This volume covers a diverse collection of topics dealing with some of the fundamental
concepts and applications embodied in the study of nonlinear dynamics. Each of the 15
chapters contained in this compendium generally fit into one of five topical areas: physics
applications, nonlinear oscillators, electrical and mechanical systems, biological and
behavioral applications or random processes. The authors of these chapters have
contributed a stimulating cross section of new results, which provide a fertile spectrum of
ideas that will inspire both seasoned researches and students....
All practical systems contain nonlinear dynamics. Control system development for
these systems has traditionally been based on linearized system dynamics in
conjunction with linear control techniques. Sometimes it is possible to describe the
operation of systems by a linear model around its operating points. Linearized system
can provide approximate behavior of the system. But in analyzing the overall system
behavior, the resulting system model is inadequate or inaccurate. Moreover, the
stability of the system cannot be guaranteed.
Rapid development of optoelectronic devices and laser techniques poses an important
task of creating and
studying, from one side, the structures capable of effectively converting, modulating,
and recording optical data in a wide range of radiation energy densities and
frequencies, from another side, the new schemes and approaches capable to activate and
simulate the modern features. It is well known that nonlinear optical phenomena and
nonlinear optical materials have the promising place to resolve these complicated
The book is intended to provide an introduction to the effects of nonlinear elements in feedback control systems. A central topic is the use of the Describing Function (DF) method since in combination with simulation it provides an excellent approach for the practicing engineer and follows on logically from a first course in classical control, such as the companion volume in this series. Some of the basic material on the topic can be found in my earlier book which is frequently referenced throughout the text....
This article is concerned with local well-posedness of the Cauchy problem for second order quasilinear hyperbolic equations with rough initial data. The new results obtained here are sharp in low dimension. 1. Introduction 1.1. The results. We consider in this paper second order, nonlinear hyperbolic equations of the form (1.1) gij (u) ∂i ∂j u = q ij (u) ∂i u ∂j u
on R × Rn , with Cauchy data prescribed at time 0, (1.2) u(0, x) = u0 (x) , ∂0 u(0, x) = u1 (x) .
This paper focuses on mining the hyponymy (or is-a) relation from large-scale, open-domain web documents. A nonlinear probabilistic model is exploited to model the correlation between sentences in the aggregation of pattern matching results. Based on the model, we design a set of evidence combination and propagation algorithms.
This lecture will teach you how to fit nonlinear functions by using bases functions and how to control model complexity. The goal is for you to: Learn how to derive ridge regression; understand the trade-off of fitting the data and regularizing it; Learn polynomial regression; understand that, if basis functions are given, the problem of learning the parameters is still linear; learn cross-validation; understand model complexity and generalization.
The fifth edition of this classic book continues its excellence in teaching numerical analysis and techniques. Interesting and timely applications motivate an understanding of methods and analysis of results. Suitable for students with mathematics and engineering backgrounds, the breadth of topics (partial differential equations, systems of nonlinear equations, and matrix algebra), provide comprehensive and flexible coverage of all aspects of all numerical analysis.
The Nonlinear Optical Susceptibility Phi tuyến quang học là nghiên cứu các hiện tượng xảy ra do hậu quả của
sửa đổi, bổ sung các tính chất quang học của một hệ thống vật chất bởi sự hiện diện
của ánh sáng. Thông thường, chỉ có ánh sáng laser cường độ đủ mạnh để thay đổi
tính chất quang học của một hệ thống vật chất. Sự khởi đầu của lĩnh vực phi tuyến
quang học thường được dùng để phát hiện ra hài hòa thế hệ thứ hai
Franken et al.
Wave-Equation Description of Nonlinear Optical Interactions
Các phương trình sóng cho truyền thông quang học phi tuyến
Chúng ta đã thấy trong chương cuối cùng như thế nào phi tuyến trong phản ứng của một hệ thống vật chất vào một lĩnh vực laser cường độ cao có thể gây ra sự phân cực của môi trường để phát triển các thành phần tần số mới không có mặt trong lĩnh vực bức xạ nhiệt.
Most of the material in this volume is new. The first three chapters deal with three important fiber-optic components--fiber-based gratings, couplers, and interferometers--that serve as the building blocks of lightwave technology. In view of the enormous impact of rare-earth-doped fibers, amplifiers and lasers made by using such fibers are covered in Chapters 4 and 5. The last three chapters describe important applications of nonlinear fiber optics and are devoted to pulse-compression techniques, fiber-optic communication systems, and soliton-based transmission schemes....
LEARNING STOCHASTIC NONLINEAR DYNAMICS Since the advent of cybernetics, dynamical systems have been an important modeling tool in ﬁelds ranging from engineering to the physical and social sciences. Most realistic dynamical systems models have two essential features. First, they are stochastic – the observed outputs are a noisy function of the inputs, and the dynamics itself may be driven by some unobserved noise process.
Molecular Origin of the Nonlinear Optical Response
Trong chương 3, chúng tôi trình bày một lý thuyết chung của cơ học lượng tử nhạy cảm quang học phi tuyến. Tính toán này dựa trên lý thuyết nhiễu loạn phụ thuộc thời gian và dẫn đến dự đoán rõ ràng cho sự phụ thuộc tần số hoàn toàn của các tuyến tính và phi tuyến tính nhạy cảm quang. Thật không may, tuy nhiên, những biểu hiện cơ học lượng tử thường quá phức tạp để được sử dụng cho các tính toán thực tế.
This chapter starts by reviewing some of the early research efforts in independent component analysis (ICA), especially the technique based on nonlinear decorrelation, that was successfully used by Jutten, H´ rault, and Ans to solve the ﬁrst ICA problems. e Today, this work is mainly of historical interest, because there exist several more efﬁcient algorithms for ICA. Nonlinear decorrelation can be seen as an extension of second-order methods such as whitening and principal component analysis (PCA)....
It has been a great pleasure for me to have prepared the latest edition of my
book on nonlinear optics. My intrigue in the subject matter of this book is as
strong as it was when the first edition was published in 1992.
The principal changes present in the third edition are as follows: (1) The
book has been entirely rewritten using the SI system of units. I personally
prefer the elegance of the gaussian system of units, which was used in the first
two editions, but I realize that most readers would prefer the SI system, and
the change was made for this reason. (2) In...
A new type of semiconductor laser is studied, in which injected carriers in the active region
are quantum mechanically confined in localized finite self-assembled wire-like quantumdash
(Qdash) structures that are varied in sizes and compositions. Effects of such carrier
distribution and quasi three-dimensional density of states contribute to a quasisupercontinuum
interband lasing characteristics, which is a new laser design platform as
compared to continuous broad emission spectrum generated by nonlinear media pumped
with ultrashort laser pulse....