This volume collects the edited and reviewed contributions presented in the 8th iTi Conference on Turbulence, held in Bertinoro, Italy, in September 2018. In keeping with the spirit of the conference, the book was produced afterwards, so that the authors had the opportunity to incorporate comments and discussions raised during the event. The respective contributions, which address both fundamental and applied aspects of turbulence, have been structured according to the following main topics: I TheoryII Wall-bounded flowsIII Simulations and modellingIV ExperimentsV Miscellaneous topicsVI Wind energy

This book focuses on the latest applications of nonlinear approaches in engineering and addresses a range of scientific problems. Examples focus on issues in automotive technology, including automotive dynamics, control for electric and hybrid vehicles, and autodriver algorithm for autonomous vehicles. Also included are discussions on renewable energy plants, data modeling, driver-aid methods, and low-frequency vibration. Chapters are based on invited contributions from world-class experts who advance the future of engineering by discussing the development of more optimal, accurate, efficient, cost, and energy effective systems. This book is appropriate for researchers, students, and practising engineers who are interested in the applications of nonlinear approaches to solving engineering and science problems. Presents a broad range of practical topics and approaches; Explains approaches to better, safer, and cheaper systems; Emphasises automotive applications, physical meaning, and methodologies.

Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

This book offers a timely overview of theories and methods developed by an authoritative group of researchers to understand the link between criticality and brain functioning. Cortical information processing in particular and brain function in general rely heavily on the collective dynamics of neurons and networks distributed over many brain areas. A key concept for characterizing and understanding brain dynamics is the idea that networks operate near a critical state, which offers several potential benefits for computation and information processing. However, there is still a large gap between research on criticality and understanding brain function. For example, cortical networks are not homogeneous but highly structured, they are not in a state of spontaneous activation but strongly driven by changing external stimuli, and they process information with respect to behavioral goals. So far the questions relating to how critical dynamics may support computation in this complex setting, and whether they can outperform other information processing schemes remain open. Based on the workshop "Dynamical Network States, Criticality and Cortical Function", held in March 2017 at the Hanse Institute for Advanced Studies (HWK) in Delmenhorst, Germany, the book provides readers with extensive information on these topics, as well as tools and ideas to answer the above-mentioned questions. It is meant for physicists, computational and systems neuroscientists, and biologists.

This book contains the proceedings of the Seventh National Conference of the Italian Systems Society. The title, Systemics of Incompleteness and Quasi-Systems, aims to underline the need for Systemics and Systems Science to deal with the concepts of incompleteness and quasiness. Classical models of Systemics are intended to represent comprehensive aspects of phenomena and processes. They consider the phenomena in their temporal and spatial completeness. In these cases, possible incompleteness in the modelling is assumed to have a provisional or practical nature, which is still under study, and because there is no theoretical reason why the modelling cannot be complete. In principle, this is a matter of non-complex phenomena, to be considered using the concepts of the First Systemics. When dealing with emergence, there are phenomena which must be modelled by systems having multiple models, depending on the aspects being taken into consideration. Here, incompleteness in the modelling is intrinsic, theoretically relating changes in properties, structures, and status of system. Rather than consider the same system parametrically changing over time, we consider sequences of systems coherently. We consider contexts and processes for which modelling is incomplete, being related to only some properties, as well as those for which such modelling is theoretically incomplete-as in the case of processes of emergence and for approaches considered by the Second Systemics. In this regard, we consider here the generic concept of quasi explicating such incompleteness. The concept of quasi is used in various disciplines including quasi-crystals, quasi-particles, quasi-electric fields, and quasi-periodicity. In general, the concept of quasiness for systems concerns their continuous structural changes which are always meta-stable, waiting for events to collapse over other configurations and possible forms of stability; whose equivalence depends on the type of phenomenon under study. Interest in the concept of quasiness is not related to its meaning of rough approximation, but because it indicates an incompleteness which is structurally sufficient to accommodate processes of emergence and sustain coherence or generate new, equivalent or non-equivalent, levels. The conference was devoted to identifying, discussing and understanding possible interrelationships of theoretical disciplinary improvements, recognised as having prospective fundamental roles for a new Quasi-Systemics. The latter should be able to deal with problems related to complexity in more general and realistic ways, when a system is not always a system and not always the same system. In this context, the inter-disciplinarity should consist, for instance, of a constructionist, incomplete, non-ideological, multiple, contradiction-tolerant, Systemics, always in progress, and in its turn, emergent.

This is the proceedings of the IUTAM Symposium on Exploiting Nonlinear Dynamics for Engineering Systems that was held in Novi Sad, Serbia, from July 15th to 19th, 2018. The appearance of nonlinear phenomena used to be perceived as dangerous, with a general tendency to avoid them or control them. This perception has led to intensive research using various approaches and tailor-made tools developed over decades. However, the Nonlinear Dynamics of today is experiencing a profound shift of paradigm since recent investigations rely on a different strategy which brings good effects of nonlinear phenomena to the forefront. This strategy has a positive impact on different fields in science and engineering, such as vibration isolation, energy harvesting, micro/nano-electro-mechanical systems, etc. Therefore, the ENOLIDES Symposium was devoted to demonstrate the benefits and to unlock the potential of exploiting nonlinear dynamical behaviour in these but also in other emerging fields of science and engineering. This proceedings is useful for researchers in the fields of nonlinear dynamics of mechanical systems and structures, and in Mechanical and Civil Engineering.

This book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric. In this metric, two words are close if one needs a morphism on a large finite monoid to distinguish them. The main focus is on a natural correspondence between minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal J-classes (certain subsets of free profinite semigroups). This correspondence sheds light on many aspects of both profinite semigroups and symbolic dynamics. For example, the return words to a given word in a shift space can be related to the generators of the group of the corresponding J-class. The book is aimed at researchers and graduate students in mathematics or theoretical computer science.

Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos-control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity - chaos - corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman's sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.

This book explores the diverse types of Schroedinger equations that appear in nonlinear systems in general, with a specific focus on nonlinear transmission networks and Bose-Einstein Condensates. In the context of nonlinear transmission networks, it employs various methods to rigorously model the phenomena of modulated matter-wave propagation in the network, leading to nonlinear Schroedinger (NLS) equations. Modeling these phenomena is largely based on the reductive perturbation method, and the derived NLS equations are then used to methodically investigate the dynamics of matter-wave solitons in the network. In the context of Bose-Einstein condensates (BECs), the book analyzes the dynamical properties of NLS equations with the external potential of different types, which govern the dynamics of modulated matter-waves in BECs with either two-body interactions or both two- and three-body interatomic interactions. It also discusses the method of investigating both the well-posedness and the ill-posedness of the boundary problem for linear and nonlinear Schroedinger equations and presents new results. Using simple examples, it then illustrates the results on the boundary problems. For both nonlinear transmission networks and Bose-Einstein condensates, the results obtained are supplemented by numerical calculations and presented as figures.

Nonlinear Structures & Systems, Volume 1: Proceedings of the 37th IMAC, A Conference and Exposition on Structural Dynamics, 2019, the first volume of eight from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Nonlinear Dynamics, including papers on: Nonlinear Reduced-order Modeling Jointed Structures: Identification, Mechanics, Dynamics Experimental Nonlinear Dynamics Nonlinear Model & Modal Interactions Nonlinear Damping Nonlinear Modeling & Simulation Nonlinearity & System Identification

This book, the first English-language translation of Acoustique des instruments de musique, Second Edition, presents the necessary foundations for understanding the complex physical phenomena involved in musical instruments. What is the function of the labium in a flute? Which features of an instrument allow us to make a clear audible distinction between a clarinet and a trumpet? With the help of numerous examples, these questions are addressed in detail. The authors focus in particular on the significant results obtained in the field during the last fifteen years. Their goal is to show that elementary physical models can be used with benefit for various applications in sound synthesis, instrument making, and sound recording. The book is primarily addressed to graduate students and researchers; however it could also be of interest for engineers, musicians, craftsmen, and music lovers who wish to learn about the basics of musical acoustics.

Nobody has to tell you that when things go bad, they go bad quickly and seemingly in bunches. Complicated structures like buildings or bridges are slow and laborious to build but, with a design flaw or enough explosive energy, take only seconds to collapse. This fate can befall a company, the stock market, or your house or town after a natural disaster, and the metaphor extends to economies, governments, and even whole societies. As we proceed blindly and incrementally in one direction or another, collapse often takes us by surprise. We step over what you will come to know as a "Seneca cliff", which is named after the ancient Roman philosopher, Lucius Annaeus Seneca, who was the first to observe the ubiquitous truth that growth is slow but ruin is rapid. Modern science, like ancient philosophy, tell us that collapse is not a bug; it is a feature of the universe. Understanding this reality will help you to see and navigate the Seneca cliffs of life, or what Malcolm Gladwell called "tipping points." Efforts to stave off collapse often mean that the cliff will be even steeper when you step over it. But the good news is that what looks to you like a collapse may be nothing more than the passage to a new condition that is better than the old. This book gives deeper meaning to familiar adages such as "it's a house of cards", "let nature take its course", "reach a tipping point", or the popular Silicon Valley expression, "fail fast, fail often." As the old Roman philosopher noted, "nothing that exists today is not the result of a past collapse", and this is the basis of what we call "The Seneca Strategy." This engaging and insightful book will help you to use the Seneca Strategy to face failure and collapse at all scales, to understand why change may be inevitable, and to navigate the swirl of events that frequently threaten your balance and happiness. You will learn: How ancient philosophy and modern science agree that failure and collapse are normal features of the universe Principles that help us manage, rather than be managed by, the biggest challenges of our lives and times Why technological progress may not prevent economic or societal collapse Why the best strategy to oppose failure is not to resist at all costs How you can "rebound" after collapse, to do better than before, and to avoid the same mistakes.

In the face of growing challenges, we need modes of thinking that allow us to not only grasp complexity but also perform it. In this book, the author approaches complexity from the standpoint of a relational worldview. The author recasts complex thinking as a mode of coupling between an observer and the world. Further, she explores the process and outcome of that coupling, namely, meaningful information that may have transformative effects and impact the management of change in the 'real world'. The author presents a new framework for operationalising complex thinking in a set of dimensions and properties through which it may be enacted. This framework may inform the development and coordination of new tools and strategies to support the practice and evaluation of complex thinking across a variety of domains. Intended for a wide interdisciplinary audience of academics, practitioners and policymakers alike, the book is an invitation to pursue inter- and transdisciplinary dialogues and collaborations.

Written by leading experts in an emerging field, this book offers a unique view of the theory of stochastic partial differential equations, with lectures on the stationary KPZ equation, fully nonlinear SPDEs, and random data wave equations. This subject has recently attracted a great deal of attention, partly as a consequence of Martin Hairer's contributions and in particular his creation of a theory of regularity structures for SPDEs, for which he was awarded the Fields Medal in 2014. The text comprises three lectures covering: the theory of stochastic Hamilton-Jacobi equations, one of the most intriguing and rich new chapters of this subject; singular SPDEs, which are at the cutting edge of innovation in the field following the breakthroughs of regularity structures and related theories, with the KPZ equation as a central example; and the study of dispersive equations with random initial conditions, which gives new insights into classical problems and at the same time provides a surprising parallel to the theory of singular SPDEs, viewed from many different perspectives. These notes are aimed at graduate students and researchers who want to familiarize themselves with this new field, which lies at the interface between analysis and probability.

This book contains a collection of recent advanced contributions in the field of nonlinear dynamics and synchronization, including selected applications in the area of theoretical electrical engineering. The present book is divided into twenty-one chapters grouped in five parts. The first part focuses on theoretical issues related to chaos and synchronization and their potential applications in mechanics, transportation, communication and security. The second part handles dynamic systems modelling and simulation with special applications to real physical systems and phenomena. The third part discusses some fundamentals of electromagnetics (EM) and addresses the modelling and simulation in some real physical electromagnetic scenarios. The fourth part mainly addresses stability concerns. Finally, the last part assembles some sample applications in the area of optimization, data mining, pattern recognition and image processing.

The 20 papers contained in this volume span the areas of mathematical physics, dynamical systems, and probability. Yakov Sinai is one of the most important and influential mathematicians of our time, having won the Boltzmann Medal (1986), the Dirac Medal (1992), Dannie Heinemann Prize for Mathematical Physics (1989), Nemmers Prize (2002), and the Wolf Prize in Mathematics (1997). He is well-known as both a mathematician and a physicist, with numerous theorems and proofs bearing his name in both fields, and this book should be of interest to researchers from all fields of the physical sciences.This volume follows Volume I. From the reviews: "The second volume covers statistical mechanics and related topics. It contains 22 papers divided into four groups: Part I: Probability Theory; Part II: Statistical Mechanics; Part III: Mathematical Physics; Part IV: Mathematical Fluid Dynamics. The volume represents Sinai's work on the above topics spanning almost 40 years: the earliest paper is dated 1972, and the latest 2008. The choice of papers was made by Sinai himself, and he provides commentary for each one. The reader will find a wealth of information and ideas that can still ignite inspiration and motivate students as well as senior researchers. The reader will also have a touch of Sinai's personality, his taste, enthusiasm, and optimism, which are just as invaluable as his mathematical results." (Nikolai Chernov, Mathematical Reviews 2012e)

This book features papers presented during a special session on dynamical systems, mathematical physics, and partial differential equations. Research articles are devoted to broad complex systems and models such as qualitative theory of dynamical systems, theory of games, circle diffeomorphisms, piecewise smooth circle maps, nonlinear parabolic systems, quadtratic dynamical systems, billiards, and intermittent maps. Focusing on a variety of topics from dynamical properties to stochastic properties of dynamical systems, this volume includes discussion on discrete-numerical tracking, conjugation between two critical circle maps, invariance principles, and the central limit theorem. Applications to game theory and networks are also included. Graduate students and researchers interested in complex systems, differential equations, dynamical systems, functional analysis, and mathematical physics will find this book useful for their studies. The special session was part of the second USA-Uzbekistan Conference on Analysis and Mathematical Physics held on August 8-12, 2017 at Urgench State University (Uzbekistan). The conference encouraged communication and future collaboration among U.S. mathematicians and their counterparts in Uzbekistan and other countries. Main themes included algebra and functional analysis, dynamical systems, mathematical physics and partial differential equations, probability theory and mathematical statistics, and pluripotential theory. A number of significant, recently established results were disseminated at the conference's scheduled plenary talks, while invited talks presented a broad spectrum of findings in several sessions. Based on a different session from the conference, Algebra, Complex Analysis, and Pluripotential Theory is also published in the Springer Proceedings in Mathematics & Statistics Series.

From the reviews: "The first volume is devoted to ergodic theory and dynamical systems. It contains 19 papers divided into four groups ... . The reader will find a wealth of information and ideas that can still ignite inspiration and motivate students as well as senior researchers. The reader will also have a touch of Sinai's personality, his taste, enthusiasm, and optimism, which are just as invaluable as his mathematical results." (Nikolai Chernov, Mathematical Reviews, Issue 2012 e)

This book addresses the basic physical phenomenon of small-angle scattering (SAS) of neutrons, x-rays or light from complex hierarchical nano- and micro-structures. The emphasis is on developing theoretical models for the material structure containing self-similar or fractal clusters. Within the suggested framework, key approaches for extracting structural information from experimental scattering data are investigated and presented in detail. The range of parameters which can be obtained pave the road towards a better understanding of the correlations between geometrical and various physical properties (electrical, magnetic, mechanical, optical, dynamical, transport etc.) in fractal nano- and micro-materials.

This book provides some recent advance in the study of stochastic nonlinear Schroedinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schroedinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schroedinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.

This book deals with randomly moving objects and their spreading. The objects considered are particles like atoms and molecules, but also living beings such as humans, animals, plants, bacteria and even abstract entities like ideas, rumors, information, innovations and linguistic features. The book explores and communicates the laws behind these movements and reports about astonishing similarities and very specific features typical of the given object under considerations. Leading scientists in disciplines as diverse as archeology, epidemics, linguistics and sociology, in collaboration with their colleagues from engineering, natural sciences and mathematics, introduce the phenomena of spreading as relevant for their fields. An introductory chapter on "Spreading Fundamentals" provides a common basis for all these considerations, with a minimum of mathematics, selected and presented for enjoying rather than frustrating the reader.

This book analyzes the updated principles and applications of nonlinear approaches to solve engineering and physics problems. The knowledge on nonlinearity and the comprehension of nonlinear approaches are inevitable to future engineers and scientists, making this an ideal book for engineers, engineering students, and researchers in engineering, physics, and mathematics. Chapters are of specific interest to readers who seek expertise in optimization, nonlinear analysis, mathematical modeling of complex forms, and non-classical engineering problems. The book covers methodologies and applications from diverse areas such as vehicle dynamics, surgery simulation, path planning, mobile robots, contact and scratch analysis at the micro and nano scale, sub-structuring techniques, ballistic projectiles, and many more.

Theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volume that resulted from the conference Patterns in Dynamics held in honor of Bernold Fiedler, in Berlin, July 25-29, 2016.The contributions build and develop mathematical techniques, and use mathematical approaches for prediction and control of complex systems. The underlying mathematical theories help extract structures from experimental observations and, conversely, shed light on the formation, dynamics, and control of spatio-temporal patterns in applications. Theoretical areas covered include geometric analysis, spatial dynamics, spectral theory, traveling-wave theory, and topological data analysis; also discussed are their applications to chemotaxis, self-organization at interfaces, neuroscience, and transport processes.

This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs. The book is intended for all researchers and graduate students specializing in dynamical systems who are looking for a comprehensive overview of the foundations of the theory and a sample of its applications.

This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques involved in numerical simulations. Though primarily intended for graduate students, it can also be considered a reference book for any researcher interested in the dynamics of resonant phenomena.