scholarly journals Nematic director fields and topographies of solid shells of revolution

2018 ◽  
Vol 474 (2210) ◽  
pp. 20170566 ◽  
Author(s):  
Mark Warner ◽  
Cyrus Mostajeran
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Gaussian Curvature ◽  
Energy Cost ◽  
Shape Change ◽  
Mechanical Deformation ◽  
Surfaces Of Revolution ◽  
Shells Of Revolution ◽  
Director Field ◽  
Nematic Director

We solve the forward and inverse problems associated with the transformation of flat sheets with circularly symmetric director fields to surfaces of revolution with non-trivial topography, including Gaussian curvature, without a stretch elastic cost. We deal with systems slender enough to have a small bend energy cost. Shape change is induced by light or heat causing contraction along a non-uniform director field in the plane of an initially flat nematic sheet. The forward problem is, given a director distribution, what shape is induced? Along the way, we determine the Gaussian curvature and the evolution with induced mechanical deformation of the director field and of material curves in the surface (proto-radii) that will become radii in the final surface. The inverse problem is, given a target shape, what director field does one need to specify? Analytic examples of director fields are fully calculated that will, for specific deformations, yield catenoids and paraboloids of revolution. The general prescription is given in terms of an integral equation and yields a method that is generally applicable to surfaces of revolution.

scholarly journals Optical manipulation of the nematic director field around microspheres covered with an azo-dendrimer monolayer

2014 ◽  
Vol 22 (17) ◽  
pp. 20087 ◽  
Author(s):  
Pemika Hirankittiwong ◽  
Nattaporn Chattham ◽  
Jumras Limtrakul ◽  
Osamu Haba ◽  
Koichiro Yonetake ◽  
...  
Keyword(s):  
Optical Manipulation ◽  
Director Field ◽  
Nematic Director

An existence theorem for Robin's equation

1972 ◽  
Vol 72 (3) ◽  
pp. 489-498 ◽  
Author(s):  
R. Cade
Keyword(s):  
Integral Equation ◽  
Existence Theorem ◽  
Electric Charge ◽  
Gaussian Curvature ◽  
Closed Surface ◽  
Arithmetic Mean ◽  
Main Argument

AbstractAn existence theorem is proved for Robin's integral equation for the density of electric charge on a closed surface, under the assumptions that the surface is convex, smooth and twice continuously differentiable. The technique is essentially Neumann's method of the arithmetic mean, used by Robin himself to show that the solution, assumed to exist, can be successively approximated by a sequence. In order to facilitate the main argument of the proof, it is assumed initially that the Gaussian curvature is everywhere positive, but this restriction is subsequently removed.

scholarly journals Inverse problem: acoustic potential vs acoustic length

1988 ◽  
Vol 123 ◽  
pp. 133-136
Author(s):  
Hiromoto Shibahashi
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Sound Velocity ◽  
Internal Structure ◽  
Asymptotic Method ◽  
The Sun ◽  
Quantization Rule ◽  
Rule Based ◽  
Deep Interior

By using the quantization rule based on the WKB asymptotic method, we present an integral equation to infer the form of the acoustic potential of a fixed ℓ as a function of the acoustic length. Since we analyze the acoustic potential itself by taking account of some factors other than the sound velocity and we can analyze the radial modes by this scheme as well as nonradial modes, this method improves the accuracy and effectiveness of the inverse problem to infer the internal structure of the Sun, in particular, the deep interior of the Sun.

scholarly journals Integral equation methods for the inverse problem with discontinuous wave speed

1996 ◽  
Vol 37 (7) ◽  
pp. 3218-3245 ◽  
Author(s):  
Tuncay Aktosun ◽  
Martin Klaus ◽  
Cornelis van der Mee
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Wave Speed ◽  
Discontinuous Wave ◽  
Integral Equation Methods

One dimensional model of dye-doped nematic layer for holography

2006 ◽  
Vol 14 (2) ◽  
Author(s):  
G. Derfel ◽  
M. Buczkowska ◽  
J. Parka
Keyword(s):  
Ion Concentration ◽  
Dimensional Model ◽  
Director Field ◽  
One Dimensional ◽  
Ion Concentrations ◽  
Electrically Conducting ◽  
Nematic Director ◽  
Extraordinary Refractive Index ◽  
Director Orientation ◽  
Coated Electrodes

AbstractThe layer of electrically conducting nematic liquid crystal doped with photosensitive dye and confined between polyimide coated electrodes can serve as a diffraction grating. In this paper, the deformations of the nematic director field induced in such a system by external voltage were studied numerically by means of one-dimensional model. The dissociation and recombination of ions were taken into account according to weak electrolyte model. The director orientation in the deformed layers and the distributions of the electric field and of the ion concentrations were calculated for blocking and for conducting electrodes. The effective extraordinary refractive index was also determined as a function of average ion concentration.

scholarly journals On a nonlinear inverse problem in viscoelasticity

2009 ◽  
Vol 31 (3-4) ◽  
Author(s):  
H. D. Bui ◽  
S. Chaillat
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Volterra Integral Equation ◽  
Boundary Data ◽  
Viscoelastic Body ◽  
Low Frequency ◽  
Cyclic Loads ◽  
Nonlinear Inverse Problem ◽  
Method Of Solution ◽  
The One

We consider an inverse problem for determining an inhomogeneity in a viscoelastic body of the Zener type, using Cauchy boundary data, under cyclic loads at low frequency. We show that the inverse problem reduces to the one for the Helmholtz equation and to the same nonlinear Calderon equation given for the harmonic case. A method of solution is proposed which consists in two steps: solution of a source inverse problem, then solution of a linear Volterra integral equation.

scholarly journals Inverse problem on the semi-axis: local approach

2011 ◽  
Vol 42 (3) ◽  
pp. 275-293
Author(s):  
S. A. Avdonin ◽  
B. P. Belinskiy ◽  
John V. Matthews
Keyword(s):  
Inverse Problem ◽  
Integral Equation ◽  
Wave Equation ◽  
Volterra Integral Equation ◽  
Accurate Data ◽  
Data Preparation ◽  
Local Approach ◽  
Numerical Examples ◽  
Linear Version ◽  
The Right

We consider the problem of reconstruction of the potential for the wave equation on the semi-axis. We use the local versions of the Gelfand-Levitan and Krein equations, and the linear version of Simon's approach. For all methods, we reduce the problem of reconstruction to a second kind Fredholm integral equation, the kernel and the right-hand-side of which arise from an auxiliary second kind Volterra integral equation. A second-order accurate numerical method for the equations is described and implemented. Then several numerical examples verify that the algorithms can be used to reconstruct an unknown potential accurately. The practicality of each approach is briefly discussed. Accurate data preparation is described and implemented.

An Efficient Computational Inverse Approach for Optimal Design of Localized Activation and Actuation for Morphing SMP Structures

2012 ◽  
Author(s):  
Shuang Wang ◽  
John C. Brigham
Keyword(s):  
Inverse Problem ◽  
Optimal Design ◽  
Shape Change ◽  
Mechanical Energy ◽  
Optimization Methods ◽  
Future Directions ◽  
Inverse Approach ◽  
Thermally Activated ◽  
Nonlinear Optimization Methods ◽  
Numerical Representations

A strategy is presented to identify the optimal localized activation and actuation for a morphing thermally-activated SMP structure or structural component to obtain a targeted shape change subject to design objectives such as minimal total required energy and time. This strategy combines numerical representations of the SMP structure’s thermo-mechanical behavior subject to activation and actuation with nonlinear optimization methods to efficiently solve the morphing inverse problem that includes minimizing cost functions which address thermal and mechanical energy, morphing time, and damage. The details of this strategy are presented along with simulated examples to display the capabilities and limitations, as well as potential future directions for improving these techniques.

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