scholarly journals Analysis of time-fractional hunter-saxton equation: a model of neumatic liquid crystal

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 145-149 ◽  
Author(s):  
Abdon Atangana ◽  
Dumitru Baleanu ◽  
Ahmed Alsaedi
Keyword(s):  
Hilbert Space ◽  
Liquid Crystal ◽  
Fractional Derivative ◽  
Iteration Method ◽  
Decomposition Method ◽  
Theoretical Study ◽  
Physical Phenomenon ◽  
Mathematical Equation ◽  
Homotopy Decomposition ◽  
Almost All

AbstractIn this work, a theoretical study of diffusion of neumatic liquid crystals was done using the concept of fractional order derivative. This version of fractional derivative is very easy to handle and obey to almost all the properties satisfied by the conventional Newtonian concept of derivative. The mathematical equation underpinning this physical phenomenon was solved analytically via the so-called homotopy decomposition method. In order to show the accuracy of this iteration method, we constructed a Hilbert space in which we proved its stability for the time-fractional Hunder-Saxton equation.

On the photophysical properties of a liquid crystal dimer based on 4-nitrostilbene: a combined experimental and theoretical study

2021 ◽  
pp. 116969
Author(s):  
Kristina Gak Simić ◽  
Ivana Đorđević ◽  
Goran Janjić ◽  
Dániel Datz ◽  
Tibor Tóth-Katona ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Theoretical Study ◽  
Photophysical Properties

Strains in Aluminum-Adhesive-Ceramic Trilayers

1990 ◽  
Vol 112 (4) ◽  
pp. 288-302 ◽  
Author(s):  
P. M. Hall ◽  
F. L. Howland ◽  
Y. S. Kim ◽  
L. H. Herring
Keyword(s):  
Elastic Modulus ◽  
High Speed ◽  
Theoretical Study ◽  
Alumina Ceramic ◽  
Strain Gages ◽  
Wire Bonds ◽  
Large Expansion ◽  
Trilayer Structure ◽  
Almost All ◽  
Increasing Temperature

In many of today’s high speed, high density circuits, there is a need to remove large amounts of heat. To facilitate this removal of heat, it is common to adhere a sheet of a high thermal conductivity material (such as aluminum or copper) to the substrate (which may be alumina ceramic). This can result in large expansion mismatches which cause stresses and bowing, with the possibility of delamination, cracking, stressing solder joints, loss of hermeticity, or shorting of a metal lid to wire bonds inside a cavity. One approach to this problem is to use a compliant adhesive to decouple the materials. The present paper is an experimental and theoretical study of the strains as a function of temperature from −40° C to 140° C in a trilayer structure of 0.030 in. or 0.76 mm thick aluminum, 0.006 in. or 0.15 mm thick adhesive, and 0.021 in. or 0.5 mm thick low-temperature cofired (glassy) ceramic. The strains are analyzed using E. Suhir’s theory, and they are measured using strain gages for three adhesives: an epoxy, a fabric-reinforced epoxy, and a silcone elastopolymer. If the adhesive has an elastic modulus below 10 psi or 70 kPa, theory predicts almost complete de-coupling. Between 100 and 105 psi or 700 kPa and 700 MPa, there is partial decoupling, depending on the in-plane dimensions. Above 10,000 psi or 700 MPa, the decoupling is negligible, and the same bowing results for any elastic modulus between 10,000 and 1,000,000 psi or 70 MPa and 7 GPa. For temperatures below 80° C, only the elastomer has enough compliance to provide any de-coupling. Above 80° C, the elastomer de-couples the most, and the unreinforced epoxy the least. Almost all of the observed effects are understandable in terms of the Suhir theory, along with the fact that the elastic modulus of the epoxy materials decreases with increasing temperature. In particular, when there is some decoupling of the materials, the amount of decoupling depends on the in-plane dimensions of the sample.

Theoretical study of the surface anchoring effect on the full leaky waveguide mode of liquid crystal

2018 ◽  
Vol 33 (6) ◽  
pp. 483-489
Author(s):  
孙婷婷 SUN Ting-ting ◽  
袁 瑞 YUAN Rui ◽  
李振杰 LI Zhen-jie ◽  
朱吉亮 ZHU Ji-liang ◽  
邢红玉 XING Hong-yu ◽  
...  
Keyword(s):  
Liquid Crystal ◽  
Waveguide Mode ◽  
Theoretical Study ◽  
Surface Anchoring ◽  
Anchoring Effect ◽  
Leaky Waveguide

scholarly journals Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 555
Author(s):  
Rafał Brociek ◽  
Agata Chmielowska ◽  
Damian Słota
Keyword(s):  
Fractional Derivative ◽  
Ant Colony Optimization ◽  
Optimization Algorithm ◽  
Iteration Method ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Ant Colony ◽  
Inverse Heat Conduction ◽  
Ant Colony Optimization Algorithm ◽  
Undetermined Coefficient

This paper presents the algorithms for solving the inverse problems on models with the fractional derivative. The presented algorithm is based on the Real Ant Colony Optimization algorithm. In this paper, the examples of the algorithm application for the inverse heat conduction problem on the model with the fractional derivative of the Caputo type is also presented. Based on those examples, the authors are comparing the proposed algorithm with the iteration method presented in the paper: Zhang, Z. An undetermined coefficient problem for a fractional diffusion equation. Inverse Probl. 2016, 32.

scholarly journals Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Abdon Atangana ◽  
Adem Kılıçman
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Biharmonic Equations ◽  
Poisson Equations ◽  
Physical Problems ◽  
Adomian Decomposition ◽  
Homotopy Decomposition ◽  
2D And 3D ◽  
Corrected Function

The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. The approximated solutions obtained converge to the exact solution as tends to infinity.

Theoretical Study of Temperature Tuning and Anisotropy of Liquid Crystal Infiltrated Synthetic Opal as Photonic Crystal

2001 ◽  
Vol 40 (Part 1, No. 7) ◽  
pp. 4565-4569 ◽  
Author(s):  
Gajendra K. Johri ◽  
Akhilesh Tiwari ◽  
Manoj Johri ◽  
Katsumi Yoshino
Keyword(s):  
Liquid Crystal ◽  
Photonic Crystal ◽  
Theoretical Study ◽  
Synthetic Opal ◽  
Temperature Tuning
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