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1 Zhu, Jian-Xin Bogoliubov-de Gennes Method and Its Applications I10464 2016 eBook  
2 Rodrigues, Jr, Waldyr A The Many Faces of Maxwell, Dirac and Einstein Equations I10404 2016 eBook  
3 Kato, Shoji Oscillations of Disks I10403 2016 eBook  
4 Vallejo, Juan C Predictability of Chaotic Dynamics I10399 2017 eBook  
5 Vaid, Deepak LQG for the Bewildered I10381 2017 eBook  
6 Vassiliev, Oleg N Monte Carlo Methods for Radiation Transport I10359 2017 eBook  
7 Timberlake, Todd Keene Classical Mechanics with Maxima I10330 2016 eBook  
8 Fan, Tian-You Mathematical Theory of Elasticity of Quasicrystals and Its Applications I10304 2016 eBook  
9 de Gosson, Maurice A Born-Jordan Quantization I10290 2016 eBook  
10 Skokos, Charalampos (Haris) Chaos Detection and Predictability I10263 2016 eBook  
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TitleBogoliubov-de Gennes Method and Its Applications
Author(s)Zhu, Jian-Xin
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2016.
DescriptionXI, 188 p. 50 illus., 33 illus. in color : online resource
Abstract NoteThe purpose of this book is to provide an elementary yet systematic description of the Bogoliubov-de Gennes (BdG) equations, their unique symmetry properties and their relation to Green???s function theory. Specifically, it introduces readers to the supercell technique for the solutions of the BdG equations, as well as other related techniques for more rapidly solving the equations in practical applications. The BdG equations are derived from a microscopic model Hamiltonian with an effective pairing interaction and fully capture the local electronic structure through self-consistent solutions via exact diagonalization. This approach has been successfully generalized to study many aspects of conventional and unconventional superconductors with inhomogeneities ??? including defects, disorder or the presence of a magnetic field ??? and becomes an even more attractive choice when the first-principles information of a typical superconductor is incorporated via the construction of a low-energy tight-binding model. Further, the lattice BdG approach is essential when theoretical results for local electronic states around such defects are compared with the scanning tunneling microscopy measurements. Altogether, these lectures provide a timely primer for graduate students and non-specialist researchers, while also offering a useful reference guide for experts in the field
ISBN,Price9783319313146
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. Mathematical Applications in the Physical Sciences 4. Mathematical Methods in Physics 5. MATHEMATICAL PHYSICS 6. Nanoscale science 7. Nanoscale Science and Technology 8. NANOSCIENCE 9. Nanostructures 10. Numerical and Computational Physics, Simulation 11. PHYSICS 12. Strongly Correlated Systems, Superconductivity 13. SUPERCONDUCTIVITY 14. SUPERCONDUCTORS
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TitleThe Many Faces of Maxwell, Dirac and Einstein Equations : A Clifford Bundle Approach
Author(s)Rodrigues, Jr, Waldyr A;Capelas de Oliveira, Edmundo
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2016.
DescriptionXVI, 587 p. 14 illus : online resource
Abstract NoteThis book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research. This thoroughly revised second edition also adds three new chapters: on the Clifford bundle approach to the Riemannian or semi-Riemannian differential geometry of branes; on Komar currents in the context of the General Relativity theory; and an analysis of the similarities and main differences between Dirac, Majorana and ELKO spinor fields. The exercises with solutions, the comprehensive list of mathematical symbols, and the list of acronyms and abbreviations are provided for self-study for students as well as for classes. From the reviews of the first edition: ???The text is written in a very readable manner and is complemented with plenty of worked-out exercises which are in the style of extended examples. ... their book could also serve as a textbook for graduate students in physics or mathematics." (Alberto Molgado, Mathematical Reviews, 2008 k)
ISBN,Price9783319276373
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. GRAVITATION 6. Mathematical Applications in the Physical Sciences 7. MATHEMATICAL PHYSICS
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TitleOscillations of Disks
Author(s)Kato, Shoji
PublicationTokyo, 1. Imprint: Springer 2. Springer Japan, 2016.
DescriptionXV, 261 p. 49 illus., 6 illus. in color : online resource
Abstract NoteThis book presents the current state of research on disk oscillation theory, focusing on relativistic disks and tidally deformed disks. Since the launch of the Rossi X-ray Timing Explorer (RXTE) in 1996, many high-frequency quasiperiodic oscillations (HFQPOs) have been observed in X-ray binaries. Subsequently, similar quasi-periodic oscillations have been found in such relativistic objects as microquasars, ultra-luminous X-ray sources, and galactic nuclei. One of the most promising explanations of their origin is based on oscillations in relativistic disks, and a new field called discoseismology is currently developing. After reviewing observational aspects, the book presents the basic characteristics of disk oscillations, especially focusing on those in relativistic disks. Relativistic disks are essentially different from Newtonian disks in terms of several basic characteristics of their disk oscillations, including the radial distributions of epicyclic frequencies. In order to understand the basic processes of disk oscillations, studies on binary systems are of importance, as they offer valuable information on wave???wave coupling processes in disk oscillations. Accordingly, some characteristics of oscillations in deformed disks are also presented in this book. The book consists of two parts. Points covered in Part I include, for instance, the basic characteristics of disk oscillations, classification of oscillation modes, and trapping of oscillations. In Part II, the focus is mainly on excitation processes of oscillations, while applications to observations are also discussed
ISBN,Price9784431562085
Keyword(s)1. ASTRONOMY 2. Astronomy, Astrophysics and Cosmology 3. ASTROPHYSICS 4. EBOOK 5. EBOOK - SPRINGER 6. Mathematical Applications in the Physical Sciences 7. MATHEMATICAL PHYSICS 8. PLANETOLOGY 9. Theoretical, Mathematical and Computational Physics
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TitlePredictability of Chaotic Dynamics : A Finite-time Lyapunov Exponents Approach
Author(s)Vallejo, Juan C;Sanjuan, Miguel A. F
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXV, 136 p. 47 illus., 22 illus. in color : online resource
Abstract NoteThis book is primarily concerned with the computational aspects of predictability of dynamical systems ??? in particular those where observation, modeling and computation are strongly interdependent. Unlike with physical systems under control in laboratories, for instance in celestial mechanics, one is confronted with the observation and modeling of systems without the possibility of altering the key parameters of the objects studied. Therefore, the numerical simulations offer an essential tool for analyzing these systems. With the widespread use of computer simulations to solve complex dynamical systems, the reliability of the numerical calculations is of ever-increasing interest and importance. This reliability is directly related to the regularity and instability properties of the modeled flow. In this interdisciplinary scenario, the underlying physics provide the simulated models, nonlinear dynamics provides their chaoticity and instability properties, and the computer sciences provide the actual numerical implementation. This book introduces and explores precisely this link between the models and their predictability characterization based on concepts derived from the field of nonlinear dynamics, with a focus on the finite-time Lyapunov exponents approach. The method is illustrated using a number of well-known continuous dynamical systems, including the Contopoulos, H??non-Heiles and R??ssler systems. To help students and newcomers quickly learn to apply these techniques, the appendix provides descriptions of the algorithms used throughout the text and details how to implement them in order to solve a given continuous dynamical system
ISBN,Price9783319518930
Keyword(s)1. Applications of Nonlinear Dynamics and Chaos Theory 2. EBOOK 3. EBOOK - SPRINGER 4. Mathematical Applications in the Physical Sciences 5. MATHEMATICAL PHYSICS 6. Numerical and Computational Physics, Simulation 7. PHYSICS 8. SPACE SCIENCES 9. Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics) 10. STATISTICAL PHYSICS
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TitleLQG for the Bewildered : The Self-Dual Approach Revisited
Author(s)Vaid, Deepak;Bilson-Thompson, Sundance
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionIX, 138 p. 16 illus., 4 illus. in color : online resource
Abstract NoteThis primer offers a concise introduction to Loop Quantum Gravity (LQG) - a theoretical framework for uniting Quantum Mechanics (QM) with General Relativity (GR). The emphasis is on the physical aspects of the framework and its historical development in terms of self-dual variables, still most suited for a first, pedagogical encounter with LQG. The text starts by reviewing GR and the very basics of Quantum Field Theory (QFT), and then explains in a concise and clear manner the steps leading from the Einstein-Hilbert action for gravity to the construction of the quantum states of geometry, known as spin-networks, and which provide the basis for the kinematical Hilbert space of quantum general relativity. Along the way the various associated concepts of tetrads, spin-connection and holonomies are introduced. Having thus provided a minimal introduction to the LQG framework, some applications to the problems of black hole entropy and of quantum cosmology are briefly surveyed. Last but not least, a list of the most common criticisms of LQG is presented, which are then tackled one by one in order to convince the reader of the physical viability of the theory. A set of appendices provides accessible introductions to several key notions such as the Peter-Weyl theorem, duality of differential forms and Regge calculus, among others. The presentation is aimed at graduate students and researchers who have some familiarity with the tools of QM and GR, but are intimidated by the technicalities required to browse through the existing LQG literature. This primer aims at making the formalism appear a little less bewildering to the uninitiated and helps lower the barrier for entry into the field
ISBN,Price9783319431840
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. EBOOK 3. EBOOK - SPRINGER 4. GRAVITATION 5. Mathematical Applications in the Physical Sciences 6. Mathematical Methods in Physics 7. MATHEMATICAL PHYSICS 8. PHYSICS
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TitleMonte Carlo Methods for Radiation Transport : Fundamentals and Advanced Topics
Author(s)Vassiliev, Oleg N
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXVII, 281 p. 38 illus., 32 illus. in color : online resource
Abstract NoteThis book is a guide to the use of Monte Carlo techniques in radiation transport. This topic is of great interest for medical physicists. Praised as a "gold standard" for accurate radiotherapy dose calculations, Monte Carlo has stimulated a high level of research activity that has produced thousands of papers within the past few years. The book is designed primarily to address the needs of an academically inclined medical physicist who wishes to learn the technique, as well as experienced users of standard Monte Carlo codes who wish to gain insight into the underlying mathematics of Monte Carlo algorithms. The book focuses on the fundamentals???giving full attention to and explaining the very basic concepts. It also includes advanced topics and covers recent advances such as transport of charged particles in magnetic fields and the grid-based solvers of the Boltzmann equation
ISBN,Price9783319441412
Keyword(s)1. Biological and Medical Physics, Biophysics 2. BIOLOGICAL PHYSICS 3. BIOPHYSICS 4. Diagnostic Radiology 5. EBOOK 6. EBOOK - SPRINGER 7. Mathematical Applications in the Physical Sciences 8. MATHEMATICAL PHYSICS 9. Medical and Radiation Physics 10. Medical physics 11. Numerical and Computational Physics, Simulation 12. Particle acceleration 13. Particle Acceleration and Detection, Beam Physics 14. PHYSICS 15. RADIATION 16. Radiology
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TitleClassical Mechanics with Maxima
Author(s)Timberlake, Todd Keene;Mixon, J. Wilson
PublicationNew York, NY, 1. Imprint: Springer 2. Springer New York, 2016.
DescriptionXI, 258 p. 156 illus : online resource
Abstract NoteThis book guides undergraduate students in the use of Maxima???a computer algebra system???in solving problems in classical mechanics. It functions well as a supplement to a typical classical mechanics textbook. When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool. Maxima is particularly attractive in that it is open-source, multiple-platform software that students can download and install free of charge. Lessons learned and capabilities developed using Maxima are easily transferred to other, proprietary software
ISBN,Price9781493932078
Keyword(s)1. ALGEBRA 2. CLASSICAL MECHANICS 3. Computational Mathematics and Numerical Analysis 4. Computer mathematics 5. EBOOK 6. EBOOK - SPRINGER 7. General Algebraic Systems 8. Mathematical Applications in the Physical Sciences 9. Mathematical Methods in Physics 10. MATHEMATICAL PHYSICS 11. MECHANICS 12. PHYSICS
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TitleMathematical Theory of Elasticity of Quasicrystals and Its Applications
Author(s)Fan, Tian-You
PublicationSingapore, 1. Imprint: Springer 2. Springer Singapore, 2016.
DescriptionXVI, 452 p. 103 illus., 40 illus. in color : online resource
Abstract NoteThis interdisciplinary work on condensed matter physics, the continuum mechanics of novel materials, and partial differential equations, discusses the mathematical theory of elasticity and hydrodynamics of quasicrystals, as well as its applications. By establishing new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions, the theories developed here dramatically simplify the solution of complex elasticity problems. Comprehensive and detailed mathematical derivations guide readers through the work. By combining theoretical analysis and experimental data, mathematical studies and practical applications, readers will gain a systematic, comprehensive and in-depth understanding of condensed matter physics, new continuum mechanics and applied mathematics. This new edition covers the latest developments in quasicrystal studies. In particular, it pays special attention to the hydrodynamics, soft-matter quasicrystals, and the Poisson bracket method and its application in deriving hydrodynamic equations. These new sections make the book an even more useful and comprehensive reference guide for researchers working in Condensed Matter Physics, Chemistry and Materials Science
ISBN,Price9789811019845
Keyword(s)1. Amorphous substances 2. Characterization and Evaluation of Materials 3. Complex fluids 4. EBOOK 5. EBOOK - SPRINGER 6. MATERIALS SCIENCE 7. Mathematical Applications in the Physical Sciences 8. MATHEMATICAL PHYSICS 9. MECHANICS 10. Mechanics, Applied 11. Soft and Granular Matter, Complex Fluids and Microfluidics 12. Solid Mechanics 13. SOLID STATE PHYSICS
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TitleBorn-Jordan Quantization : Theory and Applications
Author(s)de Gosson, Maurice A
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2016.
DescriptionXIII, 226 p : online resource
Abstract NoteThis book presents a comprehensive mathematical study of the operators behind the Born???Jordan quantization scheme. The Schr??dinger and Heisenberg pictures of quantum mechanics are equivalent only if the Born???Jordan scheme is used. Thus, Born???Jordan quantization provides the only physically consistent quantization scheme, as opposed to the Weyl quantization commonly used by physicists. In this book we develop Born???Jordan quantization from an operator-theoretical point of view, and analyze in depth the conceptual differences between the two schemes. We discuss various physically motivated approaches, in particular the Feynman-integral point of view. One important and intriguing feature of Born-Jordan quantization is that it is not one-to-one: there are infinitely many classical observables whose quantization is zero
ISBN,Price9783319279022
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. History and Philosophical Foundations of Physics 4. Mathematical Applications in the Physical Sciences 5. MATHEMATICAL PHYSICS 6. OPERATOR THEORY 7. PHYSICS 8. QUANTUM PHYSICS
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TitleChaos Detection and Predictability
Author(s)Skokos, Charalampos (Haris);Gottwald, Georg A;Laskar, Jacques
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2016.
DescriptionXI, 269 p. 122 illus., 44 illus. in color : online resource
Abstract NoteDistinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book covers theoretical and computational aspects of traditional methods to calculate Lyapunov exponents, as well as of modern techniques like the Fast (FLI), the Orthogonal (OFLI) and the Relative (RLI) Lyapunov Indicators, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), the Smaller (SALI) and the Generalized (GALI) Alignment Index and the ???0-1??? test for chaos
ISBN,Price9783662484104
Keyword(s)1. Applications of Nonlinear Dynamics and Chaos Theory 2. Earth System Sciences 3. EBOOK 4. EBOOK - SPRINGER 5. Mathematical Applications in the Physical Sciences 6. Mathematical Methods in Physics 7. MATHEMATICAL PHYSICS 8. Physical geography 9. PHYSICS 10. SPACE SCIENCES 11. Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics) 12. STATISTICAL PHYSICS
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