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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 study examines a significant development within late medieval and early modern European government, set in the context of the tense relations between the young Emperor Charles V and his ageing chancellor Mercurino de Gattrina. It focuses upon an important transformation in the administrative reorganisation of European monarchies: the shift in the political centre of gravity from the medieval institution of the chancellery as the secretariat for all government business and authentication to a small group of secretaries, the minister of a later age, acting directly in collaboration with the prince. In the collision between the traditional judicial and administrative pre-eminence of the late medieval chancellor and the new secretaries as expediters of the Renaissance prince's will. Charles gave his support to the latter, thus associating himself with the previous work of Ferdinand the Catholic. Against the background of this struggle with the state secretaries the imperial chancellery is analysing in its relations to the individual chancelleries of Charles V's disparate lands.
Liquid crystal displays were discovered in the 1960s, and today we continue to enjoy the benefits of that fundamental discovery and its translation into a wide variety of products. Like liquid crystals, polymers are unusual materials, and have similarly enjoyed a great deal of research attention because of their vast applications and uses and compl
Despite the large quantity of phenomenological information concerning the bulk properties of nematic phase liquid crystals, little is understood about the origin of the surface energy, particularly the surface, interfacial, and anchoring properties of liquid crystals that affect the performance of liquid crystal devices. Self-contained and unique,
Evolutionally optimized biomolecules and their complexes present attractive objects in the production of functionalized nanoobjects. Indeed, nucleic acid-based molecules are primary candidates as building blocks for development of nanoscale systems and devices. Written for chemists, physicists, molecular biologists, and students in related fields, Nanostructures and Nanoconstructions Based on DNA covers specific properties of metallic nanoparticles, and compares their properties with those related to nanoobjects formed by biological molecules. It also discloses details of formation and physicochemical peculiarities of the DNA nanostructures and DNA-based nanoconstructions. Furthermore, the b...
The discovery of the spatial structure of the double-stranded DNA molecule is one of the greatest achievements of science. It would not be an exaggeration to say that the DNA double helix is a distinguished symbol of modern biology. Divided into three parts, DNA Liquid-Crystalline Dispersions and Nanoconstructions covers the information presently a
Focusing on the applied and basic aspects of confined liquid crystals, this book provides a current treatise of the subject matter and places it in the broader context of electrooptic applications. The book takes an interdisciplinary approach to the
Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs, which model real-life situations. Owing to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering. Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. This book focuses on the no...
Based on graduate lectures given by the authors, Smectic and Columnar Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments examines lamellar (smectic) and columnar liquid crystals, which, in addition to orientational order, possess 1D, 2D or 3D positional order. Topics include rheology and plasticity, ferroelectricity, analogies with superconductors, hexatic order and 2D-melting, equilibrium shapes, facetting, and the Mullins-Sekerka instability, as well as phase transitions in free films and membrane vibrations. Nematic and cholesteric liquid crystals are covered by the authors in a separate volume entitled Nematic and Cholesteric Liquid Crystals: Concepts and Physical Properties Illustrated by Experiments.
The self-contained properties of discotic liquid crystals (DLCs) render them powerful functional materials for many semiconducting device applications and models for energy and charge migration in self-organized dynamic functional soft materials. The past three decades have seen tremendous interest in this area, fueled primarily by the possibility