Variational Theories For Liquid Crystals PDF Download
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Author | : E.G. Virga |
Publisher | : Routledge |
Total Pages | : 284 |
Release | : 2018-12-12 |
Genre | : Mathematics |
ISBN | : 1351405640 |
Download Variational Theories for Liquid Crystals Book in PDF, ePub and Kindle
Essentially there are two variational theories of liquid crystals explained in this book. The theory put forward by Zocher, Oseen and Frank is classical, while that proposed by Ericksen is newer in its mathematical formulation although it has been postulated in the physical literature for the past two decades. The newer theory provides a better explanation of defects in liquid crystals, especially of those concentrated on lines and surfaces, which escape the scope of the classical theory. The book opens the way to the wealth of applications that will follow.
Author | : E. G. Virga |
Publisher | : Applied Mathematics |
Total Pages | : 376 |
Release | : 2019-11-29 |
Genre | : |
ISBN | : 9780367449063 |
Download Variational Theories for Liquid Crystals Book in PDF, ePub and Kindle
Essentially there are two variational theories of liquid crystals explained in this book. The theory put forward by Zocher, Oseen and Frank is classical, while that proposed by Ericksen is newer in its mathematical formulation although it has been postulated in the physical literature for the past two decades. The newer theory provides a better explanation of defects in liquid crystals, especially of those concentrated on lines and surfaces, which escape the scope of the classical theory. The book opens the way to the wealth of applications that will follow.
Author | : E.G. Virga |
Publisher | : CRC Press |
Total Pages | : 398 |
Release | : 2018-12-12 |
Genre | : Mathematics |
ISBN | : 1351405659 |
Download Variational Theories for Liquid Crystals Book in PDF, ePub and Kindle
Essentially there are two variational theories of liquid crystals explained in this book. The theory put forward by Zocher, Oseen and Frank is classical, while that proposed by Ericksen is newer in its mathematical formulation although it has been postulated in the physical literature for the past two decades. The newer theory provides a better explanation of defects in liquid crystals, especially of those concentrated on lines and surfaces, which escape the scope of the classical theory. The book opens the way to the wealth of applications that will follow.
Author | : Zdzisław Naniewicz |
Publisher | : |
Total Pages | : 25 |
Release | : 1997 |
Genre | : |
ISBN | : |
Download Variational Theory for Liquid Crystals with Variable Degree of Orientation Book in PDF, ePub and Kindle
Author | : Iain W. Stewart |
Publisher | : CRC Press |
Total Pages | : 351 |
Release | : 2004-06-29 |
Genre | : Science |
ISBN | : 0203646339 |
Download The Static and Dynamic Continuum Theory of Liquid Crystals Book in PDF, ePub and Kindle
Given the widespread interest in macroscopic phenomena in liquid crystals, stemming from their applications in displays and devices. The need has arisen for a rigorous yet accessible text suitable for graduate students, whatever their scientific background. This book satisfies that need. The approach taken in this text, is to introduce the basic continuum theory for nematic liquid crystals in equilibria, then it proceeds to simple application of this theory- in particular, there is a discussion of electrical and magnetic field effects which give rise to Freedericksz transitions, which are important in devices. This is followed by an account of dynamic theory and elementary viscometry of nemantics Discussions of backflow and flow-induced instabilities are also included. Smetic theory is also briefly introduced and summarised with some examples of equilibrium solutions as well as those with dynamic effects. A number of mathematical techniques, such as Cartesian tensors and some variational calculus, are presented in the appendices.
Author | : G Barbero |
Publisher | : World Scientific Publishing Company |
Total Pages | : 384 |
Release | : 2000-10-27 |
Genre | : Science |
ISBN | : 9814365637 |
Download An Elementary Course on the Continuum Theory for Nematic Liquid Crystals Book in PDF, ePub and Kindle
This book was written to enable physicists and engineers to learn, within a single course, some topics in variational calculus, theory of elasticity, molecular models, and surface properties of nematic materials. It prepares graduate students for studies that require a simple knowledge in the physics of nematic liquid crystals. With this consideration in mind, the authors have formulated the problems concerning the continuum theory of liquid crystals into a precise form. In working out the solutions, they have analyzed, systematically and naturally, the techniques and methods of variational calculus. Special attention is dedicated to the analysis of well-posed and ill-posed variational problems. The presence of sub-surface discontinuity in the nematic orientation is analyzed using different techniques. A full chapter is devoted to this aspect of the theory of elasticity of nematic media.
Author | : Victor J. Mizel |
Publisher | : |
Total Pages | : 24 |
Release | : 1990 |
Genre | : Calculus of variations |
ISBN | : |
Download A Variational Problem for Nematic Liquid Crystals with Variable Degree of Orientation Book in PDF, ePub and Kindle
Abstract: "A version of Ericksen's order parameter theory of liquid crystals is studied in the case of a cylindrical container with anchoring on the curved surface only. The solutions are determined rather explicitly and the equilibrium orientation field is shown to vary between that of the Frank solution (possessing an axial disclination) and that of the disclination-free Cladis-Kleman solution as a scalar parameter in the free energy varies from 0 to [infinity]."
Author | : André M. Sonnet |
Publisher | : Springer Science & Business Media |
Total Pages | : 333 |
Release | : 2012-01-24 |
Genre | : Science |
ISBN | : 0387878157 |
Download Dissipative Ordered Fluids Book in PDF, ePub and Kindle
This is a book on the dissipative dynamics of ordered fluids, with a particular focus on liquid crystals. It covers a whole range of different theories, mainly concerned with nematic liquid crystals in both their chiral and nonchiral variants. The authors begin by giving a detailed account of the molecular origins of orientational order in fluids. They then go on to develop a general framework in which continuum theories for ordered fluids can be phrased. Within this unified setting, they cover both well-established classical theories and new ones with aspects that are not yet completely settled. The book treats a wide range of hydrodynamic theories for liquid crystals, from the original 1960s works by Ericksen and Leslie to new, fast-developing ideas of liquid crystal science. The final chapter is devoted to nematoacoustics and its applications. Old experiments on the propagation of ultrasound waves in nematic liquid crystals are interpreted and explained in the light of a new theory developed within the general theoretical infrastructure proposed in the body of the book. This book is intended both for graduate students and professional scholars in mathematics, physics, and engineering of advanced materials. It delivers a solid framework for liquid crystal hydrodynamics and shows the unifying concepts at the basis of the classical theories. It illustrates how these concepts can also be applied to a wide variety of modern topics. Andre M. Sonnet is in the Department of Mathematics and Statistics at the University of Strathclyde, Glasgow (Scotland) and Epifanio G. Virga is in the Department of Mathematics at the University of Pavia (Italy). They have a long history of working together in liquid crystal science and have contributed, in particular, to the theories of defects and biaxial nematics.
Author | : Oleg D. Lavrentovich |
Publisher | : Springer Science & Business Media |
Total Pages | : 356 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9401005125 |
Download Defects in Liquid Crystals: Computer Simulations, Theory and Experiments Book in PDF, ePub and Kindle
Topological defects are the subject of intensive studies in many different branches of physics ranging from cosmology to liquid crystals and from elementary particles to colloids and biological systems. Liquid crystals are fascinating materials which present a great variety of these mathematical objects and can therefore be considered as an extremely useful laboratory for topological defects. This book is the first attempt to present together complementary approaches to the investigations of topological defects in liquid crystals using theory, experiments and computer simulations.
Author | : Jianzhong Wu |
Publisher | : Springer |
Total Pages | : 324 |
Release | : 2016-12-17 |
Genre | : Science |
ISBN | : 9811025029 |
Download Variational Methods in Molecular Modeling Book in PDF, ePub and Kindle
This book presents tutorial overviews for many applications of variational methods to molecular modeling. Topics discussed include the Gibbs-Bogoliubov-Feynman variational principle, square-gradient models, classical density functional theories, self-consistent-field theories, phase-field methods, Ginzburg-Landau and Helfrich-type phenomenological models, dynamical density functional theory, and variational Monte Carlo methods. Illustrative examples are given to facilitate understanding of the basic concepts and quantitative prediction of the properties and rich behavior of diverse many-body systems ranging from inhomogeneous fluids, electrolytes and ionic liquids in micropores, colloidal dispersions, liquid crystals, polymer blends, lipid membranes, microemulsions, magnetic materials and high-temperature superconductors. All chapters are written by leading experts in the field and illustrated with tutorial examples for their practical applications to specific subjects. With emphasis placed on physical understanding rather than on rigorous mathematical derivations, the content is accessible to graduate students and researchers in the broad areas of materials science and engineering, chemistry, chemical and biomolecular engineering, applied mathematics, condensed-matter physics, without specific training in theoretical physics or calculus of variations.