Download or read book Variational Theories for Liquid Crystals written by E.G. Virga and published by CRC Press. This book was released on 1995-05-15 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Theories for Liquid Crystals written by Epifanio G. Virga and published by . This book was released on 1994 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Theories for Liquid Crystals written by E.G. Virga and published by CRC Press. This book was released on 2018-12-12 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Theory for Liquid Crystals with Variable Degree of Orientation written by Zdzisław Naniewicz and published by . This book was released on 1997 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Variational Problem for Nematic Liquid Crystals with Variable Degree of Orientation written by Victor J. Mizel and published by . This book was released on 1990 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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]."
Download or read book The Static and Dynamic Continuum Theory of Liquid Crystals written by Iain W. Stewart and published by CRC Press. This book was released on 2004-06-29 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Problems for Liquid Crystals with Variable Degree of Orientation written by Victor J. Mizel and published by . This book was released on 1991 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "The analysis of a nematic liquid crystal, filling a bounded cylindrical container, whose free energy is a (simplified) version of Ericksen's model with variable degree of orientation, leads to a variational problem of the form F[s, [phi]] = [integral]10[k (sʹ)2 + s2 (([phi]ʹ)2 + cos2[phi]/r2)]rdr subject to s(1) = s0, [phi](1) = 0, with k a positive constant. It will be shown that a surprisingly explicit solution is obtainable. Moreover an interesting bifurcation takes place at k = 1."
Download or read book Dissipative Ordered Fluids written by André M. Sonnet and published by Springer Science & Business Media. This book was released on 2012-01-21 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Variational Problems in Materials Science written by Gianni Dal Maso and published by Springer Science & Business Media. This book was released on 2006-06-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism and ferroelectricity, and much more.
Download or read book New Variational Problems in the Statics of Liquid Crystals written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Elementary Course on the Continuum Theory for Nematic Liquid Crystals written by Giovanni Barbero and published by World Scientific Publishing Company Incorporated. This book was released on 2001 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Static and Dynamic Continuum Theory of Liquid Crystals written by Iain W. Stewart and published by CRC Press. This book was released on 2019-01-10 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Asymptotic and Variational Methods for the Study of Defects in Liquid Crystals written by Aaron Pim and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Problems in Materials Science written by Gianni Dal Maso and published by Birkhäuser. This book was released on 2006-03-17 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism and ferroelectricity, and much more.
Download or read book Defects in Liquid Crystals Computer Simulations Theory and Experiments written by Oleg D. Lavrentovich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of Liquid Crystals 8 Volume Set written by John W. Goodby and published by John Wiley & Sons. This book was released on 2014-04-14 with total page 5240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Much more than a slight revision, this second edition of the successful "Handbook of Liquid Crystals" is completely restructured and streamlined, with updated as well as completely new topics, 100% more content and a new team of editors and authors. As such, it fills the gap for a definitive, single source reference for all those working in the field of organized fluids and will set the standard for the next decade. The Handbook's new structure facilitates navigation and combines the presentation of the content by topic and by liquid-crystal type: A fundamentals volume sets the stage for an understanding of the liquid crystal state of matter, while individual volumes cover the main types and forms, with a final volume bringing together the diverse liquid crystal phases through their applications. This unrivaled, all-embracing coverage represents the undiluted knowledge on liquid crystals, making the Handbook a must-have wherever liquid crystals are investigated, produced or used, and in institutions where their science and technology is taught. Also available electronically on Wiley Online Library, www.wileyonlinelibrary.com/ref/holc Volume 1: Fundamentals of Liquid Crystals Volume 2: Physical Properties and Phase Behavior of Liquid Crystals Volume 3: Nematic and Chiral Nematic Liquid Crystals Volume 4: Smectic and Columnar Liquid Crystals Volume 5: Non-Conventional Liquid Crystals Volume 6: Nanostructured and Amphiphilic Liquid Crystals Volume 7: Supermolecular and Polymeric Liquid Crystals Volume 8: Applications of Liquid Crystals
Download or read book A Variational Approach to Fracture and Other Inelastic Phenomena written by Gianpietro Del Piero and published by Springer Science & Business Media. This book was released on 2013-08-30 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book exposes a number of mathematical models for fracture of growing difficulty. All models are treated in a unified way, based on incremental energy minimization. They differ from each other by the assumptions made on the inelastic part of the total energy, here called the "cohesive energy". Each model describes a specific aspect of material response, and particular care is devoted to underline the correspondence of each model to the experiments. The content of the book is a re-elaboration of the lectures delivered at the First Sperlonga Summer School on Mechanics and Engineering Sciences in September 2011. In the year and a half elapsed after the course, the material has been revised and enriched with new and partially unpublished results. Significant additions have been introduced in the occasion of the course "The variational approach to fracture and other inelastic phenomena", delivered at SISSA, Trieste, in March 2013. The Notes reflect a research line carried on by the writer over the years, addressed to a comprehensive description of the many aspects of the phenomenon of fracture, and to its relations with other phenomena, such as the formation of microstructure and the changes in the material’s strength induced by plasticity and damage. Reprinted from the Journal of Elasticity, volume 112, issue 1, 2013.
