isotropic state

The present methods for obtaining the optimal Lewenestein–Sanpera decomposition of a mixed state are difficult to handle analytically. We provide a simple analytical expression for the optimal Lewenstein–Sanpera decomposition by using semi-definite programming. In particular, we obtain the optimal Lewenstein–Sanpera decomposition for some examples such as: the Bell decomposable state, the iso-concurrence state, the generic two-qubit state in the Wootters basis, the 2⊗3 Bell decomposable state, the d⊗d Werner and isotropic states, a one parameter 3⊗3 state, and finally a multi-partite isotropic state.

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Electro-optic effects of the optically isotropic state induced by the incorporative effects of a polymer network and the chirality of liquid crystal

Journal of the Society for Information Display ◽

10.1889/1.2210806 ◽

2006 ◽

Vol 14 (6) ◽

pp. 551 ◽

Cited By ~ 25

Author(s):

Yasuhiro Haseba ◽

Hirotsugu Kikuchi

Keyword(s):

Liquid Crystal ◽

Polymer Network ◽

Isotropic State ◽

Electro Optic

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Field-induced optically isotropic state in bent core nematic liquid crystals: unambiguous proof of field-induced optical biaxiality

Journal of Physics D Applied Physics ◽

10.1088/0022-3727/46/45/455101 ◽

2013 ◽

Vol 46 (45) ◽

pp. 455101 ◽

Cited By ~ 6

Author(s):

Omaima Elamain ◽

Gurumurthy Hegde ◽

Katalin Fodor-Csorba ◽

Lachezar Komitov

Keyword(s):

Liquid Crystals ◽

Nematic Liquid Crystals ◽

Isotropic State

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Variety of fiber orientation tensors

Mathematics and Mechanics of Solids ◽

10.1177/10812865211057602 ◽

2021 ◽

pp. 108128652110576

Author(s):

Julian Karl Bauer ◽

Thomas Böhlke

Keyword(s):

Fiber Orientation ◽

Mechanical Response ◽

Transversely Isotropic ◽

Orientation Tensor ◽

Isotropic State ◽

Orientation Tensors ◽

Linear Invariant ◽

Parameter Ranges ◽

Independent Parameters

Fiber orientation tensors are established descriptors of fiber orientation states in (thermo-)mechanical material models for fiber-reinforced composites. In this paper, the variety of fourth-order orientation tensors is analyzed and specified by parameterizations and admissible parameter ranges. The combination of parameterizations and admissible parameter ranges allows for studies on the mechanical response of different fiber architectures. Linear invariant decomposition with focus on index symmetry leads to a novel compact hierarchical parameterization, which highlights the central role of the isotropic state. Deviation from the isotropic state is given by a triclinic harmonic tensor with simplified structure in the orientation coordinate system, which is spanned by the second-order orientation tensor. Material symmetries reduce the number of independent parameters. The requirement of positive-semi-definiteness defines admissible ranges of independent parameters. Admissible parameter ranges for transversely isotropic and planar cases are given in a compact closed form and the orthotropic variety is visualized and discussed in detail. Sets of discrete unit vectors, leading to selected orientation states, are given.

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