![]() |
![]() |
Your cart is empty |
||
Books > Science & Mathematics > Physics > Classical mechanics
Quantum mechanics is the foundation of modern technology, due to its innumerable applications in physics, chemistry and even biology. This second volume studies Schroedinger s equation and its applications in the study of wells, steps and potential barriers. It examines the properties of orthonormal bases in the space of square-summable wave functions and Dirac notations in the space of states. This book has a special focus on the notions of the linear operators, the Hermitian operators, observables, Hermitian conjugation, commutators and the representation of kets, bras and operators in the space of states. The eigenvalue equation, the characteristic equation and the evolution equation of the mean value of an observable are introduced. The book goes on to investigate the study of conservative systems through the time evolution operator and Ehrenfest s theorem. Finally, this second volume is completed by the introduction of the notions of quantum wire, quantum wells of semiconductor materials and quantum dots in the appendices.
This self-contained, interdisciplinary book encompasses mathematics, physics, computer programming, analytical solutions and numerical modelling, industrial computational fluid dynamics (CFD), academic benchmark problems and engineering applications in conjunction with the research field of anisotropic turbulence. It focuses on theoretical approaches, computational examples and numerical simulations to demonstrate the strength of a new hypothesis and anisotropic turbulence modelling approach for academic benchmark problems and industrially relevant engineering applications. This book contains MATLAB codes, and C programming language based User-Defined Function (UDF) codes which can be compiled in the ANSYS-FLUENT environment. The computer codes help to understand and use efficiently a new concept which can also be implemented in any other software packages. The simulation results are compared to classical analytical solutions and experimental data taken from the literature. A particular attention is paid to how to obtain accurate results within a reasonable computational time for wide range of benchmark problems. The provided examples and programming techniques help graduate and postgraduate students, engineers and researchers to further develop their technical skills and knowledge.
Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University. The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). Among the special applications addressed in this second volume are: stability of motion, nonlinear oscillations, dynamics and statics of the Stewart platform, mechanics under random forces, elements of control theory, relations between nonholonomic mechanics and the control theory, vibration and autobalancing of rotor systems, physical theory of impact, statics and dynamics of a thin rod. This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.
In the course of the development of electromagnetic, weak and
strong interactions, the concept of (internal) gauge invariance
grew up and established itself as an unavoidable dynamical
principle in particle physics. It is less known that the principle
of equivalence, and the basic dynamical properties of the
gravitational interaction can also be expressed as a (spacetime)
gauge symmetry.
Focuses on the methods of solving incompressible flows, although flows with significant property change due to heat transfer are also covered. Covers turbulent flow simulation, unstructured mesh, and two-phase flows. Uses a practical approach for CFD to build a foundation for those planning to work on low-speed flows. Provides detailed steps of solving 1-D and 2-D flow examples and MATLAB (R) codes of important algorithms. Includes numerous real-word examples and worked problems.
Intumescent Coating and Fire Protection of Steel Structures establishes the thermo insulation characteristics of intumescent coating under various fire and hydrothermal aging circumstances and shows how to predict the temperature elevation of steel structures protected with intumescent coatings in fires for avoiding structural damage. Introduced are the features and applications of intumescent coatings for protecting steel structures against fire. The constant effective thermal conductivity is defined and employed to simplify the quantification for the thermo-resistance of intumescent coatings. An experimental investigation into the hydrothermal aging effects on insulative properties of intumescent coatings is presented, as well as the influence of topcoat on insulation and aging of intumescent coatings. Also described is a practical method for calculating the temperature of the protected steel structures with intumescent coatings in order to evaluate the fire safety of a structure. The book suits fire and structural engineers, as well as researchers and students concerned with the protection of steel structures.
Externally tunable properties allow for new applications of magnetic hybrid materials containing magnetic micro- and nanoparticles in sensors and actuators in technical and medical applications. By means of easy to generate and control magnetic fields, changes of the internal particle arrangements and the macroscopic properties can be achieved. This monograph delivers the latest insights into multi-scale modelling, experimental characterization, manufacturing and application of those magnetic hybrid materials.
This textbook provides materials for an introductory course in Engineering Acoustics for students with a basic knowledge of mathematics. The contents are based on extensive teaching experience at the graduate level. Each of the 14 main chapters deals with a well-defined topic and represents the material for a two-hour lecture. The chapters alternate between more theoretical and more application-oriented concepts. The presentation is organized to be suitable for self-study as well. For this third edition, the complete text and many figures have been revised. Several current amendments take account of advancements in the field. Further, a completely new chapter has been added which presents approaches and solutions to all assigned exercise problems. The new chapter offers the opportunity to explore the underlying theoretical background in more detail. However, the study of the problems and their proposed solutions is no prerequisite for comprehending the material presented in the book's lecture part.
This book offers a compact primer on advanced numerical flux functions in computational fluid dynamics (CFD). It comprehensively introduces readers to methods used at the forefront of compressible flow simulation research. Further, it provides a comparative evaluation of the methods discussed, helping readers select the best numerical flux function for their specific needs. The first two chapters of the book reviews finite volume methods and numerical functions, before discussing issues commonly encountered in connection with each. The third and fourth chapter, respectively, address numerical flux functions for ideal gases and more complex fluid flow cases- multiphase flows, supercritical fluids and magnetohydrodynamics. In closing, the book highlights methods that provide high levels of accuracy. The concise content provides an overview of recent advances in CFD methods for shockwaves. Further, it presents the author's insights into the advantages and disadvantages of each method, helping readers implement the numerical methods in their own research.
This book delivers a comprehensive and up-to-date treatment of practical applications of metamaterials, structured media, and conventional porous materials. With increasing levels of urbanization, a growing demand for motorized transport, and inefficient urban planning, environmental noise exposure is rapidly becoming a pressing societal and health concern. Phononic and sonic crystals, acoustic metamaterials, and metasurfaces can revolutionize noise and vibration control and, in many cases, replace traditional porous materials for these applications. In this collection of contributed chapters, a group of international researchers reviews the essentials of acoustic wave propagation in metamaterials and porous absorbers with viscothermal losses, as well as the most recent advances in the design of acoustic metamaterial absorbers. The book features a detailed theoretical introduction describing commonly used modelling techniques such as plane wave expansion, multiple scattering theory, and the transfer matrix method. The following chapters give a detailed consideration of acoustic wave propagation in viscothermal fluids and porous media, and the extension of this theory to non-local models for fluid saturated metamaterials, along with a description of the relevant numerical methods. Finally, the book reviews a range of practical industrial applications, making it especially attractive as a white book targeted at the building, automotive, and aeronautic industries.
This book is intended for researchers, graduate students and engineers in the fields of structure-borne sound, structural dynamics, and noise and vibration control. Based on vibration differential equations, it presents equations derived from the exponential function in the time domain, providing a unified framework for structural vibration analysis, which makes it more regular and normalized. This wave propagation approach (WPA) divides structures at "discontinuity points," and the waves show characteristics of propagation, reflection, attenuation, and waveform conversion. In each segment of the system between two "discontinuity points," the governing equation and constraint are expressed accurately, allowing the dynamic properties of complex systems to be precisely obtained. Starting with basic structures such as beams and plates, the book then discusses theoretical research on complicated and hybrid dynamical systems, and demonstrates that structural vibration can be analyzed from the perspective of elastic waves by applying WPA.
This book reviews the mathematical modeling and experimental study of systems involving two or more different length scales. The effects of phenomena occurring at the lower length scales on the behavior at higher scales are of intrinsic scientific interest, but can also be very effectively used to determine the behavior at higher length scales or at the macro-level. Efforts to exploit this micro- and macro-coupling are, naturally, being pursued with regard to every aspect of mechanical phenomena. This book focuses on the changes imposed on the dynamics, strength of materials and durability of mechanical systems by related multiscale phenomena. In particular, it addresses: 1: the impacts of effective dissipation due to kinetic energy trapped at lower scales 2: wave propagation in generalized continua 3: nonlinear phenomena in metamaterials 4: the formalization of more general models to describe the exotic behavior of meta-materials 5: the design and study of microstructures aimed at increasing the toughness and durability of novel materials
This book focusses on structural bonding, including many facets, like fundamental aspects of adhesion, science and technology of surfaces, adhesive materials, mechanical properties of bonded joints, innovative designs and applications, testing and standardization, industrial aspects, quality procedures, environmental and ecological aspects. This first volume of the new series gathers selected contributions of the 6th international conference on structural adhesive bonding AB 2021, held in Porto, Portugal, 8-9 July 2021, represents the latest trends and serves as a reference volume for researchers and graduate students working in this field.
This book focuses on the rapidly maturing solar photovoltaic (PV) industry, which is achieving an ever-increasing share of U.S. and global power production. There is a growing need for all stakeholders - owners, maintenance technicians, utilities, and installers - to fully understand the operations and maintenance of PV systems, and how to monitor and diagnose systems post installation. Recognizing this need, this book covers monitoring and diagnostic techniques and technologies, including how to identify the causes of poor performance, and measure and verify power production. Drawing on global case studies, it details how to achieve optimal PV power output in the field through an overview of basic electrical, the solar PV module and Balance of System, and processes and software for monitoring, measurement, and verification. It also provides an overview of the North American Board of Certified Energy Practitioner's (NABCEP) new PV System Inspector credential, which will be outlined in the final chapter. Equipping the reader with the knowledge and confidence required to maximize the output of solar PV installations, Solar Photovoltaics Power Optimization will be an essential resource for PV practitioners and students.
This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics, magnetohydrodynamics (MHD), shallow water, and solid dynamics equations. This treatment provides-for the first time in book form-a collection of recipes for applying higher-order non-oscillatory shock-capturing schemes to MHD modelling of physical phenomena.
This volume collects the edited and reviewed contribution presented in the 9th iTi Conference that took place virtually, covering fundamental and applied aspects in turbulence. In the spirit of the iTi conference, the volume is produced after the conference so that the authors had the opportunity to incorporate comments and discussions raised during the meeting. In the present book, the contributions have been structured according to the topics: I Experiments II Simulations and Modelling III Data Processing and Scaling IV Theory V Miscellaneous topics
This book applies the convex integration method to multi-dimensional compressible Euler equations in the barotropic case as well as the full system with temperature. The convex integration technique, originally developed in the context of differential inclusions, was applied in the groundbreaking work of De Lellis and Szekelyhidi to the incompressible Euler equations, leading to infinitely many solutions. This theory was later refined to prove non-uniqueness of solutions of the compressible Euler system, too. These non-uniqueness results all use an ansatz which reduces the equations to a kind of incompressible system to which a slight modification of the incompressible theory can be applied. This book presents, for the first time, a generalization of the De Lellis-Szekelyhidi approach to the setting of compressible Euler equations. The structure of this book is as follows: after providing an accessible introduction to the subject, including the essentials of hyperbolic conservation laws, the idea of convex integration in the compressible framework is developed. The main result proves that under a certain assumption there exist infinitely many solutions to an abstract initial boundary value problem for the Euler system. Next some applications of this theorem are discussed, in particular concerning the Riemann problem. Finally there is a survey of some related results. This self-contained book is suitable for both beginners in the field of hyperbolic conservation laws as well as for advanced readers who already know about convex integration in the incompressible framework.
This monograph deals with the mechanics and thermodynamics of materials with memory, including properties of the dynamical equations that describe their evolution in time under varying loads. A work in four parts, the first is an introduction to continuum mechanics, including classical fluid mechanics, linear and non-linear elasticity. The second part considers continuum thermodynamics and its use to derive constitutive equations of materials with memory, including viscoelastic solids, fluids, heat conductors and some examples of non-simple materials. In the third part, free energies for materials with linear memory constitutive relations are discussed. The concept of a minimal state is introduced. Explicit formulae are presented for the minimum and related free energies. The final part deals with existence, uniqueness, and stability results for the integrodifferential equations describing the dynamical evolution of viscoelastic materials, including a new approach based on minimal states rather than histories. There are also chapters on the controllability of thermoelastic systems with memory, the Saint-Venant problem for viscoelastic materials and on the theory of inverse problems. The second edition includes a new chapter on thermoelectromagnetism as well as recent findings on minimal states and free energies. It considers the case of minimum free energies for non-simple materials and dielectrics, together with an introduction to fractional derivative models.
This book focuses on the need for an Eulerian formulation of constitutive equations. After introducing tensor analysis using both index and direct notation, nonlinear kinematics of continua is presented. The balance laws of the purely mechanical theory are discussed along with restrictions on constitutive equations due to superposed rigid body motion. The balance laws of the thermomechanical theory are discussed and specific constitutive equations are presented for: hyperelastic materials; elastic-inelastic materials; thermoelastic-inelastic materials with application to shock waves; thermoelastic-inelastic porous materials; and thermoelastic-inelastic growing biological tissues.
Current standard numerical methods are of little use in solving mathematical problems involving boundary layers. In Robust Computational Techniques for Boundary Layers, the authors construct numerical methods for solving problems involving differential equations that have non-smooth solutions with singularities related to boundary layers. They present a new numerical technique that provides precise results in the boundary layer regions for the problems discussed in the book. They show that this technique can be adapted in a natural way to a real flow problem, and that it can be used to construct benchmark solutions for comparison with solutions found using other numerical techniques.
A comprehensive and easy to understand introduction to a wide range of tools to help designers to optimize their projects. The authors are engineers and therefore many of the examples are on engineering applications, but the techniques presented are common to various areas of knowledge and pervade disciplinary divisions. The book describes the fundamental ideas, mathematical and graphic methods and shows how to use Matlab and EXCEL for optimization.
This book presents theoretical and experimental investigations of mechanical behavior of solids under shock loading and highlights a multi-scale exchange process of energy and momentum between meso and macroscopic hierarchy. It also widely covers experimental approaches for the multi-scale response of solids to impacts including uniaxial strain conditions and high-velocity penetration processes. The content comprises two parts. The first part overviews modeling and theory of dynamically deformed solids from the multi-scale point of view. The second part describes experimental characterization of shock-induced solids and experimental probing of mesostructured and mesoscale dynamic processes in solids. The theory presented in the first part is then verified as it is compared with i) experiments of shock loading into different kinds of solids and ii) probed microstructure of post-shocked specimens by scanning electron microscopy, transmission electron microscopy and optical microscopy. The text is written on the basis of author's lectures at universities and thus is concisely described for postgraduate students. It is also useful for researchers who work on the theory of multi-scale mechanics of solids and engineers who work on testing materials under dynamic loading.
Predicting Motion presents the core ideas of Newtonian mechanics, starting from Newton's laws and the idea that changes in motion are predictable given the forces that cause them. Richly illustrated with questions and answers for self-assessment, it carefully introduces concepts, such as kinetics and potential energy, linear momentum, torque (the rotational analogue of force), and angular momentum, and explains their role in predicting motion. Although no prior knowledge of this topic is required, the book focuses on the significance of differential equations in making such predictions. It also provides an up-to-date treatment of mechanics with accounts of relativistic collisions and the implications of chaos theory for the future of the solar system and for galaxies that contain black holes.
This book provides a comprehensive overview of statistical descriptions of turbulent flows. Its main objectives are to point out why ordinary perturbative treatments of the Navier-Stokes equation have been rather futile, and to present recent advances in non-perturbative treatments, e.g., the instanton method and a stochastic interpretation of turbulent energy transfer. After a brief introduction to the basic equations of turbulent fluid motion, the book outlines a probabilistic treatment of the Navier-Stokes equation and chiefly focuses on the emergence of a multi-point hierarchy and the notion of the closure problem of turbulence. Furthermore, empirically observed multiscaling features and their impact on possible closure methods are discussed, and each is put into the context of its original field of use, e.g., the renormalization group method is addressed in relation to the theory of critical phenomena. The intended readership consists of physicists and engineers who want to get acquainted with the prevalent concepts and methods in this research area. |
![]() ![]() You may like...
Reliability, Risk and Safety - Back to…
Ben J. M. Ale, Ioannis A. Papazoglou, …
CD-ROM
Munson, Young and Okiishi's Fundamentals…
Andrew L Gerhart, John I Hochstein, …
Paperback
R1,520
Discovery Miles 15 200
The Navier-Stokes Problem in the 21st…
Pierre-Gilles Lemarie-Rieusset
Paperback
R1,342
Discovery Miles 13 420
Advances in Energy, Environment and…
Ahmad Zuhairi Abdullah, Azlin Fazlina Osman
Hardcover
R6,558
Discovery Miles 65 580
Transport and Mixing in Laminar Flows…
Roman Grigoriev
Hardcover
|