First published in 1868, soon after the death of Michael Faraday (1791 1867), this short work assesses the discoveries made by a humble bookbinder who became one of the foremost scientific investigators of the nineteenth century. Eminently qualified, John Tyndall (1820 93), who received Faraday's support in taking up the professorship of natural philosophy at the Royal Institution in 1853, gives an informed appraisal of a remarkable scientific career. The protege of Sir Humphry Davy, Faraday went on to carry out pioneering work in the fields of electromagnetism, diamagnetism and electrolysis. Tyndall focuses here on Faraday's research, describing his influences and how he approached his investigations, although insights into his character are also incorporated: 'Underneath his sweetness and gentleness was the heat of a volcano.' Also reissued in this series are The Life and Letters of Faraday (1870), compiled by Henry Bence Jones, and John Hall Gladstone's Michael Faraday (1872)."

Mathematical Physics in Theoretical Chemistry deals with important topics in theoretical and computational chemistry. Topics covered include density functional theory, computational methods in biological chemistry, and Hartree-Fock methods. As the second volume in the Developments in Physical & Theoretical Chemistry series, this volume further highlights the major advances and developments in research, also serving as a basis for advanced study. With a multidisciplinary and encompassing structure guided by a highly experienced editor, the series is designed to enable researchers in both academia and industry stay abreast of developments in physical and theoretical chemistry.

This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.

This book is the second of a two volume series. Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book features fully-refereed, high-quality papers exploring new results and trends in weighted norm inequalities, Schur-Agler class functions, complex analysis, dynamical systems, and dyadic harmonic analysis. Graduate students and researchers in analysis will find inspiration in the articles collected in this volume, which emphasize the remarkable connections between harmonic analysis and operator theory. A survey of the two weight problem for the Hilbert transform and an expository article on the Clark model to the case of non-singular measures and applications to the study of rank-one perturbations are included. The material for this volume is based on the 13th New Mexico Analysis Seminar held at the University of New Mexico, April 3-4, 2014 and on several special sections of the Western Spring Sectional Meeting at the University of New Mexico, April 4-6,2014. During the event, participants honored the memory of Cora Sadosky-a great mathematician who recently passed away and who made significant contributions to the field of harmonic analysis. Cora was an exceptional scientist and human being. She was a world expert in harmonic analysis and operator theory, publishing over fifty-five research papers and authoring a major textbook in the field. Participants of the conference include new and senior researchers, recent doctorates as well as leading experts in the area.

This monograph presents a new model of mathematical structures called weak n-categories. These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic. While strict n-categories are easily defined in terms associative and unital composition operations they are of limited use in applications, which often call for weakened variants of these laws. The author proposes a new approach to this weakening, whose generality arises not from a weakening of such laws but from the very geometric structure of its cells; a geometry dubbed weak globularity. The new model, called weakly globular n-fold categories, is one of the simplest known algebraic structures yielding a model of weak n-categories. The central result is the equivalence of this model to one of the existing models, due to Tamsamani and further studied by Simpson. This theory has intended applications to homotopy theory, mathematical physics and to long-standing open questions in category theory. As the theory is described in elementary terms and the book is largely self-contained, it is accessible to beginning graduate students and to mathematicians from a wide range of disciplines well beyond higher category theory. The new model makes a transparent connection between higher category theory and homotopy theory, rendering it particularly suitable for category theorists and algebraic topologists. Although the results are complex, readers are guided with an intuitive explanation before each concept is introduced, and with diagrams showing the interconnections between the main ideas and results.

This textbook provides everything you need to get through a basic physics course. It guides students through all the essentials with a concise review of the concept, simple illustrations to demonstrate it, worked problems to showcase how to apply it, and a short quiz for self-testing. Whereas other standard books can be overwhelming to students, the author shares what has worked with his own students, trimming back unnecessary detail and focusing on the core basic physical concepts required to gain solid footing. The full range of topics are addressed in a manner that facilitates understanding and will encourage students to continue forward with their learning.

This book presents a unified study of dynamically coupled systems involving a rigid body and an ideal fluid flow from the perspective of Lagrangian and Hamiltonian mechanics. It compiles theoretical investigations on the topic of dynamically coupled systems using a framework grounded in Kirchhoff's equations. The text achieves a balance between geometric mechanics, or the modern theories of reduction of Lagrangian and Hamiltonian systems, and classical fluid mechanics, with a special focus on the applications of these principles. Following an introduction to Kirchhoff's equations of motion, the book discusses several extensions of Kirchhoff's work, particularly related to vortices. It addresses the equations of motions of these systems and their Lagrangian and Hamiltonian formulations. The book is suitable to mathematicians, physicists and engineers with a background in Lagrangian and Hamiltonian mechanics and theoretical fluid mechanics. It includes a brief introductory overview of geometric mechanics in the appendix.

Quantum theory is one of the most important and successful theories of modern physical science. It has been estimated that its principles form the basis for about 30 per cent of the world's manufacturing economy. This is all the more remarkable because quantum theory is a theory that nobody understands. Baggott brings the reader up to date with the results of experimental tests of quantum non-locality and complementarity that have been successfully carried out. He also reviews the latest thinking on alternative interpretations - pilot waves, decoherence, consciousness, many worlds and God - and the frontiers of quantum cosmology, quantum gravity and potential applications of quantum entanglement in computing, cryptography and teleportation. Quantum theory emerges largely unscathed, only serving to reinforce the point that the theory remains the most powerful framework for explaining observations of the quantum world, but that its orthodox interpretation continues to offer little in the way of understanding in terms of underlying physical processes. Quantum theory remains a mysterious theoretical black top hat from which white rabbits continue to be pulled. Students are usually advised not to ask how this particular conjuring trick is done.

This book offers a comprehensive and timely report of size-dependent continuum mechanics approaches. Written by scientists with worldwide reputation and established expertise, it covers the most recent findings, advanced theoretical developments and computational techniques, as well as a range of applications, in the field of nonlocal continuum mechanics. Chapters are concerned with lattice-based nonlocal models, Eringen's nonlocal models, gradient theories of elasticity, strain- and stress-driven nonlocal models, and peridynamic theory, among other topics. This book provides researchers and practitioners with extensive and specialized information on cutting-edge theories and methods, innovative solutions to current problems and a timely insight into the behavior of some advanced materials and structures. It also offers a useful reference guide to senior undergraduate and graduate students in mechanical engineering, materials science, and applied physics.

What is econophysics? What makes an econophysicist? Why are financial economists reluctant to use results from econophysics? Can we overcome disputes concerning hypotheses used in financial economics and that make no sense for econophysicists? How can we create a profitable dialogue between financial economists and econophysicists? How do we develop a common theoretical framework allowing the creation of more efficient models for the financial industry? This book moves beyond the disciplinary frontiers in order to initiate the development of a common theoretical framework that makes sense for both traditionally trained financial economists and econophysicists. Unlike other publications dedicated to econophysics, this book is written by two financial economists and it situates econophysics in the evolution of financial economics. The major issues that concern the collaboration between the two fields are analyzed in detail. More specifically, this book explains the theoretical and methodological foundations of these two fields in an accessible vocabulary providing the first extensive analytic comparison between models and results from both fields. The book also identifies the major conceptual gate-keepers that complicate dialogue between the two communities while it provides elements to overcome them. By mixing conceptual, historical, theoretical and formal arguments our analysis bridges the current deaf dialogue between financial economists and econophysicists. This book details the recent results in econophysics that bring it closer to financial economics. So doing, it identifies what remains to be done for econophysicists to contribute significantly to financial economics. Beyond the clarification of the current situation, this book also proposes a generic model compatible with the two fields, defining minimal conditions for common models. Finally, this book provides a research agenda for a more fruitful collaboration between econophysicists and financial economists, creating new research opportunities. In this perspective, it lays the foundations for common theoretical framework and models.

This book revitalizes the relevance of the ideas of Henri Bergson (1859-1941) for current developments in exact sciences. It explores the relevance of Bergson's thought for contemporary philosophical reflections on three of the most important scientific research areas of today, namely physics, the life sciences and the neurosciences. It does so on the basis of the three interrelated topics of time, life and memory. Henri Bergson (1859-1941) was one of the most widely read philosophers of his era. The European public was seeking for answers to questions of the soul and the nature of life and fitting within a historical niche between intellectual rationalism and intuitive spiritualism, his writings drew much attention. This work focuses on the relevance of his philosophy for developments in exact sciences today. The discussion of physics in relation to the abstract and the concrete, the life sciences in relation to concepts of life in relation to new and emerging biotechnology, and the neurosciences in relation to the dual nature of human identity, focuses on one main topic: time. Time, isolated from experience, as the measure of the events in the universe in modern physics; time as the measure of emergent systems in evolution as the backdrop of the theory of evolution in biology; time in relation to memory and imagination in neuropsychological accounts of memory. The author thus discusses the ideas of Henri Bergson as a basis to unveil time as a living process, rather than as an instrument for the measure of events. This view forms the basis of a novel approach to the philosophy of technology. An exciting book for academics interested in the interplay between hard sciences and philosophy.

The book includes both invited and contributed chapters dealing with advanced methods and theoretical development for the analysis of social networks and applications in numerous disciplines. Some authors explore new trends related to network measures, multilevel networks and clustering on networks, while other contributions deepen the relationship among statistical methods for data mining and social network analysis. Along with the new methodological developments, the book offers interesting applications to a wide set of fields, ranging from the organizational and economic studies, collaboration and innovation, to the less usual field of poetry. In addition, the case studies are related to local context, showing how the substantive reasoning is fundamental in social network analysis. The list of authors includes both top scholars in the field of social networks and promising young researchers. All chapters passed a double blind review process followed by the guest editors. This edited volume will appeal to students, researchers and professionals.

This book presents a thoroughly empiricist account of physics. By providing an overview of the development of empiricism from Ockham to van Fraassen the book lays the foundation for its own version of empiricism. Empiricism for the author consists of three ideas: nominalism, i.e. dismissing second order quantification as unnecessary, epistemological naturalism, and viewing classification of things in natural kinds as a human habit not in need for any justification. The book offers views on the realism-antirealism debate as well as on the individuation of theories as a thoroughly neglected aspect of underdetermination. The book next discusses a broad range of topics, including the predicates body, spatial distance and time interval, the ontology of electromagnetism, propensities, the measurement problem and other philosophical issues in quantum theory. Discussions about the direction of time and about string theory make up the final part of the book.

The book is written for advanced graduate students. The topics have been selected to present methods and models that have applications in both particle physics and polymer physics. The lectures may serve as a guide through more recent research activities and illustrate the applicability of joint methods in different contexts. The book deals with analytic tools (e.g. random walk models, polymer expansion), numerical tools (e.g. Langevin dynamics), and common models (the three-dimensional Gross-Neveu-Model).

Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This new edition of Applied PDEs contains many new sections and exercises Including, American options, transform methods, free surface flows, linear elasticity and complex characteristics.

Nonlinearity and Chaos in Molecular Vibrations deals systematically with a Lie algebraic approach to the study of nonlinear properties of molecular highly excited vibrations. The fundamental concepts of nonlinear dynamics such as chaos, fractals, quasiperiodicity, resonance, and the Lyapunov exponent, and their roles in the study of molecular vibrations are presented.
The 20 chapters cover the basic ideas, the concept of dynamical groups, the integrable two-mode SU(2) system, the unintegrable three-mode SU(3) system, the noncompact su(1,1) algebraic application, su(3) symmetry breaking and its application and the quantal effect of asymmetric molecular rotation. Emphasis is given to: resonance and chaos, the fractal structure of eigencoefficients, the C-H bend motion of acetylene, regular and chaotic motion of DCN, the existence of approximately conserved quantum numbers, one-electronic motion in multi-sites, the Lyapunov exponent, actions of periodic trajectories and quantization, the H function and its application in vibrational relaxation as well as the Dixon dip and its destruction and chaos in the transitional states. This approach bridges the gap between molecular vibrational spectroscopy and nonlinear dynamics.
The book presents a framework of information that readers can use to build their knowledge, and is therefore highly recommended for all those working in or studying molecular physics, molecular spectroscopy, chemical physics and theoretical physics.
* Discusses nonlinearity and chaotic phenomena in molecular vibrations
* Approaches the complicated highly excited molecular vibration
* Provides clear information for students and researchers looking to expand knowledge in this field

"Multi-finger Haptic Interaction "presents a panorama of technologies and methods for multi-finger haptic interaction, together with an analysis of the benefits and implications of adding multiple-fingers to haptic applications.

Research topics covered include: design and control of advanced haptic devices;multi-contact point simulation algorithms;interaction techniques and implications in human perception when interacting with multiple fingers.

These multi-disciplinary results are integrated into applications such as medical simulators for training manual skills, simulators for virtual prototyping and precise manipulations in remote environments.

"Multi-finger Haptic Interaction "presents the current and potential applications that can be developed with these systems, and details the systems' complexity. The research is focused on enhancing haptic interaction by providing multiple contact points to the user.

This state-of-the-art volume is oriented towards researchers who are involved in haptic device design, rendering methods and perception studies, as well as readers from different disciplines who are interested in applying multi-finger haptic technologies and methods to their field of interest.

This state of the art book takes an applications based approach to teaching mathematics to engineering and applied sciences students. The book lays emphasis on associating mathematical concepts with their physical counterparts, training students of engineering in mathematics to help them learn how things work. The book covers the concepts of number systems, algebra equations and calculus through discussions on mathematics and physics, discussing their intertwined history in a chronological order. The book includes examples, homework problems, and exercises. This book can be used to teach a first course in engineering mathematics or as a refresher on basic mathematical physics. Besides serving as core textbook, this book will also appeal to undergraduate students with cross-disciplinary interests as a supplementary text or reader.

This book is both an introduction and a demonstration of how Visual Basic for Applications (VBA) can greatly enhance Microsoft Excel (R) by giving users the ability to create their own functions within a worksheet and to create subroutines to perform repetitive actions. The book is written so readers are encouraged to experiment with VBA programming with examples using fairly simple physics or non-complicated mathematics such as root finding and numerical integration. Tested Excel (R) workbooks are available for each chapter and there is nothing to buy or install.

Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peer-reviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, super-symmetry and super-integrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods. The SDEA III, held in honour of the Centenary of Noether's Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups. This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance.

This book reconceptualizes the ancient philosophy of 'dualism' and a 'trinity' applied to classical and quantum nonequilibrium phenomena. In addition to classical mechanics and electrodynamics, a remarkable connection of this philosophy with quantum mechanics is established, which can be useful for quantum computing and the development of quantum artificial intelligence. Packed with the recent theoretical models, quantum simulations of black holes, and experimental observations of quantum phase transitions, this book brings a holistic approach that can be useful to refine the concept of the 'Creation', i.e., the evolution of the Universe from the condensed state of matter, and explain the artificial vision. The approch is:

Unique: Connects ancient philosophy, classical and quantum mechanics, materials, and the latest quantum technologies

Novelty: High level of scientific interpretation of ancient philosophy, creation, interactions, and disorder

Multidisciplinary: Guides students to learn quantum simulations and develop philosophical ideas

The book contains over ten years of in-depth research by the author on the ancient eastern (Indian) philosophy and the latest scientific research in condensed matter and quantum technology. This book will simplify the picture of ancient eastern philosophy, which can be read by the general audience, particularly undergraduate/postgraduate students interested in quantum information science without any mathematical treatment. However, some parts of the book will be ideal for senior academicians and professional researchers in both worlds.

Table of Contents

Preamble: Philosophy through careful observation and self-realization—the birth of cycles. 1. Creation? A cosmic model: Birth of Matter and Mind: Two Cycles 2. Background/history—Understanding creation: Gods and Goddesses. 3. Life Begins on Earth—Creation of the Devices, Deities, and the Concept of God: Creation of Cycles 4. Theory of evolution—(Sankhya) Philosophy of dualism: Creation of a Cycle 5. Interactions at the Macroscale—Classical mechanics—Equilibrium and Rotation: One Cycle 6. Energy/Light and Space (Matter) Application in Condensed Matter Physics: Two Cycles 7.Condensed matter physics—Creation of particles—Bosonic vs. fermionic: One and a half cycle 8: Creation through interactions at the microscale—Quantum mechanics 9. Space–Time Distortion: Black holes, Condensates, and quantum devices 10. Quantum Simulation, Artificial Intelligence, and Vision . Conclusion References.

The book is devoted to several topical questions in modern mathematical and theoretical physics, astrophysics, geophysics, and cosmology that remain unsolved within the framework of the standard approaches. To them, one can attribute unexplained properties of the magnetic fields of stars and planets, puzzles of the Earth's atmosphere, the phenomenon of ball lightning, the problem of a qualitative description for nuclear forces and their well-known property of saturation, enigmatic properties of spiral galaxies, the problem of the cosmological singularity, mysteries of the dark matter and dark energy, amongst others. To find theoretical ways for understanding such phenomena, new nonlinear generalizations of the classical field theories and advanced methods to solve nonlinear equations arising in them are studied and presented in this book.

This monograph deals with theoretical aspects and numerical simulations of the interaction of electromagnetic fields with nonlinear materials. It focuses in particular on media with nonlinear polarization properties. It addresses the direct problem of nonlinear Electrodynamics, that is to understand the nonlinear behavior in the induced polarization and to analyze or even to control its impact on the propagation of electromagnetic fields in the matter. The book gives a comprehensive presentation of the results obtained by the authors during the last decade and put those findings in a broader, unified context and extends them in several directions.It is divided into eight chapters and three appendices. Chapter 1 starts from the Maxwell's equations and develops a wave propagation theory in plate-like media with nonlinear polarizability. In chapter 2 a theoretical framework in terms of weak solutions is given in order to prove the existence and uniqueness of a solution of the semilinear boundary-value problem derived in the first chapter. Chapter 3 presents a different approach to the solvability theory of the reduced frequency-domain model. Here the boundary-value problem is reduced to finding solutions of a system of one-dimensional nonlinear Hammerstein integral equations. Chapter 4 describes an approach to the spectral analysis of the linearized system of integral equations. Chapters 5 and 6 are devoted to the numerical approximation of the solutions of the corresponding mathematical models. Chapter 7 contains detailed descriptions, discussions and evaluations of the numerical experiments. Finally, chapter 8 gives a summary of the results and an outlook for future work.

The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ... etc. This problem has been studied by many communities of researchers, mostly combinatorists, probabilists, and physicists. Since 1978, physicists have invented a method called "matrix models" to address that problem, and many results have been obtained. Besides, another important problem in mathematics and physics (in particular string theory), is to count Riemann surfaces. Riemann surfaces of a given topology are parametrized by a finite number of real parameters (called moduli), and the moduli space is a finite dimensional compact manifold or orbifold of complicated topology. The number of Riemann surfaces is the volume of that moduli space. Mor e generally, an important problem in algebraic geometry is to characterize the moduli spaces, by computing not only their volumes, but also other characteristic numbers called intersection numbers. Witten's conjecture (which was first proved by Kontsevich), was the assertion that Riemann surfaces can be obtained as limits of polygonal surfaces (maps), made of a very large number of very small polygons. In other words, the number of maps in a certain limit, should give the intersection numbers of moduli spaces. In this book, we show how that limit takes place. The goal of this book is to explain the "matrix model" method, to show the main results obtained with it, and to compare it with methods used in combinatorics (bijective proofs, Tutte's equations), or algebraic geometry (Mirzakhani's recursions). The book intends to be self-contained and accessible to graduate students, and provides comprehensive proofs, several examples, and give s the general formula for the enumeration of maps on surfaces of any topology. In the end, the link with more general topics such as algebraic geometry, string theory, is discussed, and in particular a proof of the Witten-Kontsevich conjecture is provided.

This volume contains the best papers presented at the 2nd ECCOMAS International Conference on Multiscale Computations for Solids and Fluids, held June 10-12, 2015. Topics dealt with include multiscale strategy for efficient development of scientific software for large-scale computations, coupled probability-nonlinear-mechanics problems and solution methods, and modern mathematical and computational setting for multi-phase flows and fluid-structure interaction. The papers consist of contributions by six experts who taught short courses prior to the conference, along with several selected articles from other participants dealing with complementary issues, covering both solid mechanics and applied mathematics.