turned is of the order of (a 0/d 0)1/2. The equations governing the amplitude and direction of the waves are reduced to a quasi-linear, hyperbolic systemof two first-order partial differential equations. Explicit results are obtained for diffraction by a convex bend and by a concave corner, and it is found that a solitary wave of initial amplitudea 0 cannot be turned through a convex angle greater than (3a 0/d 0)1/2 without separating or otherwise losing its identity. An empirical generalization for larger amplitudes and turning angles is proposed. General solutions are obtained (in an appendix) through a hodograph transformation.

Calculation of the Hall coefficient for a mixed curvature, mixed field energy surface by the PFES approach

Abstract A simple calculation of the Hall coefficient for a polyhedral Fermi surface having both convex and concave angles between its faces gave a result having the opposite sign from conventional low or high-field calculations. This is shown to be due to a breakdown in the low-field condition over parts of the energy surface. The possibility of observing the effect experimentally is considered.

Transonic flows behind a receding shock wave

MUCH attention has recently been given to the investigation of transonic problems of gas dynamics. Such flows occur, for instance, in nozzles, in the circulation round bodies with a receding shock wave, in the development of the flow about a break point forming a convex angle, and also on aerofoils with local supersonic regions, etc. Aerodynamic and stability characteristics and questions of control and stability of motion have clearly been insufficiently studied under transonic conditions. Difficulties arise in the theoretical consideration of such problems firstly because in a number of cases there is no complete mathematical formulation of the problem. In regions of mixed gas flows complicated phenomena take place. Behind the main shock wave so-called secondary “suspended” shock waves may occur and in the critical circulation round bodies local supersonic regions are formed which may also be closed by shock waves, etc. The mechanism by which such phenomena occur has not been sufficiently studied and the question of the form of the minimum region of influence and its reconstruction with change of the circulation parameters etc. also remains open. It must also be remarked that for rotational plane and three-dimensional transonic problems no analytical and numerical methods have been developed in practice. Classical analytical methods, developed for plane potential flows and based principally on the use of the hodograph plane and a different simplification and linearization, do not as a rule apply here. Numerical solution of the problem is very difficult and requires the construction of special schemes for the integration of elliptico-hyperbolic equations. In this paper we consider some problems of transonic gas-dynamics related to the theory of plane space rotational flows of an ideal gas, worked out basically by the authors or under their direction. The first part of the paper gives the results of the analytical investigation of a number of exact properties of solutions of proplems of the circulation round bodies with a receding shock wave. The results obtained are given without proof in the forms of theorems (the proofs are in the listed works or will be published in the near future). The second part considers numerical schemes and gives results of circulation for the solution of the complete problem of the supersonic circulation round blunt bodies with a break in the generating contour, and also at low supersonic speeds. We also study here the limits of existence of various types of minimum regions of influence of a mixed flow with blunting. Only numerical schemes using high-speed computers and carefully conducted experiments enable us to obtain quantitative data and a complete picture of the flow in such complicated problems. Here we make an attempt to examine and discuss some properties of transonic flows (solutions in the neighbourhood of the sonic line, the formation of secondary shock waves, the form of the minimum zone of influence etc.) with the positions of the analytical and numerical solutions. It should be pointed out that by this numerical method it is possible to discover and construct secondary shock waves, non-monotonic sonic lines, etc. At the same time the conditions for the collapse of a continuous flow and rules connected with various types of regions of influence were discovered analytically. In the consideration of flows round an angle the effective construction of numerical schemes turns out to be possible only by using asymptotic methods of solving differential equations, etc. Thus the amalgamation of both methods appears to be very fruitful. This work is extended in these directions.