Dynamics and statics Books

Book SynopsisThis textbook teaches students the principles, materials and applications they need to understand and analyze heat transfer problems they will encounter in practice. The emphasis on modern practical problems (including thermoelectric cooling) in the numerous examples, sets this work apart from other available works.Table of Contents1. Introduction and preliminaries; 2. Energy equation; 3. Conduction; 4. Radiation; 5. Convection: unbounded fluid streams; 6. Convection: semi-bounded fluid streams; 7. Convection: bounded fluid streams; 8. Heat transfer in thermal systems.

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Book SynopsisThis second edition describes atomic-level kinetics of thermal energy storage, transport, and transformation by principal energy carriers. It includes applications in energy conversion, expanded examples of size effects, inclusion of junction quantum transport, and discussion of graphene and its phonon and electronic conductances. Examples, illustrations, and problems are included.Table of Contents1. Introduction and preliminaries; 2. Molecular orbitals/potentials/dynamics and quantum energy states; 3. Carrier energy transport and transformation theories; 4. Phonon energy storage, transport, and transformation kinetics; 5. Electron energy storage, transport, and transformation kinetics; 6. Fluid particle energy storage, transport, and transformation kinetics; 7. Photon energy storage, transport, and transformation kinetics; Appendices A-I.

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Book SynopsisA modern introduction to synchronization phenomena, this text presents recent discoveries and the current state of research in the field, from low-dimensional systems to complex networks. The book describes some of the main mechanisms of collective behaviour in dynamical systems, including simple coupled systems, chaotic systems, and systems of infinite-dimension. After introducing the reader to the basic concepts of nonlinear dynamics, the book explores the main synchronized states of coupled systems and describes the influence of noise and the occurrence of synchronous motion in multistable and spatially-extended systems. Finally, the authors discuss the underlying principles of collective dynamics on complex networks, providing an understanding of how networked systems are able to function as a whole in order to process information, perform coordinated tasks, and respond collectively to external perturbations. The demonstrations, numerous illustrations and application examples will Table of ContentsPreface; 1. Introduction and main concepts; 2. Low-dimensional systems; 3. Multistable systems, coupled neurons and applications; 4. High-dimensional systems; 5. Complex networks; References; Index.

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Book SynopsisThe availability of large data sets has allowed researchers to uncover complex properties such as large-scale fluctuations and heterogeneities in many networks, leading to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. This book presents a comprehensive account of these effects. A vast number of systems, from the brain to ecosystems, power grids and the internet, can be represented as large complex networks. This book will interest graduate students and researchers in many disciplines, from physics and statistical mechanics to mathematical biology and information science. Its modular approach allows readers to readily access the sections of most interest to them, and complicated maths is avoided so the text can be easily followed by non-expertTrade ReviewReview of the hardback: 'With a focus in dynamical processes, this book is an excellent introduction … on the statistical mechanics approach of networks … Not only [does] it consist of a wide array of commonly used techniques in the discipline but also it provides multitudes of the techniques' applied examples … this book could serve as an introduction book and a reference to new-to-the-topic JASSS readers. To conclude, I believe that this book has contributed another step in integrating the vast multidisciplinary approaches in network science.' Journal of Artificial Societies and Social SimulationReview of the hardback: '… the book does a terrific and admirable job at putting some order into the wealth of research that has emerged during the last decade … a fantastic resource book on dynamical processes on complex networks, and its wide scope promises to keep it relevant for several years to come.' Journal of Statistical PhysicsReview of the hardback: '… a very useful book that fills an important gap in the market of books on networks … I will be opening this book whenever I want to start modelling a dynamical process on a network.' Contemporary Physics'The book does a remarkably good job in getting to the mathematical foundations of dynamical processes and complex networks. Hence, it should belong in the bookshelf of any sociologist who is seriously interested in complex and dynamic networks. It gives a great overview of techniques in the field and provides the mathematical depth one wishes for in a manner sociologists can understand. In sum, the book has potential to become a reference like Wasserman and Faust (1994) and offers significant (technical) value to sociologists who seriously want to get into the mathematics behind dynamical processes and complex networks.' Thomas U. Grund, Journal of Mathematical SociologyTable of ContentsPreface; Acknowledgements; List of abbreviations; 1. Preliminaries: networks and graphs; 2. Networks and complexity; 3. Network models; 4. Introduction to dynamical processes: theory and simulation; 5. Phase transitions on complex networks; 6. Resilience and robustness of networks; 7. Synchronization phenomena in networks; 8. Walking and searching on networks; 9. Epidemic spreading in population networks; 10. Social networks and collective behavior; 11. Traffic on complex networks; 12. Networks in biology: from the cell to ecosystems; 13. Postface: critically examining complex networks science; Appendixes; References; Index.

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Book SynopsisSystems with mechanical degrees of freedom containing unstable objects are analysed in this monograph and algorithms for their control are developed, discussed, and numerically tested. This is achieved by identifying unstable modes of motion and using all available resources to suppress them. By using this approach the region of states from which a stable regime can be reached is maximised. The systems discussed in this book are models for pendula and vehicles and find applications in mechatronics, robotics as well as in mechanical and automotive engineering.Table of ContentsPreface Chapter 1. Devices Containing One-Link Pendulum § 1. Physical pendulum with fixed suspension point 1. Motion equations 2. Controllability domain 3. Maximization of attraction domain 4. Delay in feedback loop 5. Nonlinear control 6. Controllability domain for nonlinear model § 2. Pendulum with suspension point located at the center of a wheel 1. Motion equations 2. Controllability domain 3. Maximization of attraction domain 4. Nonlinear control § 3. Pendulum with flywheel 1. Design of the pendulum with flywheel 2. Motion equations 3. Local stabilization of the pendulum in the upper unstable equilibrium 4. Damping of the flywheel angular speed 5. Rocking and damping of the pendulum 6. Transferring the pendulum from the lower equilibrium to the upper one 7. Numerical study 8. Experiments § 4. Wheel rolling control using a pendulum 1. Mathematical model of the device 2. Steady motions 3. Stability of steady motions § 5. Optimal rocking and damping of the swing 1. On design of optimal feedback control for second-order systems 2. Mathematical model of the swing 3. Maximization of the swing amplitude 4. Minimization of the swing amplitude 5. Control of the swing with consideration of aerodynamic resistance and dry friction § 6. Pendulum control with minimal energy cost 1. Energy cost estimation 2. Transferring the pendulum to the unstable equilibrium 3. Transferring the pendulum to the stable equilibrium Chapter 2. Two-link Physical Pendulum § 7. Local stabilization of inverted pendulum with one control torque 1. Mathematical model of the pendulum 2. Linearized model 3. Controllability domains 4. Feedback control design, maximization of the attraction domain 5. Numerical study § 8. Optimal control design of two-link pendulum rocking and damping 1. Mathematical model 2. Reduced angle 3. Optimal control for rocking the pendulum 4. Optimal control for damping the pendulum 5. On transferring the pendulum from the lower equilibrium to the upper one § 9. Global stabilization of inverted pendulum with control applied at the hinge between links 1. Mathematical model 2. Cascade form of dynamics equations 3. Control for rocking the pendulum 4. Tracking of desired inter-link angle variation 5. Local stabilization of the inverted pendulum 6. Numerical study § 10. Global stabilization of the inverted pendulum with control applied at the suspension point 1. Mathematical model 2. Pendulum rocking 3. Straightening of the pendulum 4. Linear model, local stabilization 5. Numerical study § 11. Multilink pendulum on a movable base 1. Multilink pendulum on a wheel 2. One-link pendulum on a wheel 3. Global stabilization of inverted pendulum 4. Controllability domain 5. Design of time-optimal trajectories 6. Pendulum on a cart 7. Decrease of frequencies under imposed constraint Chapter 3. Ball on a Beam § 12. Stabilization of a ball on a rectilinear beam 1. Mathematical model of the system 2. Linearized model 3. Feedback control synthesis 4. Numerical study § 13. Stabilization of a ball on a circular beam 1. Mathematical model 2. Linearized model 3. Feedback control 4. Numerical study Chapter 4. Gyroscopic Stabilization of Robot-Bicycle § 14. Designs of two bicycle types 1. Bicycle with one steering wheel 2. Bicycle with two steering wheels 3. Gyroscopic stabilizer 4. Equations of bicycle roll oscillations § 15. Control law for stabilizing bicycle in the upright position 1. Measurement of bicycle roll angle with accelerometers 2. Bicycle motion along a straight line 3. Bicycle motion along a circular line 4. Numerical and experimental study References

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Book SynopsisThis updated revision gives a complete and topical overview on Nonconservative Stability which is essential for many areas of science and technology ranging from particles trapping in optical tweezers and dynamics of subcellular structures to dissipative and radiative instabilities in fluid mechanics, astrophysics and celestial mechanics. The author presents relevant mathematical concepts as well as rigorous stability results and numerous classical and contemporary examples from non-conservative mechanics and non-Hermitian physics. New coverage of ponderomotive magnetism, experimental detection of Ziegler’s destabilization phenomenon and theory of double-diffusive instabilities in magnetohydrodynamics.

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Book SynopsisThe revised edition gives a comprehensive mathematical and physical presentation of fluid flows in non-classical models of convection - relevant in nature as well as in industry. After the concise coverage of fluid dynamics and heat transfer theory it discusses recent research. This monograph provides the theoretical foundation on a topic relevant to metallurgy, ecology, meteorology, geo-and astrophysics, aerospace industry, chemistry, crystal physics, and many other fields.

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Book SynopsisStatistical mechanics is one of the most important areas of physics, and it also has applications to subjects as diverse as economics, social behavior, algorithmic theory, and evolutionary biology. This bokk introduces important developments in classical statistical mechanics, and guides readers to the very threshold of research.Trade Review"Unlike typical textbooks ... [Statistical Mechanics in a Nutshell] presents statistical mechanics as a more general theory with broader applications... A graduate student or researcher who wants to explore the applications of statistical mechanics would be very well served by this book."--Choice "Peliti's Statistical Mechanics in a Nutshell is a fantastic reference for those who know the subject, teach it, or need a quick technical reminder, especially on the topic of phase transitions, which are consistently featured in modern-day discussions... Statistical Mechanics in a Nutshell provides the more general overview, with topics such as the renormalization group method. It includes a good mix of fundamental thermodynamics, phase behaviour, and other key subjects."--Physics TodayTable of ContentsPreface to the English Edition xi Preface xiii Chapter 1: Introduction 1 1.1 The Subject Matter of Statistical Mechanics 1 1.2 Statistical Postulates 3 1.3 An Example: The Ideal Gas 3 1.4 Conclusions 7 Recommended Reading 8 Chapter 2: Thermodynamics 9 2.1 Thermodynamic Systems 9 2.2 Extensive Variables 11 2.3 The Central Problem of Thermodynamics 12 2.4 Entropy 13 2.5 Simple Problems 14 2.6 Heat and Work 18 2.7 The Fundamental Equation 23 2.8 Energy Scheme 24 2.9 Intensive Variables and Thermodynamic Potentials 26 2.10 Free Energy and Maxwell Relations 30 2.11 Gibbs Free Energy and Enthalpy 31 2.12 The Measure of Chemical Potential 33 2.13 The Koenig Born Diagram 35 2.14 Other Thermodynamic Potentials 36 2.15 The Euler and Gibbs-Duhem Equations 37 2.16 Magnetic Systems 39 2.17 Equations of State 40 2.18 Stability 41 2.19 Chemical Reactions 44 2.20 Phase Coexistence 45 2.21 The Clausius-Clapeyron Equation 47 2.22 The Coexistence Curve 48 2.23 Coexistence of Several Phases 49 2.24 The Critical Point 50 2.25 Planar Interfaces 51 Recommended Reading 54 Chapter 3: The Fundamental Postulate 55 3.1 Phase Space 55 3.2 Observables 57 3.3 The Fundamental Postulate: Entropy as Phase-Space Volume 58 3.4 Liouville's Theorem 59 3.5 Quantum States 63 3.6 Systems in Contact 66 3.7 Variational Principle 67 3.8 The Ideal Gas 68 3.9 The Probability Distribution 70 3.10 Maxwell Distribution 71 3.11 The Ising Paramagnet 71 3.12 The Canonical Ensemble 74 3.13 Generalized Ensembles 77 3.14 The p-T Ensemble 80 3.15 The Grand Canonical Ensemble 82 3.16 The Gibbs Formula for the Entropy 84 3.17 Variational Derivation of the Ensembles 86 3.18 Fluctuations of Uncorrelated Particles 87 Recommended Reading 88 Chapter 4: Interaction-Free Systems 89 4.1 Harmonic Oscillators 89 4.2 Photons and Phonons 93 4.3 Boson and Fermion Gases 102 4.4 Einstein Condensation 112 4.5 Adsorption 114 4.6 Internal Degrees of Freedom 116 4.7 Chemical Equilibria in Gases 123 Recommended Reading 124 Chapter 5: Phase Transitions 125 5.1 Liquid-Gas Coexistence and Critical Point 125 5.2 Van der Waals Equation 127 5.3. Other Singularities 129 5.4 Binary Mixtures 130 5.5 Lattice Gas 131 5.6 Symmetry 133 5.7 Symmetry Breaking 134 5.8 The Order Parameter 135 5.9 Peierls Argument 137 5.10 The One-Dimensional Ising Model 140 5.11 Duality 142 5.12 Mean-Field Theory 144 5.13 Variational Principle 147 5.14 Correlation Functions 150 5.15 The Landau Theory 153 5.16 Critical Exponents 156 5.17 The Einstein Theory of Fluctuations 157 5.18 Ginzburg Criterion 160 5.19 Universality and Scaling 161 5.20 Partition Function of the Two-Dimensional Ising Model 165 Recommended Reading 170 Chapter 6: Renormalization Group 173 6.1 Block Transformation 173 6.2 Decimation in the One-Dimensional Ising Model 176 6.3 Two-Dimensional Ising Model 179 6.4 Relevant and Irrelevant Operators 183 6.5 Finite Lattice Method 187 6.6 Renormalization in Fourier Space 189 6.7 Quadratic Anisotropy and Crossover 202 6.8 Critical Crossover 203 6.9 Cubic Anisotrophy 208 6.10 Limit n 209 6.11 Lower and Upper Critical Dimensions 213 Recommended Reading 214 Chapter 7: Classical Fluids 215 7.1 Partition Function for a Classical Fluid 215 7.2 Reduced Densities 219 7.3 Virial Expansion 227 7.4 Perturbation Theory 244 7.5 Liquid Solutions 246 Recommended Reading 249 Chapter 8: Numerical Simulation 251 8.1 Introduction 251 8.2 Molecular Dynamics 253 8.3 Random Sequences 259 8.4 Monte Carlo Method 261 8.5 Umbrella Sampling 272 8.6 Discussion 274 Recommended Reading 275 Chapter 9: Dynamics 277 9.1 Brownian Motion 277 9.2 Fractal Properties of Brownian Trajectories 282 9.3 Smoluchowski Equation 285 9.4 Diffusion Processes and the Fokker-Planck Equation 288 9.5 Correlation Functions 289 9.6 Kubo Formula and Sum Rules 292 9.7 Generalized Brownian Motion 293 9.8 Time Reversal 296 9.9 Response Functions 296 9.10 Fluctuation-Dissipation Theorem 299 9.11 Onsager Reciprocity Relations 301 9.12 Affinities and Fluxes 303 9.13 Variational Principle 306 9.14 An Application 308 Recommended Reading 310 Chapter 10: Complex Systems 311 10.1 Linear Polymers in Solution 312 10.2 Percolation 321 10.3 Disordered Systems 338 Recommended Reading 356 Appendices 357 Appendix A Legendre Transformation 359 A.1 Legendre Transform 359 A.2 Properties of the Legendre Transform 360 A.3 Lagrange Multipliers 361 Appendix B Saddle Point Method 364 B.1 Euler Integrals and the Saddle Point Method 364 B.2 The Euler Gamma Function 366 B.3 Properties of N-Dimensional Space 367 B.4 Integral Representation of the Delta Function 368 Appendix C A Probability Refresher 369 C.1 Events and Probability 369 C.2 Random Variables 369 C.3 Averages and Moments 370 C.4 Conditional Probability: Independence 371 C.5 Generating Function 372 C.6 Central Limit Theorem 372 C.7 Correlations 373 Appendix D Markov Chains 375 D.1 Introduction 375 D.2 Definitions 375 D.3 Spectral Properties 376 D.4 Ergodic Properties 377 D.5 Convergence to Equilibrium 378 Appendix E Fundamental Physical Constants 380 Bibliography 383 Index 389

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