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Tensor Algebra and Tensor Analysis for Engineers
by Mikhail ItskovThere is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area. This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.
Tensor Algebra and Tensor Analysis for Engineers: With Applications To Continuum Mechanics (Mathematical Engineering Ser.)
by Mikhail ItskovThis is the fifth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. In accordance with the contemporary way of scientific publication, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. As such, this new edition also discusses such modern topics of solid mechanics as electro- and magnetoelasticity. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this textbook addresses graduate students as well as scientists working in this field and in particular dealing with multi-physical problems. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers (Mathematical Engineering #21)
by Hung Nguyen-Schäfer Jan-Philip SchmidtThis book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world.The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation• Tensor Analysis• Elementary Differential Geometry• Differential Forms• Applications of Tensors and Differential Geometry• Tensors and Bra-Ket Notation in Quantum MechanicsThe text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics.Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.
Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers (Mathematical Engineering)
by Hung Nguyen-Schäfer Jan-Philip SchmidtTensors and methods of differential geometry are very useful mathematical tools in many fields of modern physics and computational engineering including relativity physics, electrodynamics, computational fluid dynamics (CFD), continuum mechanics, aero and vibroacoustics and cybernetics.This book comprehensively presents topics, such as bra-ket notation, tensor analysis and elementary differential geometry of a moving surface. Moreover, authors intentionally abstain from giving mathematically rigorous definitions and derivations that are however dealt with as precisely as possible. The reader is provided with hands-on calculations and worked-out examples at which he will learn how to handle the bra-ket notation, tensors and differential geometry and to use them in the physical and engineering world. The target audience primarily comprises graduate students in physics and engineering, research scientists and practicing engineers.
Tensor-Based Dynamical Systems: Theory and Applications (Synthesis Lectures on Mathematics & Statistics)
by Can ChenThis book provides a comprehensive review on tensor algebra, including tensor products, tensor unfolding, tensor eigenvalues, and tensor decompositions. Tensors are multidimensional arrays generalized from vectors and matrices, which can capture higher-order interactions within multiway data. In addition, tensors have wide applications in many domains such as signal processing, machine learning, and data analysis, and the author explores the role of tensors/tensor algebra in tensor-based dynamical systems where system evolutions are captured through various tensor products. The author provides an overview of existing literature on the topic and aims to inspire readers to learn, develop, and apply the framework of tensor-based dynamical systems.
Tensor Calculus and Analytical Dynamics (Engineering Mathematics Ser. #4)
by John G. PapastavridisTensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints.Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of FrobeniusThe book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.
Tensor Calculus and Applications: Simplified Tools and Techniques (Mathematics and its Applications)
by Bhaben KalitaThe aim of this book is to make the subject easier to understand. This book provides clear concepts, tools, and techniques to master the subject -tensor, and can be used in many fields of research. Special applications are discussed in the book, to remove any confusion, and for absolute understanding of the subject. In most books, they emphasize only the theoretical development, but not the methods of presentation, to develop concepts. Without knowing how to change the dummy indices, or the real indices, the concept cannot be understood. This book takes it down a notch and simplifies the topic for easy comprehension. Features Provides a clear indication and understanding of the subject on how to change indices Describes the original evolution of symbols necessary for tensors Offers a pictorial representation of referential systems required for different kinds of tensors for physical problems Presents the correlation between critical concepts Covers general operations and concepts
Tensor Calculus and Differential Geometry for Engineers: With Solved Exercises
by Shahab Sahraee Peter WriggersThe book contains the basics of tensor algebra as well as a comprehensive description of tensor calculus, both in Cartesian and curvilinear coordinates. Some recent developments in representation theorems and differential forms are included. The last part of the book presents a detailed introduction to differential geometry of surfaces and curves which is based on tensor calculus. By solving numerous exercises, the reader is equipped to properly understand the theoretical background and derivations. Many solved problems are provided at the end of each chapter for in-depth learning. All derivations in this text are carried out line by line which will help the reader to understand the basic ideas. Each figure in the book includes descriptive text that corresponds with the theoretical derivations to facilitate rapid learning.
Tensor Computation for Data Analysis
by Yipeng Liu Jiani Liu Zhen Long Ce ZhuTensor is a natural representation for multi-dimensional data, and tensor computation can avoid possible multi-linear data structure loss in classical matrix computation-based data analysis. This book is intended to provide non-specialists an overall understanding of tensor computation and its applications in data analysis, and benefits researchers, engineers, and students with theoretical, computational, technical and experimental details. It presents a systematic and up-to-date overview of tensor decompositions from the engineer's point of view, and comprehensive coverage of tensor computation based data analysis techniques. In addition, some practical examples in machine learning, signal processing, data mining, computer vision, remote sensing, and biomedical engineering are also presented for easy understanding and implementation. These data analysis techniques may be further applied in other applications on neuroscience, communication, psychometrics, chemometrics, biometrics, quantum physics, quantum chemistry, etc. The discussion begins with basic coverage of notations, preliminary operations in tensor computations, main tensor decompositions and their properties. Based on them, a series of tensor-based data analysis techniques are presented as the tensor extensions of their classical matrix counterparts, including tensor dictionary learning, low rank tensor recovery, tensor completion, coupled tensor analysis, robust principal tensor component analysis, tensor regression, logistical tensor regression, support tensor machine, multilinear discriminate analysis, tensor subspace clustering, tensor-based deep learning, tensor graphical model and tensor sketch. The discussion also includes a number of typical applications with experimental results, such as image reconstruction, image enhancement, data fusion, signal recovery, recommendation system, knowledge graph acquisition, traffic flow prediction, link prediction, environmental prediction, weather forecasting, background extraction, human pose estimation, cognitive state classification from fMRI, infrared small target detection, heterogeneous information networks clustering, multi-view image clustering, and deep neural network compression.
Tensor Product Model Transformation in Polytopic Model-Based Control (Automation and Control Engineering)
by Péter Baranyi Yeung Yam Péter VárlakiTensor Product Model Transformation in Polytopic Model-Based Control offers a new perspective of control system design. Instead of relying solely on the formulation of more effective LMIs, which is the widely adopted approach in existing LMI-related studies, this cutting-edge book calls for a systematic modification and reshaping of the polytopic convex hull to achieve enhanced performance. Varying the convexity of the resulting TP canonical form is a key new feature of the approach. The book concentrates on reducing analytical derivations in the design process, echoing the recent paradigm shift on the acceptance of numerical solution as a valid form of output to control system problems. The salient features of the book include: Presents a new HOSVD-based canonical representation for (qLPV) models that enables trade-offs between approximation accuracy and computation complexity Supports a conceptually new control design methodology by proposing TP model transformation that offers a straightforward way of manipulating different types of convexity to appear in polytopic representation Introduces a numerical transformation that has the advantage of readily accommodating models described by non-conventional modeling and identification approaches, such as neural networks and fuzzy rules Presents a number of practical examples to demonstrate the application of the approach to generate control system design for complex (qLPV) systems and multiple control objectives. The authors’ approach is based on an extended version of singular value decomposition applicable to hyperdimensional tensors. Under the approach, trade-offs between approximation accuracy and computation complexity can be performed through the singular values to be retained in the process. The use of LMIs enables the incorporation of multiple performance objectives into the control design problem and assurance of a solution via convex optimization if feasible. Tensor Product Model Transformation in Polytopic Model-Based Control includes examples and incorporates MATLAB® Toolbox TPtool. It provides a reference guide for graduate students, researchers, engineers, and practitioners who are dealing with nonlinear systems control applications.
Tensor Properties of Crystals
by D LovettThe use of single crystals for scientific and technological applications is now widespread in solid-state physics, optics, electronics, materials science, and geophysics. An understanding of the variation of physical properties with crystalline direction is essential to maximize the performance of solid-state devices.Written from a physical viewpoint and avoiding advanced mathematics, Tensor Properties of Crystals provides a concise introduction to the tensor properties of crystals at a level suitable for advanced undergraduate and graduate students. While retaining the successful basic format of the well-known first edition, this second edition brings the material up to date with the latest developments in nonlinear optics and modulated structures. Because of the increasing importance of nonlinear optics, a new chapter on optoelectronics has been added. This edition also includes a short discussion on incommensurate modulated structures in the final chapter because they are relevant to high temperature superconductors and to ferroelectric and ferromagnetic materials. The book extensively contains diagrams, worked examples, and problems with answers throughout.
Tenth Annual Symposium On Frontiers Of Engineering
by National Academy of Engineering StaffThis volume includes 14 papers from the National Academy of Engineering's Tenth Annual U.S. Frontiers of Engineering Symposium held in September 2004. The U.S. Frontiers meeting brings together 100 outstanding engineers (ages 30-45) to learn from their peers and discuss leading-edge technologies in a range of fields. The 2004 symposium covered these four areas: engineering for extreme environments, designer materials, multiscale modeling, and engineering and entertainment. Papers in the book cover topics such as scalable mobile robots for deployment in polar climates, the challenges of landing on Mars, thin-film active materials, vascular tissue engineering, small-scale processes and large-scale simulations of the climate system, simulating physically accurate illumination in computer graphics, and designing socially intelligent robots, among others. Appendixes include information about the contributors, the symposium program, and a list of the meeting participants. The book is the tenth in a series covering the topics of the U.S. Frontiers of Engineering meetings.
Tenth International Conference on Applications and Techniques in Cyber Intelligence: Volume 2 (Lecture Notes on Data Engineering and Communications Technologies #169)
by Jemal H. Abawajy Zheng Xu Mohammed Atiquzzaman Xiaolu ZhangThis book presents innovative ideas, cutting-edge findings, and novel techniques, methods, and applications in a broad range of cybersecurity and cyberthreat intelligence areas. As our society becomes smarter, there is a corresponding need to secure our cyberfuture. The book describes approaches and findings that are of interest to business professionals and governments seeking to secure our data and underpin infrastructures, as well as to individual users.
Tenth International Conference on Applications and Techniques in Cyber Intelligence: Volume 1 (Lecture Notes on Data Engineering and Communications Technologies #170)
by Jemal H. Abawajy Xiaolu Zhang Mohammed Atiquzzaman Zheng XuThis book presents innovative ideas, cutting-edge findings, and novel techniques, methods, and applications in a broad range of cybersecurity and cyberthreat intelligence areas. As our society becomes smarter, there is a corresponding need to secure our cyberfuture. The book describes approaches and findings that are of interest to business professionals and governments seeking to secure our data and underpin infrastructures, as well as to individual users.
Tenth Planet: Book 2
by Kristine Kathryn Rusch Dean Wesley SmithFor aeons, Earth has been ravaged by so-called natural disasters. Now we know the primary cause: over- harvesting of our limited resources-not by humans but by the residents of our solar system's tenth planet. Since before the birth of humanity, this dark planet has plundered our world every two thousand years. But in 2017, Earth fought back. Now thousands of aliens face starvation. To survive, they must harvest Earth when their orbit brings them back from behind the sun. But the humans are not waiting for Earth to become as parched and barren as Mars. Every nuclear weapon has been aimed at the tenth planet. Their ultimate goal-to blow the tenth planet to OBLIVION.
Terahertz (NATO Science for Peace and Security Series B: Physics and Biophysics)
by Mauro Fernandes Pereira Apostolos ApostolakisCritical infrastructures are targets for terrorism and deliver a valuable vector through which the proliferation of CBRN and explosive precursors can be detected. Recent technological breakthroughs, notably in the field of near infrared (NIR), mid infrared (MIR), Terahertz (THz) and Gigahertz (GHz) sources and detectors, have led to rugged commercial devices, capable of standoff sensing a range of these dangerous substances. However, at the same time criminal and terrorist organizations have also benefited from the availability of technologies to increase the threat they pose to the security of citizens and a concerted effort is needed to improve early detection measures to identify activities, such as the production of homemade explosives or CBRN that can be potentially dangerous to society. The key global technological bottleneck to be overcome is the current lack of integration and networking of mature detection technology into early warning systems for critical infrastructures. Thus, this book brings together complementary information connecting the research of leading teams working on critical Infrastructure protection with academic developers and industrial producers of state of the art sensors.
Terahertz and Mid Infrared Radiation
by Oleksiy Shulika Mauro F. PereiraTerahertz (THz) and Mid-Infrared (MIR) radiation (TERA-MIR) can be transmitted through nearly any material without causing biological harm. Novel and rapid methods of detection can be created with devices operation in these spectral ranges allowing scanning for weapons, detecting hidden explosives (including plastic landmines), controlling the quality of food and a host of other exciting applications. This book focuses on mathematical and physical aspects of the field, on unifying these two spectral domains (THz and MIR) with regard to common sources, detectors, materials and applications, and on key interdisciplinary topics. The main THz and MIR source is the quantum cascade laser (QCL). Thus significant attention is paid to the challenge of turning this advanced technology into affordable commercial devices so as to exploit its enormous potential. However other alternatives to THz QCLs are also presented, e.g. sub-terahertz imaging from avalanching GaAs bipolar transistors, Josephson junctions as THz sources, semiconductor materials for pulsed THz sources, superconducting THz electronics with Josephson vortices. In summary this book delivers a global picture of the state of the art in TERA-MIR generation, detection and applications.
Terahertz Antenna Technology for Imaging and Sensing Applications
by Isha Malhotra Ghanshyam SinghThis book covers terahertz antenna technology for imaging and sensing, along with its various applications. The authors discuss the use of terahertz frequency and photoconductive antenna technology for imaging applications, such as biological and bio-medical applications, non-destructive inspection of fabrics and plastics, analysis of hydration levels or detecting the presence of metallic components in samples, and detecting a variety of materials with unique spectral fingerprints in the terahertz frequency range, such as different types of explosives or several compounds used in the fabrication of medicines.Provides a comprehensive review of terahertz source and detector for imaging and sensing;Discusses photoconductive antenna technology for imaging and sensing;Presents modalities for improving the photoconductive dipole antenna performance for imaging and sensing;Explores applications in tomographic imaging, art conservation and the pharmaceutical and aerospace industries.
Terahertz Antenna Technology for Space Applications
by Balamati Choudhury Aniruddha R. Sonde Rakesh Mohan JhaThis book explores the terahertz antenna technology towards implementation of compact, consistent and cheap terahertz sources, as well as the high sensitivity terahertz detectors. The terahertz EM band provides a transition between the electronic and the photonic regions thus adopting important characteristics from these regimes. These characteristics, along with the progress in semiconductor technology, have enabled researchers to exploit hitherto unexplored domains including satellite communication, bio-medical imaging, and security systems. The advances in new materials and nanostructures such as graphene will be helpful in miniaturization of antenna technology while simultaneously maintaining the desired output levels. Terahertz antenna characterization of bandwidth, impedance, polarization, etc. has not yet been methodically structured and it continues to be a major research challenge. This book addresses these issues besides including the advances of terahertz technology in space applications worldwide, along with possibilities of using this technology in deep space networks.
Terahertz Antenna Technology for Space Applications (SpringerBriefs in Electrical and Computer Engineering)
by Balamati Choudhury Aniruddha R. Sonde Rakesh Mohan JhaThis book explores the terahertz antenna technology towards implementation of compact, consistent and cheap terahertz sources, as well as the high sensitivity terahertz detectors. The terahertz EM band provides a transition between the electronic and the photonic regions thus adopting important characteristics from these regimes. These characteristics, along with the progress in semiconductor technology, have enabled researchers to exploit hitherto unexplored domains including satellite communication, bio-medical imaging, and security systems. The advances in new materials and nanostructures such as graphene will be helpful in miniaturization of antenna technology while simultaneously maintaining the desired output levels. Terahertz antenna characterization of bandwidth, impedance, polarization, etc. has not yet been methodically structured and it continues to be a major research challenge. This book addresses these issues besides including the advances of terahertz technology in space applications worldwide, along with possibilities of using this technology in deep space networks.
Terahertz Astronomy
by Christopher K. WalkerA Powerful Window into Cosmic EvolutionTerahertz (THz) observations of interstellar atoms, molecules, and dust serve as powerful probes of the conditions within the interstellar medium that permeates our galaxy, providing insights into the origins of stars, planets, galaxies, and the Universe. Taking a cross-disciplinary approach to the subject, Te
Terahertz Biomedical Science and Technology
by Joo-Hiuk SonA number of applications including scientific spectroscopy, security screening, and medical imaging have benefitted from the development and utilization of new and emerging terahertz (THz) generation and detection techniques. Exploring recent discoveries and the advancements of biological behaviors through THz spectroscopy and imaging and the devel
Terahertz Devices, Circuits and Systems: Materials, Methods and Applications
by Sudipta Das Anveshkumar Nella Shobhit K. PatelThis book is aimed to bring the emerging application aspects of THz technology and various modules used for its successful realization. It gathers scientific technological novelties and advancements already developed or under development in the academic and research communities. This book focuses on recent advances, different research issues in terahertz technology and would also seek out theoretical, methodological, well-established and validated empirical work dealing with these different topics. In particular, this textbook covers design considerations and current trends of THz antennas and antenna arrays to deal with the transmission and reception of THz EM waves. It also presents a discussion on metamaterial structures, meta-surfaces, and absorbers to be used for some kind of sensing and detection applications. Furthermore, it reports on THz wireless communication aspects, 6G network issues and challenges, advantages and disadvantages, generation and detection of THz waves, Signal and Communication Processing for THz communication, reconfigurable low-noise amplifier (LNA) design, III-Nitride HEMTs for THz Applications, photonic crystal fiber for sensing applications, THz Design Variable Estimation by Deep Optimization, and THz Imaging issues. Once the readers finish studying this book then they will learn about the importance of THz technology, advancement in the field, applications, THz modules like antennas, MIMO and DRAs, communication aspects, LNAs, generation of THz waves, etc and future scope. It also leads to enhancement in their knowledge in THz technology, gives a platform to future technology and novel applications realization.
Terahertz Imaging for Biomedical Applications
by Brian W.-H. Ng Xiaoxia Yin Derek AbbottTerahertz biomedical imaging has become an area of interest due to its ability to simultaneously acquire both image and spectral information. Terahertz imaging systems are being commercialized, with increasing trials performed in a biomedical setting. As a result, advanced digital image processing algorithms are needed to assist screening, diagnosis, and treatment. "Pattern Recognition and Tomographic Reconstruction" presents these necessary algorithms, which will play a critical role in the accurate detection of abnormalities present in biomedical imaging. Terhazertz tomographic imaging and detection technology contributes to the ability to identify opaque objects with clear boundaries, and would be useful to both in vivo and ex vivo environments, making this book a must-read for anyone in the field of biomedical engineering and digital imaging.
Terahertz Planar Antennas for Next Generation Communication
by Kumud Ranjan Jha Ghanshyam SinghThis book describes various methods to enhance the directivity of planar antennas, enabling the next generation of high frequency, wireless communication. The authors discuss various applications to the terahertz regime of the electromagnetic spectrum, with an emphasis on gain enhancement mechanisms. The numerical models of these antennas are presented and the analytical results are supported, using commercial simulators. The multilayer substrate microstrip transmission line at terahertz frequency is also explored and a method to obtain the various parameters of this interconnect at high frequency is described. This book will be a valuable resource for anyone needing to explore the terahertz band gap for future wireless communication, in an effort to solve the bandwidth (spectrum scarcity) problem.