Zhong-can Ou-yang – författare

"The book is highly recommended as a reference for advanced graduate students and scholars involved in geometric analysis of membranes and other elastic surfaces. Valuable techniques may be learned from the book’s model constructions and sequential derivations and presentations of governing equations. Detailed analysis and solutions enable the reader with an increased understanding of the physical characteristics of membranes in liquid crystal phases such as their preferred shapes."Contemporary PhysicsThis is the second edition of the book Geometric Methods in Elastic Theory of Membranes in Liquid Crystal Phases published by World Scientific in 1999. This book gives a comprehensive treatment of the conditions of mechanical equilibrium and the deformation of membranes as a surface problem in differential geometry. It is aimed at readers engaging in the field of investigation of the shape formation of membranes in liquid crystalline state with differential geometry. The material chosen in this book is mainly limited to analytical results. The main changes in this second edition are: we add a chapter (Chapter 4) to explain how to calculate variational problems on a surface with a free edge by using a new mathematical tool — moving frame method and exterior differential forms — and how to derive the shape equation and boundary conditions for open lipid membranes through this new method. In addition, we include the recent concise work on chiral lipid membranes as a section in Chapter 5, and in Chapter 6 we mention some topics that we have not fully investigated but are also important to geometric theory of membrane elasticity.

This book addresses the physical mechanisms involved in the characteristic electrical properties and the geometrical structures that are observed from dipolar monolayers composed of organic molecules by using dielectric physics, electrostatics, the physics of liquid crystal, and soft matter physics. The orientational order parameters, introduced to quantify the orientational structures of monolayers, guide us towards this goal. Dielectric polarizations are spontaneously generated from monolayers because of their orientational structures, and electrostatic energies due to these dielectric polarizations play a key role in forming the geometrical structures that are observed from monolayers. Free energy minimization is a powerful tool to understand the physical mechanisms that stabilize these geometrical structures because of the soft matter nature of monolayers. The approach using mathematical differential geometry method makes this book unique among the literatures of monolayers.