scholarly journals Director Fluctuations in Two-Dimensional Liquid Crystal Disclinations

Crystals ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 1
Author(s):  
Olaf Stenull ◽  
Tom C. Lubensky
Keyword(s):  
Boundary Conditions ◽  
Normal Modes ◽  
Critical Value ◽  
Outer Radius ◽  
Two Dimensional ◽  
Free Energies ◽  
Excitation Energies ◽  
Smectic C ◽  
Inner Radius ◽  
Decay Times

We present analytical calculations of the energies and eigenfunctions of all normal modes of excitation of charge +1 two-dimensional splay (bend) disclinations confined to an annular region with inner radius R1 and outer radius R2 and with perpendicular (tangential) boundary conditions on the region’s inner and outer perimeters. Defects such as these appear in islands in smectic-C films and can in principle be created in bolaamphiphilic nematic films. Under perpendicular boundary conditions on the two surfaces and when the ratio β=Ks/Kb of the splay to bend 2D Frank constants is less than one, the splay configuration is stable for all values μ=R2/R1. When β>1, the splay configuration is stable only for μ less than a critical value μc(β), becoming unstable to a “spiral” mixed splay-bend configuration for μ>μc. The same behavior occurs in trapped bend defects with tangential boundary conditions but with Ks and Kb interchanged. By calculating free energies, we verify that the transition from a splay or bend configuration to a mixed one is continuous. We discuss the differences between our calculations that yield expressions for experimentally observable excitation energies and other calculations that produce the same critical points and spiral configurations as ours but not the same excitation energies. We also calculate measurable correlation functions and associated decay times of angular fluctuations.

scholarly journals Impact of Radii Ratios on a Two-Dimensional Cloaking Structure and Corresponding Analysis for Practical Design at Optical Wavelengths

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Nadia Anam ◽  
Ebad Zahir
Keyword(s):  
Fdtd Method ◽  
Visible Spectrum ◽  
Outer Radius ◽  
Visible Range ◽  
Two Dimensional ◽  
Real Component ◽  
Average Value ◽  
Inner Radius ◽  
Practical Design ◽  
Selection Of

This work is an extension to the evaluation and analysis of a two-dimensional cylindrical cloak in the Terahertz or visible range spectrum using Finite Difference Time-Domain (FDTD) method. It was concluded that it is possible to expand the frequency range of a cylindrical cloaking model by careful scaling of the inner and outer radius of the simulation geometry with respect to cell size and/or number of time steps in the simulation grid while maintaining appropriate stability conditions. Analysis in this study is based on a change in the radii ratio, that is, outer radius to inner radius, of the cloaking structure for an array of wavelengths in the visible spectrum. Corresponding outputs show inconsistency in the cloaking pattern with respect to frequency. The inconsistency is further increased as the radii ratio is decreased. The results also help to establish a linear relationship between the transmission coefficient and the real component of refractive index with respect to different radii ratios which may simplify the selection of the material for practical design purposes. Additional performance analysis is carried out such that the dimensions of the cloak are held constant at an average value and the frequency varied to determine how a cloaked object may be perceived by the human eye which considers different wavelengths to be superimposed on each other simultaneously.

scholarly journals Voltage-Induced Wrinkling in a Constrained Annular Dielectric Elastomer Film

2017 ◽  
Vol 85 (1) ◽  
Author(s):  
Kai Li ◽  
Wanfang Wu ◽  
Ziyang Jiang ◽  
Shengqiang Cai
Keyword(s):  
Applied Voltage ◽  
Plate Theory ◽  
Critical Value ◽  
Dielectric Elastomer ◽  
Outer Radius ◽  
Material Failure ◽  
System Failure ◽  
Mechanical Forces ◽  
Inner Radius ◽  
Deformation Modes

Wrinkles can be often observed in dielectric elastomer (DE) films when they are subjected to electrical voltage and mechanical forces. In the applications of DEs, wrinkle formation is often regarded as an indication of system failure. However, in some scenarios, wrinkling in DE does not necessarily result in material failure and can be even controllable. Although tremendous efforts have been made to analyze and calculate a variety of deformation modes in DE structures and devices, a model which is capable of analyzing wrinkling phenomena including the critical electromechanical conditions for the onset of wrinkles and wrinkle morphology in DE structures is currently unavailable. In this paper, we experimentally demonstrate controllable wrinkling in annular DE films with the central part being mechanically constrained. By changing the ratio between the inner radius and outer radius of the annular films, wrinkles with different wavelength can be induced in the films when externally applied voltage exceeds a critical value. To analyze wrinkling phenomena in DE films, we formulate a linear plate theory of DE films subjected to electromechanical loadings. Using the model, we successfully predict the wavelength of the voltage-induced wrinkles in annular DE films. The model developed in this paper can be used to design voltage-induced wrinkling in DE structures for different engineering applications.

Vibration of a Fluid Conveying Pipe Carrying a Discrete Mass

1974 ◽  
Vol 96 (4) ◽  
pp. 268-272 ◽  
Author(s):  
T. T. Wu ◽  
P. P. Raju
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Flow Velocity ◽  
General Expression ◽  
Normal Modes ◽  
Critical Value ◽  
Numerical Results ◽  
Simply Supported ◽  
Various Boundary Conditions ◽  
Discrete Mass

This paper presents a method to predict the dynamic response of a fluid conveying pipe carrying a discrete mass when the flow velocity is less than its critical value. A general expression for the normal modes of a vibrating pipe with various boundary conditions is newly derived herein. Also presented for a particular case are the numerical results of eigenfunctions and eigenvalues which can be used to calculate the dynamic response of a simply-supported pipe with an attached discrete mass at its mid-span.

scholarly journals Theoretical analysis of inertially irrotational and solenoidal flow in two-dimensional radial-flow pump and turbine impellers with equiangular blades

1994 ◽  
Vol 269 ◽  
pp. 107-141 ◽  
Author(s):  
F. C. Visser ◽  
J. J. H. Brouwers ◽  
R. Badie
Keyword(s):  
Reverse Flow ◽  
Fluid Velocity ◽  
Beta Function ◽  
Logarithmic Spiral ◽  
Outer Radius ◽  
Gauss Hypergeometric Function ◽  
Two Dimensional ◽  
Pump Impeller ◽  
Inner Radius ◽  
Radial Pump

Using the theory of functions of a complex variable, in particular the method of conformal mapping, the irrotational and solenoidal flow in two-dimensional radialflow pump and turbine impellers fitted with equiangular blades is analysed. Exact solutions are given for the fluid velocity along straight radial pump and turbine impeller blades, while for logarithmic spiral pump impeller blades solutions are given which hold asymptotically as (r1/r2)n→0, in whichr1is impeller inner radius,r2is impeller outer radius andnis the number of blades. Both solutions are given in terms of a Fourier series, with the Fourier coefficients being given by the (Gauss) hypergeometric function and the beta function respectively. The solutions are used to derive analytical expressions for a number of parameters which are important for practical design of radial turbomachinery, and which reflect the two-dimensional nature of the flow field. Parameters include rotational slip of the flow leaving radial impellers, conditions to avoid reverse flow between impeller blades, and conditions for shockless flow at impeller entry, with the number of blades and blade curvature as variables. Furthermore, analytical extensions to classical one-dimensional Eulerian-based expressions for developed head of pumps and delivered work of turbines are given.

Computer Analysis of Flexural Vibrations of a Rotating Disk With an Arbitrary Profile

1965 ◽  
Author(s):  
J. J. Blech
Keyword(s):  
Boundary Conditions ◽  
Turbine Blades ◽  
Rotating Disk ◽  
Outer Radius ◽  
Mode Shapes ◽  
Determinantal Equation ◽  
Arbitrary Profile ◽  
Solid Disk ◽  
Inner Radius ◽  
Flexural Vibrations

A collocation method is applied to the differential equation and boundary conditions which govern the flexural vibrations of a rotating thin solid disk with an arbitrary profile, clamped at the inner radius and having a flexible ring carrying masses (turbine blades) at the outer radius. The determinantal equation, from which approximations to the reasonance frequencies and mode shapes are extracted, is derived. The results of sample calculations are compared with theoretical and test results. The treatment of other types of boundary conditions is straightforward. A brief discussion of the convergence of this method is given.

Symbolic computation to estimate two-sided boundary conditions in two-dimensional conduction problems

10.2514/3.920 ◽  
1997 ◽  
Vol 11 ◽  
pp. 472-476
Author(s):  
Henry H. Kerr ◽  
F. C. Frank ◽  
Jae-Woo Lee ◽  
W. H. Mason ◽  
Ching-Yu Yang
Keyword(s):  
Boundary Conditions ◽  
Symbolic Computation ◽  
Two Dimensional

scholarly journals Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

scholarly journals A methodology for hygrothermal modelling of imperfect masonry interfaces

2021 ◽  
pp. 174425912198938
Author(s):  
Michael Gutland ◽  
Scott Bucking ◽  
Mario Santana Quintero
Keyword(s):  
Boundary Conditions ◽  
Material Properties ◽  
Structural Integrity ◽  
Bulk Material ◽  
Weather Conditions ◽  
Masonry Wall ◽  
Two Dimensional ◽  
Liquid Transport ◽  
Imperfect Contact ◽  
Moisture Contents

Hygrothermal models are important tools for assessing the risk of moisture-related decay mechanisms which can compromise structural integrity, loss of architectural features and material. There are several sources of uncertainty when modelling masonry, related to material properties, boundary conditions, quality of construction and two-dimensional interactions between mortar and unit. This paper examines the uncertainty at the mortar-unit interface with imperfections such as hairline cracks or imperfect contact conditions. These imperfections will alter the rate of liquid transport into and out of the wall and impede the liquid transport between mortar and masonry unit. This means that the effective liquid transport of the wall system will be different then if only properties of the bulk material were modelled. A detailed methodology for modelling this interface as a fracture is presented including definition of material properties for the fracture. The modelling methodology considers the combined effect of both the interface resistance across the mortar-unit interface and increase liquid transport in parallel to the interface, and is generalisable to various combinations of materials, geometries and fracture apertures. Two-dimensional DELPHIN models of a clay brick/cement-mortar masonry wall were created to simulate this interaction. The models were exposed to different boundary conditions to simulate wetting, drying and natural cyclic weather conditions. The results of these simulations were compared to a baseline model where the fracture model was not included. The presence of fractures increased the rate of absorption in the wetting phase and an increased rate of desorption in the drying phase. Under cyclic conditions, the result was higher peak moisture contents after rain events compared to baseline and lower moisture contents after long periods of drying. This demonstrated that detailed modelling of imperfections at the mortar-unit interface can have a definitive influence on results and conclusions from hygrothermal simulations.

scholarly journals Phase transitions in GLSMs and defects

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ilka Brunner ◽  
Fabian Klos ◽  
Daniel Roggenkamp
Keyword(s):  
Phase Transitions ◽  
Boundary Conditions ◽  
Sigma Models ◽  
Domain Walls ◽  
Two Dimensional ◽  
Linear Sigma Models

Abstract In this paper, we construct defects (domain walls) that connect different phases of two-dimensional gauged linear sigma models (GLSMs), as well as defects that embed those phases into the GLSMs. Via their action on boundary conditions these defects give rise to functors between the D-brane categories, which respectively describe the transport of D-branes between different phases, and embed the D-brane categories of the phases into the category of D-branes of the GLSMs.

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