Investigation of vortex wakes behind various aircraft, especially behind wide bodied and heavy cargo ones, is of both scientific and practical in terest. The vortex wakes shed from the wing's trailing edge are long lived and attenuate only atdistances of10-12kmbehindthe wake generating aircraft. The encounter of other aircraft with the vortex wake of a heavy aircraft is open to catastrophic hazards. For example, air refueling is adangerous operationpartly due to thepossibility of the receiver aircraft's encountering the trailing wake of the tanker aircraft. It is very important to know the behavior of vortex wakes of aircraft during theirtakeoff andlanding operations whenthe wakes canpropagate over the airport's ground surface and be a serious hazard to other depart ing or arriving aircraft. This knowledge can help in enhancing safety of aircraft's movements in the terminal areas of congested airports where the threat of vortex encounters limits passenger throughput. Theoreticalinvestigations of aircraft vortex wakes arebeingintensively performedinthe major aviationnations.Usedforthispurpose are various methods for mathematical modeling of turbulent flows: direct numerical simulation based on the Navier-Stokes equations, large eddy simulation using the Navier-Stokes equations in combination with subrigid scale modeling, simulation based on the Reynolds equations closed with a differential turbulence model. These approaches are widely used in works of Russian and other countries' scientists. It should be emphasized that the experiments in wind tunnels and studies of natural vortex wakes behind heavy and light aircraft in flight experiments are equally important.

This thesis explores the connection between gravity and thermodynamics and provides a unification scheme that opens up new directions of exploration. Further elaborating on the Hawking effect and the possibility of singularity avoidance, the author not only discusses the information loss paradox at a broader level but also provides a possible solution to it. As the final frontier, it describes some novel effects arising from the microscopic structure of spacetime. Taken as a whole, the thesis addresses three major research areas in gravitational physics: it starts with classical gravity, proceeds to the black hole information loss paradox, and closes with Planck scale physics. The thesis is written in a lucid and pedagogical style, with an introduction accessible to researchers from other branches of physics and a d iscussion presenting open questions and future directions, which will benefit and hopefully inspire next-generation researchers.

This thesis reports on experiments in which the motion of a mechanical oscillator is measured with unprecedented precision. The position fluctuations of the oscillator-a glass nanostring-are measured with an imprecision that is sufficient to resolve its quantum zero-point motion within its thermal decoherence time. The concomitant observation of measurement back-action, in accordance with Heisenberg's uncertainty principle, verifies the principles of linear quantum measurements on a macroscopic mechanical object. The record of the measurement is used to perform feedback control so as to suppress both classical thermal motion and quantum measurement back-action. These results verify some of the central and long-standing predictions of quantum measurement theory applied to a macroscopic object. The act of measurement not only perturbs the subject of the measurement-the mechanical oscillator-but also changes the state of the light used to make the measurement. This prediction is verified by demonstrating that the optical field, after having interacted with the mechanical oscillator, contains quantum correlations that render its quadrature fluctuations smaller than those of the vacuum - i.e., the light is squeezed. Lastly, the thesis reports on some of the first feedback control experiments involving macroscopic objects in the quantum regime, together with an exploration of the quantum limit of feedback control. The book offers a pedagogical account of linear measurement theory, its realization via optical interferometry, and contains a detailed guide to precision optical interferometry..

This book deals with blow-up of a solution to a system of PDEs that arise in practical situations. It begins with a relatively simple account of blow-up in systems of interaction-diffusion equations, then concentrates on mechanics. In particular it deals with the Euler equations, Navier--Stokes equations, models for glacier physics, Korteweg--de-Vries equations, and ferro-hydrodynamics. Blow-up is treated in Volterra equations, stressing how these equations arise in mechanics, e.g. in combustion theory. Further topics are chemotaxis in mathematical biology, change of type, from hyperbolic to elliptic, instability in soils, instability in sea ice dynamics, instability in pressure-dependent viscosity flow, and energy growth in parallel shear flows. It addresses graduate students and researchers in mechanics.

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, BrasilWalter D. Neumann, Columbia University, New York, USAMarkus J. Pflaum, University of Colorado, Boulder, USADierk Schleicher, Jacobs University, Bremen, GermanyKatrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

This is the fourth volume in a series of survey articles covering many aspects of mathematical fluid dynamics, a vital source of open mathematical problems and exciting physics.

This book deals with theoretical aspects of modelling the mechanical behaviour of manufacturing, processing, transportation or other systems in which the processed or supporting material is travelling through the system. Examples of such applications include paper making, transmission cables, band saws, printing presses, manufacturing of plastic films and sheets, and extrusion of aluminium foil, textiles and other materials.

The work focuses on out-of-plane dynamics and stability analysis for isotropic and orthotropic travelling elastic and viscoelastic materials, with and without fluid-structure interaction, using analytical and semi-analytical approaches. Also topics such as fracturing and fatigue are discussed in the context of moving materials. The last part of the book deals with optimization problems involving physical constraints arising from the stability and fatigue analyses, including uncertainties in the parameters.

The book is intended for researchers and specialists in the field, providing a view of the mechanics of axially moving materials. It can also be used as a textbook for advanced courses on this specific topic. Considering topics related to manufacturing and processing, the book can also be applied in industrial mathematics.
"

The question of when and how the basic concepts that characterize modern science arose in Western Europe has long been central to the history of science. This book examines the transition from Renaissance engineering and philosophy of nature to classical mechanics oriented on the central concept of velocity. For this new edition, the authors include a new discussion of the doctrine of proportions, an analysis of the role of traditional statics in the construction of Descartes' impact rules, and go deeper into the debate between Descartes and Hobbes on the explanation of refraction. They also provide significant new material on the early development of Galileo's work on mechanics and the law of fall.

This book is the first of several volumes on solids in the Shock Wave Science and Technology Reference Library. This is a unique collection, and the library as a whole sets out to comprehensively and authoritatively cover and review at research level the subject matter with all its ramifications. All the chapters are self-contained and can be read independently of each other, though they are of course thematically interrelated.

This book is a superb tool in virtually all application areas involving the Kinetic Theory of Gases, Rarefied Gas Dynamics, Transport Theory, and Aerosol Mechanics.It has been especially designed to serve a dual function, both as a teaching instrument either in a classroom environment or at home, and as a reference for scientists and engineers working in relevant fields.The Kinetic Theory of Gases has applications in many areas of science and technology as well as in our understanding of phenomena from the nano- to the cosmic scale.Some of the fields and topics affected include manufacturing, health care, defence, and aerospace science and engineering.

This book describes an effective method for modeling advanced materials like polymers, composite materials and biomaterials, which are, as a rule, inhomogeneous. The thermoelastic theory with internal variables presented here provides a general framework for predicting a material's reaction to external loading. The basic physical principles provide the primary theoretical information, including the evolution equations of the internal variables. The cornerstones of this framework are the material representation of continuum mechanics, a weak nonlocality, a non-zero extra entropy flux, and a consecutive employment of the dissipation inequality. Examples of thermoelastic phenomena are provided, accompanied by detailed procedures demonstrating how to simulate them.

This book is written for researchers as well as engineers in an industrial environment. Following a longstanding tradition of the Les Houches Summer Schools, all chapters are pedagogically presented and accessible for graduate students. The book treats 2D and 3D turbulence from the experimental, theoretical and computational points of view. The reader will find, for example, comprehensive accounts of fully developed turbulence experiments, simulating deterministically coherent vortices formation, and statistical prediction of industrial flows, and a very complete review of 2D turbulence. Fundamental concepts like topological fluid dynamics in MHD flows or finite-time singularities of the Burgers, Euler and Navier--Stokes equations complete the volume.

What do combustion engines, fusion reactors, weather forecast, ocean ?ows, our sun, and stellar explosions in outer space have in common? Of course, the physics and the length and time scales are vastly di?erent in all cases, but it is alsowellknownthatinallofthem,onsomerelevantlengthscales,thematerial ?ows that govern the dynamical and/or secular evolution of the systems are chaotic and often unpredictable: they are said to be turbulent. In fact, the term "turbulence" is used for an enormous variety of p- nomena in very di?erent ?elds, including geophysics, astrophysics, and - gineering. Unfortunately, these communities do not talk to each other too often. Therefore, back in 2005, we organized a workshop on "Interdis- plinary Aspects of Turbulence" at the Ringberg Castle in the Bavarian Alps, to discuss topics such as the basic concepts of turbulence, the di?- ent approaches of modelling and simulations used in the various areas, and also possible tests. This workshop was a great success and the proceedings can be found on the Internet (www.mpa-garching.mpg.de/mpa/publications/ proceedings/proceedings-en.html) as well as pdf-?les of several of the talks presented (www.mpa-garching. mpg.de/hydro/Turbulence/).

This book gathers the proceedings of the Fifth Symposium on Hybrid RANS-LES Methods, which was held on March 19-21 in College Station, Texas, USA. The different chapters, written by leading experts, reports on the most recent developments in flow physics modelling, and gives a special emphasis to industrially relevant applications of hybrid RANS-LES methods and other turbulence-resolving modelling approaches. The book addresses academic researchers, graduate students, industrial engineers, as well as industrial R&D managers and consultants dealing with turbulence modelling, simulation and measurement, and with multidisciplinary applications of computational fluid dynamics (CFD), such as flow control, aero-acoustics, aero-elasticity and CFD-based multidisciplinary optimization. It discusses in particular advanced hybrid RANS-LES methods. Further topics include wall-modelled Large Eddy Simulation (WMLES) methods, embedded LES, and a comparison of the LES methods with both hybrid RANS-LES and URANS methods. Overall, the book provides readers with a snapshot on the state-of-the-art in CFD and turbulence modelling, with a special focus to hybrid RANS-LES methods and their industrial applications.

In this short book, renowned theoretical physicist and author Carlo Rovelli gives a straightforward introduction to Einstein's General Relativity, our current theory of gravitation. Focusing on conceptual clarity, he derives all the basic results in the simplest way, taking care to explain the physical, philosophical and mathematical ideas at the heart of "the most beautiful of all scientific theories". Some of the main applications of General Relativity are also explored, for example, black holes, gravitational waves and cosmology, and the book concludes with a brief introduction to quantum gravity. Written by an author well known for the clarity of his presentation of scientific ideas, this concise book will appeal to university students looking to improve their understanding of the principal concepts, as well as science-literate readers who are curious about the real theory of General Relativity, at a level beyond a popular science treatment.

This volume contains eleven contributions on boundary integral equation and boundary element methods. Beside some historical and more analytical aspects in the formulation and analysis of boundary integral equations, modern fast boundary element methods are also described and analyzed from a mathematical point of view. In addition, the book presents engineering and industrial applications that show the ability of boundary element methods to solve challenging problems from different fields.

Inverse scattering theory is a major theme in applied mathematics, with applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting challenges in the development of efficient inversion algorithms. A further complication is that anisotropic materials cannot be uniquely determined from given scattering data. In the first edition of Inverse Scattering Theory and Transmission Eigenvalues, the authors discussed methods for determining the support of inhomogeneous media from measured far field data and the role of transmission eigenvalue problems in the mathematical development of these methods. In this second edition, three new chapters describe recent developments in inverse scattering theory. In particular, the authors explore the use of modified background media in the nondestructive testing of materials and methods for determining the modified transmission eigenvalues that arise in such applications from measured far field data. They also examine nonscattering wave numbers-a subset of transmission eigenvalues-using techniques taken from the theory of free boundary value problems for elliptic partial differential equations and discuss the dualism of scattering poles and transmission eigenvalues that has led to new methods for the numerical computation of scattering poles. This book will be of interest to research mathematicians and engineers and physicists working on problems in target identification. It will also be useful to advanced graduate students in many areas of applied mathematics.

This book compiles a variety of experimental data on blast waves. The book begins with an introductory chapter and proceeds to the topic of blast wave phenomenology, with a discussion on Rankine-Hugoniot equations and the Friedlander equation, used to describe the pressure-time history of a blast wave. Additional topics include arrival time measurement, the initiation of detonation by exploding wires, a discussion of TNT equivalency, and small scale experiments. Gaseous and high explosive detonations are covered as well. The topics and experiments covered were chosen based on the comparison of used scale sizes, from small to large. Each characteristic parameter of blast waves is analyzed and expressed versus scaled distance in terms of energy and mass. Finally, the appendix compiles a number of polynomial laws that will prove indispensable for engineers and researchers.

Classical plasticity theory of metals is independent of the hydrostatic pressure. However if the metal contains voids or pores or if the structure is composed of cells, this classical assumption is no more valid and the influence of the hydrostatic pressure must be incorporated in the constitutive description. Looking at the microlevel, metal plasticity is connected with the uniform planes of atoms organized with long-range order. Planes may slip past each other along their close-packed directions. The result is a permanent change of shape within the crystal and plastic deformation. The presence of dislocations increases the likelihood of planes slipping.

Nowadays, the theory of pressure sensitive plasticity is successfully applied to many other important classes of materials (polymers, concrete, bones etc.) even if the phenomena on the micro-level are different to classical plasticity of metals. The theoretical background of this phenomenological approach based on observations on the macro-level is described in detail in this monograph and applied to a wide range of different important materials in the last part of this book.

Want to know not just what makes rockets go up but how to do it optimally? Optimal control theory has become such an important field in aerospace engineering that no graduate student or practicing engineer can afford to be without a working knowledge of it. This is the first book that begins from scratch to teach the reader the basic principles of the calculus of variations, develop the necessary conditions step-by-step, and introduce the elementary computational techniques of optimal control. This book, with problems and an online solution manual, provides the graduate-level reader with enough introductory knowledge so that he or she can not only read the literature and study the next level textbook but can also apply the theory to find optimal solutions in practice. No more is needed than the usual background of an undergraduate engineering, science, or mathematics program: namely calculus, differential equations, and numerical integration. Although finding optimal solutions for these problems is a complex process involving the calculus of variations, the authors carefully lay out step-by-step the most important theorems and concepts. Numerous examples are worked to demonstrate how to apply the theories to everything from classical problems (e.g., crossing a river in minimum time) to engineering problems (e.g., minimum-fuel launch of a satellite). Throughout the book use is made of the time-optimal launch of a satellite into orbit as an important case study with detailed analysis of two examples: launch from the Moon and launch from Earth. For launching into the field of optimal solutions, look no further!