Generation Theory

This book collects papers presented in the Invited Workshop, “Liutex and Third Generation of Vortex Definition and Identification for Turbulence,” from CHAOS2020, June 9-12, 2020, which was held online as a virtual conference. Liutex is a new physical quantity introduced by Prof. Chaoqun Liu of the University of Texas at Arlington.

by Tsutomu Sasao (Author), Mitchell a Thornton (Editor)
Index generation functions are binary-input integer valued functions

This book highlights the physics, research advances, and applications of integrated optical supercontinuum generation (SCG). The authors provide a roadmap of SCG in various nonlinear media and its historical perspective. The commonly used materials of integrated platforms are discussed, which could provide the references for platform choices in various nonlinear applications. The book introduces the fundamental light-guiding mechanisms, explains the typical dispersion engineering approaches, and summarizes various types of integrated waveguides. The authors present an overview of the physical mechanisms and fundamental equations involved in the SCG. They conduct an in-depth discussion on different types of nonlinear Schrödinger equation (NLSE) to adapt to various circumstances. Through these equations, readers can numerically model the SCG processes. In particular, the book reviews recent representative SCG reports in the integrated waveguides. Moreover, because of the close relationship between the frequency combs and SC, the book discusses some basic concepts of a frequency comb. Finally, the authors raise future prospects on SCG in the integrated waveguides. The book is a comprehensive reference for graduate students and researchers interested in the subject and a handy manual for professionals engaged in related work.

This book highlights the physics, research advances, and applications of integrated optical supercontinuum generation (SCG). The authors provide a roadmap of SCG in various nonlinear media and its historical perspective. The commonly used materials of integrated platforms are discussed, which could provide the references for platform choices in various nonlinear applications. The book introduces the fundamental light-guiding mechanisms, explains the typical dispersion engineering approaches, and summarizes various types of integrated waveguides. The authors present an overview of the physical mechanisms and fundamental equations involved in the SCG. They conduct an in-depth discussion on different types of nonlinear Schrödinger equation (NLSE) to adapt to various circumstances. Through these equations, readers can numerically model the SCG processes. In particular, the book reviews recent representative SCG reports in the integrated waveguides. Moreover, because of the close relationship between the frequency combs and SC, the book discusses some basic concepts of a frequency comb. Finally, the authors raise future prospects on SCG in the integrated waveguides. The book is a comprehensive reference for graduate students and researchers interested in the subject and a handy manual for professionals engaged in related work.

Tiling theory is an elegant branch of mathematics that has applications in several areas of computer science. The most immediate application area is graphics, where tiling theory has been used in the contexts of texture generation, sampling theory, remeshing, and of course the generation of decorative patterns. The combination of a solid theoretical base (complete with tantalizing open problems), practical algorithmic techniques, and exciting applications make tiling theory a worthwhile area of study for practitioners and students in computer science.