Fractional Order Thinking in Exploring the Frontiers of STEM – serie

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9 produkter

Fractional Calculus for Skeptics I
The Fractal Paradigm
AvBruce J. West,YangQuan Chen
Inbunden, Engelska, 2024
2 983 kr
Skickas inom 10-15 vardagar
This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research.Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem.The book will appeal to students and researchers in all STEM-related fields, such as engineering, physics, biology and biomedicine, climate change, big data, and machine learning. It is also suitable for general readers interested in these fields.
On the Fractal Language of Medicine
AvBruce J. West,W. Alan C. Mutch
Inbunden, Engelska, 2024
3 072 kr
Skickas inom 10-15 vardagar
On the Fractal Language of Medicine bridges a very clear gap among the knowledge gained over the last 20 years in the physical and life sciences on network theory, organ synchronicity and communication, the understanding of fractal signatures in health and disease and the importance of fractional calculus in integrating these concepts.The authors opine that the field of medicine has not appreciated this hard-won knowledge and has suffered greatly as a result. This book addresses this perceived deficiency by introducing medical researchers, clinicians, residents, first-year medical students and members of allied fields to the work of the so-called hard sciences. It seeks to facilitate effective communication between empiricists and theorists by making interdisciplinary efforts to explain complex mathematical concepts to physicians and, equally important, to elucidate complex medical concepts to physicists or mathematicians.This book will be of great interest to medical students, professionals and academics, as well as students and researchers of applied mathematics, especially those interested in fractional calculus and fractals.
Fractional Random Vibrations I
Theories
AvMing Li
Inbunden, Engelska, 2025
1 028 kr
Skickas
This two-volume set provides a comprehensive study of fractional random vibration from the perspective of theory and practice. Volume I deals succinctly with the theories of fractional processes and fractional vibration systems.A major focus of fractional vibrations is the derivation of analytical expressions for the frequency transfer functions of seven classes of fractional vibrations using elementary functions. This is considered from the perspective of the functional form of linear vibrations with frequency-dependent mass, damping, or stiffness. The present results serve as a basis for the study of the novel and frontier topic of fractional processes passing through fractional vibration systems, which is discussed in Volume II.The title will be essential reading for students, mathematicians, physicists, and engineers interested in fractional random vibration phenomena.
Fractional Random Vibrations II
Applications
AvMing Li
Inbunden, Engelska, 2025
1 197 kr
Skickas inom 10-15 vardagar
This two-volume set provides a comprehensive study of fractional random vibration from the perspective of theory and practice. Volume II provides the analytical expressions for the responses of seven classes of fractional vibration systems excited by six types of random processes.It examines the responses of seven classes of fractional vibrations driven by five fractional processes, namely, fractional Gaussian noise, generalized fractional Gaussian noise, fractional Brownian motion, fractional Ornstein-Uhlenbeck process, the process with the von Kármán spectrum, and the process with the Pierson-Moskowitz spectrum. The present results apply the theories discussed in Volume I to the novel and cutting-edge topic of fractional processes, with a special focus on fractional vibration systems for marine structures influenced by the Pierson-Moskowitz and von Kármán spectra.The title will be essential reading for students, mathematicians, physicists, and engineers interested in fractional random vibration phenomena.
Fractional Random Vibrations
Two Volume Set
Taylor & Francis Ltd
2025
2 314 kr
Skickas inom 10-15 vardagar
This two-volume set provides a comprehensive study of fractional random vibration from the perspective of theory and practice. By fractional random vibration, we mean the random vibration of fractional vibration systems driven by fractional processes.Volume I explores the fundamentals of fractional processes and fractional vibration systems. A major focus is the derivation of analytical expressions for the frequency transfer functions of seven classes of fractional vibrations using elementary functions. Theoretical support is provided by the functional form of linear vibrations with frequency-dependent mass, damping, or stiffness. Volume II provides the analytical expressions for the responses of seven classes of fractional vibration systems subjected to fractional Gaussian noise, generalized fractional Gaussian noise, fractional Brownian motion, the fractional Ornstein-Uhlenbeck process, the process with the von Kármán spectrum, and the one with the Pierson-Moskowitz spectrum. It applies the theories discussed in Volume I to the novel and cutting-edge topic of fractional processes, with special emphasis on fractional vibration systems for marine structures influenced by the Pierson-Moskowitz and von Kármán spectra.The titles will be essential reading for students, mathematicians, physicists, and engineers interested in vibration phenomena driven by fractional processes.
Smart Sensing with Digital Twins
Methane Emission Source Determination with sUAS
AvDerek Hollenbeck,YangQuan Chen
Inbunden, Engelska, 2025
1 481 kr
Skickas inom 10-15 vardagar
This book explores the innovative use of small unmanned aircraft systems (sUAS)—commonly known as drones—for methane emissions monitoring (i.e., detection, localization, and quantification) by introducing smart sensing frameworks and digital twin technology.Based on the concept of smart sensing, which combines mobile sensor data with physics-based models to provide actionable and timely insights, this book presents novel methods for monitoring and quantifying methane emissions, a potent greenhouse gas, using digital twins in single and multiple sUAS-based approaches. The first part of the book examines the methane sensing problem for detecting, locating, and quantifying emission sources, with case studies highlighting key observations and lessons learned from field experiments. The second part proposes what, why, and how digital twins should be used in environmental monitoring applications, covering both basic detection principles and advanced source localization and quantification techniques. This section shows how digital twins can enhance sUAS-based source detection and smart sensing methods.With practical tools and field-tested examples, this book serves as both an introductory guide and advanced reference to environmental monitoring and is particularly valuable to researchers, students, engineers, and environmental professionals in engineering, environmental studies, and technology.
Fractional Order Intelligent Modeling for Lithium-Ion Batteries
Theory and Practice
AvYaNan Wang,YangQuan Chen
Inbunden, Engelska, 2025
1 481 kr
Skickas inom 10-15 vardagar
This book focuses on fractional order (non-integer order) modeling (FOM) techniques coupled with deep neural network-based intelligent modeling methods for lithium-ion batteries (LIBs) and battery management systems (BMS) in general. It provides the first one-stop resource on FOM for LIBs with case studies using real operational data sets.With the rapid growth of electric vehicles and energy storage systems, battery technology has become critical to global energy solutions. Fractional Order Intelligent Modeling for Lithium-Ion Batteries: Theory and Practice aims to provide several accurate and effective intelligent modeling algorithms for the next generation of advanced BMS. Key topics include intelligent battery modeling, fractional-order modeling, physics-informed machine learning, state estimation, and degradation analysis. By integrating AI and physics-informed machine learning techniques with fractional-order modeling methods, this book presents several innovative solutions for next-generation battery management systems.This title will serve as an invaluable resource for researchers and advanced students in the fields of transportation, energy storage, and power systems, as well as those studying electric vehicles, control theory, machine learning, and fractional calculus-based modeling.
Fractional Calculus for Skeptics II
Quantifying Roughness
AvBruce J. West,YangQuan Chen
Inbunden, Engelska, 2026
2 983 kr
Skickas inom 10-15 vardagar
This second volume of the multi-volume Fractional Calculus for Skeptics explores the concept of “roughness” and its applications in complex systems. It demonstrates how fractional calculus offers valuable insights into modeling real-world phenomena that traditional calculus struggles to address.Building on the first volume's foundational work advocating a fractal/fractional calculus paradigm shift, this volume offers an in-depth exploration of the concept of “roughness,” drawing parallels to what Benoît B. Mandelbrot originally intended to call the “Science of Roughness.” The book introduces the novel concept of “body roughness” and demonstrates its practical applications through two case studies of “roughness-informed rehabilitation therapy” with closed-loop control systems. One study involves non-invasive, 40-Hz gamma-frequency sensory stimulation for Alzheimer's disease, and the other involves biologically variable ventilation using roughness-informed, closed-loop control. The four chapters are complemented by valuable appendices and essential chapter-end references, as well as insightful “take-home messages.”This book will appeal to students, researchers, and professionals in STEM fields, including engineering, physics, biology, biomedicine, control engineering, rehabilitation, big data, and machine learning.
Nyhet
Reading Randomness I
New Horizons for Understanding Fractal and Fractional Calculus
AvRaoul R. Nigmatullin,YangQuan Chen
Inbunden, Engelska, 2026
1 778 kr
Skickas inom 10-15 vardagar
Reading Randomness I: New Horizons for Understanding Fractal and Fractional Calculus shows readers how to understand and analyze seemingly “noisy” and irregular data. It offers practical methods for comparing and labeling fluctuations, ensuring reproducible results across laboratories, industries, and research fields.The book begins with a narrative tour of how people have understood chance, from ancient divination and games to modern probability, information theory, and computing. In seven chapters, the authors provide step-by-step instructions for extracting reliable patterns from raw measurements. These instructions include removing trends, checking whether a signal has long-term memory, and identifying stable patterns hidden inside apparent randomness. The book also presents new tools for analyzing “trendless” sequences, extending Fourier-style analysis to complicated, multi-period data, and measuring correlations in a way that distinguishes between contributions from the system itself and the environment. Using a reader-friendly approach, the authors explain how “memory” kernels capture slow, history-dependent behavior. Throughout the book, the authors emphasize independent checks, surrogate tests, and instrument-path corrections to ensure that conclusions can be reliably and safely transferred across place and time.With case studies ranging from transcendental numbers and electrical circuits to earthquake records and precious metal price data, this valuable guidebook will appeal to students, researchers, and professionals working with complex data in science, engineering, and finance.

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Fractional Order Thinking in Exploring the Frontiers of STEM – serie

Fractional Calculus for Skeptics I

On the Fractal Language of Medicine

Fractional Random Vibrations I

Fractional Random Vibrations II

Fractional Random Vibrations

Smart Sensing with Digital Twins

Fractional Order Intelligent Modeling for Lithium-Ion Batteries

Fractional Calculus for Skeptics II

Reading Randomness I

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