Torsional Forces Research Articles

A Spatio-temporal Description of the Abrupt Changes in the Photospheric Magnetic and Lorentz-Force Vectors During the 15 February 2011 X2.2 Flare

The active region NOAA 11158 produced the first X-class flare of Solar Cycle 24, an X2.2 flare at 01:44 UT on 2011 February 15. Here we analyze SDO/HMI magnetograms covering a 12-hour interval centered at the time of this flare. We describe the spatial distributions of the photospheric magnetic changes associated with this flare, including the abrupt changes in the field vector, vertical electric current and Lorentz force vector. We also trace these parameters' temporal evolution. The abrupt magnetic changes were concentrated near the neutral line and in two neighboring sunspots. Near the neutral line, the field vectors became stronger and more horizontal during the flare and the shear increased. This was due to an increase in strength of the horizontal field components near the neutral line, most significant in the horizontal component parallel to the neutral line but the perpendicular component also increased in strength. The vertical component did not show a significant, permanent overall change at the neutral line. The increase in total flux at the neutral line was accompanied by a compensating flux decrease in the surrounding volume. In the two sunspots near the neutral line the azimuthal flux abruptly decreased during the flare but this change was permanent in only one of the spots. There was a large, abrupt, downward vertical Lorentz force change during the flare, consistent with results of past analyses and recent theoretical work. The horizontal Lorentz force acted in opposite directions along each side of neutral line, with the two sunspots at each end subject to abrupt torsional forces. The shearing forces were consistent with field contraction and decrease of shear near the neutral line, whereas the field itself became more sheared as a result of the flux collapsing towards the neutral line from the surrounding volume.

Imaging soft matters in water with torsional mode atomic force microscopy

We have developed a high-sensitivity atomic force microscopy (AFM) mode operated in aqueous environment based on the torsional resonance of the cantilever. It is found that the torsional mode can achieve a good spatial resolution even with a relatively large tip. We have used this mode to image different soft materials in water, including DNA molecules and purple membrane. High-resolution images of purple membrane can be obtained at a relatively low ion concentration under a long-range electrostatic force. Thus the torsional mode allows investigators to probe surface structures and their properties under a wide range of solution conditions.

Tolerance to mechanical damage in ten herbaceous grassland plant species

The establishment of plants with high damage tolerance may provide a means for soil protection on sites exposed to strong disturbance. In a pot experiment, we investigated the tolerance to mechanical strain of ten grassland plant species representing three growth form groups (cespitose: Festuca arundinacea, Lolium perenne, Taraxacum officinale; rhizomatous: Achillea millefolium, Elymus repens, Poa pratensis; stoloniferous: Agrostis stolonifera, Festuca rubra rubra, Poa supina, Trifolium repens). We hypothesised that growth form and pre-disturbance biomass allocation to the root serve as predictors of damage tolerance. With a tool imitating the action of cleated football boots or scratching chicken, we applied three standardized levels (moderate, medium, strong) of a torsional force which exceeded the shear strength of the sward and impacted on shoots and roots. Post-treatment shoot biomass in relation to shoot biomass of the non-treated control plants served as a measure of damage tolerance. Species, but not growth form groups, differed significantly in damage tolerance, with F. arundinacea and P. pratensis showing the best performance. Shoot re-growth was strongly correlated with relative post-treatment root biomass across all species and treatment levels (R<sup>2</sup> = 0.25, P < 0.001), but not with pre-treatment root biomass. We conclude that root resistance to mechanical damage is the prevalent determinant of tolerance to disturbance.  

Impact of lateral mass anatomic variation on ideal polyaxial screw head mobility: technical considerations

Objective. To assess optimal angulation characteristics of lateral mass screws for subaxial (C3 to C6) fixation of the cervical spine in the neutral position. Background. In the typical Magerl or Anderson placement technique, the screw trajectory is ideally parallel to the facet joint. For the rod and screw to align properly, the screw head must rotate enough to become perpendicular to the rod. If the optimal angle for the screw head is limited by the screw design, abnormal torsional forces will be generated at the rod/screw interface inducing kyphosis. In this paper, we examined the spinal anatomy in patients with normal CTs to determine the necessary range of motion between tulip head and screw to prevent forced persuasion and abnormal cervical spine alignment. Methods. We examined subaxial radiographs of 292 vertebrae from C3 to C6 in 73 normal subjects. Computed tomography (CT) scans of the cervical spine with multiplanar reconstructions were evaluated in the axial and sagittal planes. A planned screw entry angle of 30° based upon the midpoint of the lateral mass was used in the axial plane, and parallel to the facet joint in the sagittal plane. The screw head angle (SHA) was then calculated from this 3D measured angle. Results. The measured SHA ranged from 27 to 60°. The average SHA was 43.8°. The average SHA was not significantly different between the levels measured with consistent range and standard deviation. Seventy-six percent (223/292) of levels measured required a SHA >40°, and 12% (36/292) required a SHA >50°. Conclusion. The authors recommend using cervical instrumentation systems that allow for at least 55° of freedom of the polyaxial head to prevent abnormal segmental forces. In systems with lesser angulation, technique modifications must be applied to prevent translational forces.

Biomechanical Performance of Flexible Intramedullary Nails With End Caps Tested in Distal Segmental Defects of Pediatric Femur Models

Unstable distal femoral fractures in children are challenging lesions with restricted surgical options for adequate stabilization. Elastic nails have become popular for treating femoral shaft fractures, yet they are still challenging for using in distal fractures. The aim of this study was to test whether end caps (CAP) inserted into the nail extremity improved the mechanical stabilization of a segmental defect at the distal femoral metaphyseal-diaphyseal junction created in an artificial pediatric bone model. Two 3.5-mm titanium elastic nails (TEN) were introduced intramedullary into pediatric femur models, and a 7.0-mm-thick segmental defect was created at the distal diaphyseal-metaphyseal junction. Nondestructive 4-point bending, axial-bending, and torsion tests were conducted. After this, the end caps were inserted into the external tips of the nails and then screwed into the bone cortex. The mechanical tests were repeated. Stiffness, displacement, and torque were analyzed using the Wilcoxon nonparametric test for paired samples. In the combined axial-bending tests, the TEN+CAP combination was 8.75% stiffer than nails alone (P<0.01); in torsion tests, the TEN+CAP was 14% stiffer than nails alone (P<0.01). In contrast, the 4-point bending test did not show differences between the methods (P=0.91, stiffness; P=0.51, displacement). Thus, the end caps contributed to an increase in the construct stability for torsion and axial-bending forces but not for 4-point bending forces. These findings indicate that end caps fitted to elastic nails may contribute to the stabilization of fractures that our model mimics (small distal fragment, bone comminution, and distal bone fragment loss). Type II [therapeutic study: lesser-quality randomized controlled trial (eg, <80% follow-up, no blinding, or improper randomization)].

Bite Force Evaluation of Mandibular Fractures Treated With Microplates and Miniplates

The purpose of this study was to determine the clinical stability and efficacy of 1 microplate combined with 1 miniplate in the management of mandibular fractures of the interforaminal region compared with the standard 2-miniplate treatment using bite force measurements. Twenty patients were treated for isolated mandibular fractures of the interforaminal region. They were randomly divided into group A (test group) and group B (control group), with 10 patients per group. Group A underwent osteosynthesis using the combination of 1 microplate (subapical) and 1 miniplate (at the lower border). Group B underwent osteosynthesis using the standard 2-miniplate protocol. The bite force measurements were performed preoperatively and postoperatively at each follow-up using a bite force recorder. As a secondary outcome, the patients also were assessed for complications, such as infection, that might interfere with successful osteosynthesis at the fracture site. A statistically significant increase in incisor bite force was found in the 2 groups compared with the preoperative bite force measurements. No statistically significant difference was seen in the incisor bite force of either group at the different follow-up visits. No statistically significant difference was seen in the molar bite force (right vs left) of the test and control groups during follow-up. Molar bite force on the nonfractured side was greater than on the fractured side in the 2 groups. Infection was seen in 1 patient (ie, 10%) in each group. On surgical exploration, the fracture had united and the infection was resolved in the 2 patients, with no further complications. The replacement of an upper miniplate by a microplate in the management of mandibular fractures is stable and adequately efficacious to withstand the masticatory loads and torsional forces acting in the anterior region of the mandible.

A comparative evaluation of different treatment modalities for parasymphysis fractures: a pilot study

Maxime Champy advised the use of two miniplates for parasymphysis fractures because of the high torsional forces in the anterior region of the mandible. According to him there is no need for intraoperative or postoperative intermaxillary fixation, but most surgeons use arch bars for intraoperative or postoperative intermaxillary fixation. This study evaluated the role of the lower arch bar as a tension band eliminating the need for an upper miniplate (tension band plate) in cases of parasymphysis fractures. 3 groups underwent treatment. In the first group, two titanium miniplates were placed across the fracture site along with Erich's arch bar for 6 weeks. In the second group, two titanium miniplates were used for osteosynthesis without Erich's arch bar. In the third group, one titanium miniplate was placed along with Erich's arch bar for 6 weeks. The results of third group were statistically non-significant compared with those of the first and second groups.

Flow and force inducement using micron size dielectric barrier discharge actuators

Micron size dielectric barrier discharge actuators, designed for minimal footprint area and weight penalty, show a wall jet up to 2.0 m/s consuming 15 W/m of electrode. A torsional balance measures force up to 3 mN/m of electrode and demonstrates equivalent “thrust effectiveness” (induced force/power) to macroscale actuators. Compared with reported macroscale data, the microscale actuator shows a 31% increase in energy conversion efficiency. Per unit actuator mass, both the force and the velocity induced by microscale actuators show an order of magnitude (22.1 and 18.5 times, respectively) increase over macroscale actuators, making them suitable for distributed flow control applications.

Effects of Ice Thickness on the Aerodynamic Characteristics of Crescent Shape Iced Conductors

Aerodynamic characteristics of iced conductors were investigated by the wind tunnel test. Under the homogeneous turbulence of 5% intensity, aerodynamic force coefficients of single and bundled conductors were obtained at wind angles of 0°~180°. The variation patterns of aerodynamic forces on the iced conductors with respect to wind angels of attack were systematically studied for the ice thickness of 0.25, 0.5, 0.75 and 1 times of the conductor diameter. The difference of aerodynamic force characteristics for single and bundled conductors were identified and discussed. Based on the Den Hartog and Nigol’s mechanisms of galloping, the wind angle ranges sensitive to galloping were analyzed. The results show that lift and torsion force coefficients reach peak values at wind angles of 15°~20°. For bundled conductors, lift force curve is approximately agreed with the curve of single conductor. Drag force coefficients were smaller than these of single conductor at some wind angles. There are noticeably differences of torsion coefficients existed between bundled conductors and single conductor. According to two classical galloping mechanisms, wind angles of 15°~30°are critical for the galloping of iced conductors with crescent shapes.

Analysis and applications of the Voronoi Implicit Interface Method

We analyze a new mathematical and numerical framework, the “Voronoi Implicit Interface Method” (“VIIM”), first introduced in Saye and Sethian (2011) [R.I. Saye, J.A. Sethian, The Voronoi Implicit Interface Method for computing multiphase physics, PNAS 108 (49) (2011) 19498–19503] for tracking multiple interacting and evolving regions (“phases”) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.). From a mathematical point of view, the method provides a theoretical framework for moving interface problems that involve multiple junctions, defining the motion as the formal limit of a sequence of related problems. Discretizing this theoretical framework provides a numerical methodolology which automatically handles multiple junctions, triple points and quadruple points in two dimensions, as well as triple lines, etc. in higher dimensions. Topological changes in the system occur naturally, with no surgery required. In this paper, we present the method in detail, and demonstrate several new extensions of the method to different physical phenomena, including curvature flow with surface energy densities defined on a per-phase basis, as well as multiphase fluid flow in which density, viscosity and surface tension can be defined on a per-phase basis.We test this method in a variety of ways. We perform rigorous analysis and demonstrate convergence in both two and three dimensions for a variety of evolving interface problems, including verification of von Neumann–Mullins’ law in two dimensions (and its analog in three dimensions), as well as normal driven flow and curvature flow with and without constraints, demonstrating topological change and the effects of different boundary conditions. We couple the method to a second order projection method solver for incompressible fluid flow, and study the effects of membrane permeability and impermeability, large shearing torsional forces, and the effects of varying density, viscosity and surface tension on a per-phase basis. Finally, we demonstrate convergence in both space and time of a topological change in a multiphase foam.

An improved torsional force field for cis-enol malonaldehyde

An improved torsional force field for cis-enol malonaldehyde is presented. First, the conformational potential energy has been calculated by ab initio method at MP2/6-31G** level as a function of two torsional angles around C–C and C–O single bonds. Then, the calculated 2D potential energy surface has been fitted to a potential function, where cross terms of the two dihedrals are added to the ordinary single cosine terms of the optimised potentials for liquid simulations all atom (OPLS-aa) type. The optimised function excellently reproduces the energies with the standard deviation as small as 1.9 kJ/mol. The function may be used easily in the molecular dynamics calculation.

Analytical solution of torsion vibration of a finite cylindrical cavity in a transversely isotropic half‐space

AbstractA transversely isotropic linear elastic half‐space with depth wise axis of material symmetry containing a cylindrical cavity of finite length is considered to be under the effect of a time‐harmonic torsion force applied on a ring at an arbitrary depth on the surface of the cylindrical cavity. With the aid of cosine transforms, the boundary value problem for the fundamental solution is reduced to a generalized Cauchy singular integral equation. The Cauchy integral equation involved in this paper is analytically investigated and the final equation is numerically solved with an in‐depth attention. Integral representation of the stress and displacement are obtained, and is shown that their degenerated form to the static problem of isotropic material is coincide with existing solutions in the literature. To investigate the effect of material anisotropy, the results are numerically evaluated and illustrated.

A biomechanical study of monosegmental fixation by pedicle instrumentation in the management of thoracolumbar fractures

Objective To test the biomechanical stability of fixation of thoracolumbar burst fractures (A 3.1 by AO classification) with monosegmental pedicle instrumentation (MSPI). Methods Six specimens of T10-L2 thoracolumbar spine segment were harvested from human donors ranging in age from 27 to 46 years (mean,39 years).Incomplete burst fractures (A3.1 by AO classification) were made at the level of T12 in the specimens using a mechanical dropping hammer.The fractures were fixated with MSPI in the specimens sequentially to restore spinal stability.The specimens in conditions of integrity,fracture and MSPI fixation were tested on the mechanical testing system for biomechanical assessment of the segmental stability.Range of motions (ROM) in flexion-extension and lateral bending were recorded by a 2-camera VICON motion measurement system.The rotational stability was tested by a computer torsional testing machine. Results The ROMs of MSPI specimens in flexion,extension,left and right lateral bending were respectively 0.14°± 0.02°,0.07° ± 0.02°,0.73 ° ± 0.22° and 0.74° ± 0.13°,significantly lower than those of fracture specimens (0.84° ± 0.10°,1.94° ± 0.30°,2.33° ± 0.56° and 2.54° ± 0.44° ) and those of intact specimens (0.46° ±0.05°,1.01° ±0.23°,1.34° ± 0.24° and 1.30° ± 0.31°) ( P ＜ 0.05).The torsional force needed in MSPI specimens was 3103.00 ± 213.11 N,which was not significantly different from that in intact specimens (2654.75 ± 122.90 N) ( P ＞ 0.05) but significantly higher than that in fracture specimens ( 1519.60 ± 100.82 N) ( P ＜ 0.05). Conclusion In the treatment of thoraeolumbar burst fractures (A3.1 by AO classification),MSPI can reconstruct the spinal stability. Key words: Spinal fracture; Fracture fixation, internal; Bone nail; Biomechanics

Performance and Cost Evaluation of a Smart Tuned Mass Damper for Suppressing Wind-Induced Lateral-Torsional Motion of Tall Structures

The implementation of a vibration control system has always been associated with considerable capital and long-standing main- tenance costs, resulting in limited practical applications of damping devices. The notion of a massive implementation cost is largely the result of a lack of cost analysis of vibration control systems in the literature. This paper presents the structural design of awind-sensitive tall building at various design stages and the results of a collaborative study with two damper construction companies on the cost estimation of a control device. A series of wind tunnel pressure tests were conducted on a 1∶400 scale model to determine the translational and torsional wind forces acting on the studied building. A structural optimization was subsequently employed to reduce the excessive top deflection, and a smart tuned mass damper was implemented at the final design stage to meet occupant comfort criteria. The details of each structural design stage, the implementation of vibration control devices, and a collaborative study on damper cost are outlined in this paper. DOI: 10.1061/(ASCE)ST .1943-541X.0000486. © 2012 American Society of Civil Engineers. CE Database subject headings: Torsion; Damping; High-rise buildings; Wind forces; Costs. Author keywords: Lateral-torsional motion; Structural optimization; STMD; Damper pricing chart.

Reducing the data: Analysis of the role of vascular geometry on blood flow patterns in curved vessels

Three-dimensional simulations of blood flow usually produce such large quantities of data that they are unlikely to be of clinical use unless methods are available to simplify our understanding of the flow dynamics. We present a new method to investigate the mechanisms by which vascular curvature and torsion affect blood flow, and we apply it to the steady-state flow in single bends, helices, double bends, and a rabbit thoracic aorta based on image data. By calculating forces and accelerations in an orthogonal coordinate system following the centreline of each vessel, we obtain the inertial forces (centrifugal, Coriolis, and torsional) explicitly, which directly depend on vascular curvature and torsion. We then analyse the individual roles of the inertial, pressure gradient, and viscous forces on the patterns of primary and secondary velocities, vortical structures, and wall stresses in each cross section. We also consider cross-sectional averages of the in-plane components of these forces, which can be thought of as reducing the dynamics of secondary flows onto the vessel centreline. At Reynolds numbers between 50 and 500, secondary motions in the directions of the local normals and binormals behave as two underdamped oscillators. These oscillate around the fully developed state and are coupled by torsional forces that break the symmetry of the flow. Secondary flows are driven by the centrifugal and torsional forces, and these are counterbalanced by the in-plane pressure gradients generated by the wall reaction. The viscous force primarily opposes the pressure gradient, rather than the inertial forces. In the axial direction, and depending on the secondary motion, the curvature-dependent Coriolis force can either enhance or oppose the bulk of the axial flow, and this shapes the velocity profile. For bends with little or no torsion, the Coriolis force tends to restore flow axisymmetry. The maximum circumferential and axial wall shear stresses along the centreline correlate well with the averaged in-plane pressure gradient and the radial displacement of the peak axial velocity, respectively. We conclude with a discussion of the physiological implications of these results.

Solution of a Green’s function for a saturated porous medium in a half-space subjected to a torsional force

Based on the solutions of the Green’s function for a saturated porous medium obtained by the authors, and using transformation of axisymmetric coordinates, Sommerfeld integrals and superposition of the influence field on a free surface, the authors have obtained displacement solutions of a saturated porous medium subjected to a torsional force in a half-space. The relationship curves of the displacement solutions and various parameters (permeability, frequency, etc.) under action of a unit of torque are also given in this paper. The results are consistent with previous Reissner’s solutions, where a two-phase medium decays to a single-phase medium. The solution is useful in solving relevant dynamic problems of a two-phase saturated medium in engineering.

Torsion of monofilament and polyfilament sutures under tension decreases suture strength and increases risk of suture fracture

Background: A continuous running suture is the preferential method for abdominal closure. In this technique the suture is secured with an initial knot and successive tissue bites are taken. At each tissue bite, the needle is rotated through the tissue; in doing so, the suture can twist around the knot which acts as an anchor.Objective: To determine the effect of axial torsional forces on sutures used in abdominal closure.Methods: The effect of axial twisting on polydioxanone (PDS*II), polyglactin (Vicryl), polypropylene (Prolene) and nylon (Ethilon) sutures was investigated using a uniaxial testing device.Results: The maximum tensile force withstood for untwisted sutures was determined: polydioxanone failed at a tensile force of 116.4±0.84 N, polyglactin failed at 113.9±2.4 N, polypropylene failed at 71.1±1.5 N and nylon failed at 61.8±0.5 N. Twisting decreased the maximum tensile force of all sutures; one complete twist per 10 mm (i.e., 15 twists) decreased the tensile strength of polydioxanone by 21%, polyglactin by 23%, polypropylene by 16% and nylon by 13%, p<0.001. Excessive twisting caused a nonlinear decrease in suture strength, with one twist per 75 mm (i.e., 20 twists) of polydioxanone decreasing strength by 39%, P<0.001.Conclusion: The effect of excessive twisting on the mechanical properties of sutures is a previously unrecognised phenomenon. Surgeons should be aware that this can result in a decrease in suture strength and reduce the elasticity of the material, and therefore need to adapt their practice to reduce the torsional force placed on sutures.

Quantifying and comparing torsional strains after olecranon plating

PurposeAny torsion experienced at a fracture site will directly translate into shearing forces and has been regarded as detrimental to healing. The purpose of this study was to determine which plating system currently on the market controls torsional forces about comminuted olecranon fractures most effectively. MethodsFive olecranon plates (Acumed, Synthes-SS, Synthes-Ti, ITS/US Implants and Zimmer) were implanted to stabilise a simulated comminuted fracture pattern in 50 fresh-frozen, cadaveric elbows. All specimens were evaluated by dual energy X-ray absorptiometry (DXA) scan to determine bone density. Three-dimensional displacement analysis was conducted to assess fragment motion through physiologic cyclic arcs of motion. The specimens were cycled through progressive physiologic loads (0.18–5.6kg). Movements of the fragments were statistically compared amongst the different implants using one-way analysis of variance (ANOVA) and Tukey Honestly Significant Difference (HSD) post hoc comparisons with a critical significance level of α=0.05. ResultsDXA bone mineral densities (BMDs) ranged from 0.465 to 0.927, with an average of 0.714. The Acumed, Synthes-SS, Synthes-Ti and Zimmer plates allowed <1° of torsion up to 1.6kg of load. The differences between these plates at this load were not statistically significant. The ITS/US Implants plate, however, allowed significantly more torsion above loads of 2.6kg (p=0.045) compared with all other plates. The ITS/US Implants plate allowed over 2° of torsion at 2.6kg (p=0.012), and nearly 3° at 3.6kg (p=0.045). The Zimmer plate consistently allowed more torsion than the Acumed plate or either of the Synthes plates, but the differences were not statistically significant. ConclusionRegardless of which olecranon plate is used, the authors recommend limiting postoperative rehabilitation loads to below 1.6kg in an effort to minimise the detrimental effects of torsion on healing. If loads over 1.6kg are anticipated, the authors recommend the use of the Acumed plate or either of the Synthes plates.

Investigation on the Effect of Infilled Walls Utilizing Response Spectrum Analysis for Steel Staggered-Truss System

Considering the structure type of the steel staggered-truss (SST) system, the effect of infilled walls will be major and need to be studied amply, some scientific design regulations need to be found for referrence. Based on two different 3D models considering or ignoring the stiffness of infilled walls (SIW), a numerical investigation is presented on the structural behaviors of the SST system utilizing the finite element 3D simulation analysis soft ware ETABS. The longitudinal structure is asymmetrical due to the SIW, it causes the torsion forces in the building. Comparing to the different results of response spectrum analysis, including storey drift and equivalent base shear under frequent earth quake and rare earth quake, some conclusions were made, including the capacity of the SST system under seismic load and the effect of the SIW for SST system. The increased base shear force factors due to the effect of the SIW were suggested for SST structure design, it is different from the other steel structure types.

A procedure for rapid visual screening for seismic safety of wood-frame dwellings with plan irregularity

This paper highlights the development of a rapid visual screening (RVS) tool to quickly identify, inventory, and rank residential buildings that are potentially seismically hazardous, focusing on single-family, wood-frame dwellings with plan irregularity. The SAPWood software was used to perform a series of nonlinear time-history analyses for 480 representative models, covering different combinations of plan shapes, numbers of floors, base-rectangular areas, shape aspect ratio, area percentage cutoffs, window and door openings, and garage doors. The evolutionary parameter hysteresis model was used to represent the load–displacement relationship of structural panel-sheathed shear walls and a 10 parameter CUREE hysteresis model for gypsum wallboard sheathed walls. Ten pairs of ground motion time histories were used and scaled to four levels of spectral acceleration at 0.167, 0.5, 1.0, and 1.5g. An average seismic performance grade for each model was generated based on the predicted maximum shear wall drifts. Five seismic performance grades: 4, 3, 2, 1, and 0, are associated with the 1% immediate occupancy drift limit, 2% life safety limit, 3% collapse prevention limit, 10% drift, and exceeding 10% drift, respectively. The obtained average seismic performance grades were used to develop a new RVS tool that is applicable for checking the seismic performance of either existing or newly designed single-family, wood-frame dwellings. It examines the adequacy of the structure’s exterior shear walls to resist lateral forces resulting from ground motions, including torsional forces induced from plan irregularity.