This volume presents lectures given at the Wisla 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations, and are included here as lecture notes comprising the first three chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and mathematical physics. Specific topics covered include: Parabolic geometry Geometric methods for solving PDEs in physics, mathematical biology, and mathematical finance Darcy and Euler flows of real gases Differential invariants for fluid and gas flow Differential Geometry, Differential Equations, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry is assumed.

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 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.

This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.

This book discusses the impetus-based physics of the Jesuit natural philosopher and mathematician Honore Fabri (1608-1688), a senior representative of Jesuit scientists during the period between Galileo's death (1642) and Newton's Principia (1687). It shows how Fabri, while remaining loyal to a general Aristotelian outlook, managed to reinterpret the old concept of "impetus" in such a way as to assimilate into his physics building blocks of modern science, like Galileo's law of fall and Descartes' principle of inertia. This account of Fabri's theory is a novel one, since his physics is commonly considered as a dogmatic rejection of the New Science, not essentially different from the medieval impetus theory. This book shows how New Science principles were taught in Jesuit Colleges in the 1640s, thus depicting the sophisticated manner in which new ideas were settling within the lion's den of Catholic education.

This book describes the mathematical foundations, especially geometric, underlying the motions and force-transfers in robots. The principles developed can be applied to both control of robots and the design of their major moving parts. Containing many illustrative examples and over 300 exercises, it is ideal for graduate students, researchers and professionals in the field of robotics, robot design and development

Even though mathematics and physics have been related for centuries and this relation appears to be unproblematic, there are many questions still open: Is mathematics really necessary for physics, or could physics exist without mathematics? Should we think physically and then add the mathematics apt to formalise our physical intuition, or should we think mathematically and then interpret physically the obtained results? Do we get mathematical objects by abstraction from real objects, or vice versa? Why is mathematics effective into physics?

These are all relevant questions, whose answers are necessary to fully understand the status of physics, particularly of contemporary physics.

The aim of this book is to offer plausible answers to such questions through both historical analyses of relevant cases, and philosophical analyses of the relations between mathematics and physics.

This book examines the lives and contributions of American women physicists who were active in the years following World War II, during the middle decades of the 20th century. It covers the strategies they used to survive and thrive in a time where their gender was against them. The percentage of PhD's in physics has risen for 6% in 1983 to 20% in 2012 (an all-time high for women). By understanding the history of women in physics, these gains can continue. It discusses to major classes of women physicists; those who worked on military projects, and those who worked in industrial laboratories and at universities largely in the late 1940s and 1950s. While it includes minimal discussion of physics and physicists in the 1960s and later, this book focuses on the challenges and successes of women physicists in the years immediately following World War II and before the eras of affirmative actions and the use of the personal computer.

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.

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.

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.

The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in "small" domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schroedinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I, II, III and IV are applied to multiparticle quantum theory (asymptotics of the ground state energy and related problems), and to miscellaneous spectral problems.

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.

In this monograph we study the problem of construction of asymptotic solutions of equations for functions whose number of arguments tends to infinity as the small parameter tends to zero. Such equations arise in statistical physics and in quantum theory of a large number of fi elds. We consider the problem of renormalization of quantum field theory in the Hamiltonian formalism, which encounters additional difficulties related to the Stuckelberg divergences and the Haag theorem. Asymptotic methods for solving pseudodifferential equations with small parameter multiplying the derivatives, as well as the asymptotic methods developed in the present monograph for solving problems in statistical physics and quantum field theory, can be considered from a unified viewpoint if one introduces the notion of abstract canonical operator. The book can be of interest for researchers - specialists in asymptotic methods, statistical physics, and quantum fi eld theory as well as for graduate and undergraduate students of these specialities.

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.

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.

John Brockman brings together the world's best-known physicists and science writers--including Brian Greene, Walter Isaacson, Nobel Prize-winners Murray Gell-Mann and Frank Wilczek, and Brian Cox--to explain the universe in all wondrous splendor.

In Universe, today's most influential science writers explain the science behind our evolving understanding of the universe and everything in it, including the cutting edge research and discoveries that are shaping our knowledge.

Lee Smolin reveals how math and cosmology are helping us create a theory of the whole universe Brian Cox offers new dimensions on the Large Hadron and the existence of a Higgs-Boson particle Neil Turok analyzes the fundamental laws of nature, what came before the big bang, and the possibility of a unified theory.

Seth Lloyd investigates the impact of computational revolutions and the informational revolution Lawrence Krauss provides fresh insight into gravity, dark matter, and the energy of empty space Brian Greene and Walter Isaacson illuminate the genius who revolutionized modern science: Albert Einstein and much more.

Explore the Universe with some of today's greatest minds: what it is, how it came into being, and what may happen next.

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.

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).

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer's series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA's first funding phase, and provides an overview of SPPEXA's contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.

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 accessible and self-contained text presents the essential theoretical techniques developed to describe quantum processes, alongside a detailed review of the devices and experimental methods required in quantum measurement. Ideal for advanced undergraduate and graduate students seeking to extend their knowledge of the physics underlying quantum technologies, the book develops a thorough understanding of quantum measurement theory, quantum processes and the evolution of quantum states. A wide range of basic quantum systems are discussed, including atoms, ions, photons, and more complex macroscopic quantum devices such as opto-mechanical systems and superconducting circuits. Quantum phenomena are also covered in detail, from entanglement and quantum jumps, to quantum fluctuations in optical systems. Numerous problems at the end of each chapter problems enable the reader to consolidate key theoretical concepts and to develop their understanding of the most widely-used experimental techniques.