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Special Relativity: For Inquiring Minds (Undergraduate Lecture Notes in Physics)

This textbook introduces the special theory of relativity at a level which is accessible to undergraduate students and even high school students with a strong foundation in algebra. The presentation emphasizes clean algebraic and geometrical methods, visualized with plenty of illustrations, resulting in a textbook that is modern and serious yet accessible. Replete with many solved exercises and copious spacetime diagrams, this book will help students develop relativistic intuition when encountering the subject for the first time. The emphasis on geometric methods, combined with the pedagogically appealing k-calculus approach, makes this book ideal for a self-contained course on special relativity or as supplementary reading for modern physics courses. It will also appeal to high schoolers with a strong math background who want to get ahead.

Special Relativity in General Frames: From Particles to Astrophysics

Special relativity is the basis of many fields in modern physics: particle physics, quantum field theory, high-energy astrophysics, etc. This theory is presented here by adopting a four-dimensional point of view from the start. An outstanding feature of the book is that it doesn't restrict itself to inertial frames and to considering accelerated and rotating observers. It is thus possible to treat physical effects such as the Thomas precession or the Sagnac effect in a simple yet precise manner. In the final chapters, more advanced topics like tensorial fields in spacetime, exterior calculus and relativistic hydrodynamics are addressed. In the last, brief chapter the author gives a preview of gravity and shows where it becomes incompatible with Minkowsky spacetime. Well illustrated and enriched by many historical notes, this book also presents many applications of special relativity, ranging from particle physics (accelerators, particle collisions, quark-gluon plasma) to astrophysics (relativistic jets, active galactic nuclei), and including practical applications (Sagnac gyrometers, synchrotron radiation, GPS). In addition, the book provides some mathematical developments, such as the detailed analysis of the Lorentz group and its Lie algebra. The book is suitable for students in the third year of a physics degree or on a masters course, as well as researchers and any reader interested in relativity. Thanks to the geometric approach adopted, this book should also be beneficial for the study of general relativity. "A modern presentation of special relativity must put forward its essential structures, before illustrating them using concrete applications to specific dynamical problems. Such is the challenge (so successfully met!) of the beautiful book by Éric Gourgoulhon." (excerpt from the Foreword by Thibault Damour)

Special Sciences and the Unity of Science

Science is a dynamic process in which the assimilation of new phenomena, perspectives, and hypotheses into the scientific corpus takes place slowly. The apparent disunity of the sciences is the unavoidable consequence of this gradual integration process. Some thinkers label this dynamical circumstance a 'crisis'. However, a retrospective view of the practical results of the scientific enterprise and of science itself, grants us a clear view of the unity of the human knowledge seeking enterprise. This book provides many arguments, case studies and examples in favor of the unity of science. These contributions touch upon various scientific perspectives and disciplines such as: Physics, Computer Science, Biology, Neuroscience, Cognitive Psychology, and Economics.

The Special Theory of Relativity: Einstein’s World in New Axiomatics

This book discusses in detail the special theory of relativity without including all the instruments of theoretical physics, enabling readers who are not budding theoretical physicists to develop competence in the field. An arbitrary but fixed inertial system is chosen, where the known velocity of light is measured. With respect to this system a moving clock loses time and a moving length contracts. The book then presents a definition of simultaneity for the other inertial frames without using the velocity of light. To do so it employs the known reciprocity principle, which in this context serves to provide a definition of simultaneity in the other inertial frames. As a consequence, the Lorentz transformation is deduced and the universal constancy of light is established. With the help of a lattice model of the special theory of relativity the book provides a deeper understanding of the relativistic effects. Further, it discusses the key STR experiments and formulates and solves 54 problems in detail.

The Special Theory of Relativity

The book expounds the major topics in the special theory of relativity. It provides a detailed examination of the mathematical foundation of the special theory of relativity, relativistic mass, relativistic mechanics and relativistic electrodynamics. As well as covariant formulation of relativistic mechanics and electrodynamics, the book discusses the relativistic effect on photons. Using a mathematical approach, the text offers graduate students a clear, concise view of the special theory of relativity. Organized into 14 chapters and two appendices, the content is presented in a logical order, and every topic has been dealt with in a simple and lucid manner. To aid understanding of the subject, the book provides numerous relevant worked examples in every chapter. The book's mathematical approach helps students in their independent study and motivates them to research the topic further.

The Special Theory of Relativity: A Mathematical Approach (UNITEXT #136)

This textbook expounds the major topics in the special theory of relativity. It provides a detailed examination of the mathematical foundation of the special theory of relativity, relativistic mass, relativistic mechanics, and relativistic electrodynamics. As well as covariant formulation of relativistic mechanics and electrodynamics, the text discusses the relativistic effect on photons. A new chapter on electromagnetic waves as well as several new problems and examples have been included in the second edition of the book. Using the mathematical approach, the text offers graduate students a clear, concise view of the special theory of relativity. Organized into 15 chapters and two appendices, the content is presented in a logical order, and every topic has been dealt with in a simple and lucid manner. To aid understanding of the subject, the text provides numerous relevant worked-out examples in every chapter. The mathematical approach of the text helps students in their independent study and motivates them to research the topic further.

Special Topics in Earthquake Geotechnical Engineering

Geotechnical Earthquake Engineering and Soil Dynamics, as well as their interface with Engineering Seismology, Geophysics and Seismology, have all made remarkable progress over the past 15 years, mainly due to the development of instrumented large scale experimental facilities, to the increase in the quantity and quality of recorded earthquake data, to the numerous well-documented case studies from recent strong earthquakes as well as enhanced computer capabilities. One of the major factors contributing to the aforementioned progress is the increasing social need for a safe urban environment, large infrastructures and essential facilities. The main scope of our book is to provide the geotechnical engineers, geologists and seismologists, with the most recent advances and developments in the area of earthquake geotechnical engineering, seismology and soil dynamics.

Species at Risk: Using Economic Incentives to Shelter Endangered Species on Private Lands

Protecting endangered species of animals and plants is a goal that almost everyone supports in principle--but in practice private landowners have often opposed the regulations of the Endangered Species Act, which, they argue, unfairly limits their right to profit from their property. <P><P>To encourage private landowners to cooperate voluntarily in species conservation and to mitigate the economic burden of doing so, the government and nonprofit land trusts have created a number of incentive programs, including conservation easements, leases, habitat banking, habitat conservation planning, safe harbors, candidate conservation agreements, and the "no surprise" policy.

Species Conservation: Lessons from Islands (Ecology, Biodiversity and Conservation)

This book brings together leading conservation practitioners to reflect on their response to the current global biodiversity crisis, through the lens of island species recovery and management. Initial chapters cover the biological understanding of small population biology and the growing threat of invasive species, while subsequent chapters discuss the management of these threats and the complexity of leading projects within a dynamic and still relatively unknown system. Multiple case studies from islands worldwide illustrate key points, allowing readers to draw on the first-hand practical experience of experienced professionals. This resource will be invaluable to both current and future conservation professionals, helping them to go beyond disciplinary 'comfort zones' and develop, manage and lead projects over extensive timeframes in a way that brings others with them on the journey.

Species, Science and Society: The Role of Systematic Biology (Routledge Studies in Conservation and the Environment)

This book presents an engaging and accessible examination of the role of systematic biology in species exploration and biodiversity conservation. Our planet and systematic biology are at a crossroads. Millions of species face an imminent threat of extinction, and, with knowledge of only a fraction of earth’s species we are unprepared to respond. Species, Science and Society explains what is at stake if we continue to ignore the traditional mission of systematics. Rejecting claims that it is too late to document earth’s species, that molecular evidence is sufficient and that comparative morphology and the grand traditions of systematics are outdated, this book makes a compelling argument for a taxonomic renaissance. The book challenges readers to rethink assumptions about systematics. Shattering myths and misconceptions and clarifying the role of systematics in confronting mass extinction, it hopes to inspire a new generation of systematists. Readers are given a deeply personal view of the mission, motivations and rewards of systematic biology. Written in narrative style with passion, wit and optimism, it is the first book to question the growing dominance of molecular data, defend descriptive taxonomy and propose a mission to discover, describe and classify all species. Our evolutionary heritage, the fate of society and the future of the planet depend on what we do next. This book will be of great interest to academics, researchers and professionals working in systematics, taxonomy and biodiversity conservation, as well as students with a basic background in biology.

Species, Science and Society: The Role of Systematic Biology (Routledge Studies in Conservation and the Environment)

- presents an engaging and accessible examination of the role of systematic biology in species exploration and biodiversity conservation - clarifies misconceptions about systematic biology, reimagining it for the 21st Century - proposes an ambitious, planetary-scale project to inventory and make known every kind of plant, animal, and microbe on Earth - challenges the next and present generations of taxonomists to allow molecular data to assume it’s proper place alongside traditional data, to reembrace the fundamentally important mission of systematics - will be of great interest to those researching and working in systematics in botany and zoology, as well as professionals working in taxonomy and biodiversity conservation.

The Species–Area Relationship: Theory and Application (Ecology, Biodiversity and Conservation)

Speciesism in Biology and Culture: How Human Exceptionalism is Pushing Planetary Boundaries

This open access book explores a wide-ranging discussion about the sociopolitical, cultural, and scientific ramifications of speciesism and world views that derive from it. In this light, it integrates subjects across the natural sciences, social sciences, and humanities. The 21st-century western world is anthropocentric to an extreme; we adopt unreasonably self-centered and self-serving ideas and lifestyles. Americans consume more energy resources per person than most other nations on Earth and have little concept of how human ecology and population biology interface with global sustainability. We draw upon religion, popular culture, politics, and technology to justify our views and actions, yet remain self-centered because our considerations rarely extend beyond our immediate interests. Stepping upward on the hierarchy from “racism,” “speciesism” likewise refers to the view that unique natural kinds (species) exist and are an important structural element of biodiversity. This ideology manifests in the cultural idea that humans are distinct from and intrinsically superior to other forms of life. It further carries a plurality of implications for how we perceive ourselves in relation to nature, how we view Judeo-Christian religions and their tenets, how we respond to scientific data about social problems such as climate change, and how willing we are to change our actions in the face of evidence.

Spectral Action in Noncommutative Geometry (SpringerBriefs in Mathematical Physics #27)

What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry à la Connes, deliberately unveiling the answers to these questions.After a brief preface flashing the panorama of the spectral approach, a concise primer on spectral triples is given. Chapter 2 is designed to serve as a toolkit for computations. The third chapter offers an in-depth view into the subtle links between the asymptotic expansions of traces of heat operators and meromorphic extensions of the associated spectral zeta functions. Chapter 4 studies the behaviour of the spectral action under fluctuations by gauge potentials. A subjective list of open problems in the field is spelled out in the fifth Chapter. The book concludes with an appendix including some auxiliary tools from geometry and analysis, along with examples of spectral geometries.The book serves both as a compendium for researchers in the domain of noncommutative geometry and an invitation to mathematical physicists looking for new concepts.

Spectral Analysis of N-Body Schrödinger Operators at Two-Cluster Thresholds (Mathematical Physics Studies)

This book provides a systematic study of spectral and scattering theory for many-body Schrödinger operators at two-cluster thresholds. While the two-body problem (reduced after separation of the centre of mass motion to a one-body problem at zero energy) is a well-studied subject, the literature on many-body threshold problems is sparse. However, the authors’ analysis covers for example the system of three particles interacting by Coulomb potentials and restricted to a small energy region to the right of a fixed nonzero two-body eigenvalue. In general, the authors address the question: How do scattering quantities for the many-body atomic and molecular models behave within the limit when the total energy approaches a fixed two-cluster threshold? This includes mapping properties and singularities of the limiting scattering matrix, asymptotics of the total scattering cross section, and absence of transmission from one channel to another in the small inter-cluster kinetic energy region. The authors’ principal tools are the Feshbach–Grushin dimension reduction method and spectral analysis based on a certain Mourre estimate. Additional topics of independent interest are the limiting absorption principle, micro-local resolvent estimates, Rellich- and Sommerfeld-type theorems and asymptotics of the limiting resolvents at thresholds. The mathematical physics field under study is very rich, and there are many open problems, several of them stated explicitly in the book for the interested reader.

Spectral Approach to Transport Problems in Two-Dimensional Disordered Lattices: Physical Interpretation And Applications (Springer Theses)

This book introduces the spectral approach to transport problems in infinite disordered systems characterized by Anderson-type Hamiltonians. The spectral approach determines (with probability one) the existence of extended states for nonzero disorder in infinite lattices of any dimension and geometry. Here, the author focuses on the critical 2D case, where previous numerical and experimental results have shown disagreement with theory. Not being based on scaling theory, the proposed method avoids issues related to boundary conditions and provides an alternative approach to transport problems where interaction with various types of disorder is considered.Beginning with a general overview of Anderson-type transport problems and their relevance to physical systems, it goes on to discuss in more detail the most relevant theoretical, numerical, and experimental developments in this field of research. The mathematical formulation of the innovative spectral approach is introduced together with a physical interpretation and discussion of its applicability to physical systems, followed by a numerical study of delocalization in the 2D disordered honeycomb, triangular, and square lattices. Transport in the 2D honeycomb lattice with substitutional disorder is investigated employing a spectral analysis of the quantum percolation problem. Next, the applicability of the method is extended to the classical regime, with an examination of diffusion of lattice waves in 2D disordered complex plasma crystals, along with discussion of proposed future developments in the study of complex transport problems using spectral theory.

Spectral Functions in Mathematics and Physics

The literature on the spectral analysis of second order elliptic differential operators contains a great deal of information on the spectral functions for explicitly known spectra. The same is not true, however, for situations where the spectra are not explicitly known. Over the last several years, the author and his colleagues have developed new,

Spectral Measures and Dynamics: Typical Behaviors (Latin American Mathematics Series)

This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature. It starts with classic topics such as Wiener lemma, Strichartz inequality, and the basics of fractal dimensions of measures, progressing to more advanced material, some of them developed by the own authors.A fundamental concept to the mathematical theory of quantum mechanics, the spectral measure relates to the components of the quantum state concerning the energy levels of the Hamiltonian operator and, on the other hand, to the dynamics of such state. However, these correspondences are not immediate, with many nuances and subtleties discovered in recent years.A valuable example of such subtleties is found in the so-called “Wonderland theorem” first published by B. Simon in 1995. It shows that, for some metric space of self-adjoint operators, the set of operators whose spectral measures are singular continuous is a generic set (which, for some, is exotic). Recent works have revealed that, on top of singular continuity, there are other generic properties of spectral measures. These properties are usually associated with a number of different notions of generalized dimensions, upper and lower dimensions, with dynamical implications in quantum mechanics, ergodicity of dynamical systems, and evolution semigroups. All this opens ways to new and instigating avenues of research.Graduate students with a specific interest in the spectral properties of spectral measure are the primary target audience for this work, while researchers benefit from a selection of important results, many of them presented in the book format for the first time.

Spectral Methods for the Estimation of the Effective Elastic Thickness of the Lithosphere (Advances in Geophysical and Environmental Mechanics and Mathematics)

Although several excellent works exist that describe the effective elastic thickness (Te) of the lithosphere—its theory, significance and relevance to Earth sciences in general—none cover the details of the methods for its estimation. This book brings together the disparate knowledge required to estimate Te in one handy volume: signal processing, harmonic analysis, civil engineering, and foundational mathematics and physics, in addition to the relevant geophysics and, to a lesser extent, geology. Its two principal focus areas are spectral estimation, covering various approaches to estimating the admittance and coherence between gravity and topography using Slepian multitapers and fan wavelets; and algebraic and finite difference solutions of the plate bending partial differential equation in a variety of geological settings. This book would be suitable for postgraduate students beginning their research, up to faculty professors interested in diversifying their skills.

Spectral Methods in Geodesy and Geophysics

The text develops the principal aspects of applied Fourier analysis and methodology with the main goal to inculcate a different way of perceiving global and regional geodetic and geophysical data, namely from the perspective of the frequency, or spectral, domain rather than the spatial domain. The word "methods" in the title is meant to convey that the transformation of a geophysical signal into the spectral domain can be applied for purposes of analysis as well as rapid computation. The text is written for graduate students; however, Chapters 1 through 4 and parts of 5 can also benefit undergraduates who have a solid and fluent knowledge of integral and differential calculus, have some statistical background, and are not uncomfortable with complex numbers. Concepts are developed by starting from the one-dimensional domain and working up to the spherical domain, which is part of every chapter. Many concepts are illustrated graphically with actual geophysical data primarily from signals of gravity, magnetism, and topography.

Spectral Mixture for Remote Sensing: Linear Model and Applications (Springer Remote Sensing/Photogrammetry)

This book explains in a didactic way the basic concepts of spectral mixing, digital numbers and orbital sensors, and then presents the linear modelling technique of spectral mixing and the generation of fractional images. In addition to presenting a theoretical basis for spectral mixing, the book provides examples of practical applications such as projects for estimating and monitoring deforested areas in the Amazon. In its seven chapters, the book offers remote sensing techniques to understand the main concepts, methods, and limitations of spectral mixing for digital image processing. Chapter 1 addresses the basic concepts of spectral mixing, while chapters 2 and 3 discuss digital numbers and orbital sensors such as MODIS and Landsat MSS. Chapter 4 details the linear spectral mixing model, and chapter 5 talks about how to use this technique to create fraction images. Chapter 6 offers remote sensing applications of fraction images in deforestation monitoring, burned-area mapping, selective logging detection, and land-use/land-cover mapping. Chapter 7 gives some concluding thoughts on spectral mixing, and considers future uses in environmental remote sensing. This book will be of interest to students, teachers, and researchers using remote sensing for Earth observation and environmental modelling.

Spectral Theory and Applications of Linear Operators and Block Operator Matrices

Examining recent mathematical developments in the study of Fredholm operators, spectral theory and block operator matrices, with a rigorous treatment of classical Riesz theory of polynomially-compact operators, this volume covers both abstract and applied developments in the study of spectral theory. These topics are intimately related to the stability of underlying physical systems and play a crucial role in many branches of mathematics as well as numerous interdisciplinary applications. By studying classical Riesz theory of polynomially compact operators in order to establish the existence results of the second kind operator equations, this volume will assist the reader working to describe the spectrum, multiplicities and localization of the eigenvalues of polynomially-compact operators.

Spectral Theory and Quantum Mechanics

This book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given to spectral theory features that are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in one place a number of useful rigorous statements on the mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out to Master's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book should benefit established researchers to organise and present the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly.

Spectral Theory of Localized Resonances and Applications

This book is devoted to the spectral theory of localized resonances including surface plasmon/polariton resonances, atypical resonances, anomalous localized resonances and interior transmission resonances. Those resonance phenomena arise in different physical contexts, but share similar features. They form the fundamental basis for many cutting-edge technologies and applications including invisibility cloaking and super-resolution imaging. The book presents a systematic and comprehensive treatment on these resonance phenomena and the associated applications in a unified manner from a mathematical and spectral perspective, covering acoustic, electromagnetic and elastic wave scattering.The book can serve as a handy reference book for researchers in this field and it can also serve as a textbook or an inspiring source for postgraduate students who are interested in entering this field.

Spectroscopic Methods in the Study of Kaolin Minerals and Their Modifications (Springer Mineralogy Ser.)

This book systematically provides an overview of the use of a wide range of spectroscopic methods (Mid- and Near-Infrared, Infrared Emission, Raman, Solid-State Magic Angle Spinning Nuclear Magnetic Resonance, X-ray Photoelectron, Extended X-ray Absorption Fine Structure, X-ray Absorption Near Edge, Electron Spin and Mössbauer spectroscopy) to investigate kaolin minerals (kaolinite, dickite, nacrite and halloysite) and their modifications (intercalation compounds, nanocomposites and other modifications).