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Nonlinear Photonics
Suitable for both graduate and senior undergraduate students, this textbook offers a logical progression through the underlying principles and practical applications of nonlinear photonics.Building up from essential physics, general concepts, and fundamental mathematical formulations, it provides a robust introduction to nonlinear optical processes and phenomena, and their practical applications in real-world devices and systems.Over 45 worked problems illustrate key concepts and provide hands-on models for students, and over 160 end-of-chapter exercises supply students with plenty of scope to master the material.Accompanied by a complete solutions manual for instructors, including detailed explanations of each result, and drawing on the author's 35 years of teaching experience, this is the ideal introduction to nonlinear photonics for students in electrical engineering.
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Nonlinear Acoustics
This open access book is an introductory text on the theory of nonlinear acoustics authored by experts on their respective topics.It is written at a level appropriate for a graduate course on nonlinear acoustics, and it also serves as a useful resource for scientists and engineers.Consistent notation is employed for the principal symbols, and there is extensive cross-referencing between chapters.Chapters 1 through 8 develop the physical concepts, mathematical models, and classical methods of solution that form the theoretical framework for nonlinear acoustics.These chapters, or selected portions, form an appropriate core for an introductory course.While the emphasis is on nonlinear sound waves in fluids, Chapter 9 provides an introduction to nonlinear elastic waves in isotropic solids.Chapters 10 through 15 cover applications and additional methodologies encountered in nonlinear acoustics that include perturbation and numerical methods, ray theory for inhomogeneous moving media, statistical and parametric phenomena, and biomedical applications.The book is relevant to studies of therapeutic ultrasound, blast waves and jet noise, nondestructive testing, parametric array loudspeakers, particle manipulation with acoustic radiation force, and other applications involving nonlinear acoustics.This is an open access book.
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Nonlinear Optics
Nonlinear Optics, Fourth Edition, is a tutorial-based introduction to nonlinear optics that is suitable for graduate-level courses in electrical and electronic engineering, and for electronic and computer engineering departments, physics departments, and as a reference for industry practitioners of nonlinear optics.It will appeal to a wide audience of optics, physics and electrical and electronic engineering students, as well as practitioners in related fields, such as materials science and chemistry.
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Nonlinear : Navigating Design with Curiosity and Conviction
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What are nonlinear functions?
Nonlinear functions are mathematical functions that do not have a constant rate of change. This means that the relationship between the input and output values is not a straight line. Nonlinear functions can take on various shapes and forms, such as curves, parabolas, or exponential growth. These functions are often more complex and can exhibit behaviors like oscillations or rapid changes in output for small changes in input.
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What is a nonlinear equation?
A nonlinear equation is an equation that cannot be expressed in the form of a straight line, quadratic, or any other simple function. Instead, it involves variables raised to powers other than 1, or multiplied together, or involved in other non-linear operations. Nonlinear equations can have multiple solutions, and their graphs can take on various shapes, such as curves, loops, or other non-straight-line patterns. These equations are often more complex and challenging to solve compared to linear equations.
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What is the meaning of nonlinear?
Nonlinear refers to a system or process that does not follow a straight or predictable path. In mathematics and physics, it often refers to equations or relationships that do not have a constant rate of change or do not follow a linear pattern. Nonlinear systems can exhibit complex and unpredictable behavior, making them difficult to analyze and understand using traditional methods. In general, nonlinear can be used to describe any situation where the relationship between inputs and outputs is not proportional or straightforward.
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Which class of nonlinear equation systems?
Nonlinear equation systems can be classified into different classes based on their properties and characteristics. Some common classes of nonlinear equation systems include polynomial equations, transcendental equations, and systems of equations with constraints. Each class has its own unique features and methods for solving, making it important to identify the specific class of nonlinear equation system in order to choose the most appropriate solution technique.
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Strict-Feedback Nonlinear Systems : Gain Control Design
This book describes the research progress of the control design about strict-feedback nonlinear systems.A novel gain control design method is proposed, which greatly simplifies the construction procedure of controller for strict-feedback nonlinear systems.The control design problem of strict-feedback nonlinear systems is converted into the determination problem of gain parameters or the construction of dynamic gain equations.Therefore, the tedious iterative design procedure is effectively avoided.This book can be used as a reference for researchers in the field of control theory and engineers seeking advanced methods in practical control applications.
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Kilohearts Nonlinear Filter
The Kilohearts Nonlinear Filter allows you to shape refine and re-define your sounds - perfect for adding some vintage flavour and saturation to your input sources. Nonlinear filters have been used on countless hit records to achieve powerful and distinctive sounds. For example Jimi Hendrix used a form of nonlinear filtering to achieve his signature guitar sound. Whether youve heard of this filtering method before or not the Kilohearts Nonlinear Filter is a must-have for any music producer or sound designer. A simple and intuitive interface allows you to dial in your sound with precision featuring three dials and a range of different modes to choose from. Controls include Type Cutoff Q Drive and a selectable Mode option. There are four main filter types to choose from including low-pass band-pass high-pass and notch filter settings. You can create everything from analog-esque grit to outlandish and mangled sounds with a few twists on the dials. Please Note: This product comes in the form of a digital download code that will be sent to your email for activation.
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Nonlinear Option Pricing
New Tools to Solve Your Option Pricing ProblemsFor nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues.Written by two leaders in quantitative research—including Risk magazine’s 2013 Quant of the Year—Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing.Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods.Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise.It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems.The authors build intuition through numerous real-world examples of numerical implementation.Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs.The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + b? technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.
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Applied Nonlinear Control
Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
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Is electrical engineering linear or nonlinear now?
Electrical engineering can involve both linear and nonlinear systems. Linear systems follow the principle of superposition, meaning the output is directly proportional to the input. Nonlinear systems, on the other hand, do not follow this principle and exhibit more complex behavior. In modern electrical engineering, both linear and nonlinear systems are studied and utilized depending on the specific application and requirements.
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Is electrical engineering now linear or nonlinear?
Electrical engineering encompasses both linear and nonlinear systems. Linear systems follow the principle of superposition, meaning the output is directly proportional to the input. Nonlinear systems, on the other hand, do not follow this principle and exhibit more complex behavior. In practice, both linear and nonlinear concepts are used in electrical engineering to design and analyze a wide range of systems and devices.
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What is the root of a nonlinear function?
The root of a nonlinear function is the value of the independent variable for which the function equals zero. In other words, it is the value of the input that makes the output of the function equal to zero. Finding the root of a nonlinear function often involves using numerical methods or graphical techniques, as there may not be a simple algebraic solution. The root of a nonlinear function is important in many applications, including solving equations, optimization problems, and finding intersections of curves.
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What are examples of nonlinear systems in nature?
Examples of nonlinear systems in nature include the weather, the behavior of ecosystems, the human brain, and the movement of fluids. These systems exhibit complex and unpredictable behavior, with small changes in initial conditions leading to significant differences in outcomes. Nonlinear systems are characterized by feedback loops, chaotic behavior, and emergent properties, making them difficult to model and predict using traditional linear methods.
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