On steady Stokes flow in a trihedral rectangular corner

2003 ◽  
Vol 476 ◽  
pp. 159-177 ◽  
Author(s):  
A. M. GOMILKO ◽  
V. S. MALYUGA ◽  
V. V. MELESHKO
Keyword(s):  
Velocity Field ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Stagnation Line ◽  
Stagnation Points ◽  
Boundary Velocity ◽  
Different Types ◽  
Spiral Shape ◽  
Induced Flow

Motivated by the recent paper of Hills & Moffatt (2000), we investigate the Stokes flow in a trihedral corner formed by three mutually orthogonal planes, induced by a non-zero velocity distribution over one of the walls of the corner. It is shown that the local behaviour of the velocity field near the edges of the corner, where a discontinuity of the boundary velocity is assumed, coincides with the Goodier–Taylor solution for a two-dimensional wedge. Analysis of the streamline patterns confirms the existence of eddies near the stationary edge in the flow, induced either by uniform translation of one of the walls of the corner in the direction perpendicular to its bisectrix or by uniform rotation of a side about the vertex of the corner. These flows are shown to be quasi-two-dimensional. If the wall rotates about a centre displaced from the vertex, the induced flow is essentially three-dimensional. In the antisymmetric velocity field, a stagnation line appears composed of stagnation points of different types. Otherwise the three-dimensionality manifests itself in a non-closed spiral shape of the streamlines.

scholarly journals Cephalometric measurements from 3D reconstructed images compared with conventional 2D images

2011 ◽  
Vol 81 (5) ◽  
pp. 856-864 ◽  
Author(s):  
Natalia Zamora ◽  
Jose M. Llamas ◽  
Rosa Cibrián ◽  
Jose L. Gandia ◽  
Vanessa Paredes
Keyword(s):  
Three Dimensional ◽  
Cone Beam ◽  
Two Dimensional ◽  
Linear Measurements ◽  
3D Reconstructions ◽  
Software Packages ◽  
Mandibular Plane ◽  
Different Types ◽  
Cephalometric Measurements ◽  
2D Images

Abstract Objective: To assess whether the values of different measurements taken on three-dimensional (3D) reconstructions from cone-beam computed tomography (CBCT) are comparable with those taken on two-dimensional (2D) images from conventional lateral cephalometric radiographs (LCRs) and to examine if there are differences between the different types of CBCT software when taking those measurements. Material and Methods: Eight patients were selected who had both an LRC and a CBCT. The 3D reconstructions of each patient in the CBCT were evaluated using two different software packages, NemoCeph 3D and InVivo5. An observer took 10 angular and 3 linear measurements on each of the three types of record on two different occasions. Results: Intraobserver reliability was high except for the mandibular plane and facial cone (from the LCR), the Na-Ans distance (using NemoCeph 3D), and facial cone and the Ans-Me distance (using InVivo5). No statistically significant differences were found for the angular and linear measurements between the LCRs and the CBCTs for any measurement, and the correlation levels were high for all measurements. Conclusion: No statistically significant differences were found between the angular and linear measurements taken with the LCR and those taken with the CBCT. Neither were there any statistically significant differences between the angular or linear measurements using the two CBCT software packages.

Optimum profiles in two-dimensional Stokes flow

1995 ◽  
Vol 450 (1940) ◽  
pp. 603-622 ◽  
Keyword(s):  
Circular Cylinder ◽  
Cross Section ◽  
Stokes Flow ◽  
Unit Length ◽  
Three Dimensional ◽  
Variational Formula ◽  
Effective Radius ◽  
Two Dimensional ◽  
Equivalent Radius ◽  
Optimum Profile

We consider the problem of designing the section of a cylinder to minimize the drag per unit length it experiences when placed perpendicular to a uniform stream at low Reynolds number; we suppose the area of the cross-section to be given, and the flow to be two-dimensional. The relevant properties of a cylinder of general cross-section in a particular orientation can conveniently be expressed in terms of its equivalent radius; when the drag and flow at infinity are parallel, this equivalent radius is the radius of the circular cylinder giving rise to the same drag per unit length. We obtain a variational formula for this equivalent radius when the surface of the cylinder is perturbed; this shows that the optimum profile we seek must be such that the flow past it has a vorticity of constant magnitude at its surface, and this fact enables the optimum to be determined analytically. The efficacy of a particular section may be measured by its effective radius, this being the equivalent radius when the length scale is chosen to give the section an area π ; thus a circular cylinder has an effective radius of 1. The minimum possible effective radius, achieved by the optimum profile, is 0.88876. To illustrate some of the arguments we exploit in a more familiar setting, we also obtain a variational formula for the drag on a three-dimensional body in Stokes flow when its surface is perturbed.

On angles of separation in Stokes flows

1983 ◽  
Vol 133 ◽  
pp. 427-442 ◽  
Author(s):  
M. E. O'Neill
Keyword(s):  
Circular Cylinder ◽  
Stokes Flow ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Stokes Flows ◽  
Eddy Structure ◽  
Toroidal Vortices ◽  
Mathematical Equivalence ◽  
Infinite Sets

A two-dimensional Stokes flow close to the line of contact of two touching cylinders or three-dimensional axisymmetric Stokes flow close to the point of contact of two touching bodies is shown in general to separate into infinite sets of eddies with angles of separation from the bodies which tend to 58.61° as the line or point of contact is approached. The flow near the vertex of a conical cusp is shown to be a system of nested toroidal vortices and the separation angles tend to 45.25° as the vertex is approached. Stokes flow between parallel planes or within a circular cylinder is shown in general to separate far from the generating disturbances with cellular eddy structure and separation angles which tend to 58.61° and 45.25° respectively. The mathematical equivalence of the various problems is established.

Three-Dimensional Flow of a Newtonian Liquid Through an Annular Space with Axially Varying Eccentricity

2005 ◽  
Vol 128 (2) ◽  
pp. 223-231 ◽  
Author(s):  
Eduarda P. F. de Pina ◽  
M. S. Carvalho
Keyword(s):  
Velocity Field ◽  
Cross Section ◽  
Drill Pipe ◽  
Three Dimensional ◽  
Complete Analysis ◽  
Correct Prediction ◽  
Two Dimensional ◽  
Annular Space ◽  
Drilling Mud ◽  
Frictional Pressure Drop

Flow in annular space occurs in drilling operation of oil and gas wells. The correct prediction of the flow of the drilling mud in the annular space between the well wall and the drill pipe is essential to determine the variation in the mud pressure within the wellbore, the frictional pressure drop, and the efficiency of the transport of the rock drill cuttings. A complete analysis of this situation is extremely complex: the inner cylinder is usually rotating, the wellbore wall will depart significantly from cylindrical, the drill pipe is eccentric, and the eccentricity varies along the well. A complete analysis of this situation would require the solution of the three-dimensional momentum equation and would be computationally expensive and complex. Models available in the literature to study this situation do consider the rotation of the inner cylinder and the non-Newtonian behavior of the drilling fluids, but assume the relative position of the inner with respect to the outer cylinders fixed, i.e., they neglect the variation of the eccentricity along the length of the well, and the flow is considered to be fully developed. This approximation leads to a two-dimensional model to determine the three components of the velocity field in a cross-section of the annulus. The model presented in this work takes into account the variation of the eccentricity along the well; a more appropriate description of the geometric configuration of directional wells. As a consequence, the velocity field varies along the well length and the resulting flow model is three-dimensional. Lubrication theory is used to simplify the governing equations into a two-dimensional differential equation that describes the pressure field. The results show the effect of the variation of the eccentricity on the friction factor, maximum and minimum axial velocity in each cross section, and the presence of azimuthal flow even when the inner cylinder is not rotating.

scholarly journals Crystal structure of the two-dimensional coordination polymer poly[di-μ-bromido-bis(μ-tetrahydrothiophene)dicopper(I)]

2021 ◽  
Vol 77 (7) ◽  
pp. 744-748
Author(s):  
Michael Knorr ◽  
Lydie Viau ◽  
Yoann Rousselin ◽  
Marek M. Kubicki
Keyword(s):  
Crystal Structure ◽  
Coordination Polymer ◽  
Hydrogen Bonds ◽  
Three Dimensional ◽  
Supramolecular Network ◽  
Two Dimensional ◽  
Different Types ◽  
Secondary Building Units ◽  
Mecn Solution ◽  
Bonding Mode

The polymeric title compound, [Cu2Br2(C4H8S)2] n , CP1, represents an example of a two-dimensional coordination polymer resulting from reaction of CuBr with tetrahydrothiophene (THT) in MeCN solution. The two-dimensional layers consist of two different types of rhomboid-shaped dinuclear Cu(μ2-Br)2Cu secondary building units (SBUs); one with a quite loose Cu...Cu separation of 3.3348 (10) Å and a second one with a much closer intermetallic contact of 2.9044 (9) Å. These SBUs are interconnected through bridging THT ligands, in which the S atom acts as a four-electron donor bridging each Cu(μ2-Br)2Cu unit in a μ2-bonding mode. In the crystal, the layers are linked by very weak C—H...·Br hydrogen bonds with H...Br distances of 2.95 Å, thus giving rise to a three-dimensional supramolecular network.

scholarly journals Maximal heat transfer between two parallel plates

2018 ◽  
Vol 851 ◽  
Author(s):  
Shingo Motoki ◽  
Genta Kawahara ◽  
Masaki Shimizu
Keyword(s):  
Heat Transfer ◽  
Velocity Field ◽  
Large Scale ◽  
Three Dimensional ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Solution Branch ◽  
Search Range ◽  
Dimensional Solution

The divergence-free time-independent velocity field has been determined so as to maximise heat transfer between two parallel plates with a constant temperature difference under the constraint of fixed total enstrophy. The present variational problem is the same as that first formulated by Hassanzadeh et al. (J. Fluid Mech., vol. 751, 2014, pp. 627–662); however, the search range for optimal states has been extended to a three-dimensional velocity field. A scaling of the Nusselt number $Nu$ with the Péclet number $Pe$ (i.e., the square root of the non-dimensionalised enstrophy with thermal diffusion time scale), $Nu\sim Pe^{2/3}$, has been found in the three-dimensional optimal states, corresponding to the asymptotic scaling with the Rayleigh number $Ra$, $Nu\sim Ra^{1/2}$, expected to appear in an ultimate state, and thus to the Taylor energy dissipation law in high-Reynolds-number turbulence. At $Pe\sim 10^{0}$, a two-dimensional array of large-scale convection rolls provides maximal heat transfer. A three-dimensional optimal solution emerges from bifurcation on the two-dimensional solution branch at $Pe\sim 10^{1}$, and the three-dimensional solution branch has been tracked up to $Pe\sim 10^{4}$ (corresponding to $Ra\approx 2.7\times 10^{6}$). At $Pe\gtrsim 10^{3}$, the optimised velocity fields consist of convection cells with hierarchical self-similar vortical structures, and the temperature fields exhibit a logarithmic-like mean profile near the walls.

Social Factors and Interface Design Guidelines

2006 ◽  
pp. 523-532
Author(s):  
Zhe Xu ◽  
David John ◽  
Anthony C. Boucouvalas
Keyword(s):  
Social Presence ◽  
Interface Design ◽  
Three Dimensional ◽  
Design Guidelines ◽  
Chat Room ◽  
Two Dimensional ◽  
Contributing Factors ◽  
Business Systems ◽  
Different Types ◽  
Video And Audio

Designing an attractive user interface for Internet communication is the objective of every software developer. However, it is not an easy task as the interface will be accessed by an uncertain number of users with various purposes. To interact with users, text, sounds, images, and animations can be provided according to different situations. Originally, text was the only medium available for a user to communicate over the Internet. With technology development, multimedia channels (e.g., video and audio) emerged into the online context. Individuals’ sociability may influence human behaviour. Some people prefer a quiet environment and others enjoy more liveliness. On the other hand, the activity purpose influences the environment preference as well. Following usability principles and task analysis (Badre, 2002; Cato, 2001; Dix, Finlay, Abowd, & Beale, 1998; McCraken & Wolfe, 2004; Neilsen, 2000; Nielsen & Tahir, 2002; Preece, Rogers, & Sharp, 2002), we can predict that business-oriented systems and informal systems will require different types of interfaces: Business systems are concerned with the efficiency of performing tasks, while the effectiveness of informal systems depend more on the user’s satisfaction with the experience of interacting with the system. Suppose you are an Internet application designer; should you provide a vivid and multichannel interface or a concise and clear appearance? When individuals’ sociability and the activity purpose contradict, should the interface design follow the sociability requirement, the purpose of the activity, or even neither of them? To answer these questions, the characteristics of communication interfaces should be examined. For face-to-face communications, sounds, voices, various facial expressions, and physical movements are the most important contributing factors. These features are named physical and social presence (Loomis, Golledge, & Klatzky, 1998). In the virtual world, real physical presence does not exist anymore; however, emotional feelings, group feelings, and other social feelings are existent but vary in quantity. The essential differences of interfaces are the quantity of the presented social feelings. For example, a three-dimensional (3-D) interface may provide more geographical and social feelings than a two-dimensional (2-D) chat room may present. To assess the different feelings that may emerge from different interfaces, a two-dimensional chat room and a three-dimensional chatting environment were developed. The identification of social feelings present in the different interface styles is presented first. Then an experiment that was carried out to measure the influence the activity styles and the individuals’ sociability have on the interface preferences is discussed. The questions raised in this article are “What are the social feelings that may differ between the two interfaces (2-D vs. 3-D)?” and “Will users prefer different interfaces for different types of activities?”

Sign in / Sign up

Export Citation Format

Share Document