scholarly journals The surface-tension-driven evolution of a two-dimensional annular viscous tube

2007 ◽  
Vol 593 ◽  
pp. 181-208 ◽  
Author(s):  
I. M. GRIFFITHS ◽  
P. D. HOWELL
Keyword(s):  
Surface Tension ◽  
Numerical Solutions ◽  
Applied Pressure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Free Surfaces ◽  
Final Shape ◽  
Capillary Tubing ◽  
Well Posed

We consider the evolution of an annular two-dimensional region occupied by viscous fluid driven by surface tension and applied pressure at the free surfaces. We assume that the thickness of the domain is small compared with its circumference, so that it may be described as a thin viscous sheet whose ends are joined to form a closed loop. Analytical and numerical solutions of the resulting model are obtained and we show that it is well posed whether run forwards or backwards in time. This enables us to determine, in many cases explicitly, which initial shapes will evolve into a desired final shape. We also show how the application of an internal pressure may be used to control the evolution.This work is motivated by the production of non-axisymmetric capillary tubing via the Vello process. Molten glass is fed through a die and drawn off vertically, while the shape of the cross-section evolves under surface tension and any applied pressure as it flows downstream. Here the goal is to determine the die shape required to achieve a given desired final shape, typically square or rectangular. We conclude by discussing the role of our two-dimensional model in describing the three-dimensional tube-drawing process.

Regularization of the Kelvin–Helmholtz instability by surface tension

2007 ◽  
Vol 365 (1858) ◽  
pp. 2253-2266 ◽  
Author(s):  
David M Ambrose
Keyword(s):  
Surface Tension ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Vortex Sheet ◽  
Energy Estimates ◽  
Two Dimensional ◽  
Helmholtz Instability ◽  
Joint Work ◽  
Numerical Work ◽  
Well Posed

The Kelvin–Helmholtz instability is present in the motion of a vortex sheet without surface tension. This can be seen from the linearization of the equations of motion, and there have also been proofs of ill-posedness for the full nonlinear equations. In the presence of surface tension, the linearized equations no longer exhibit an instability, and it has been believed that the full equations should then be well-posed. In this paper, I sketch a proof that the vortex sheet with surface tension is well-posed in the case of both two- and three-dimensional fluids. The proof in the case of three-dimensional fluids is the joint work with Nader Masmoudi. The method is to first reformulate the problem using suitable variables and parametrizations, and then to perform energy estimates. The choice of variables and parametrizations in the two-dimensional case is the same as that of Hou et al . in a prior numerical work.

scholarly journals A Framework for Approximation of the Stokes Equations in an Axisymmetric Domain

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Niklas Ericsson
Keyword(s):  
Fourier Expansion ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Countable Family ◽  
Angular Variable ◽  
Two Dimensional ◽  
Sobolev Norms ◽  
Well Posed ◽  
Variational Formulations

Abstract We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an equivalent, countable family of decoupled two-dimensional problems. By using decomposition of three-dimensional Sobolev norms, we derive natural variational spaces for the two-dimensional problems, and show that the variational formulations are well-posed. We analyze the error due to Fourier truncation and conclude that, for data that are sufficiently regular, it suffices to solve a small number of two-dimensional problems.

The Role of Three Dimension Computerized Imaging in Hand Surgery

1987 ◽  
Vol 12 (3) ◽  
pp. 349-352
Author(s):  
J. ENGEL ◽  
M. SALAI ◽  
B. YAFFE ◽  
R. TADMOR
Keyword(s):  
Three Dimensional ◽  
Hand Surgery ◽  
New Technique ◽  
Silicone Implants ◽  
Three Dimension ◽  
Two Dimensional ◽  
Radiological Imaging ◽  
Preliminary Results ◽  
Dimensional Picture

Three-dimensional computerized imaging is a new modality of radiological imaging. This new technique transforms the two-dimensional slices of bi-plane CT into a three-dimensional picture by a computer’s monitor adjusted to the system. This system enables the physician to rotate the angle of viewing of the desired region to any desired angle. Moreover, this system can delete certain features of different densities from the picture, such as silicone implants, thus improving visualization. Our preliminary results using this technique are presented. The advantages, pitfalls, and suggested future applications of this new technique in hand surgery are discussed.

Role of divalent cation (Ba) substitution in the Li+ ion conductor LiTi2(PO4)3: a molecular dynamics study

2020 ◽  
Vol 22 (26) ◽  
pp. 14471-14479
Author(s):  
Kartik Sau ◽  
Tamio Ikeshoji ◽  
Supriya Roy
Keyword(s):  
Molecular Dynamics ◽  
Divalent Cation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Ion Diffusion ◽  
Ion Conductor ◽  
Li Ion ◽  
Ba Substitution

Influence of Ba2+ ordering on cationic diffusion: (a) three-dimensional low Li+ ion diffusion using randomly substituted Ba2+, and (b) two-dimensional layered type high Li+ ion diffusion using specifically ordered substitution of Ba2+.

The Role of Three-Dimension Computerized Imaging in Hand Surgery

1992 ◽  
Vol 17 (6) ◽  
pp. 702-702
Author(s):  
J. Engel ◽  
M. Salai ◽  
B. Yaffe ◽  
R. Tadmor
Keyword(s):  
Three Dimensional ◽  
Hand Surgery ◽  
New Technique ◽  
Silicone Implants ◽  
Three Dimension ◽  
Two Dimensional ◽  
Radiological Imaging ◽  
Preliminary Results ◽  
Dimensional Picture

Three-dimensional computerized imaging is a new modality of radiological imaging. This new technique transforms the two-dimensional slices of bi-plane CT into a three-dimensional picture by a computer's monitor adjusted to the system. This system enables the physician to rotate the angle of viewing of the desired region to any desired angle. Moreover, this system can delete certain features of different densities from the picture, such as silicone implants, thus improving visualization. Our preliminary results using this technique are presented. The advantages, pitfalls, and suggested future applications of this new technique in hand surgery are discussed.

ON THE ROLE OF KINKS AND STRAIN IN HETEROEPITAXIAL GROWTH: AN STM STUDY

2000 ◽  
Vol 07 (05n06) ◽  
pp. 673-677
Author(s):  
E. LUNDGREN ◽  
M. SCHMID ◽  
G. LEONARDELLI ◽  
A. HAMMERSCHMID ◽  
B. STANKA ◽  
...  
Keyword(s):  
Diffusion Process ◽  
Scanning Tunneling Microscopy ◽  
Three Dimensional ◽  
Growth Mode ◽  
Scanning Tunneling ◽  
Two Dimensional ◽  
Heteroepitaxial Growth ◽  
Tunneling Microscopy ◽  
Exchange Diffusion

Interlayer diffusion of Co over steps of vacancy islands on the Pt(111) surface as studied by scanning tunneling microscopy is presented. It is demonstrated that Co atoms descend Pt steps by an exchange diffusion process at the step edge with the Pt atoms. Further, the exchange diffusion process is observed to occur at the corners (kinks) of the vacancy islands. The importance of kinks concerning whether the growth mode of a heteropitaxial film is two-dimensional or three-dimensional is demonstrated for the case of thin Co films on Pt(111). We argue that the strain in the Co film is to a large extent responsible for the kink formation.

scholarly journals Nonlinear evolution of interacting oblique waves on two-dimensional shear layers

1989 ◽  
Vol 207 ◽  
pp. 97-120 ◽  
Author(s):  
M. E. Goldstein ◽  
S.-W. Choi
Keyword(s):  
Wave Amplitude ◽  
Numerical Solutions ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Shear Layers ◽  
Instability Wave ◽  
Two Dimensional ◽  
Instability Waves ◽  
Downstream Distance ◽  
Parallel Streams

We consider the effects of critical-layer nonlinearity on spatially growing oblique instability waves on nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. We show that they always end in a singularity at a finite downstream distance.

Zn/Mn–MOFs with `S-shaped' packing modes

2014 ◽  
Vol 70 (5) ◽  
pp. 502-507
Author(s):  
Hong-Jie Fan ◽  
Qian-Qian Xu ◽  
Tie-Zhen Ren ◽  
Xiang-Ying Xing ◽  
Kirsten E. Christensen
Keyword(s):  
Metal Ion ◽  
Metal Organic Frameworks ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Hydrothermal Conditions ◽  
Dimensional Network ◽  
Metal Organic

Two novel polymers exhibiting metal–organic frameworks (MOFs) have been synthesized by the combination of a metal ion with a benzene-1,3,5-tricarboxylate ligand (BTC) and 1,10-phenanthroline (phen) under hydrothermal conditions. The first compound, poly[[(μ4-benzene-1,3,5-tricarboxylato-κ4 O:O′:O′′:O′′′)(μ-hydroxido-κ2 O:O)bis(1,10-phenanthroline-κ2 N,N′)dizinc(II)] 0.32-hydrate], {[Zn2(C9H3O6)(OH)(C12H8N2)2]·0.32H2O} n , denoted Zn–MOF, forms a two-dimensional network in which a binuclear Zn2 cluster serves as a 3-connecting node; the BTC trianion also acts as a 3-connecting centre. The overall topology is that of a 63 net. The phen ligands serve as appendages to the network and interdigitate with phen ligands belonging to adjacent parallel sheets. The second compound, poly[[(μ6-benzene-1,3,5-tricarboxylato-κ7 O 1,O 1′:O 1:O 3:O 3′:O 5:O 5′)(μ3-hydroxido-κ2 O:O:O)(1,10-phenanthroline-κ2 N,N′)dimanganese(II)] 1.26-hydrate], {[Mn2(C9H3O6)(OH)(C12H8N2)]·1.26H2O} n , denoted Mn–MOF, exists as a three-dimensional network in which an Mn4 cluster serves as a 6-connecting unit, while the BTC trianion again plays the role of a 3-connecting centre. The overall topology is that of the rutile net. Phen ligands act as appendages to the network and form the `S-shaped' packing mode.

scholarly journals The Role of 2D and 3D Echo in Mitral Stenosis

2021 ◽  
Vol 8 (12) ◽  
pp. 171
Author(s):  
Juan Manuel Monteagudo Ruiz ◽  
José Luis Zamorano Gómez
Keyword(s):  
Heart Valve ◽  
Transthoracic Echocardiography ◽  
Mitral Stenosis ◽  
Imaging Modality ◽  
Three Dimensional ◽  
Heart Valve Disease ◽  
Two Dimensional ◽  
3D Echo ◽  
2D And 3D

Mitral stenosis is an important cause of heart valve disease globally. Echocardiography is the main imaging modality used to diagnose and assess the severity and hemodynamic consequences of mitral stenosis as well as valve morphology. Transthoracic echocardiography (TTE) is sufficient for the management of most patients. The focus of this review is the role of current two-dimensional (2D) and three-dimensional (3D) echocardiographic imaging for the evaluation of mitral stenosis.

Linear and nonlinear statistics of extreme waves

2017 ◽  
Vol 32 (2) ◽  
Author(s):  
Dmitry V. Chalikov
Keyword(s):  
Nonlinear Model ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Extreme Waves ◽  
Linear Waves ◽  
Wave Heights ◽  
Linear And Nonlinear ◽  
Nonlinear Statistics ◽  
Integral Probability

AbstractThe probability of extremely high waves is calculated by two methods. The first method is based on the direct numerical simulation of two-dimensional wave field using a three-dimensional nonlinear model. The second method consists in calculation of the probability of wave heights over ensemble of fields representing a superposition of linear waves with random phases and a spectrum similar to that obtained in the nonlinear model. It is shown that the integral probability of extreme waves are very close to each other in both cases. This implies that the role of nonlinearity in the generation of extreme waves is probably not so important as it was assumed in most papers considering this phenomenon.

Sign in / Sign up

Export Citation Format

Share Document