# krainaksiazek basic physics equations and complex phenomena 20124260

- znaleziono 28 produktów w 3 sklepach

### Selected problems in physics with examples and exercises Politechnika Gdańska

**FIZYKA**

What is physics? The answer to this question has been changing, because physics also changes with time. But physics has always dealt with the basic rules governing the world: the macro-world as well as the world of atoms, electrons and nucleons. Physicists are concerned with various kinds of matter and radiation and their interactions. Their main purpose is to find, understand and use the basic laws that govern the natural world. The foundation of physics is experiment. Experimental observation of the phenomena of nature allows physicists to find the rules and principles that relate these phenomena. This leads to formulation of models and theories, which form our perceptions of the investigated phenomena. Any physical model or theory must always be confronted with experiment. Essential contradictions between a particular model or theory and experimental data are a signal that the model or theory should be corrected or replaced by a new one. This confrontation is a source of development of physics and its continuous approaching a truth of nature. Contemporary physics is a highly developed basic science with many fields, which are the foundation of all engineering and technology. Especially strong relations exist between physics and chemistry. Ever since chemistry ceased to be a purely phenomenological science, chemists not only employ certain laws of physics, but even include some complex and subtle physical phenomena and physics' arcane methods of measurement in their own research. This results in a gradual obliteration of the border line between some branches of chemistry and physics. Spis treści: 1. INTRODUCTION 1.1. The nature of physics 1.2. The language and units. of physics 1.3. How to study physics? Questions and problems 2. FUNDAMENTAL LAWS AND LAWS OF CONSERVATION IN PHYSICS 2.1. The meaning of fundamental laws 2.2. On the laws of conservation in physics 2.2.1. Newton's laws of motion 2.2.2. Conservation of momentum 2.2.3. Conservation of angular momentum 2.3. Work and energy 2.3.1. Definition of work in physics 2.3.2. Energy 2.3.3. The law of conservation of energy 2..3.3.1. Conservation of mechanical energy 2.3.3.2. Conservation of total energy Questions and problems 3. KINETIC THEORY AND LAWS OF THERMODYNAMICS 3.1. The microscopic interpretation of temperature 3.2. Measuring temperature 3.3. Internal energy and equipartition of energy 3.4. Laws of thermodynamics 3.4.1. The first law of thermodynamics 3.4.2. The second law of thermodynamics Questions and problems 4. ELECTROMAGNETIC INTERACTIONS 4.1. Static electric force 4.1.1. Electric charges 4.1.2. Quantization and conservation of charge 4.1.3. Electrical interaction between two charged particles - Coulomb's law 4.1.4. Electrical interactions in a system of several charges 4.2. Electric field 4.2.1. Graphic representation of electric fields 4.3. Gauss's law 4.3.1. Flux of electric field 4.3.2. Gauss's law 4.4. Electric potential and voltage 4.4.1. Electric potential energy 4.4.2. Electric potential 4.5. Capacitance and electric energy storage 4.5.1. Capacitors and capacitance 4.5.2. Energy storage 4.6. Electric current and magnetic force 4.6.1. Electric current 4.6.2. Ohm's law 4.6.3. Magnetic force and magnetic field 4.6.4. Magnetic field of linear current. Ampere's law 4.6.5. Gauss's law for magnetic field 4.7. Electromagnetic induction 4.7.1. Faraday's law of induction 4.7.2. Self-induced emf (? s) 4.8. Maxwell's equations Questions and problems 5. SELECTED PROBLEMS OF MODERN PHYSICS 5.1. The photoelectric effect 5.1.1. Photoelectrons 5.1.2. Fundamental features of the photoelectric effect 5.1.3. Einstein's theory of the photoelectric effect 5.2. Photons and electrons 5.2.1. X-ray photons 5.2.2. The Compton effect 5.3. The Bohr model of the atom of hydrogen 5.3. 1. Bohr's assumptions and postulates 5.3.2. Quantization of electron's total energy5.3.3. Electron jumps 5.3.4. Advantages and limitations of the Bohr model 5.4. Wave-particle duality 5.4.1. De Broglie's hypothesis 5.4.2. Experimental verification of de Broglie's hypothesis Questions and problems 6. NUCLEAR PHYSICS 6.1. Nuclear size and structure 6.1.1. Constituents of the nucleus 6.1.2. Nuclear size 6.1.3. Nuclear forces 6.2. Radioactivity 6.2.1. Kinetics of radioactive decay 6.2.2. Beta decay 6.2.3. Alpha decay 6.2.4. Gamma decay 6.3. Nuclear reactions 6.3.1. General remarks 6.3.2. The fission reaction 6.3.3. Nuclear fusion Questions and problems EXERCISES APPENDIX A. Mathematics A.1. Vector algebra A.2. Derivatives A.3. Integrals APPENDIX B. ENGLISH-POLISH PHYSICS DICTIONARY.

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### Nonlinear Dynamics and Chaotic Phenomena Springer Netherlands

**Książki / Literatura obcojęzyczna**

FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.

Sklep: Libristo.pl

### Navier-Stokes Equations Springer, Berlin

**Książki / Literatura obcojęzyczna**

This volume is devoted to the study of the Navier-Stokes equations, providing a comprehensive reference for a range of applications: from advanced undergraduate students to engineers and professional mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier-Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier-Stokes equations. § Incompressible Navier-Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior of the fluid, assuming knowledge of its initial and boundary states. These equations are one of the most important models of mathematical physics: although they have been a subject of vivid research for more than 150 years, there are still many open problems due to the nature of nonlinearity present in the equations. The nonlinear convective term present in the equations leads to phenomena such as eddy flows and turbulence. In particular, the question of solution regularity for three-dimensional problem was appointed by Clay Institute as one of the Millennium Problems, the key problems in modern mathematics. The problem remains challenging and fascinating for mathematicians, and the applications of the Navier-Stokes equations range from aerodynamics (drag and lift forces), to the design of watercraft and hydroelectric power plants, to medical applications such as modeling the flow of blood in the circulatory system.

Sklep: Libristo.pl

### Boundaries of a Complex World Springer, Berlin

**Książki / Literatura obcojęzyczna**

The central§theme of this book is the extent to which the structure of the free dynamical§boundaries of a system controls the evolution of the system as a whole. Applying§three orthogonal types of thinking - mathematical, constructivist and§morphological, it illustrates these concepts using applications to selected§problems from the social and life sciences, as well as economics.§§In a broader§context, it introduces and reviews some modern mathematical approaches to the§science of complex systems. Standard modeling approaches (based on non-linear§differential equations, dynamic systems, graph theory, cellular automata,§stochastic processes, or information theory) are suitable for studying local§problems. However they cannot simultaneously take into account all the different§facets and phenomena of a complex system, and new approaches are required to solve§the challenging problem of correlations between phenomena at different levels§and hierarchies, their self-organization and memory-evolutive aspects, the growth§of additional structures and are ultimately required to explain why and how§such complex systems can display both robustness and flexibility.§§ This graduate-level§text also addresses a broader interdisciplinary audience, keeping the§mathematical level essentially uniform throughout the book, and involving only§basic elements from calculus, algebra, geometry and systems theory.§§

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### Invitation To Contemporary Physics (2nd Edition) World Scientific Publishing Co Pte Ltd

**Książki / Literatura obcojęzyczna**

This revised second edition invites the reader to explore ten of the most important areas of modern physics: symmetry, lasers, superconductivity, Bose-Einstein condensation, nanoscience, quantum computation, chaos and fractals, stellar evolution, particles and cosmology. The authors give an up-to-date account of the exciting advances in these fast-moving fields. Their emphasis is as much on describing natural phenomena as on attempting to explain them in terms of basic principles, replacing equations with physical insight. General readers and university undergraduates alike should find this book a useful guide to the worlds of modern physics, while the mature scientist will get an insightful survey of neighbouring fields of research. For the teacher who takes a thematic approach to teaching physics, this book should be a complete source of current topics at the frontiers of research; and for the student, a valuable tool of study, made even more useful by numerous pertinent problems (with complete solutions) and references found at the end of each chapter.

Sklep: Libristo.pl

### Introduction to Mathematical Physics Oxford University Press

**Książki / Literatura obcojęzyczna**

Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages the reader to use computer-aided algebra to solve problems in mathematical physics. A free Instructor's Solutions Manual is available to instructors who order the book for course adoption.

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### Fuzzy Arbitrary Order System John Wiley & Sons Inc

**Książki / Literatura obcojęzyczna**

Presents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems Complete with comprehensive results and solutions, Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications details newly developed methods of fuzzy computational techniquesneeded to model solve uncertainty. Fuzzy differential equations are solved via various analytical andnumerical methodologies, and this book presents their importance for problem solving, prototypeengineering design, and systems testing in uncertain environments. In recent years, modeling of differential equations for arbitrary and fractional order systems has been increasing in its applicability, and as such, the authors feature examples from a variety of disciplines to illustrate the practicality and importance of the methods within physics, applied mathematics, engineering, and chemistry, to name a few. The fundamentals of fractional differential equations and the basic preliminaries of fuzzy fractional differential equations are first introduced, followed by numerical solutions, comparisons of various methods, and simulated results. In addition, fuzzy ordinary, partial, linear, and nonlinear fractional differential equations are addressed to solve uncertainty in physical systems. In addition, this book features: * Basic preliminaries of fuzzy set theory, an introduction of fuzzy arbitrary order differential equations, and various analytical and numerical procedures for solving associated problems * Coverage on a variety of fuzzy fractional differential equations including structural, diffusion, and chemical problems as well as heat equations and biomathematical applications * Discussions on how to model physical problems in terms of nonprobabilistic methods and provides systematic coverage of fuzzy fractional differential equations and its applications * Uncertainties in systems and processes with a fuzzy concept Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications is an ideal resource for practitioners, researchers, and academicians in applied mathematics, physics, biology, engineering, computer science, and chemistry who need to model uncertain physical phenomena and problems. The book is appropriate for graduate-level courses on fractional differential equations for students majoring in applied mathematics, engineering, physics, and computer science. Snehashish Chakraverty, PhD, is Professor and Head of the Department of Mathematics at the National Institute of Technology, Rourkela in India. The author of five books and approximately 140 journal articles, his research interests include mathematical modeling, machine intelligence, uncertainty modeling, numerical analysis, and differential equations. Smita Tapaswini, PhD, is Assistant Professor in the Department of Mathematics at the Kalinga Institute of Industrial Technology University in India and is also Post-Doctoral Fellow at the College of Mathematics and Statistics at Chongqing University in China. Her research interests include fuzzy differential equations, fuzzy fractional differential equations, and numerical analysis. Diptiranjan Behera, PhD, is Post-Doctoral Fellow at the Institute of Reliability Engineering in the School of Mechatronics Engineering at the University of Electronic Science and Technology of China. His current research interests include interval and fuzzy mathematics, fuzzy finite element methods, and fuzzy structural analysis.

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### Combustion Waves and Fronts in Flows Cambridge University Press

**Książki / Literatura obcojęzyczna**

Combustion is a fascinating phenomenon coupling complex chemistry to transport mechanisms and nonlinear fluid dynamics. This book provides an up-to-date and comprehensive presentation of the nonlinear dynamics of combustion waves and other non-equilibrium energetic systems. The major advances in this field have resulted from analytical studies of simplified models performed in close relation with carefully controlled laboratory experiments. The key to understanding the complex phenomena is a systematic reduction of the complexity of the basic equations. Focusing on this fundamental approach, the book is split into three parts. Part I provides physical insights for physics-oriented readers, Part II presents detailed technical analysis using perturbation methods for theoreticians, and Part III recalls the necessary background knowledge in physics, chemistry and fluid dynamics. This structure makes the content accessible to newcomers to the physics of unstable fronts in flows, whilst also offering advanced material for scientists who wish to improve their knowledge.

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### Solitons, Instantons, and Twistors Oxford University Press

**Książki / Literatura obcojęzyczna**

Most nonlinear differential equations arising in natural sciences admit chaotic behaviour and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topologically different from vacuum. While integrable equations in lower space-time dimensions can be solved using the inverse scattering transform, the higher-dimensional examples of anti-self-dual Yang-Mills and Einstein equations require twistor theory. Both techniques rely on an ability to represent nonlinear equations as compatibility conditions for overdetermined systems of linear differential equations. The book provides a self-contained and accessible introduction to the subject. It starts with an introduction to integrability of ordinary and partial differential equations. Subsequent chapters explore symmetry analysis, gauge theory, gravitational instantons, twistor transforms, and anti-self-duality equations. The three appendices cover basic differential geometry, complex manifold theory, and the exterior differential system.

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### Singularities: Formation, Structure, and Propagation Cambridge University Press

**Książki / Literatura obcojęzyczna**

Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.

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### Superlinear Parabolic Problems Birkhäuser

**Książki / Literatura obcojęzyczna**

This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. §The first two chapters introduce to the field and enable the reader to get acquainted with the main ideas by studying simple model problems, respectively of elliptic and parabolic type. The subsequent three chapters are devoted to problems with more complex structure; namely, elliptic and parabolic systems, equations with gradient depending nonlinearities, and nonlocal equations. They include many developments which reflect several aspects of current research. Although the techniques introduced in the first two chapters provide efficient tools to attack some aspects of these problems, they often display new phenomena and specifically different behaviors, whose study requires new ideas. Many open problems are mentioned and commented.§The book is self-contained and up-to-date, it has a high didactic quality. It is devoted to problems that are intensively studied but have not been treated so far in depth in the book literature. The intended audience includes graduate and postgraduate students and researchers working in the field of partial differential equations and applied mathematics.

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### Atoms in Intense Laser Fields Cambridge University Press

**Książki / Literatura obcojęzyczna**

The development of lasers capable of producing high-intensity pulses has opened a new area in the study of light-matter interactions. The corresponding laser fields are strong enough to compete with the Coulomb forces in controlling the dynamics of atomic systems and give rise to multiphoton processes. This book presents a unified account of this rapidly developing field of physics. The first part describes the fundamental phenomena occurring in intense laser-atom interactions and gives the basic theoretical framework to analyze them. The second part contains a detailed discussion of Floquet theory, the numerical integration of the wave equations and approximation methods for the low- and high-frequency regimes. In the third part, the main multiphoton processes are discussed: multiphoton ionization, high harmonic and attosecond pulse generation, and laser-assisted electron-atom collisions. Aimed at graduate students in atomic, molecular and optical physics, the book will also interest researchers working on laser interactions with matter.

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### Introduction to the Theory of Soft Matter Springer, Berlin

**Książki / Literatura obcojęzyczna**

This book presents the theory of soft matter to students at the advanced undergraduate or beginning graduate level. It provides a basic introduction to theoretical physics as applied to soft matter, explaining the concepts of symmetry, broken symmetry and order parameters; phases and phase transitions; mean-field theory; and the mathematics of variational calculus and tensors. It is written in an informal, conversational style, which is accessible to students from a diverse range of backgrounds. The book begins with a simple "toy model" to demonstrate the physical significance of free energy. It then introduces two standard theories of phase transitions-the Ising model for ferromagnetism and van der Waals theory of gases and liquids and uses them to illustrate principles of statistical mechanics. From those examples, it moves on to discuss order, disorder and broken symmetry in many states of matter and to explain the theoretical methods that are used to model the phenomena. It concludes with a chapter on liquid crystals, which brings together all of these physical and mathematical concepts. The book is accompanied by a set of "interactive figures," which can be downloaded from the publisher's website. Some of these figures allow users to change parameters and see what happens to a graph, some allow users to rotate a plot or other graphics in 3D, and some do both. These interactive figures help students to develop their intuition for the physical meaning of equations. The book will be useful for advanced undergraduate or early graduate students going into theoretical research, to prepare them for more advanced studies-as well as for students going into experimental physics, chemistry and engineering, who will be prepared to understand theoretical seminars, read theoretical articles and collaborate with theorists.

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### Synergetics of Molecular Systems Springer, Berlin

**Książki / Literatura obcojęzyczna**

Synergetics is the quantitative study of multi-component systems that exhibit nonlinear dynamics and cooperativity. This book specifically considers basic models of the nonlinear dynamics of molecular systems and discusses relevant applications in biological physics and the polymer sciences.§Emphasis is placed on specific solutions to the dynamical equations that correspond to the coherent formation of spatial-temporal structures, such as solitons, kinks and breathers, in particular. The emergence of these patterns in molecular structures provides a variety of information on their structural properties and plays a significant part in energy transfer processes, topological defects, dislocations, and related structure transitions. §Real media, in which solitons take the form of solitary waves, are also considered. In this context, the formation of nonlinear waves in a continuous medium described by non-linear equations is associated with spontaneous breaking of the local symmetry of the homogeneous system, which produces a range of interesting phenomena. §A particular feature of this text is its combination of analytic and computational strategies to tackle difficult nonlinear problems at the molecular level of matter.§

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### Introduction to Hydrodynamic Stability Cambridge University Press

**Książki / Literatura obcojęzyczna**

Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.

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