Computing and Analysing Energy Minimisation Problems in Liquid Crystals

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How does one numerically analyse different phases of liquid crystals? With the help of some open-source libraries, what can we do in exploiting the mathematical models of liquid crystals and numerical aspects of their typical defects? There are many excellent books on liquid crystals, but none on their numerics to the knowledge of the author. This book presents some of the latest work on numerical investigations of liquid crystals, addressing some mathematical modelling and numerical problems. This book consists of three major parts, each of which focuses on different problems for different phases of liquid crystals: nematics and cholesterics, ferronematics and smectics. The associated topics include robust solvers for cholesterics, multiple solutions for ferronematics, and mathematical modelling theory for smectics, etc. This interdisciplinary book can be helpful in utilising the open-source libraries Firedrake (for solving problems using finite element methods) and Defcon (for computing multiple solutions) to solve general energy minimisation problems. Sample Chapter(s) Preface Chapter 1: Introduction Chapter 2: A Mathematical Model of Nematics and Cholesterics Contents: Introduction Nematic and Cholesteric Liquid Crystals: A Mathematical Model of Nematics and Cholesterics A Robust Multigrid Algorithm for the Augmented Director Block Numerical Experiments for Nematics and Cholesterics Ferronematic Liquid Crystals: A Mathematical Model of Ferronematics Computing Multiple Solutions Using Deflation Numerical Verifications for Ferronematics Smectic Liquid Crystals: A Mathematical Model of Smectics Finite Element Discretisation Numerical Experiments for Smectics Conclusions and Perspectives: Summary and Conclusions Appendices: Stability of the Newton System Equilibrium Equations in Two Dimensions Readership: Advanced undergraduate and graduate students interested in numerical modelling of liquid crystals; researchers in the fields of mathematical theories and numerical aspects in liquid crystals.

Liquid Crystals: New Perspectives

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DESCRIPTION This book on liquid crystals reports on the new perspectives that have been brought about by the recent expansion of frontiers and overhaul of common beliefs. First, it explores the interaction of light with mesophases, when the light or matter is endowed with topological defects. It goes on to show how electrophoresis, electro-osmosis and the swimming of flagellated bacteria are affected by the anisotropic properties of liquid crystals. It also reports on the recent progress in the understanding of thermomechanical and thermohydrodynamical effects in cholesterics and deformed nematics and refutes the common belief that these effects could explain Lehmann’s observations of the rotation of cholesteric droplets subjected to a temperature gradient. It then studies the physics of the dowser texture, which has remarkable properties. This is of particular interest in regards to nematic monopoles, which can easily be generated, set into motion and collided within it. Finally, this book deals with the spontaneous emergence of chirality in nematics made of achiral molecules, and provides a brief historical context of chirality

LIQUID CRYSTALS (3版)

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The latest edition of the leading resource on the properties and applications of liquid crystals In the newly revised Third Edition of Liquid Crystals, Professor Iam Choon Khoo delivers a comprehensive treatment of the fundamentals and applied aspects of optical physics, light scattering, electro-optics, and non-linear optics of liquid crystals. The book's opening chapters include coverage of the foundational physics and optical properties of liquid crystals and lead to more advanced content on the display, photonics and nonlinear optics applications of liquid crystals. New topics, including photonic crystals, metamaterials, ultrafast nonlinear optics, and fabrication methods for massive cholesteric and blue phase liquid crystals are discussed at length. Analytical methods and experimental observations of nonlinear light propagation through liquid crystalline and anisotropic materials and devices are also discussed. Liquid Crystals offers an insightful and unique treatment of the nonlinear optics of liquid crystals. New and expanded sections round out this new edition and add to the most up-to-date resource on this topic available today. The book also includes: A thorough introduction to liquid crystals, including their molecular structures, chemical compositions, order parameter, phase transition, and free energies Practical discussions of nematic, cholesteric, smectic, and ferroelectric liquid crystals, and explorations of linear and nonlinear light scattering in these phases. A detailed quantum mechanical treatment of the linear and nonlinear electronic optical response of liquid crystal molecules to optical fields. A self-contained discussion of the fundamentals of nonlinear optics/photonics and comprehensive review of all liquid crystalline materials-based nonlinear optical processes and applications. The latest edition of Liquid Crystals is an indispensable resource for graduate students, professors, research scientists and engineers in industrial or government laboratories. It's also an ideal reference for anyone seeking a one-stop textbook with complete coverage of the optical, electro-optical, and non-linear optical properties and processes of liquid crystals.