The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers- The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics. The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular. Prof. Vladimir V. UCHAIKIN is a known Russian scientist and pedagogue, a Honored Worker of Russian High School, a member of the Russian Academy of Natural Sciences. He is the author of about three hundreds articles and more than a dozen books (mostly in Russian) in Cosmic ray physics, Mathematical physics, Levy stable statistics, Monte Carlo methods with applications to anomalous processes in complex systems of various levels: from quantum dots to the Milky Way galaxy.

Based on a two-semester course aimed at illustrating various interactions of "pure mathematics" with other sciences, such as hydrodynamics, thermodynamics, statistical physics and information theory, this text unifies three general topics of analysis and physics, which are as follows: the dimensional analysis of physical quantities, which contains various applications including Kolmogorov's model for turbulence; functions of very large number of variables and the principle of concentration along with the non-linear law of large numbers, the geometric meaning of the Gauss and Maxwell distributions, and the Kotelnikov-Shannon theorem; and, finally, classical thermodynamics and contact geometry, which covers two main principles of thermodynamics in the language of differential forms, contact distributions, the Frobenius theorem and the Carnot-Caratheodory metric. It includes problems, historical remarks, and Zorich's popular article, "Mathematics as language and method."

The only textbook that completely covers the OxfordAQA International AS & A Level Physics specification (9630), for first teaching in September 2016. Written by experienced authors, the engaging, international approach ensures a thorough understanding of complex concepts and provides exam-focused practice to build assessment confidence. Help students develop the scientific, mathematical and practical skills and knowledge needed for Oxford AQA assessment success and the step up to university. Ensure students understand the bigger picture, supporting their progression to further study, with synoptic links and a focus on how scientists and engineers apply their knowledge in real life. This pack includes one print textbook and one online textbook. The online textbook can be accessed on a wide range of devices and the licence is valid until 31st December 2026, for use by one student or teacher. Your first login will be sent to you in the mail on a printed access card.

Perhaps the most distinct question in science throughout the ages has been the one of perceivable "reality," treated both in physics and philosophy.Reality is acting upon us, and we, and life in general, are acting upon reality. "Potentiality," found both in quantum reality and in the activity of life, plays a key role. In quantum reality observation turns potentiality into reality. Again, life computes possibilities in various ways based on past actions, and acts on the basis of these computations.

This book is about a new approach to biology (and physics, of course ). Its subtitle suggests a perpetual movement and interplay between two elusive aspects of modern science reality/matter and potentiality/mind, between physics and biology both captured and triggered by mathematics to understand and explain emergence, development and life all the way up to consciousness.

But what is the real/potential difference between living and non-living matter? How does time in potentiality differ from time in reality? What we need to understand these differences is an integrative approach. This book contemplates how to encircle life to obtain a formal system, equivalent to the ones in physics. "Integral Biomathics" attempts to explore the interplay between reality and potentiality.

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Philosophy of the Text This text presents an introductory survey of the basic concepts and applied mathematical methods of nonlinear science as well as an introduction to some simple related nonlinear experimental activities. Students in engineering, phys ics, chemistry, mathematics, computing science, and biology should be able to successfully use this book. In an effort to provide the reader with a cutting edge approach to one of the most dynamic, often subtle, complex, and still rapidly evolving, areas of modern research-nonlinear physics-we have made extensive use of the symbolic, numeric, and plotting capabilities of the Maple software sys tem applied to examples from these disciplines. No prior knowledge of Maple or computer programming is assumed, the reader being gently introduced to Maple as an auxiliary tool as the concepts of nonlinear science are developed. The CD-ROM provided with this book gives a wide variety of illustrative non linear examples solved with Maple. In addition, numerous annotated examples are sprinkled throughout the text and also placed on the CD. An accompanying set of experimental activities keyed to the theory developed in Part I of the book is given in Part II. These activities allow the student the option of "hands on" experience in exploring nonlinear phenomena in the REAL world. Although the experiments are easy to perform, they give rise to experimental and theoretical complexities which are not to be underestimated."

The subject of this book is the hierarchies of integrable equations connected with the one-component and multi component loop groups. There are many publications on this subject, and it is rather well defined. Thus, the author would like t.o explain why he has taken the risk of revisiting the subject. The Sato Grassmannian approach, and other approaches standard in this context, reveal deep mathematical structures in the base of the integrable hi erarchies. These approaches concentrate mostly on the algebraic picture, and they use a language suitable for applications to quantum field theory. Another well-known approach, the a-dressing method, developed by S. V. Manakov and V.E. Zakharov, is oriented mostly to particular systems and ex act classes of their solutions. There is more emphasis on analytic properties, and the technique is connected with standard complex analysis. The language of the a-dressing method is suitable for applications to integrable nonlinear PDEs, integrable nonlinear discrete equations, and, as recently discovered, for t.he applications of integrable systems to continuous and discret.e geometry. The primary motivation of the author was to formalize the approach to int.e grable hierarchies that was developed in the context of the a-dressing method, preserving the analytic struetures characteristic for this method, but omitting the peculiarit.ies of the construetive scheme. And it was desirable to find a start."

The only textbook that completely covers the OxfordAQA International AS & A Level Physics specification (9630), for first teaching in September 2016. Written by experienced authors, the engaging, international approach ensures a thorough understanding of complex concepts and provides exam-focused practice to build assessment confidence. Help students develop the scientific, mathematical and practical skills and knowledge needed for Oxford AQA assessment success and the step up to university. Ensure students understand the bigger picture, supporting their progression to further study, with synoptic links and a focus on how scientists and engineers apply their knowledge in real life. The online textbook can be accessed on a wide range of devices and the licence is valid until 31st December 2026, for use by one student or teacher. Your first login will be sent to you in the mail on a printed access card.

Without listing his works, all of which are highly notable both for the originality of the methods utilized as well as for the importance of the results achieved, we limit ourselves to the following: Inmodernnucleartheories, thecontributionmadebythisresearcher to the introduction of the forces called 'Majorana forces' is universally recognized as the one, among the most fundamental, that permits us to theoretically comprehend the reasons for nuclear stability. The work of Majorana today serves as a basis for the most important research in this ?eld. In atomic physics, the merit of having resolved some of the most - tricate questions on the structure of spectra through simple and elegant considerations of symmetry is due to Majorana. Lastly, he devised a brilliant method that permits us to treat the positive and negative electron in a symmetrical way, ?nally elimin- ing the necessity to rely on the extremely arti?cial and unsatisfactory hypothesis of an in?nitely large electrical charge di?used in space, a question that had been tackled in vain by many other scholars [4].

These proceedings of the international Conference "Ill-Posed and Non-Classical Problems of Mathematical Physics and Analysis," held at the Samarkand State University, Uzbekistan in September 2000 bring together fundamental research articles in the major areas of the numerated fields of analysis and mathematical physics. The book covers the following topics: theory of ill-posed problems inverse problems for differential equations boundary value problems for equations of mixed type integral geometry mathematical modelling and numerical methods in natural sciences

COMSOL 5 and MATLAB are valuable software modeling tools for engineers and scientists. This updated edition includes five new models and explores a wide range of models in coordinate systems from 0D to 3D, introducing the numerical analysis techniques employed in COMSOL 5.6 and MATLAB software. The text presents electromagnetic, electronic,optical, thermal physics, and biomedical models as examples. It presents the fundamental concepts in the models and the step-by-step instructions needed to build each model. The companion files include all the built models for each step-by-step example presented in the text and the related animations, as specified. The book is designed to introduce modeling to an experienced engineer or can also be used for upper level undergraduate or graduate courses. FEATURES: Focuses on COMSOL 5.x and MATLAB models that demonstrate the use of concepts for later application in engineering, science, medicine, and biophysics for the development of devices and systems Includes companion files with executable copies of each model and related animations Includes detailed discussions of possible modeling errors and results Uses a step-by-step modeling methodology linked to the Fundamental Laws of Physics.

Exam Board: Salters Horner Level: A level Subject: Science / Physics First teaching: September 2015 First exams: June 2017 An ActiveBook is included with every Student Book, giving your students easy online access to the content in the Student Book. They can make it their own with notes, highlights and links to their wider reading. Perfect for supporting revision activities. Student Book 1 supports a standalone AS course and provides the first year of a two-year A level course; Student Books 1and 2 together support the full A level course. A cumulative approach to learning constantly builds on what has previously been learnt. Each topic is introduced within a wider context. Concepts are revisited and developed in later chapters. Link the Learning sections require students to use knowledge from throughout the chapter and apply it to new contexts. Practical skills section provides guidance on practical work within an investigative framework. End of chapter questions provide opportunities for students to check understanding and apply what they have learnt in a variety of contexts. Maths notes section provides guidance on key maths skills that students can refer to throughout the course. Achievements list the specification points covered in each chapter and show where each is addressed.

This book explains how standard micro-founded macroeconomics is misguided and proposes an alternative method based on statistical physics. The Great Recession following the bankruptcy of Lehman Brothers in September 2015 amply demonstrated that mainstream micro-founded macroeconomics was in trouble. The new approach advanced in this book reasonably explains important macro-problems such as employment, business cycles, growth, and inflation/deflation. The key concept is demand failures, which modern micro-founded macroeconomics has ignored. "It (Chapter 3) captures analytically a good part of the intuition that underlies the Keynesian economics of people like Tobin and me." Robert Solow, Emeritus Institute Professor of Economics, Massachusetts Institute of Technology, Nobel Laureate in Economics, 1987 "Professor Hiroshi Yoshikawa provides a unique synthesis of statistical physics and macro-economic theory in order to confront the dismal failure in economics and in finance to understand how an economy or a financial market works, given the heterogeneous decision making of many different individual interacting actors. Economics has failed in this regard with the naive and often misleading concept of "representative agents." The author presents many insights on the historical development, concepts, and errors made by the most illustrious economists in the past. This book should be essential readings for any economics students as well as academic researchers and policy makers, who should learn to bring back good-sense thinking in their impactful decisions." Didier Sornette, Professor on the Chair of Entrepreneurial Risks at the Swiss Federal Institute of Technology Zurich (ETH Zurich)

Nonlinear science is by now a well established field of research at the interface of many traditional disciplines and draws on the theoretical concepts developed in physics and mathematics. The present volume gathers the contributions of leading scientists to give the state of the art in many areas strongly influenced by nonlinear research, such as superconduction, optics, lattice dynamics, biology and biomolecular dynamics. While this volume is primarily intended for researchers working in the field care, has been taken that it will also be of benefit to graduate students or nonexpert scientist wishing to familiarize themselves with the current status of research.

To protect the Earth, China has launched its target of peaking carbon dioxide emissions by 2030, and achieving carbon neutrality by 2060 , which greatly encourages the use and development of renewable energy. Supercritical CO2 power cycle is a promising technology and the radial inflow turbine is the most important component of it, whose design and optimisation are considered as great challenges. This book introduces simulation tools and methods for supercritical CO2 radial inflow turbine, including a high fidelity quasi-one-dimensional design procedure, a non-ideal compressible fluid dynamics Riemann solver within open-source CFD software OpenFOAM framework, and a multi-objective Nelder-Mead geometry optimiser. Enhanced one-dimensional loss models are presented for providing a new insight towards the preliminary design of the supercritical CO2 radial inflow turbine. Since the flow phenomena within the blade channels are complex, involving fluid flow, shock wave transmission and boundary layer separation, only employing the ideal gas model is inadequate to predict the performance of the turbine. Thus, a non-ideal compressible fluid dynamics Riemann solver based on OpenFOAM library is developed. This book addresses the issues related to the turbine design and blade optimization and provides leading techniques. Hence, this book is of great value for the readers working on the supercritical CO2 radial inflow turbine and understanding the knowledge of CFD and turbomachinery.

This volume contains a collection of review articles that are extended versions of invited lectures given at the First Pamporovo Winter Workshop on Cooperative Phe nomena in Condensed Matter held in villa "Orlitza" (7th-15th March 1998, Pamporovo Ski Resort, Bulgaria). Selected research works reported at the Workshop have been published in the Journal of Physical Studies - a new International Journal for research papers in experimental and theoretical physics (Lviv University, Lviv, Ukraine). These reviews are supposed to be status reports and present new insights gained from the rapidly developing research of outstanding problems in condensed matter physics such as structural properties and phase transitions in fullerene crystals, super conductivity ofstrongly interacting electrons in copper oxides, spin polarized Fermi liq uids, chaotic vortex filaments in superfluid turbulent Helium-II, desorption induced by electronic transitions in ionic compounds, fluctuation phenomena in superconductors, and quantum critical phenomena in low dimensional magnets and quantum liquids. We have set the material according to the alphabetic order of authors' names although the high temperature superconductivity seems to be the hard kernel in condensed matter physics. The authors have taken care to present the recent advances in their research in a form which is readable and useful not only to experts in the respective field, but also to young scientists. That is why the lectures include a comprehensive introduction to the matter and also an extended discussion of methodical details."

The Scaled Boundary Finite Element Method describes a fundamental solution-less boundary element method, based on finite elements. As such, it combines the advantages of the boundary element method:

• spatial discretisation reduced by one
  
• boundary condition at infinity satisfied exactly

• no fundamental solution required
  
• no singular integrals
  
• the processing of anisotropic material without any additional computational effort

The scaled boundary finite element method can be used to analyse any bounded and unbounded media governed by linear elliptic, parabolic and hyperbolic partial differential equations.

The book serves two goals which can be pursued independently. Part I is a primer, with a model problem addressing the simplest wave propagation but still containing all essential features. Part II derives the fundamental equations for statics, elastodynamics and diffusion, and discusses the solution procedures from scratch in great detail.

In summary this comprehensive text presents a novel procedure which will be of interest not only to engineers, researchers and students working in engineering mechanics, acoustics, heat-transfer, earthquake engineering, electromagnetism, and computational mathematics, but also consulting engineers dealing with nuclear structures, offshore platforms, hardened structures, critical facilities, dams, machine foundations and other structures subjected to earthquakes, wave loads, explosions and traffic.

Learn about Einstein's theory of relativity from a physics Nobel laureate and "one of the greatest minds of the twentieth century" (New York Review of Books) in six memorable lessons It was Richard Feynman's outrageous and scintillating method of teaching that earned him legendary status among students and professors of physics. From 1961 to 1963, Feynman delivered a series of lectures at the California Institute of Technology that revolutionized the teaching of physics. In Six Not-So-Easy Pieces, taken from these famous Lectures on Physics, Feynman delves into one of the most revolutionary discoveries in twentieth-century physics: Einstein's theory of relativity. The idea that the flow of time is not a constant, that the mass of an object depends on its velocity, and that the speed of light is a constant no matter what the motion of the observer, at first seemed shocking to scientists and laymen alike. But as Feynman shows, these tricky ideas are not merely dry principles of physics, but things of beauty and elegance. No one - not even Einstein himself - explained these difficult, anti-intuitive concepts more clearly, or with more verve and gusto, than Feynman. Filled with wonderful examples and clever illustrations, Six Not-So-Easy Pieces is the ideal introduction to the fundamentals of physics by one of the most admired and accessible physicists of all time. "There is no better explanation for the scientifically literate layman." -Washington Post Book World

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich's book is a must.'' The second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kahler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics.

The ASI Quarks, Leptons and Beyond, held in Munich from the 5th to the 16th of September 1983 was dedicated to the study of what we now believe are the fundamental building blocks of nature: quarks and leptons. The subject was approached on two levels. On the one hand, a thorough discussion was given of the status of our knowledge of quarks and leptons and their interactions, both from an experi mental and a theoretical standpoint. On the other hand, open problems presented by the so called standard model of quark and lepton interact ions were explored along various ways that lead one beyond this frame work. One of the principal predictions of the standard model is that weak interactions are mediated by heavy Wand Z vector bosons. These particles were discovered in 1983 at CERN and their relevant proper ties were discussed at the ASI by C. Rubbia. Further theoretical predictions concerning these Z and W bosons, yet to be checked by future experimentation, were discussed by G. Altarelli with a view of seeing where the standard model might fail and new physics ensue. The strong interactions of quarks, based on Quantum Chromodynamics (QeD), are presumed to cause the quarks to bind into hadrons. Pro gress in attempts to calculate the observed hadronic spectrum, ab initio, starting from QCD and employing lattice methods were reviewed at the ASI by P. Hasenfratz."

Provides a new and more realistic framework for describing the dynamics of non-linear systems. A number of issues arising in applied dynamical systems from the viewpoint of problems of phase space transport are raised in this monograph. Illustrating phase space transport problems arising in a variety of applications that can be modeled as time-periodic perturbations of planar Hamiltonian systems, the book begins with the study of transport in the associated two-dimensional Poincare Map. This serves as a starting point for the further motivation of the transport issues through the development of ideas in a non-perturbative framework with generalizations to higher dimensions as well as more general time dependence. A timely and important contribution to those concerned with the applications of mathematics.

Spaces of homogeneous type were introduced as a generalization to the Euclidean space and serve as a suffi cient setting in which one can generalize the classical isotropic Harmonic analysis and function space theory. This setting is sometimes too general, and the theory is limited. Here, we present a set of fl exible ellipsoid covers of n that replace the Euclidean balls and support a generalization of the theory with fewer limitations.

Fundamentals of Physics, 12th Edition guides students through the process of learning how to effectively read scientific material, identify fundamental concepts, reason through scientific questions, and solve quantitative problems. The 12th edition includes a renewed focus on several contemporary areas of research to help challenge students to recognize how scientific and engineering applications are fundamental to the world's clockwork. A wide array of tools will support students' active learning as they work through and engage in this course. Fundamentals of Physics, 12e is built to be a learning center with practice opportunities, interactive challenges, activities, simulations, and videos. Practice and assessment questions are available with immediate feedback and detailed solutions, to ensure that students understand the problem-solving processes behind key concepts and understand their mistakes while working through problems.

This text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favorite problems to understand their strengths and weaknesses, also making the text suitable for a self-study. Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation and numerous application areas in science and engineering. This text is designed as an introduction to UQ for senior undergraduate and graduate students with a mathematical or statistical background and also for researchers from the mathematical sciences or from applications areas who are interested in the field. T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.