Fractional Calculus View of Complexity

Author: Bruce J. West
Publisher: CRC Press
ISBN: 149873801X
Format: PDF, Kindle
Download Now
This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research. It accomplishes both these things while providing a rationale for why the reader ought to be interested in learning about fractional calculus. This book is for researchers who has heard about many of these scientifically exotic activities, but could not see how they fit into their own scientific interests, or how they could be made compatible with the way they understand science. It is also for beginners who have not yet decided where their scientific talents could be most productively applied. The book provides insight into the long-term direction of science and show how to develop the skills necessary to successfully do research in the twenty-first century.

Nature s Patterns and the Fractional Calculus

Author: Bruce J. West
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110535130
Format: PDF, ePub, Mobi
Download Now
Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. Contents Complexity Empirical allometry Statistics, scaling and simulation Allometry theories Strange kinetics Fractional probability calculus

Simplifying Complexity Life is Uncertain Unfair and Unequal

Author: Bruce J. West
Publisher: Bentham Science Publishers
ISBN: 1681082179
Format: PDF, ePub
Download Now
In life, we often face unavoidable complexities in terms of our ability to understand or influence outcomes. Some questions which arise due to these complexities are: Why can’t the future be made certain? Why do the some people or events always end up at the center of controversy? Why do only a select few get ahead of their peers? Each question pertains to three central elements of complexities and these elements are: uncertainty, inequality and unfairness. Simplifying Complexity explains the scientific study of complex cognitive networks, as well as the methods scientists use to parse difficult problems into manageable pieces. Readers are introduced to scientific methodology and thought processes, followed by a discourse on perspectives on the three elements of complexity through concepts such as normal and non-normal statistics, scaling and complexity management. Simplifying Complexity combines basic cognitive science and scientific philosophy for both advanced students (in the fields of sociology, cognitive science, complex networks and change management) and for general readers looking for a more scientific guide to understanding and managing the nature of change in a complex world.

Fractional Order Devices

Author: Karabi Biswas
Publisher: Springer
ISBN: 3319544608
Format: PDF, Mobi
Download Now
This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new types of integrated circuits. The majority of the book addresses FOEs. The interest in these topics is related to the need to produce “analogue” electronic devices characterized by non-integer order impedance, and to the characterization of natural phenomena, which are systems with memory or aftereffects and for which the fractional-order calculus tool is the ideal choice for analysis. FOEs represent the building blocks for designing and realizing analogue integrated electronic circuits, which the authors believe hold the potential for a wealth of mass-market applications. The freedom to choose either an integer- or non-integer-order analogue integrator/derivator is a new one for electronic circuit designers. The book shows how specific non-integer-order impedance elements can be created using materials with specific structural properties. EIS measures the electrical impedance of a specimen across a given range of frequencies, producing a spectrum that represents the variation of the impedance versus frequency – a technique that has the advantage of avoiding aggressive examinations. Biological tissues are complex systems characterized by dynamic processes that occur at different lengths and time scales; this book proposes a model for vegetable tissues that describes the behavior of such materials by considering the interactions among various relaxing phenomena and memory effects.

Fractional Order Control Systems

Author: Dingyü Xue
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110497972
Format: PDF, ePub, Mobi
Download Now
This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design. It presents original research to improve the solution of fractional differential equations and to analyze fractional-order control systems with multi-variables. Through high-quality Matlab programs, it provides engineers and applied mathematicians with theoretical and numerical tools to design control systems.

Artificial Neural Networks for Engineers and Scientists

Author: S. Chakraverty
Publisher: CRC Press
ISBN: 1351651315
Format: PDF, ePub, Mobi
Download Now
Differential equations play a vital role in the fields of engineering and science. Problems in engineering and science can be modeled using ordinary or partial differential equations. Analytical solutions of differential equations may not be obtained easily, so numerical methods have been developed to handle them. Machine intelligence methods, such as Artificial Neural Networks (ANN), are being used to solve differential equations, and these methods are presented in Artificial Neural Networks for Engineers and Scientists: Solving Ordinary Differential Equations. This book shows how computation of differential equation becomes faster once the ANN model is properly developed and applied.

Complexity

Author: Mitchell M. Waldrop
Publisher: Simon and Schuster
ISBN: 0671872346
Format: PDF, Kindle
Download Now
A look at the rebellious thinkers who are challenging old ideas with their insights into the ways countless elements of complex systems interact to produce spontaneous order out of confusion

Fractional order Systems and Controls

Author: Concepción A. Monje
Publisher: Springer Science & Business Media
ISBN: 9781849963350
Format: PDF, Kindle
Download Now
Fractional-order Systems and Controls details the use of fractional calculus in the description and modeling of systems, and in a range of control design and practical applications. It is largely self-contained, covering the fundamentals of fractional calculus together with some analytical and numerical techniques and providing MATLAB® codes for the simulation of fractional-order control (FOC) systems. Many different FOC schemes are presented for control and dynamic systems problems. Practical material relating to a wide variety of applications is also provided. All the control schemes and applications are presented in the monograph with either system simulation results or real experimental results, or both. Fractional-order Systems and Controls provides readers with a basic understanding of FOC concepts and methods, so they can extend their use of FOC in other industrial system applications, thereby expanding their range of disciplines by exploiting this versatile new set of control techniques.

A First Course in Differential Equations Modeling and Simulation

Author: Carlos A. Smith
Publisher: CRC Press
ISBN: 1439850887
Format: PDF, ePub, Mobi
Download Now
Emphasizing a practical approach for engineers and scientists, A First Course in Differential Equations, Modeling, and Simulation avoids overly theoretical explanations and shows readers how differential equations arise from applying basic physical principles and experimental observations to engineering systems. It also covers classical methods for obtaining the analytical solution of differential equations and Laplace transforms. In addition, the authors discuss how these equations describe mathematical systems and how to use software to solve sets of equations where analytical solutions cannot be obtained. Using simple physics, the book introduces dynamic modeling, the definition of differential equations, two simple methods for obtaining their analytical solution, and a method to follow when modeling. It then presents classical methods for solving differential equations, discusses the engineering importance of the roots of a characteristic equation, and describes the response of first- and second-order differential equations. A study of the Laplace transform method follows with explanations of the transfer function and the power of Laplace transform for obtaining the analytical solution of coupled differential equations. The next several chapters present the modeling of translational and rotational mechanical systems, fluid systems, thermal systems, and electrical systems. The final chapter explores many simulation examples using a typical software package for the solution of the models developed in previous chapters. Providing the necessary tools to apply differential equations in engineering and science, this text helps readers understand differential equations, their meaning, and their analytical and computer solutions. It illustrates how and where differential equations develop, how they describe engineering systems, how to obtain the analytical solution, and how to use software to simulate the systems.

Differential Equations with Applications and Historical Notes Third Edition

Author: George F. Simmons
Publisher: CRC Press
ISBN: 1498702600
Format: PDF, Kindle
Download Now
Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one’s own time. An unfortunate effect of the predominance of fads is that if a student doesn’t learn about such worthwhile topics as the wave equation, Gauss’s hypergeometric function, the gamma function, and the basic problems of the calculus of variations—among others—as an undergraduate, then he/she is unlikely to do so later. The natural place for an informal acquaintance with such ideas is a leisurely introductory course on differential equations. Specially designed for just such a course, Differential Equations with Applications and Historical Notes takes great pleasure in the journey into the world of differential equations and their wide range of applications. The author—a highly respected educator—advocates a careful approach, using explicit explanation to ensure students fully comprehend the subject matter. With an emphasis on modeling and applications, the long-awaited Third Edition of this classic textbook presents a substantial new section on Gauss’s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity—i.e., identifying why and how mathematics is used—the text includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout. Provides an ideal text for a one- or two-semester introductory course on differential equations Emphasizes modeling and applications Presents a substantial new section on Gauss’s bell curve Improves coverage of Fourier analysis, numerical methods, and linear algebra Relates the development of mathematics to human activity—i.e., identifying why and how mathematics is used Includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout Uses explicit explanation to ensure students fully comprehend the subject matter Outstanding Academic Title of the Year, Choice magazine, American Library Association.