scholarly journals Effect of the presence of orthodontic brackets on intraoral scans

2020 ◽  
Vol 91 (1) ◽  
pp. 98-104
Author(s):  
Sung-Ja Kang ◽  
Youn-Ju Kee ◽  
Kyungmin Clara Lee
Keyword(s):  
Cross Sections ◽  
Tooth Movement ◽  
Vertical Section ◽  
Three Dimensional ◽  
Orthodontic Brackets ◽  
Horizontal Section ◽  
Arch Width ◽  
Tooth Surfaces ◽  
The Cross ◽  
Width Measurements

ABSTRACT Objectives The need for intraoral scanning in the presence of brackets has increased for monitoring tooth movement during orthodontic treatment. The purpose of this study was to evaluate the effect of orthodontic brackets bonded to tooth surfaces on intraoral scans. Materials and Methods Intraoral scans were performed in 30 patients using both iTero and Trios scanners before and after bonding of the brackets. The two sets of intraoral scans of each patient and intraoral scans with and without brackets were superimposed using a best-fit algorithm, and three-dimensional (3D) surface analysis was performed. In each superimposition, discrepancies in the 3D axes and arch-width measurements in the incisor and molar regions were compared. In addition, the range of distortion around the brackets was evaluated on the cross sections of each superimposition. Results The overall discrepancies between the intraoral scans with and without brackets were within 0.30 mm. The arch-width discrepancies in the molar region were greater than those in the incisor region, but the differences were not statistically significant (P = .972 for iTero; P = .960 for Trios). The cross sections of the superimposed intraoral scans with and without brackets showed that the deviations were within 0.40 mm in the horizontal section and within 0.35 mm in the vertical section around the brackets. Conclusions The results of this study indicate that the accuracy of intraoral scans, even in the presence of brackets, is clinically acceptable, and the regions beyond 0.50 mm around the brackets should be used for superimposition on images without brackets.

Convection in a box: linear theory

1967 ◽  
Vol 30 (3) ◽  
pp. 465-478 ◽  
Author(s):  
Stephen H. Davis
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Linear Theory ◽  
Cross Sections ◽  
Critical Rayleigh Number ◽  
Three Dimensional ◽  
Wave Number ◽  
Spatial Variables ◽  
Zero Velocity ◽  
The Cross

The linear stability of a quiescent, three-dimensional rectangular box of fluid heated from below is considered. It is found that finite rolls (cells with two non-zero velocity components dependent on all three spatial variables) with axes parallel to the shorter side are predicted. When the depth is the shortest dimension, the cross-sections of these finite rolls are near-square, but otherwise (in wafer-shaped boxes) narrower cells appear. The value of the critical Rayleigh number and preferred wave-number (number of finite rolls) for a given size box is determined for boxes with horizontal dimensions h, ¼ ≤ h/d ≤ 6, where d is the depth.

Interference in a three-dimensional array of jets

2015 ◽  
Vol 26 (5) ◽  
pp. 795-819
Author(s):  
P. E. WESTWOOD ◽  
F. T. SMITH
Keyword(s):  
Cross Sections ◽  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Longitudinal Vortex ◽  
Cross Sectional ◽  
Dimensional Array ◽  
Unsteady Jets ◽  
The Cross ◽  
Jet Cross Sections

The theoretical investigation here of a three-dimensional array of jets of fluid (air guns) and their interference is motivated by applications to the food sorting industry especially. Three-dimensional motion without symmetry is addressed for arbitrary jet cross-sections and incident velocity profiles. Asymptotic analysis based on the comparatively long axial length scale of the configuration leads to a reduced longitudinal vortex system providing a slender flow model for the complete array response. Analytical and numerical studies, along with comparisons and asymptotic limits or checks, are presented for various cross-sectional shapes of nozzle and velocity inputs. The influences of swirl and of unsteady jets are examined. Substantial cross-flows are found to occur due to the interference. The flow solution is non-periodic in the cross-plane even if the nozzle array itself is periodic. The analysis shows that in general the bulk of the three-dimensional motion can be described simply in a cross-plane problem but the induced flow in the cross-plane is sensitively controlled by edge effects and incident conditions, a feature which applies to any of the array configurations examined. Interference readily alters the cross-flow direction and misdirects the jets. Design considerations centre on target positioning and jet swirling.

A super-convergent thin-walled 3D beam element for analysis of laminated composite structures with arbitrary cross-section

2021 ◽  
pp. 1-23
Author(s):  
M. Talele ◽  
M. van Tooren ◽  
A. Elham
Keyword(s):  
Cross Sections ◽  
Composite Structures ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Beam Element ◽  
Arbitrary Cross Section ◽  
Beam Model ◽  
Cross Sectional ◽  
Thin Walled ◽  
The Cross

Abstract An efficient, fully coupled beam model is developed to analyse laminated composite thin-walled structures with arbitrary cross-sections. The Euler–Lagrangian equations are derived from the kinematic relationships for a One-Dimensional (1D) beam representing Three-Dimensional (3D) deformations that take into account the cross-sectional stiffness of the composite structure. The formulation of the cross-sectional stiffness includes all the deformation effects and related elastic couplings. To circumvent the problem of shear locking, exact solutions to the approximating Partial Differential Equations (PDEs) are obtained symbolically instead of by numerical integration. The developed locking-free composite beam element results in an exact stiffness matrix and has super-convergent characteristics. The beam model is tested for different types of layup, and the results are validated by comparison with experimental results from literature.

scholarly journals Three-dimensional extension of Lighthill's large-amplitude elongated-body theory of fish locomotion

2011 ◽  
Vol 674 ◽  
pp. 196-226 ◽  
Author(s):  
FABIEN CANDELIER ◽  
FREDERIC BOYER ◽  
ALBAN LEROYER
Keyword(s):  
Cross Sections ◽  
Velocity Potential ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Neumann Boundary ◽  
The Body ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Curvature Effects ◽  
The Cross

The goal of this paper is to derive expressions for the pressure forces and moments acting on an elongated body swimming in a quiescent fluid. The body is modelled as an inextensible and unshearable (Kirchhoff) beam, whose cross-sections are elliptic, undergoing prescribed deformations, consisting of yaw and pitch bending. The surrounding fluid is assumed to be inviscid, and irrotational everywhere, except in a thin vortical wake. The Laplace equation and the corresponding Neumann boundary conditions are first written in terms of the body coordinates of a beam treating the body as a fixed surface. They are then simplified according to the slenderness of the body and its kinematics. Because the equations are linear, the velocity potential is sought as a sum of two terms which are linked respectively to the axial movements of the beam and to its lateral movements. The lateral component of the velocity potential is decomposed further into two sub-components, in order to exhibit explicitly the role of the two-dimensional potential flow produced by the lateral motion of the cross-section, and the role played by the curvature effects of the beam on the cross-sectional flow. The pressure, which is given by Bernoulli's equation, is integrated along the body surface, and the expressions for the resultant and the moment are derived analytically. Thereafter, the validity of the force and moment obtained analytically is checked by comparisons with Navier–Stokes simulations (using Reynolds-averaged Navier–Stokes equations), and relatively good agreements are observed.

THE AHARONOV–CASHER SCATTERING: THE EFFECT OF THE ∇ · E TERM

2010 ◽  
Vol 25 (18) ◽  
pp. 1531-1540 ◽  
Author(s):  
E. AL-QAQ ◽  
M. S. SHIKAKHWA
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Structural Difference ◽  
Scalar Particle ◽  
Delta Function ◽  
Spin Orientation ◽  
The Cross ◽  
Attractive Case ◽  
Aharonov Bohm

In the Aharonov–Casher (AC) scattering, a neutral particle interacts with an infinitesimally thin, long charge filament resulting in a phase shift. In the original AC treatment, a ∇ · E term proportional to the charge density at the filament's position is dropped from the Hamiltonian on the basis that the particle is banned from the filament, thus, the resulting Hamiltonian compares with the Aharonov–Bohm Hamiltonian of a scalar particle. Here, we consider AC scattering with this term included. Starting from the three-dimensional nonrelativistic Aharonov–Casher (AC) Schrödinger equation with the ∇ · E term included, we find the wave functions — in particular their singular component — the phase shifts and thus compute the scattering amplitudes and cross-sections. We show that singular solutions in the AC case appear only when the delta function interaction introduced is attractive regardless of the spin orientation of the particle. We find that the inclusion of this term does not introduce a structural difference in the general form of the cross-section even for polarized particles. Its mere effect, is in shifting the parameter N (the greatest integer in α) that appears in the cross-section, in the attractive case, by one. Interesting situation appears when N = 0, thus α=δ, in the case α≻0, and N = -1, so α = 1-δ in the case α≺0: At these values of the parameter N, where αis just any fraction, the cross-section for a particle polarized in the scattering plane to scatter in a state with the same polarization, is isotropic. It also vanishes, at these values of N, for transitions between same-helicity eigenstates. For these values of the parameter N and at the special values α = ±1/2, the cross-sections for both signs of α coincide. The main differences between this model and the "mathematically equivalent" spin-1/2 AB theory are outlined.

The dynamics of the near field of strong jets in crossflows

1989 ◽  
Vol 200 ◽  
pp. 95-120 ◽  
Author(s):  
Sergio L. V. Coelho ◽  
J. C. R. Hunt
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Near Field ◽  
Three Dimensional ◽  
Vortex Sheet ◽  
Transverse Component ◽  
Viscous Effects ◽  
Mean Velocity ◽  
Pressure Drag ◽  
The Cross

An inviscid three-dimensional vortex-sheet model for the near field of a strong jet issuing from a pipe into a crossflow is derived. The solution for this model shows that the essential mechanisms governing this idealized flow are the distortion of the main transverse vorticity by the generation of additional axial and transverse vorticity within the pipe owing to the pressure gradients induced by the external flow, and the convection of both components of vorticity from the upwind side of the jet to its downwind side.The deformation of the cross-section of the jet which is predicted by this model is compared with the deformation predicted by the commonly used time-dependent two-dimensional vortex-sheet model. Differences arise because the latter model does not take into account the effects of the transport of the transverse component of vorticity. The complete three-dimensional vortex-sheet model leads to a symmetrical deformation of the jet cross-section and no overall deflection of the jet in the direction of the stream.To account for viscous effects, the initial region of a strong jet issuing into a uniform crossflow is modelled as an entraining three-dimensional vortex sheet, which acts like a sheet of vortices and sinks, redistributing the vorticity in the bounding shear layer and inducing non-symmetrical deformations of the cross-section of the jet. This leads to a deflection of the jet in the direction of the stream, and the loci of the centroids of the cross-sections of the jet describe a quadratic curve.Deformations predicted by each of the three models are compared with measurements obtained from photographs of the cross-sections of a jet of air emerging into a uniform crossflow in a wind tunnel. Mean velocity measurements around the jet made with a hot-wire anemometer agree with the theory; they clearly invalidate models of jets based on ‘pressure drag’.

The Nature of Centroidal Locus in Misaligned Flip-Chip Solder Joints

1997 ◽  
Vol 119 (3) ◽  
pp. 156-162
Author(s):  
G. Subbarayan ◽  
A. Deshpande
Keyword(s):  
Solder Joint ◽  
Cross Sections ◽  
Flip Chip ◽  
Solder Joints ◽  
Three Dimensional ◽  
Diameter Ratio ◽  
Straight Line ◽  
Dimensional Models ◽  
The Cross ◽  
Three Dimensional Models

The self-alignment mechanism of molten flip-chip solder joints is being increasingly used in passive alignment of optoelectronic devices. For these applications, three-dimensional models of misaligned solder joints are necessary to understand the effect of solder joint design parameters on self alignment. To reduce the complexity of fully three-dimensional models, intuitively reasonable assumptions are often made in their theoretical development. Two such assumptions for misaligned flip-chip solder joints with circular pads are that the locus of centroids is a straight line and that the cross sections are circular in shape. In the present paper, the limits of validity of these two assumptions are explored. In general, if either the top and bottom pad radii are identical, or if there is no misalignment between the pads, then the centroidal locus is a straight line and the cross sections are circular. The extent of deviation from straight line centroidal locus or circular cross section depends on the ratio of the top and bottom pad radii and on the extent of misalignment between the pads. For a misalignment equal to 20 percent of the solder joint height and a joint with 90 percent pad diameter ratio, the deviation from straight line locus is 7 percent and the deviation from circularity is less than 1 percent. However, as the pad ratio is decreased to 50 percent, and as the misalignment is increased to 100 percent, the deviation in centroidal locus increases to 43 percent and the deviation from circularity increases to 33 percent. Thus, straight line locus and circular cross sections are reasonable assumptions for flip-chip solder joints provided the pad diameter ratio and misalignment are small.

Three-Dimensional Vibration Analysis of Toroidal Sectors With Solid Circular Cross-Sections

2010 ◽  
Vol 77 (4) ◽  
Author(s):  
D. Zhou ◽  
Y. K. Cheung ◽  
S. H. Lo
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Small Strain ◽  
Boundary Function ◽  
Mode Shapes ◽  
Curvature Radius ◽  
Linear Elasticity Theory ◽  
Energy Principle ◽  
Cross Sectional ◽  
The Cross

This paper studies the free vibration of circular toroidal sectors with circular cross-sections based on the three-dimensional small-strain, linear elasticity theory. A set of orthogonal coordinates, composing the polar coordinate (r,θ) with the origin on the cross-sectional centerline of the sector and the circumferential coordinate φ with the origin at the curvature center of the centerline, is developed to describe the displacements, strains, and stresses in the sector. Each of the displacement components is taken as a product of four functions: a set of Chebyshev polynomials in φ and r coordinates, a set of trigonometric series in θ coordinate, and a boundary function in terms of φ. Frequency parameters and mode shapes have been obtained via a displacement-based extremum energy principle. The upper bound convergence of the first eight frequency parameters accurate up to five figures has been achieved. The present results agree with those from the finite element solutions. The effect of the ratio of curvature radius R to the cross-sectional radius a and the subtended angle φ0 on the frequency parameters of the sectors are discussed in detail. The three-dimensional vibration mode shapes are also plotted.

scholarly journals 3D IMAGE BASED GEOMETRIC DOCUMENTATION OF THE TOWER OF WINDS

2016 ◽  
Vol XLI-B5 ◽  
pp. 969-975
Author(s):  
M. S. Tryfona ◽  
A. Georgopoulos
Keyword(s):  
Point Cloud ◽  
3D Model ◽  
Vertical Section ◽  
Three Dimensional ◽  
Horizontal Section ◽  
Extreme Caution ◽  
Cartesian Coordinate ◽  
Data Acquisition And Processing ◽  
Selection Of ◽  
At Will

This paper describes and investigates the implementation of almost entirely image based contemporary techniques for the three dimensional geometric documentation of the Tower of the Winds in Athens, which is a unique and very special monument of the Roman era. These techniques and related algorithms were implemented using a well-known piece of commercial software with extreme caution in the selection of the various parameters. Problems related to data acquisition and processing, but also to the algorithms and to the software implementation are identified and discussed. The resulting point cloud has been georeferenced, i.e. referenced to a local Cartesian coordinate system through minimum geodetic measurements, and subsequently the surface, i.e. the mesh was created and finally the three dimensional textured model was produced. In this way, the geometric documentation drawings, i.e. the horizontal section plans, the vertical section plans and the elevations, which include orthophotos of the monument, can be produced at will from that 3D model, for the complete geometric documentation. Finally, a 3D tour of the Tower of the Winds has also been created for a more integrated view of the monument. The results are presented and are evaluated for their completeness, efficiency, accuracy and ease of production.

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