The development of man's understanding of planetary motions is the crown jewel of Newtonian mechanics. This book offers a concise but self-contained handbook-length treatment of this historically important topic for students at about the third-year-level of an undergraduate physics curriculum. After opening with a review of Kepler's three laws of planetary motion, it proceeds to analyze the general dynamics of "central force" orbits in spherical coordinates, how elliptical orbits satisfy Newton's gravitational law and how the geometry of ellipses relates to physical quantities such as energy and momentum. Exercises are provided and derivations are set up in such a way that readers can gain analytic practice by filling in missing steps. A brief bibliography lists sources for readers who wish to pursue further study on their own.

Functional Gaussian Approximation for Dependent Structures develops and analyses mathematical models for phenomena that evolve in time and influence each another. It provides a better understanding of the structure and asymptotic behaviour of stochastic processes. Two approaches are taken. Firstly, the authors present tools for dealing with the dependent structures used to obtain normal approximations. Secondly, they apply normal approximations to various examples. The main tools consist of inequalities for dependent sequences of random variables, leading to limit theorems, including the functional central limit theorem and functional moderate deviation principle. The results point out large classes of dependent random variables which satisfy invariance principles, making possible the statistical study of data coming from stochastic processes both with short and long memory. The dependence structures considered throughout the book include the traditional mixing structures, martingale-like structures, and weakly negatively dependent structures, which link the notion of mixing to the notions of association and negative dependence. Several applications are carefully selected to exhibit the importance of the theoretical results. They include random walks in random scenery and determinantal processes. In addition, due to their importance in analysing new data in economics, linear processes with dependent innovations will also be considered and analysed.

Electroencephalography and magnetoencephalography are the two most efficient techniques to study the functional brain. This book completely aswers the fundamental mathematical question of uniqueness of the representations obtained using these techniques, and also covers many other concrete results for special geometric models of the brain, presenting the research of the authors and their groups in the last two decades.

This book introduces the fundamental concepts, methods, and applications of Hausdorff calculus, with a focus on its applications in fractal systems. Topics such as the Hausdorff diffusion equation, Hausdorff radial basis function, Hausdorff derivative nonlinear systems, PDE modeling, statistics on fractals, etc. are discussed in detail. It is an essential reference for researchers in mathematics, physics, geomechanics, and mechanics.

This book demonstrates some of the ways in which Microsoft Excel (R) may be used to solve numerical problems in the field of physics.

This book addresses the mechanism of enrichment of heavy elements in galaxies, a long standing problem in astronomy. It mainly focuses on explaining the origin of heavy elements by performing state-of-the-art, high-resolution hydrodynamic simulations of dwarf galaxies. In this book, the author successfully develops a model of galactic chemodynamical evolution by means of which the neutron star mergers can be used to explain the observed abundance pattern of the heavy elements synthesized by the rapid neutron capture process, such as europium, gold, and uranium in the Local Group dwarf galaxies. The book argues that heavy elements are significant indicators of the evolutionary history of the early galaxies, and presents theoretical findings that open new avenues to understanding the formation and evolution of galaxies based on the abundance of heavy elements in metal-poor stars.

Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field.

This book focuses on theoretical aspects of dynamical systems in the broadest sense. It highlights novel and relevant results on mathematical and numerical problems that can be found in the fields of applied mathematics, physics, mechanics, engineering and the life sciences. The book consists of contributed research chapters addressing a diverse range of problems. The issues discussed include (among others): numerical-analytical algorithms for nonlinear optimal control problems on a large time interval; gravity waves in a reservoir with an uneven bottom; value distribution and growth of solutions for certain Painleve equations; optimal control of hybrid systems with sliding modes; a mathematical model of the two types of atrioventricular nodal reentrant tachycardia; non-conservative instability of cantilevered nanotubes using the Cell Discretization Method; dynamic analysis of a compliant tensegrity structure for use in a gripper application; and Jeffcott rotor bifurcation behavior using various models of hydrodynamic bearings.

This book discusses recent advances and research in applied mathematics, statistics and their applications in computing. It features papers presented at the fourth conference in the series organized at the Indian Institute of Technology (Banaras Hindu University), Varanasi, India, on 9 - 11 January 2018 on areas of current interest, including operations research, soft computing, applied mathematical modelling, cryptology, and security analysis. The conference has emerged as a powerful forum, bringing together leading academic scientists, experts from industry, and researchers and offering a venue to discuss, interact and collaborate to stimulate the advancement of mathematics and its applications in computer science. The education of future consumers, users, producers, developers and researchers of mathematics and its applications is an important challenge in modern society, and as such, mathematics and its application in computer science are of vital significance to all spectrums of the community, as well as to mathematicians and computing professionals across different educational levels and disciplines. With contributions by leading international experts, this book motivates and creates interest among young researchers.

The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Seminaire de Mathematiques Superieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.

This book presents a generalised computational model for the degradation of resorbable composites, using analytic expressions to represent the interwoven phenomena present during degradation. It then combines this modelling framework with a comprehensive database of quantitative degradation data mined from existing literature and from novel experiments, to provide new insights into the interrelated factors controlling degradation. Resorbable composites made of biodegradable polyesters and calcium-based ceramics have significant therapeutic potential as tissue engineering scaffolds, as temporary implants and as drug-loaded matrices for controlled release. However, their degradation is complex and the rate of resorption depends on multiple connected factors such as the shape and size of the device, polymer chemistry and molecular weight, particle phase, size, volume fraction, distribution and pH-dependent dissolution properties. Understanding and ultimately predicting the degradation of resorbable composites is of central importance if we are to fully unlock the promise of these materials.

This book provides a concise introduction to the special theory of relativity and the general theory of relativity. The format has been chosen to provide the basis for a single semester course that can take the students all the way from the foundations of special relativity to the core results of general relativity: the Einstein equation, and the equations of motion for particles and light in curved spacetime. To facilitate access to the topics of special and general relativity for science and engineering students, without prior training in relativity or geometry, the relevant geometric notions are also introduced.

The revised edition gives a comprehensive mathematical and physical presentation of fluid flows in non-classical models of convection - relevant in nature as well as in industry. After the concise coverage of fluid dynamics and heat transfer theory it discusses recent research. This monograph provides the theoretical foundation on a topic relevant to metallurgy, ecology, meteorology, geo-and astrophysics, aerospace industry, chemistry, crystal physics, and many other fields.

This book provides a detailed introduction to maintenance policies and the current and future research in these fields, highlighting mathematical formulation and optimization techniques. It comprehensively describes the state of art in maintenance modelling and optimization for single- and multi-unit technical systems, and also investigates the problem of the estimation process of delay-time parameters and how this affects system performance. The book discusses delay-time modelling for multi-unit technical systems in various reliability structures, examining the optimum maintenance policies both analytically and practically, focusing on a delay-time modelling technique that has been employed by researchers in the field of maintenance engineering to model inspection intervals. It organizes the existing work into several fields, based mainly on the classification of single- and multi-unit models and assesses the applicability of the reviewed works and maintenance models. Lastly, it identifies potential future research directions and suggests research agendas. This book is a valuable resource for maintenance engineers, reliability specialists, and researchers, as it demonstrates the latest developments in maintenance, inspection and delay-time-based maintenance modelling issues. It is also of interest to graduate and senior undergraduate students, as it introduces current theory and practice in maintenance modelling issues, especially in the field of delay-time modelling.

Blockchain Technology: Platforms, Tools and Use Cases, Volume 111, the latest release in the Advances in Computers series published since 1960, presents detailed coverage of innovations in computer hardware, software, theory, design and applications. In addition, it provides contributors with a medium in which they can explore their subjects in greater depth and breadth than journal articles usually allow. This volume has 8 Chapters that discuss the various aspects of Blockchain technology.

The Generator Coordinate Method (GCM) is a mathematical tool for the understanding of stable atomic nuclei. Electronic, Atomic and Molecular Calculations is designed to assist scientists applying GCM in the analysis of the electronic structure of atoms and molecules. There have been numerous publications covering nuclear physics and electronic structure of atoms and molecules, but this book is unique in the sense that it specifically addresses the application of GCM for such purposes. Using this book, researchers will be able to understand and calculate the electronic structure in a novel manner.
* Only book that covers the Generator Coordinate Method and applications for atoms, molecules and nuclei
* Clearly describes how the GCM can be used as a powerful tool for design of atomic basis sets
* Reviews current literature on GCM in atomic and molecular fields and a large part of the literature of the method in nuclear physics

Reliability is one of the fundamental criteria in engineering systems. Design and maintenance serve to support it throughout the systems life. As such, maintenance acts in parallel to production and can have a great impact on the availability and capacity of production and the quality of the products. The authors describe current and innovative methods useful to industry and society.

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.

This volume gathers selected contributions from the participants of the Banff International Research Station (BIRS) workshop Coupled Mathematical Models for Physical and Biological Nanoscale Systems and their Applications, who explore various aspects of the analysis, modeling and applications of nanoscale systems, with a particular focus on low dimensional nanostructures and coupled mathematical models for their description. Due to the vastness, novelty and complexity of the interfaces between mathematical modeling and nanoscience and nanotechnology, many important areas in these disciplines remain largely unexplored. In their efforts to move forward, multidisciplinary research communities have come to a clear understanding that, along with experimental techniques, mathematical modeling and analysis have become crucial to the study, development and application of systems at the nanoscale. The conference, held at BIRS in autumn 2016, brought together experts from three different communities working in fields where coupled mathematical models for nanoscale and biosystems are especially relevant: mathematicians, physicists (both theorists and experimentalists), and computational scientists, including those dealing with biological nanostructures. Its objectives: summarize the state-of-the-art; identify and prioritize critical problems of major importance that require solutions; analyze existing methodologies; and explore promising approaches to addressing the challenges identified. The contributions offer up-to-date introductions to a range of topics in nano and biosystems, identify important challenges, assess current methodologies and explore promising approaches. As such, this book will benefit researchers in applied mathematics, as well as physicists and biologists interested in coupled mathematical models and their analysis for physical and biological nanoscale systems that concern applications in biotechnology and medicine, quantum information processing and optoelectronics.

This book aims to bring together researchers and practitioners working across domains and research disciplines to measure, model, and visualize complex networks. It collects the works presented at the 9th International Conference on Complex Networks (CompleNet) in Boston, MA, March, 2018. With roots in physical, information and social science, the study of complex networks provides a formal set of mathematical methods, computational tools and theories to describe, prescribe and predict dynamics and behaviors of complex systems. Despite their diversity, whether the systems are made up of physical, technological, informational, or social networks, they share many common organizing principles and thus can be studied with similar approaches. This book provides a view of the state-of-the-art in this dynamic field and covers topics such as group decision-making, brain and cellular connectivity, network controllability and resiliency, online activism, recommendation systems, and cyber security.

This is the third volume in a three-part series that uses art photography as a point of departure for learning about physics, while also using physics to ask fundamental questions about the nature of photography as an art.

In Pi ( ) in Nature, Art, and Culture Marcel Danesi revisits the importance of as a pattern in the structure of reality, fitting in with the Pythagorean view of Order. Pi has cropped up in formulas that describe natural and physical structures which, on the surface, seem to have nothing to do with a circle, but might harbor the archetype of circularity as a principle. Through , this book thus revisits the implicit ancient Greek view that geometry was a 'hermeneutic science,' a discipline aiming to investigate the connectivity among numbers, shapes, and natural phenomena. It also examines its manifestations in aesthetic, symbolic and cultural structures, which point to an abiding fascination with the circle as an unconscious archetype. Hermeneutic geometry is ultimately about the exploration of the meanings of geometric-mathematical notions to science and human life.

This book provides a comprehensive and systematic approach to the study of the qualitative theory of boundedness, periodicity, and stability of Volterra difference equations. The book bridges together the theoretical aspects of Volterra difference equations with its applications to population dynamics. Applications to real-world problems and open-ended problems are included throughout. This book will be of use as a primary reference to researchers and graduate students who are interested in the study of boundedness of solutions, the stability of the zero solution, or in the existence of periodic solutions using Lyapunov functionals and the notion of fixed point theory.

This monograph provides a concise overview of the main theoretical and numerical tools to solve homogenization problems in solids with finite elements. Starting from simple cases (linear thermal case) the problems are progressively complexified to finish with nonlinear problems. The book is not an overview of current research in that field, but a course book, and summarizes established knowledge in this area such that students or researchers who would like to start working on this subject will acquire the basics without any preliminary knowledge about homogenization. More specifically, the book is written with the objective of practical implementation of the methodologies in simple programs such as Matlab. The presentation is kept at a level where no deep mathematics are required.