This book provides state-of-the-art results and theories in homogeneous turbulence, including anisotropy and compressibility effects with extension to quantum turbulence, magneto-hydodynamic turbulence and turbulence in non-newtonian fluids. Each chapter is devoted to a given type of interaction (strain, rotation, shear, etc.), and presents and compares experimental data, numerical results, analysis of the Reynolds stress budget equations and advanced multipoint spectral theories. The role of both linear and non-linear mechanisms is emphasized. The link between the statistical properties and the dynamics of coherent structures is also addressed. Despite its restriction to homogeneous turbulence, the book is of interest to all people working in turbulence, since the basic physical mechanisms which are present in all turbulent flows are explained. The reader will find a unified presentation of the results and a clear presentation of existing controversies. Special attention is given to bridge the results obtained in different research communities. Mathematical tools and advanced physical models are detailed in dedicated chapters.
This book presents the basic elements of Analytical Mechanics, starting from the physical motivations that favor it with respect to the Newtonian Mechanics in Cartesian coordinates. Rather than presenting Analytical Mechanics mainly as a formal development of Newtonian Mechanics, it highlights its effectiveness due to the following five important achievements: 1) the most economical description of time evolution in terms of the minimal set of coordinates, so that there are no constraint forces in their evolution equations; 2) the form invariance of the evolution equations, which automatically solves the problem of fictitious forces; 3) only one scalar function encodes the formulation of the dynamics, rather than the full set of vectors which describe the forces in Cartesian Newtonian Mechanics; 4) in the Hamiltonian formulation, the corresponding evolution equations are of first order in time and are fully governed by the Hamiltonian function (usually corresponding to the energy); 5) the emergence of the Hamiltonian canonical algebra and its effectiveness in simplifying the control of the dynamical problem (e.g. the constant of motions identified by the Poisson brackets with the Hamiltonian, the relation between symmetries and conservations laws, the use of canonical transformations to reduce the Hamiltonian to a simpler form etc.). The book also addresses a number of points usually not included in textbook presentations of Analytical Mechanics, such as 1) the characterization of the cases in which the Hamiltonian differs from the energy, 2) the characterization of the non-uniqueness of the Lagrangian and of the Hamiltonian and its relation to a ´´gauge´´ transformation, 3) the Hamiltonian formulation of the Noether theorem, with the possibility that the constant of motion corresponding to a continuous symmetry of the dynamics is not the canonical generator of the symmetry transformation but also involves the generator of a gauge transformation. In turn, the book´s closing chapter is devoted to explaining the extraordinary analogy between the canonical structure of Classical and Quantum Mechanics. By correcting the Dirac proposal for such an explanation, it demonstrates that there is a common Poisson algebra shared by Classical and Quantum Mechanics, the differences between the two theories being reducible to the value of the central variable of that algebra.
This book describes physical, mathematical and experimental methods to model flows in micro- and nanofluidic devices. It takes in consideration flows in channels with a characteristic size between several hundreds of micrometers to several nanometers. Methods based on solving kinetic equations, coupled kinetic-hydrodynamic description, and molecular dynamics method are used. Based on detailed measurements of pressure distributions along the straight and bent microchannels, the hydraulic resistance coefficients are refined. Flows of disperse fluids (including disperse nanofluids) are considered in detail. Results of hydrodynamic modeling of the simplest micromixers are reported. Mixing of fluids in a Y-type and T-type micromixers is considered. The authors present a systematic study of jet flows, jets structure and laminar-turbulent transition. The influence of sound on the microjet structure is considered. New phenomena associated with turbulization and relaminarization of the mixing layer of microjets are discussed. Based on the conducted experimental investigations, the authors propose a chart of microjet flow regimes. When addressing the modeling of microflows of nanofluids, the authors show where conventional hydrodynamic approaches can be applied and where more complicated models are needed, and they analyze the hydrodynamic stability of the nanofluid flows. The last part of the book is devoted the statistical theory of the transport processes in fluids under confined conditions. The authors present the constitutive relations and the formulas for transport coefficients. In conclusion the authors present a rigorous analysis of the viscosity and diffusion in nanochannels and in porous media.
For thirty years this has been the acknowledged standard in advanced classical mechanics courses. This classic text enables students to make connections between classical and modern physics - an indispensable part of a physicist´s education. In this new edition, Beams Medal winner Charles Poole and John Safko have updated the text to include the latest topics, applications, and notation, to reflect today´s physics curriculum. They introduce students to the increasingly important role that nonlinearities play in contemporary applications of classical mechanics. New numerical exercises help students to develop skills in how to use computer techniques to solve problems in physics. Mathematical techniques are presented in detail so that the text remains fully accessible to students who have not had an intermediate course in classical mechanics. Product Description For 30 years, this book has been the acknowledged standard in advanced classical mechanics courses. This classic book enables readers to make connections between classical and modern physics ? an indispensable part of a physicist´s education. In this new edition, Beams Medal winner Charles Poole and John Safko have updated the book to include the latest topics, applications, and notation to reflect today´s physics curriculum. Features + Benefits The classic approach of this leading text has been revised and updated without increasing the overall length of the book. NEW - NEW! Chapter 11 on classical chaos theory builds from the Hamilton-Jacobi theory to introduce nonlinear dynamics and fractal dimensionality as it relates to classical mechanics. REVISED! Chapter 7 now presents special relativity using the standard real metric (in lieu of the complex Minkowski space) and coordinate-free notation, and includes a brief introduction to the concepts of general relativity. UPDATED! A section on the Euler and Lagrange exact solutions to the three-body problem has been added to Chapter 3. UPDATED! A section on the damped driven oscillator as an example of the workings of the Josephson junction has been added to Chapter 6. REVISED! Chapter 12 on Canonical Perturbation Theory has been streamlined and the mathematics has been simplified. NEW - NEW! Approximately 45 new problems, mostly in Chapters One through Eight and Eleven. Problem sets are now helpfully divided into ´´Derivations´´ and ´´Exercises.´´ 1. Survey of the Elementary Principles. 2. Variational Principles and Lagrange´s Equations. UPDATED! 3. The Central Force Problem. 4. The Kinematics of Rigid Body Motion. 5. The Rigid Body Equations of Motion. UPDATED! 6. Oscillations. REVISED! 7. The Classical Mechanics of the Special Theory of Relativity. 8. The Hamiltonian Equations of Motion. 9. Canonical Transformations. 10. Hamilton-Jacobi Theory and Action Angle Variables. NEW! 11. Classical Chaos. REVISED! 12. Canonical Perturbation Theory. 13. Introduction to Lagrangian and Hamiltonian Formulations for Continuous Systems and Fields. Appendixes. Select Bibliography. Index. For thirty years this has been the acknowledged standard in advanced classical mechanics courses. This classic text enables students to make connections between classical and modern physics - an indispensable part of a physicist´s education. In this new edition, Beams Medal winner Charles Poole and John Safko have updated the text to include the latest topics, applications, and notation, to reflect today´s physics curriculum. They introduce students to the increasingly important role that nonlinearities play in contemporary applications of classical mechanics. New numerical exercises help students to develop skills in how to use computer techniques to solve problems in physics. Mathematical techniques are presented in detail so that the text remains fully accessible to students who have not had an intermediate course in classical mechanics.
This book covers all topics in mechanics from elementary Newtonian mechanics, the principles of canonical mechanics and rigid body mechanics to relativistic mechanics and nonlinear dynamics. It was among the first textbooks to include dynamical systems and deterministic chaos in due detail. As compared to the previous editions the present 6th edition is updated and revised with more explanations, additional examples and problems with solutions, together with new sections on applications in science. Symmetries and invariance principles, the basic geometric aspects of mechanics as well as elements of continuum mechanics also play an important role. The book will enable the reader to develop general principles from which equations of motion follow, to understand the importance of canonical mechanics and of symmetries as a basis for quantum mechanics, and to get practice in using general theoretical concepts and tools that are essential for all branches of physics. The book contains more than 150 problems with complete solutions, as well as some practical examples which make moderate use of personal computers. This will be appreciated in particular by students using this textbook to accompany lectures on mechanics. The book ends with some historical notes on scientists who made important contributions to the development of mechanics.
In a nutshell, it´s an eleven string, fretless, acoustic/electric instrument, strung with nylon strings and tuned to standard guitar tuning. More than ever before, musicians are mixing sounds and musical styles from all over the world. This often involves the mixing of Eastern and Western music, such as using a Sitar in a western musical setting or using western instruments to imitate the sounds in eastern music. The Glissentar was inspired by a similar desire to mix elements of East and West, but in this case, in the instrument itself. The Western part of the equation is easy to recognize as a variation on the guitar. All of the instruments basic dimensions, scale length, body size, depth, fingerboard radius, and string height, are fairly standard for acoustic/electric guitars. The Eastern influence in the Glissentar comes from the Oud, an ancestor of the Mandolin that dates back to the seventh century. The Oud is also an eleven-string fretless instrument and is still in use today primarily in Armenia and Egypt. Adapting to this new instrument is actually a great deal easier than it appears. The shape and scale of the neck and the easily visible side position markers help to give the Glissentar a very familiar feel. The Glissentar opens the door to microtonal playing as well as some incredible and unique new sounds for adventurous guitar players.SpecsRock Maple neckEbony Fingerboard16 fingerboard radius25 1/2 Scale1 3/4 nut widthTwo-Chamber Silver Leaf Maple bodySolid Cedar TopGodin Custom under-saddle Transducer & custom preampVolume, Mid, Treble and Bass controls
Diese Arbeit befasst sich mit der Lösung des direkten und inversen Streuproblems im Anwendungsbereich der zerstörungsfreien Prüfungen von Materialien mittels Ultraschallecho-Verfahren. Am Modell eines Spannbetonbauteils werden mit Hilfe numerischer Methoden ?Messdaten? erzeugt. Diese ?Messdaten? werden mit verschiedenen Inversionsalgorithmen unter Berücksichtigung von Materialinhomogenitäten analysiert und zur Abbildung von Materialfehlern verwendet. Dazu werden u.a. der ?konventionelle? Inversionsalgorithmus Synthetic Aperture Focusing Technique und die One-Way Wave-Equation-Methode vorgestellt. Die Algorithmen werden anhand des Impuls-Echo- und Linear-Array-Messverfahrens für akustische ?Messdaten? gegenübergestellt. Der Vergleich der Ergebnisse zeigt die Vor- und Nachteile beider Verfahren auf. Die Ergebnisse der SAFT- und Phasenauswertung für verschiedene Litzen- und Lufteinschlusskonstellationen veranschaulichen, wie schwierig ein Lufteinschluss in einem Spannbetonbauteil zu identifizieren ist.