Plenty of biographies glamorize Tesla and his eccentricities, but until now none has carefully examined what, how, and why he invented. In this groundbreaking book, W. Bernard Carlson demystifies the legendary inventor, placing him within the cultural and technological context of his time, and focusing on his inventions themselves as well as the creation and maintenance of his celebrity. Drawing on original documents from Tesla's private and public life, Carlson shows how he was an "idealist" inventor who sought the perfect experimental realization of a great idea or principle, and who skillfully sold his inventions to the public through mythmaking and illusion.
This major biography sheds new light on Tesla's visionary approach to invention and the business strategies behind his most important technological breakthroughs.
The book begins at the simplest level, develops the basics, and reinforces fundamentals, ensuring a solid foundation in the principles and methods of physics. It provides an ideal introduction for college-level students of physics, chemistry, and engineering; for motivated AP Physics students; and for general readers interested in advances in the sciences.
Nikola Tesla—a poet of invention—left behind a vast and intriguing legacy. He was a scientist, physicist, mathematician, electrical engineer, and extensively published author who spent his last decades scraping for funding for celestial projects and living out his final days in penurious solitude with a pigeon.
As digital devices continue to be produced at increasingly lower costs and with higher speeds, the need for effective electromagnetic compatibility (EMC) design practices has become more critical than ever to avoid unnecessary costs in bringing products into compliance with governmental regulations. The Second Edition of this landmark text has been thoroughly updated and revised to reflect these major developments that affect both academia and the electronics industry. Readers familiar with the First Edition will find much new material, including:
* Latest U.S. and international regulatory requirements
* PSpice used throughout the textbook to simulate EMC analysis solutions
* Methods of designing for Signal Integrity
* Fortran programs for the simulation of Crosstalk supplied on a CD
* OrCAD(r) PSpice(r) Release 10.0 and Version 8 Demo Edition software supplied on a CD
* The final chapter on System Design for EMC completely rewritten
* The chapter on Crosstalk rewritten to simplify the mathematics
Detailed, worked-out examples are now included throughout the text. In addition, review exercises are now included following the discussion of each important topic to help readers assess their grasp of the material. Several appendices are new to this edition including Phasor Analysis of Electric Circuits, The Electromagnetic Field Equations and Waves, Computer Codes for Calculating the Per-Unit-Length Parameters and Crosstalk of Multiconductor Transmission Lines, and a SPICE (PSPICE) tutorial.
Now thoroughly updated, the Second Edition of Introduction to Electromagnetic Compatibility remains the textbook of choice for university/college EMC courses as well as a reference for EMC design engineers.
An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.
"Now a new laboratory bible for optics researchers has joined the list: it is Phil Hobbs's Building Electro-Optical Systems: Making It All Work."
—Tony Siegman, Optics & Photonics News
Building a modern electro-optical instrument may be the most interdisciplinary job in all of engineering. Be it a DVD player or a laboratory one-off, it involves physics, electrical engineering, optical engineering, and computer science interacting in complex ways. This book will help all kinds of technical people sort through the complexity and build electro-optical systems that just work, with maximum insight and minimum trial and error.
Written in an engaging and conversational style, this Second Edition has been updated and expanded over the previous edition to reflect technical advances and a great many conversations with working designers. Key features of this new edition include:Expanded coverage of detectors, lasers, photon budgets, signal processing scheme planning, and front ends Coverage of everything from basic theory and measurement principles to design debugging and integration of optical and electronic systems Supplementary material is available on an ftp site, including an additional chapter on thermal Control and Chapter problems highly relevant to real-world design Extensive coverage of high performance optical detection and laser noise cancellation
Each chapter is full of useful lore from the author's years of experience building advanced instruments. For more background, an appendix lists 100 good books in all relevant areas, introductory as well as advanced. Building Electro-Optical Systems: Making It All Work, Second Edition is essential reading for researchers, students, and professionals who have systems to build.
Starting with chapters on vector analysis and electrostatics, the text covers electrostatic boundary value problems, formal and microscopic theories of dielectric electrostatics and of magnetism and matter, electrostatic energy, steady currents, and induction. Additional topics include magnetic energy, circuits with nonsteady currents, Maxwell's equations, radiation, electromagnetic boundary value problems, and the special theory of relativity. Exercises appear at the end of each chapter and answers to odd-numbered problems are included in one of several helpful appendixes.
There are very few other books available even though EMI is constantly discussed and cursed. Most of the books on the market are about how to prevent EMI in circuit design or approaches to understanding the theory behind EMI. Though this information is important, especially to an engineering audience, these books hold no value at all to the technicians and hands-on practitioners in the fields of communications and servicing.These savvy professionals know that the book they are looking for and need is just not on the market. To get the information they need, this group is forced to read every magazine article they can find on the subject and rely on the advice of other professionals whether through technician groups or newsgroups. This book fills a void in the telecommunications and electronics industries by providing practical troubleshooting information.Addresses the technician's needs and interestsWritten by an eminent authority in the fieldCovers correction and prevention of problems with EMI
This edition has been thoroughly revised and updated to reflect the large extensions to LTE as introduced in 3GPP Releases 12 and 13 and the role of LTE in the upcoming 5G era. New to this edition includes updated content on:
4G and 5G Radio Access Spectrum for 4G and 5G Machine-Type Communication Device-to-Device Communication License-assisted Access Full-dimension MIMOSmall-cell enhancements, eIMTA, FDD+TDD aggregation, dual connectivity Requirements on and general structure of 5G wireless access, addressing the existing and new usage scenarios for 5GTechnical solutions for the new 5G radio-access technology
The authors of this book all work at Ericsson Research and have been deeply involved in 3G and 4G development and standardization. They are leading experts in the field and are today actively contributing to the standardization of 4G and 5G within 3GPP.The leading book on 3GPP specifications for LTE, LTE-Advanced, and LTE-Advanced Pro covering up to and including Release 13, written by Ericsson engineers who are heavily involved in the development of 3GPP specificationsTen new chapters and coverage of all major features introduced with Release 12 and 13Two completely new chapters on 5G wireless access including a detailed description of the key technology components under development by 3GPP
In 1600 he published De Magnete in Latin. As lively and entertaining as it was scientifically scrupulous, it summarized everything that had previously been known about electricity and magnetism, founded a new science and earned Gilbert the title of "the father of modern electricity." In it Gilbert explores magnetism and electricity, lodestones, phenomena of magnetism, direction of the earth's magnetic lines of force, variation in the compass, dip, the concept of the earth as a giant magnet, and much else.
This Dover edition is a complete, unabridged reprinting of the definitive English translation of De Magnete prepared by Dr. P. Fleury Mottelay. Dr. Mottelay has added a number of footnotes that explain points that might be obscure to today's readers, who will find in this historically important text invaluable insights into the origins of modern science and physics. Translation by P. F. Mottelay. Biographical introduction. 90 illustrations.
This book explains the basic principles of spectroscopy, including the fundamental optical constraints and all mathematical aspects needed to understand the working principles in detail. It covers the complete theoretical and practical design of standard and Echelle spectrographs. Readers are guided through all necessary calculations, enabling them to engage in spectrograph design. The book also examines data acquisition with CCD cameras and fiber optics, as well as the constraints of specific data reduction and possible sources of error. In closing it briefly highlights some main aspects of the research on massive stars and spectropolarimetry as an extension of spectroscopy. The book offers a comprehensive introduction to spectroscopy for students of physics and astronomy, as well as a valuable resource for amateur astronomers interested in learning the principles of spectroscopy and spectrograph design.
This new version of Barrett's book has been updated for today's world with annotations and updates from Windell Oskay of Evil Mad Scientist Laboratories, including extensive notes about modern safety practices, suggestions on where to find the parts you need, and tips for building upon Barrett's ideas with modern technology. With this book, you'll be ready to take on your own scientific explorations at school, work, or home.
This book presents an overview of the technological advances that have occurred since the publication of the Editors earlier book High Voltage Vacuum Insulation: The Physical Basis. In this latest book, contributions from internationally recognized professionals and researchers in the field provide expanded treatment of the practical aspects of the subject. High Voltage Vacuum Insulation: Basic Concepts and Technological Practice provides a modern working manual for this specialized technology that is generic to a wide range of applications. The format makes the text suitable for use as a basis for special topic lecture courses at either the undergraduate or graduate level.Provides the fundamental physical concepts of the subjectFocuses on practical applicationsGives a historical survey of the fieldIncludes a detailed account of system design criteriaReviews theoretical models developed to explain the pinhole phenomenaPresents results of a series of experimental investigations on the subject
In order to be able to reflect the development of today's science and to cover all modern aspects of thin films, the series, starting with Volume 20, has moved beyond the basic physics of thin films. It now addresses the most important aspects of both inorganic and organic thin films, in both their theoretical as well as technological aspects. Therefore, in order to reflect the modern technology-oriented problems, the title has been slightly modified from Physics of Thin Films to Thin Films.
This volume, part of the Thin Films Series, has been wholly written by two authors instead of showcasing several edited manuscripts.
Nikola Tesla (1856-1943), credited as the inspiration for radio, robots, and even radar, has been called the patron saint of modern electricity. Based on original material and previously unavailable documents, this acclaimed book is the definitive biography of the man considered by many to be the founding father of modern electrical technology. Among Tesla’s creations were the channeling of alternating current, fluorescent and neon lighting, wireless telegraphy, and the giant turbines that harnessed the power of Niagara Falls.
This essential biography is illustrated with sixteen pages of photographs, including the July 20, 1931, Time magazine cover for an issue celebrating the inventor’s career.
“A deep and comprehensive biography of a great engineer of early electrical science--likely to become the definitive biography. Highly recommended.”--American Association for the Advancement of Science
“Seifer's vivid, revelatory, exhaustively researched biography rescues pioneer inventor Nikola Tesla from cult status and restores him to his rightful place as a principal architect of the modern age.” --Publishers Weekly Starred Review
“[Wizard] brings the many complex facets of [Tesla's] personal and technical life together in to a cohesive whole....I highly recommend this biography of a great technologist.” --A.A. Mullin, U.S. Army Space and Strategic Defense Command, COMPUTING REVIEWS
“[Along with A Beautiful Mind] one of the five best biographies written on the brilliantly disturbed.”--WALL STREET JOURNAL
“Wizard is a compelling tale presenting a teeming, vivid world of science, technology, culture and human lives.”--NEW SCIENTIST
“Marc Seifer is an excellent writer and scholar, who has produced a wonderfully readable and illuminating biography of one of the most intriguing men of this century...mak[ing] us understand not only the man, but also the times in which he lived....[A] masterpiece.”--NELSON DEMILLE
“The author presents much new material...[and] bases his book on a large number of archival and primary sources....Underneath the layers of hero worship, the core of Seifer's book is a serious piece of scholarship.” --Ronald Kline, SCIENTIFIC AMERICAN
“Seifer has done a remarkable job going through all the Tesla manuscripts...ferret[ing] out hundreds of newspaper and magazine articles in which he traces out Tesla's public image [and] offers a reasonable reconstruction of Tesla's emotional world...Seifer has significantly advanced our understanding of Tesla.”--Bernard Carlson, author of Tesla: Inventor of the Electrical Age, for ISIS
“It is my opinion that Dr. Seifer leads the world as the most authoritative of all the Tesla researchers.”--J.W. McGINNIS, President, International Tesla Society
“Far and away the best job among Tesla biographies.”--Jeffrey D. Kooistra, INFINITE ENERGY
“Wizard is...utterly absorbing with chapters charting all stages of Tesla's life...Seifer treats his prodigious subject with sympathy and realism.”--NEXUS
“Wizard...presents a much more accurate...picture of Tesla.... [It] is thorough, informative, entertaining and a valuable addition to electrotechnological history, past and future.”--ELECTRONIC ENGINEERING TIMES
“In modern times, Tesla may be enjoying a comeback thanks to books like Wizard.”--THE NEW YORK TIMES
This book will be mandatory reading for anyone working on the foundations of modern devices such as free electron lasers, plasma accelerators, synchroton sources and other modern sources of bright, coherent radiation with high spectral density.
assumes only basic mathematical knowledge on the part of the reader and includes more than 100 discussion questions and some 70 problems, with solutions as well as further supplementary material available free to lecturers from the Wiley-VCH website.
In this simple, descriptive treatment of Tesla's work:
- We start with the analysis of Tesla's experiment in his US patent 787412, providing explanations for his lower bounds, requirements, and superluminal speeds. Modes of operation of Tesla transformer are analyzed, and the true nature of the so-called Tesla-wave explained, considering what renders it to be the most significant technological discovery to date.
- We recognize that the very discovery of radio is a witness to the physical existence of invisible, exclusively 3-dimensional worlds, and spherical potential waves in a fully three-dimensional imaginary space are a fundamental phenomenon and physical reality.
- We progress to discuss implications and applications, and claim that properly constructed radio waves do not travel through our visible domain, allowing for efficient wireless energy transfer irrespective of distance.
- Finally, concentrated in one of the last of the 12 chapters, we present a concise mathematical treatment based on Maxwell's equations in characterizing the Tesla effect.
Redefining the thinking outside-the-box and challenging the state of the art in modern physics, I submit this innovation to your careful scrutiny. This descriptive work is accessible to any reader, including physics and mathematics scholars skilled in the art. The combined experience in the above treatment yields a novel, simple, yet comprehensive view of the spatial construction of the universe, above and beyond the everyday three-dimensional reality experienced by physical senses.
No sensationalist descriptions involving time travel, weapons of global destruction, Soviet military research, mind alteration, age reversal, UFOs, aliens, and a myriad of other manufactured and unrelated topics, are contained in this text. No strings, tensors, elementary particles, or any of the traditional special relativity effects are associated with Tesla waves, and are not mentioned in this text. The most significant problem in theoretical interpretation of Tesla's ideas to date - was the avoidance of the most obvious solution.
Read this flagship book, and discover that the universe is so small that we are all intimately connected through a countably infinite set of pathways of ever decreasing length, and that it is yet so large, that it escapes our senses.
Universe is a lattice of countably infinitely many, mutually embedded, distinct, experientially equivalent, fully-fledged three-dimensional worlds, with all corresponding lengths ratio of Pi/2. Illustrated in C^3 , universe is simply a sphere of radius zero.
Maxwell made numerous other contributions to the advancement of science, but the greatest work of his life was devoted to electricity. An Elementary Treatise on Electricity appeared at a time when very few books on electrical measurements were available to students, and its compact treatment not only elucidates the theory of electricity but also serves to develop electrical ideas in readers' minds. The author describes experiments that demonstrate the principal facts relating an electric charge as a quantity capable of being measured, deductions from these facts, and the exhibition of electrical phenomena.
This volume, published posthumously from Maxwell's lecture notes at the Cavendish Laboratory — which he founded at the University of Cambridge — is supplemented by a selection of articles from his landmark book, Electricity and Magnetism. A classic of science, this volume is an eminently suitable text for upper-level undergraduates and graduate students.
Laser Fabrication and Machining of Materials introduces readers to the fundamental properties and physical phenomena of laser machining and its applications on the macro, micro, and nano scales. Examples of existing, emerging, and potential techniques are discussed, giving students and practicing engineers alike the opportunity to expand their use of lasers in such disciplines as mechanical processes, electronics, materials, and manufacturing.
Each topic is carefully introduced at three levels to aid student understanding. First, theoretical ideas and background information are discussed, then explanations of mathematical solutions follow and finally practical solutions are presented using MATLAB. The content includes:A compendium of equations and numerical data required by the modern colour and imaging scientist. Numerous examples of solutions and algorithms for a wide-range of computational problems in colour science. Example scripts using the MATLAB programming language.
This 2nd edition contains substantial new and revised material, including three innovative chapters on colour imaging, psychophysical methods, and physiological colour spaces; the MATLAB toolbox has been extended with a professional, optimized, toolbox to go alongside the current teaching toolbox; and a java toolbox has been added which will interest users who are writing web applications and/or applets or mobile phone applications.
Computational Colour Science Using MATLAB 2nd Edition is an invaluable resource for students taking courses in colour science, colour chemistry and colour physics as well as technicians and researchers working in the area. In addition, it acts a useful reference for professionals and researchers working in colour dependent industries such as textiles, paints, print & electronic imaging.
Review from First Edition:
“…highly recommended as a concise introduction to the practicalities of colour science…” (Color Technology, 2004)
An adaptive lens is a lens whose shape has been changed to a different focal length by an external stimulus such as pressure, electric field, magnetic field, or temperature. Introduction to Adaptive Lenses is the first book ever to address all of the fundamental operation principles, device characteristics, and potential applications of various types of adaptive lenses.
This comprehensive book covers basic material properties, device structures and performance, image processing and zooming, optical communications, and biomedical imaging. Readers will find homework problems and solutions included at the end of each chapter—and based on the described device structures, they will have the knowledge to fabricate adaptive lenses for practical applications or develop new adaptive devices or concepts for advanced investigation.
Introduction to Adaptive Lenses includes chapters on:
Elastomeric membrane lenses
Liquid crystal lenses
This is an important reference for optical engineers, research scientists, graduate students, and undergraduate seniors.
Written and edited by leading experts in the field, with contributors belonging to the European Commission's FP7 Network of Excellence NEWCOM++ Applications to a wide range of fields, including sensor networks, emergency services, military use, location-based billing, location-based advertising, intelligent transportation, and leisure
Location-aware personal devices and location-based services have become ever more prominent in the past few years, thanks to the significant advances in position location technology. Sensor networks, geographic information, emergency services, location management, location-based billing, location-based advertising, intelligent transportation, and leisure applications are just some of the potential applications that can be enabled by these techniques.
Increasingly, satellite and terrestrial positioning techniques are being combined for maximum performance; to produce the next wave of location-based devices and services, engineers need to combine both components. This book is the first to present a holistic view, covering all aspects of positioning: both terrestrial and satellite, both theory and practice, both performance bounds and signal processing techniques. It will provide a valuable resource for product developers and R&D engineers, allowing them to improve existing location techniques and develop future approaches for new systems.Combines satellite and terrestrial positioning techniques, using a signal processing approach. Discusses the applicability of developed techniques to emerging standards, such as LTE Advanced or WiMAX II, through the issue of ranging measurement with multicarrier signals.Contains quantitative performance results for ranging, positioning, and tracking for various systems.
Classical Electromagnetism in a Nutshell is ideal for a yearlong graduate course and features more than 300 problems, with solutions to many of the advanced ones. Key formulas are given in both SI and Gaussian units; the book includes a discussion of how to convert between them, making it accessible to adherents of both systems.Offers a complete treatment of classical electromagnetism Emphasizes physical ideas Separates the treatment of electromagnetism in vacuum and material media Presents key formulas in both SI and Gaussian units Covers applications to other areas of physics Includes more than 300 problems
The book begins with a brief history of the effort to enable the device that generates light through modern organic LEDs and reviews the fundamentals and principles of light prior to a detailed explanation of how LEDs generate different colors. After forming this basic foundation, the book examines the key LEDs in lighting and communications. It then discusses the latest opportunities and advancements in high brightness (HB) LED technology, solid state lighting, and handheld electronic applications.
As we approach a new decade the role of LEDs is literally set to explode, with organic light emitting diodes emerging as a leading next generation technology for electronic displays and lighting. Challenges still exist, including light extraction, luminosity, and white light generation, not to mention non-technical obstacles such as IP disputes and the lack of standards. This book provides a foundation for resolving these issues and developing new applications for LEDs in the promising general illumination market.
This book guides the reader through the mathematics, physics and practical techniques needed to use telescopes (from small amateur models to the larger instruments installed in many colleges) and to observe objects in the sky. Mathematics to around Advanced Placement standard (US) or A level (UK) is assumed, although High School Diploma (US) or GCSE-level (UK) mathematics plus some basic trigonometry will suffice most of the time. Most of the physics and engineering involved is described fully and requires no prior knowledge or experience.
This is a ‘how to’ book that provides the knowledge and background required to understand how and why telescopes work. Equipped with the techniques discussed in this book, the observer will be able to operate with confidence his or her telescope and to optimize its performance for a particular purpose. In principle the observer could calculate his or her own predictions of planetary positions (ephemerides), but more realistically the observer will be able to understand the published data lists properly instead of just treating them as ‘recipes.’ When the observer has obtained measurements, he/she will be able to analyze them in a scientific manner and to understand the significance and meaning of the results.
“Telescopes and Techniques, 3rd Edition” fills a niche at the start of an undergraduate astronomer’s university studies, as shown by it having been widely adopted as a set textbook. This third edition is now needed to update its material with the many new observing developments and study areas that have come into prominence since it was published. The book concentrates on the knowledge needed to understand how small(ish) optical telescopes function, their main designs and how to set them up, plus introducing the reader to the many ways in which objects in the sky change their positions and how they may be observed. Both visual and electronic imaging techniques are covered, together with an introduction to how data (measurements) should be processed and analyzed. A simple introduction to radio telescopes is also included. Brief coverage of the most advanced topics of photometry and spectroscopy are included, but mainly to enable the reader to see some of the developments possible from the basic observing techniques covered in the main parts of the book.
This comprehensive reference provides up-to-date information on component and subsystem technologies, fundamental limitations, and approaches to reach those limits. It covers basic concepts and state-of-the-art technologies, emphasizing device technology, implementation techniques, and system trades. The authors discuss hardware technologies and their applications, and also explore ongoing research activities and those planned for the near future.
The analytical aspects of laser communication have been covered to a great extent in several books. However, a detailed approach to system design and development, including trades on subsystem choices and implications of the hardware selection for satellite and aircraft telecommunications, is missing. Highlighting key design variations and critical differences between them, this book distills decades’ worth of experience into a practical resource on hardware technologies.
The text discusses the practical aspects of building a confocal scanning optical microscope or optical interference microscope, and the applications of these microscopes to phase imaging, biological imaging, and semiconductor inspection and metrology.A comprehensive theoretical discussion of the depth and transverse resolution is given with emphasis placed on the practical results of the theoretical calculations and how these can be used to help understand the operation of these microscopes.Provides a comprehensive introduction to the field of scanning optical microscopy for scientists and engineersExplains many practical applications of scanning optical and interference microscopy in such diverse fields as biology and semiconductor metrologyDiscusses in theoretical terms the origin of the improved depth and transverse resolution of scanning optical and interference microscopes with emphasis on the practical results of the theoretical calculationsConsiders the practical aspects of building a confocal scanning or interference microscope and explores some of the design tradeoffs made for microscopes used in various applicationsDiscusses the theory and design of near-field optical microscopesExplains phase imaging in the scanning optical and interference microscopes
Edison struggled to introduce his radical new direct current (DC) technology into the hurly-burly of New York City as Tesla and Westinghouse challenged his dominance with their alternating current (AC), thus setting the stage for one of the eeriest feuds in American corporate history, the War of the Electric Currents. The battlegrounds: Wall Street, the 1893 Chicago World’s Fair, Niagara Falls, and, finally, the death chamber—Jonnes takes us on the tense walk down a prison hallway and into the sunlit room where William Kemmler, convicted ax murderer, became the first man to die in the electric chair.
Empires of Light is the gripping history of electricity, the “mysterious fluid,” and how the fateful collision of Edison, Tesla, and Westinghouse left the world utterly transformed.
From the Hardcover edition.
The overall layout of the book is similar to that of the previous two editions however, there are considerable changes in emphasis and several key additions including:
•up-to-date presentation of modern theories of liquid-vapour coexistence and criticality
•areas of considerable present and future interest such as super-cooled liquids and the glass transition
•the area of liquid metals, which has grown into a mature subject area, now presented as part of the chapter ionic liquids
•Provides cutting-edge research in the principles of liquid-state theory
•Includes frequent comparisons of theoretical predictions with experimental and simulation data
•Suitable for researchers and post-graduates in the field of condensed matter science (Physics, Chemistry, Material Science), biophysics as well as those in the oil industry
Magnetic fields are found in every corner of the cosmos. For decades, astrophysicists have identified them by their effects on visible light, radio waves, and x-rays. J. B. Zirker summarizes our deep knowledge of magnetism, pointing to what is yet unknown about its astrophysical applications.
In clear, nonmathematical prose, Zirker follows the trail of magnetic exploration from the auroral belts of Earth to the farthest reaches of space. He guides readers on a fascinating journey of discovery to understand how magnetic forces are created and how they shape the universe. He provides the historical background needed to appreciate exciting new research by introducing readers to the great scientists who have studied magnetic fields.
Students and amateur astronomers alike will appreciate the readable prose and comprehensive coverage of The Magnetic Universe.
The selection and organization of the material is in a form to prepare the reader to reason independently and to deal just as independently with available theoretical results and experimental data. The subjects dealt with include:
- electronic transport theory based on the test-particle and correlation-function concepts;
- scattering by phonons, impurities, surfaces, magnons, dislocations, electron-electron scattering and electron temperature;
- two-phonon scattering, spin-flip scattering, scattering in degenerate and many-band models.