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This book demonstrates Microsoft EXCEL-based Fourier transform of selected physics examples. Spectral density of the auto-regression process is also described in relation to Fourier transform. Rather than offering rigorous mathematics, readers will «try and feel» Fourier transform for themselves through the examples. Readers can also acquire and analyze their own data following the step-by-step procedure explained in this book. A hands-on acoustic spectral analysis can be one of the ideal long-term student projects.

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This book begins with the history and fundamentals of optical fiber communications. Then, briefly introduces existing optical multiplexing techniques and finally focuses on spatial domain multiplexing (SDM), aka space division multiplexing, and orbital angular momentum of photon based multiplexing. These are two emerging multiplexing techniques that have added two new degrees of photon freedom to optical fibers.

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Domain theory, a subject that arose as a response to natural concerns in the semantics of computation, studies ordered sets which possess an unusual amount of mathematical structure. This book explores its connection with quantum information science and the concept that relates them: disorder. This is not a literary work. It can be argued that its subject, domain theory and quantum information science, does not even really exist, which makes the scope of this alleged 'work' irrelevant. BUT, it does have a purpose and to some extent, it can also be said to have a method. I leave the determination of both of those largely to you, the reader. Except to say, I am hoping to convince the uninitiated to take a look. A look at what? Twenty years ago, I failed to satisfactorily prove a claim that I still believe: that there is substantial domain theoretic structure in quantum mechanics and that we can learn a lot from it. One day it will be proven to the point that people will be comfortable dismissing it as a 'well-known' idea that many (possibly including themselves) had long suspected but simply never bothered to write down. They may even call it «obvious!» I will not bore you with a brief history lesson on why it is not obvious, except to say that we have never been interested in the difficulty of proving the claim only in establishing its validity. This book then documents various attempts on my part to do just that.

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The Boussinesq equation is the first model of surface waves in shallow water that considers the nonlinearity and the dispersion and their interaction as a reason for wave stability known as the Boussinesq paradigm. This balance bears solitary waves that behave like quasi-particles. At present, there are some Boussinesq-like equations. The prevalent part of the known analytical and numerical solutions, however, relates to the 1d case while for multidimensional cases, almost nothing is known so far. An exclusion is the solutions of the Kadomtsev-Petviashvili equation. The difficulties originate from the lack of known analytic initial conditions and the nonintegrability in the multidimensional case. Another problem is which kind of nonlinearity will keep the temporal stability of localized solutions. The system of coupled nonlinear Schroedinger equations known as well as the vector Schroedinger equation is a soliton supporting dynamical system. It is considered as a model of light propagation in Kerr isotropic media. Along with that, the phenomenology of the equation opens a prospect of investigating the quasi-particle behavior of the interacting solitons. The initial polarization of the vector Schroedinger equation and its evolution evolves from the vector nature of the model. The existence of exact (analytical) solutions usually is rendered to simpler models, while for the vector Schroedinger equation such solutions are not known. This determines the role of the numerical schemes and approaches. The vector Schroedinger equation is a spring-board for combining the reduced integrability and conservation laws in a discrete level. The experimental observation and measurement of ultrashort pulses in waveguides is a hard job and this is the reason and stimulus to create mathematical models for computer simulations, as well as reliable algorithms for treating the governing equations. Along with the nonintegrability, one more problem appears here – the multidimensionality and necessity to split and linearize the operators in the appropriate way.

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Prior to the 1920s it was generally thought, with a few exceptions, that our galaxy, the Milky Way, was the entire Universe. Based on the work of Henrietta Leavitt with Cepheid variables, astronomer Edwin Hubble was able to determine that the Andromeda Galaxy and others had to lie outside our own. Moreover, based on the work of Vesto Slipher, involving the redshifts of these galaxies, Hubble was able to determine that the Universe was not static, as had been previously thought, but expanding. The number of galaxies has also been expanding, with estimates varying from 100 billion to 2 trillion. While every galaxy in the Universe is interesting just by its very fact of being, the author has selected 51 of those that possess some unusual qualities that make them of some particular interest. These galaxies have complex evolutionary histories, with some having supermassive black holes at their core, others are powerful radio sources, a very few are relatively nearby and even visible to the naked eye, whereas the light from one recent discovery has been travelling for the past 13.4 billion years to show us its infancy, and from a time when the Universe was in its infancy. And in spite of the vastness of the Universe, some galaxies are colliding with others, embraced in a graceful gravitational dance. Indeed, as the Andromeda Galaxy is heading towards us, a similar fate awaits our Milky Way. When looking at a modern image of a galaxy, one is in awe at the shear wondrous nature of such a magnificent creation, with its boundless secrets that it is keeping from us, its endless possibilities for harboring alien civilizations, and we remain left with the ultimate knowledge that we are connected to its glory.

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This book contains an extensive illustration of use of finite difference method in solving the boundary value problem numerically. A wide class of differential equations has been numerically solved in this book. Starting with differential equations of elementary functions like hyperbolic, sine and cosine, we have solved those of special functions like Hermite, Laguerre and Legendre. Those of Airy function, of stationary localised wavepacket, of the quantum mechanical problem of a particle in a 1D box, and the polar equation of motion under gravitational interaction have also been solved. Mathematica 6.0 has been used to solve the system of linear equations that we encountered and to plot the numerical data. Comparison with known analytic solutions showed nearly perfect agreement in every case. On reading this book, readers will become adept in using the method.

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This book is a short introduction to classical field theory, most suitable for undergraduate students who have had at least intermediate-level courses in electromagnetism and classical mechanics. The main theme of the book is showcasing role of fields in mediating action-at-a-distance interactions. Suitable technical machinery is developed to explore at least some aspect of each of the four known fundamental forces in nature. Beginning with the physically-motivated introduction to field theory, the text covers the relativistic formulation of electromagnetism in great detail so that aspects of gravity and the nuclear interaction not usually encountered at the undergraduate level can be covered by using analogies with familiar electromagentism. Special topics such as the behavior of gravity in extra, compactified dimensions, magnetic monopoles and electromagnetic duality, and the Higgs mechanism are also briefly considered.

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In the field of particle and astrophysics, one of the major unresolved problems is to understand the nature and properties of dark matter, which constitutes almost 80% of the matter content of the universe. This book gives a pedagogical introduction to the field of dark matter in general, and in particular to the model building perspective. Starting from the evidence and need for dark matter, it goes into the deeper understanding of how to accommodate a dark matter candidate in a particle physics model. This book focuses on teaching the basic tools for model building of dark matter, starting from the easiest to gradually the difficult one. Although there are plenty of dark matter models available in the literature, this book concentrates on the important ones. This book aims to motivate the reader to propose a new dark matter model complying with all observational constraints.

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This book presents simple interdisciplinary stochastic models meant as a gentle introduction to the field of non-equilibrium statistical physics. It focuses on the analysis of two-state models with cooperative effects, which are versatile enough to be applied to many physical and social systems. The book also explores a variety of mathematical techniques to solve the master equations that govern these models: matrix theory, empty-interval methods, mean field theory, a quantum approach, and mapping onto classical Ising models. The models discussed are at the confluence of nanophysics, biology, mathematics, and the social sciences and provide a pedagogical path toward understanding the complex dynamics of particle self-assembly with the tools of statistical physics.

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Electric glow discharges (glows) can be found almost everywhere, from atmospheric electricity to modern plasma technologies, and have long been the object of research. The main purpose of this book is to provide simple illustrations of the basic physical mechanisms and principles that determine the properties of electric glow discharges. It should enable readers to successfully participate in scientific and technical progress.

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