Variational Theories For Liquid Crystals

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.

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.

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.

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.

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.

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.

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.