Polymers on a Random Liquid Surface

1989 ◽  
Vol 177 ◽  
Author(s):  
Bertrand Duplantier
Keyword(s):  
Surface Tension ◽  
Critical Exponents ◽  
Degrees Of Freedom ◽  
Liquid Membrane ◽  
Theoretical Study ◽  
Liquid Surface ◽  
Experimental Studies ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Universal Values

ABSTRACTWe report a recent theoretical study of polymers moving on a random two-dimensional fluid surface. The metric of the liquid membrane is free to fluctuate and these new degrees of freedom couple to those of the polymers - as a result, the critical exponents describing the polymers are changed, but are nevertheless related to those in two dimensions. The relation to possible experimental studies on membranes with vanishing surface tension, which should search for new universal values of exponents u and 7, is discussed.

AN INTEGRABLE MODEL WITH SOLITON SOLUTIONS WHICH HAVE APPLICATIONS TO TWO-DIMENSIONAL GRAVITY

2005 ◽  
Vol 20 (07) ◽  
pp. 1503-1514 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Integrable Model ◽  
Soliton Solutions ◽  
Integrable Equation ◽  
Two Dimensions ◽  
Spin Connection ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Chern Simons

The equations of motion for a theory described by a Chern–Simons type of action in two dimensions are obtained and investigated. The equation for the classical, continuous Heisenberg model is used as a form of gauge constraint to obtain a result which provides a completely integrable dynamics and which partially fixes the gauge degrees of freedom. Under a particular form of the spin connection, an integrable equation which can be analytically extended to a form of the nonlinear Schrödinger equation is obtained. Some explicit solutions are presented, and in particular a soliton solution is shown to lead to an integrable two-dimensional model of gravity.

scholarly journals THE “DUAL” VARIABLES OF YANG-MILLS THEORY AND LOCAL GAUGE-INVARIANT VARIABLES

1996 ◽  
Vol 11 (32) ◽  
pp. 5701-5728 ◽  
Author(s):  
ORI GANOR ◽  
J. SONNENSCHEIN
Keyword(s):  
Degrees Of Freedom ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Six Degrees Of Freedom ◽  
Local Gauge ◽  
Dual Variables ◽  
Topological Part

After adding auxiliary fields and integrating out the original variables, the Yang-Mills action can be expressed in terms of local gauge-invariant variables. This method reproduces the known solution of the two-dimensional SU (N) theory. In more than two dimensions the action splits into a topological part and a part proportional to αs. We demonstrate the procedure for SU (2) in three dimensions where we reproduce a gravitylike theory. We discuss the four-dimensional case as well. We use a cubic expression in the fields as a space-time metric to obtain a covariant Lagrangian. We also show how the four-dimensional SU (2) theory can be expressed in terms of a local action with six degrees of freedom only.

A New Method for Measuring Contact Angle and Liquid Surface Tension Applying Detachment of Two-Dimensional Meniscus

1998 ◽  
Vol 202 (1) ◽  
pp. 54-62 ◽  
Author(s):  
Kenji Katoh ◽  
Yu Tsao ◽  
Masayoshi Yamamoto ◽  
Tsuneo Azuma ◽  
Hideomi Fujita
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Liquid Surface ◽  
New Method ◽  
Two Dimensional ◽  
Liquid Surface Tension

scholarly journals A two-dimensional propensity score matching method for longitudinal quasi-experimental studies: A focus on travel behavior and the built environment

2020 ◽  
pp. 239980832098230
Author(s):  
Haotian Zhong ◽  
Wei Li ◽  
Marlon G Boarnet
Keyword(s):  
Propensity Score ◽  
Built Environment ◽  
Propensity Score Matching ◽  
Treatment Effect ◽  
Travel Behavior ◽  
Experimental Studies ◽  
Two Dimensions ◽  
Superior Performance ◽  
Two Dimensional ◽  
Matching Method

The lack of longitudinal studies of the relationship between the built environment and travel behavior has been widely discussed in the literature. This paper discusses how standard propensity score matching estimators can be extended to enable such studies by pairing observations across two dimensions: longitudinal and cross-sectional. Researchers mimic randomized controlled trials and match observations in both dimensions to find synthetic control groups that are similar to the treatment group and to match subjects across before- and after-treatment periods. We call this a two-dimensional propensity score matching method. This method demonstrates superior performance for improving treatment effect estimation based on Monte Carlo evidence. A near-term opportunity for such matching is identifying the treatment effect of transportation infrastructure on travel behavior.

Experimental study of the stability and dynamics of a two-dimensional ideal vortex under external strain

2018 ◽  
Vol 848 ◽  
pp. 256-287 ◽  
Author(s):  
N. C. Hurst ◽  
J. R. Danielson ◽  
D. H. E. Dubin ◽  
C. M. Surko
Keyword(s):  
Ideal Fluid ◽  
Experimental Studies ◽  
Quantitative Agreement ◽  
Two Dimensions ◽  
Global Dynamics ◽  
Two Dimensional ◽  
Plasma Dynamics ◽  
Electron Plasmas ◽  
Precise Control ◽  
The Stability

The dynamics of two-dimensional (2-D) ideal fluid vortices is studied experimentally in the presence of an irrotational strain flow. Laboratory experiments are conducted using strongly magnetized pure electron plasmas, a technique which is made possible by the isomorphism between the drift–Poisson equations describing plasma dynamics transverse to the field and the 2-D Euler equations describing an ideal fluid. The electron plasma system provides an excellent opportunity to study the dynamics of a 2-D Euler fluid due to weak dissipation and weak 3-D effects, simple diagnosis and precise control. The plasma confinement apparatus used here was designed specifically to study vortex dynamics under the influence of external flow by applying boundary conditions in two dimensions. Additionally, vortex-in-cell simulations are carried out to complement the experimental results and to extend the parameter range of the studies. It is shown that the global dynamics of a quasi-flat vorticity profile is in good quantitative agreement with the theory of a piecewise-constant elliptical patch of vorticity, including the equilibria, dynamical orbits and stability properties. Deviations from the elliptical patch theory are observed for non-flat vorticity profiles; they include inviscid damping of the orbits and modified stability limits. The dependence of these phenomena on the flatness of the initial profile is discussed. The relationship of these results to other theoretical, numerical and experimental studies is also discussed.

scholarly journals Free surface flow over an obstacle. Theoretical study of the fluvial case

2001 ◽  
Vol 6 (7) ◽  
pp. 413-429 ◽  
Author(s):  
D. Boukari ◽  
R. Djouadi ◽  
D. Teniou
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Implicit Function Theorem ◽  
Theoretical Study ◽  
Free Surface Flow ◽  
Stationary Flow ◽  
Surface Flow ◽  
Existence Theory ◽  
Two Dimensional ◽  
Implicit Function

The two-dimensional stationary flow of a fluid over an obstacle lying on the bottom of a stream is discussed. We take into account the gravity and we neglect the effects of the surface tension. An existence theory for the solution of this problem is established by the implicit function theorem, for small obstacles and Froude numbers in an interval included in]0,1[.

scholarly journals A numerical study of the Bénard cell

1971 ◽  
Vol 45 (4) ◽  
pp. 805-829 ◽  
Author(s):  
André Cabelli ◽  
G. de Vahl Davis
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Numerical Method ◽  
Liquid Surface ◽  
Numerical Study ◽  
Three Dimensional ◽  
Critical Value ◽  
Two Dimensional ◽  
Surface Tension Forces ◽  
Biot Numbers

When a layer of liquid is heated from below at a rate which exceeds a certain critical value, a two- or three-dimensional motion is generated. This motion arises from the action of buoyancy and surface tension forces, the latter being due to variations in the temperature of the liquid surface.The two-dimensional form of the flow has been studied by a numerical method. It consists of a series of rolls, rotating alternately clockwise and anticlockwise, which are shown to be symmetrical about the dividing streamlines. As well as a detailed description of the motion and temperature of the liquid, and of the effects on these characteristics of variations in the Rayleigh, Marangoni, Prandtl and Biot numbers, a study has been made of the conditions under which the motion first starts, the wavelength of the rolls and the rate of heat transfer across the liquid layer.

On the evolution of packets of water waves

1979 ◽  
Vol 92 (4) ◽  
pp. 691-715 ◽  
Author(s):  
Mark J. Ablowitz ◽  
Harvey Segur
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Evolution Equations ◽  
Wave Packets ◽  
Short Wave ◽  
Similarity Solutions ◽  
Two Dimensions ◽  
Long Waves ◽  
Two Dimensional ◽  
One Dimensional

We consider the evolution of packets of water waves that travel predominantly in one direction, but in which the wave amplitudes are modulated slowly in both horizontal directions. Two separate models are discussed, depending on whether or not the waves are long in comparison with the fluid depth. These models are two-dimensional generalizations of the Korteweg-de Vries equation (for long waves) and the cubic nonlinear Schrödinger equation (for short waves). In either case, we find that the two-dimensional evolution of the wave packets depends fundamentally on the dimensionless surface tension and fluid depth. In particular, for the long waves, one-dimensional (KdV) solitons become unstable with respect to even longer transverse perturbations when the surface-tension parameter becomes large enough, i.e. in very thin sheets of water. Two-dimensional long waves (‘lumps’) that decay algebraically in all horizontal directions and interact like solitons exist only when the one-dimensional solitons are found to be unstable.The most dramatic consequence of surface tension and depth, however, occurs for capillary-type waves in sufficiently deep water. Here a packet of waves that are everywhere small (but not infinitesimal) and modulated in both horizontal dimensions can ‘focus’ in a finite time, producing a region in which the wave amplitudes are finite. This nonlinear instability should be stronger and more apparent than the linear instabilities examined to date; it should be readily observable.Another feature of the evolution of short wave packets in two dimensions is that all one-dimensional solitons are unstable with respect to long transverse perturbations. Finally, we identify some exact similarity solutions to the evolution equations.

On the Shear Modulus of Two-Dimensional Liquid Foams: A Theoretical Study of the Effect of Geometrical Disorder

2006 ◽  
Vol 74 (3) ◽  
pp. 560-567 ◽  
Author(s):  
N. P. Kruyt
Keyword(s):  
Surface Tension ◽  
Shear Modulus ◽  
Theoretical Study ◽  
Two Dimensional ◽  
Liquid Content ◽  
Geometrical Characteristics ◽  
Liquid Foams ◽  
Theoretical Predictions ◽  
Nonaffine Deformation

The shear modulus of two-dimensional liquid foams in the dry limit of low liquid content has been studied theoretically. The focus is on the effect of geometrical disorder on the shear modulus (besides the influence of surface tension). Various theoretical predictions are formulated that are all based on the assumptions of isotropic geometrical characteristics, incompressible bubbles, and negligible edge curvature. Three of these predictions are based on a transformation of Princen’s theory that is strictly valid only for regular hexagonal bubbles. Another prediction takes into account variations in bubble areas by considering the foam as consisting of approximately regular hexagonal bubbles with varying areas. Two other predictions are solely based on the characteristics of the bubble edges. The first of these is based on the assumption of affine movement of bubble vertices, while the second accounts for nonaffine deformation by considering the interaction with neighboring edges. The theoretical predictions for the shear modulus are compared with the result from a single foam simulation. For the single simulation considered, all predictions, except that based on affine movement of bubble vertices, are close to the value obtained from this simulation.

scholarly journals On the collapse of locally isostatic networks

2009 ◽  
Vol 465 (2111) ◽  
pp. 3517-3530 ◽  
Author(s):  
V. Kapko ◽  
M. M. J. Treacy ◽  
M. F. Thorpe ◽  
S. D. Guest
Keyword(s):  
Degrees Of Freedom ◽  
Two Dimensions ◽  
Unit Cell ◽  
Three Dimensions ◽  
Collapse Mechanism ◽  
Two Dimensional ◽  
Higher Symmetry ◽  
Collapse Mechanisms ◽  
Equilateral Triangles ◽  
As If

We examine the flexibility of periodic planar networks built from rigid corner-connected equilateral triangles. Such systems are locally isostatic, since for each triangle the total number of degrees of freedom equals the total number of constraints. These nets are two-dimensional analogues of zeolite frameworks, which are periodic assemblies of corner-sharing tetrahedra. If the corner connections are permitted to rotate, as if pin-jointed, there is always at least one collapse mechanism in two dimensions (and at least three mechanisms in three dimensions). We present a number of examples of such collapse modes for different topologies of triangular net. We show that the number of collapse mechanisms grows with the size of unit cell. The collapsible mechanisms that preserve higher symmetry of the network tend to exhibit the widest range of densities without sterical overlap.

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