ELECTRICAL AND GEOMETRICAL PROPERTIES OF ORGANIC M

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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. Sample Chapter(s) Preface Chapter 1: Introduction Contents: Introduction Dielectric Physics of Monolayers; Theory of Dielectric Polarization of Monolayers Dielectric Physics of Monolayers: Experimental Techniques to Measure Dielectric Polarizations of Monolayers Liquid Crystalline Properties of Monolayers on Water Surface Differential Geometry Method for Analyzing Domain Shapes Differential Geometry Method for Analyzing Domain Shapes II Comprehensive Approach for Analyzing Domain Shapes Readership: This book would be useful for physicists, chemists, biologists and electronic engineers of the field to understand their experimental results and to develop new theories.

Geometric Gems: An Appreciation for Geometric Curiosities - Volume III: The Wonders of Circles (1版)

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【簡介】 Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The circle, one of the basic aspects of geometry, has a plethora of unexpected curiosities, which the authors present in an easily understandable fashion requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general readership, whose love for geometry should be greatly enhanced through exploring these many unexpected relationships. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating circle properties.

Geometric Deformations of Discriminants and Apparent Contours (1版)

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【簡介】 This book presents new and original results on the deformations of apparent contours of surfaces in Euclidean 3-space and the discriminants of plane-to-plane map-germs. Given a viewing direction, the apparent contour (also called the profile or outline) is the projection of the set of points on the surface where the viewing direction is tangent to the surface. Apparent contours are extensively used in computer vision and image analysis and pose significant mathematical challenges. As the viewing direction varies, the apparent contour deforms, with emerging and vanishing inflections and vertices. The book provides a complete catalog of these bifurcations for generic surfaces as the viewing direction changes. Additionally, it explores geometric invariants that determine the maximum number of inflections and vertices that may appear in such deformations of an apparent contour. Aimed at researchers working in differential geometry, singularity theory, computer vision, and related areas, the text can also serve as material for an undergraduate reading course.

GEOMETRIC GEMS (V2)

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Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The quadrilateral, one of the basic instruments in geometry, has a plethora of unexpected curiosities. The authors present these in an easily understood fashion, requiring nothing more than the very basics of school geometry to appreciate these curiosities and their justifications or proofs. The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating quadrilateral properties. Request Inspection Copy Sample Chapter(s) Introduction Contents: About the Authors Acknowledgments Introduction Quadrilateral Curiosities Proofs of Quadrilateral Curiosities Toolbox Index Readership: The book is intended for the general readership, mathematics teachers, and mathematicians interested in extending their appreciation for geometry.