This book, provides a general introduction to the ideas and methods of statistical mechanics with the principal aim of meeting the needs of Master's students in chemical, mechanical, and materials science engineering. Extensive introductory information is presented on many general physics topics in which students in engineering are inadequately trained, ranging from the Hamiltonian formulation of classical mechanics to basic quantum mechanics, electromagnetic fields in matter, intermolecular forces, and transport phenomena. Since engineers should be able to apply physical concepts, the book also focuses on the practical applications of statistical physics to material science and to cutting-edge technologies, with brief but informative sections on, for example, interfacial properties, disperse systems, nucleation, magnetic materials, superfluidity, and ultralow temperature technologies. The book adopts a graded approach to learning, the opening four basic-level chapters being followed by advanced "starred" sections in which special topics are discussed. Its relatively informal style, including the use of musical metaphors to guide the reader through the text, will aid self-learning.

The revised edition of this advanced textbook provides the reader with a solid grounding in the formalism of classical mechanics, underlying a number of powerful mathematical methods that are widely used in modern theoretical and mathematical physics. It reviews the fundamentals of Lagrangian and Hamiltonian mechanics, and goes on to cover related topics such as canonical transformations, integral invariants, potential motion in geometric setting, symmetries, the Noether theorem and systems with constraints. While in some cases the formalism is developed beyond the traditional level adopted in the standard textbooks on classical mechanics, only elementary mathematical methods are used in the exposition of the material. New material for the revised edition includes additional sections on the Euler-Lagrange equation, the Cartan two-form in Lagrangian theory, and Newtonian equations of motion in context of general relativity. Also new for this edition is the inclusion of problem sets and solutions to aid in the understanding of the material presented. The mathematical constructions involved are explicitly described and explained, so the book is a good starting point for the student new to this field. Where possible, intuitive motivations are replaced by explicit proofs and direct computations, preserving the level of rigor that makes the book useful for more advanced students intending to work in one of the branches of the vast field of theoretical physics. To illustrate how classical-mechanics formalism works in other branches of theoretical physics, examples related to electrodynamics, as well as to relativistic and quantum mechanics, are included.

This new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.

This book compiles solutions of linear theory of elasticity problems for isotropic and anisotropic bodies with sharp and rounded notches. It contains an overview of established and recent achievements, and presents the authors' original solutions in the field considered with extensive discussion. The volume demonstrates through numerous, useful examples the effectiveness of singular integral equations for obtaining exact solutions of boundary problems of the theory of elasticity for bodies with cracks and notches. Incorporating analytical and numerical solutions of the problems of stress concentrations in solid bodies with crack-like defects, this volume is ideal for scientists and PhD students dealing with the problems of theory of elasticity and fracture mechanics.

1 Introduction.- 2 Equations of motion.- 2.1 incompressible flow.- 2.2 the Boussinesq approximation.- 2.3 coordinate system.- 3 Stability and Transition.- 3.1 stability analysis.- 3.2 Kelvin-Helmholtz instability.- 3.3 Rayleigh stability criterion.- 3.4 stability of a one-dimensional flow.- 3.5 routes to chaos.- 4 The characteristics of turbulence.- 4.1 the Burgers equation.- 4.2 phenomenology.- 4.3 experimental and numerical methods.- 5 Statistical description of turbulence.- 5.1 statistics.- 5.2 stationarity and homogeneity.- 5.3 the Reynolds equations.- 5.4 kinetic theory of momentum transfer.- 6 Turbulent flows.- 6.1 channel flow.- 6.2 mean velocity profile.- 6.3 scaling of turbulent wall flows.- 6.4 wall roughness.- 6.5 pressure gradient.- 6.6 free turbulent flows.- 6.7 the free jet.- 7 Kinetic energy.- 7.1 kinetic energy of the mean flow.- 7.2 kinetic energy of turbulence.- 7.3 Prandtl's one-equation model.- 7.4 energy equation per component.- 7.5 convective turbulence.- 7.6 the convective boundary layer.- 8 Vorticity.- 8.1 vorticity equation.- 8.2 coherent structures.- 8.3 enstrophy.- 8.4 the k- (e- ) model.- 8.5 second-order closure and algebraic stress models.- 8.6 large eddy simulation of turbulence.- 9 Correlation function and spectrum.- 9.1 time correlations.- 9.2 the spectrum.- 9.3 spatial correlations and spectra.- 9.4 the Taylor hypothesis.- 9.5 scaling of turbulence spectra.- 9.6 isotropic turbulence.- 10 Turbulent diffusion.- 10.1 statistical approach.- 10.2 the diffusion equation.- 10.3 inertial transport.- A Equations of motion.- B Special topics.- B.1 Monin-Obukhov similarity.- B.2 rapid distortion theory.- B.3 aeroacoustics.- B.4 rotating turbulence (by Herman Clercx).- B.5 drag reduction by polymer additives.- Bibliography.- Index.

This book provides comprehensive, graduate-level treatment of analog and digital signal analysis suitable for course use and self-guided learning. This expert text guides the reader from the basics of signal theory through a range of application tools for use in acoustic analysis, geophysics, and data compression. Each concept is introduced and explained step by step, and the necessary mathematical formulae are integrated in an accessible and intuitive way. The first part of the book explores how analog systems and signals form the basics of signal analysis. This section covers Fourier series and integral transforms of analog signals, Laplace and Hilbert transforms, the main analog filter classes, and signal modulations. Part II covers digital signals, demonstrating their key advantages. It presents z and Fourier transforms, digital filtering, inverse filters, deconvolution, and parametric modeling for deterministic signals. Wavelet decomposition and reconstruction of non-stationary signals are also discussed. The third part of the book is devoted to random signals, including spectral estimation, parametric modeling, and Tikhonov regularization. It covers statistics of one and two random variables and the principles and methods of spectral analysis. Estimation of signal properties is discussed in the context of ergodicity conditions and parameter estimations, including the use of Wiener and Kalman filters. Two appendices cover the basics of integration in the complex plane and linear algebra. A third appendix presents a basic Matlab toolkit for computer signal analysis. This expert text provides both a solid theoretical understanding and tools for real-world applications.

This thesis covers several important topics relevant to our understanding of quark-gluon plasma. It describes measurement of the third-order harmonic flow using two-particle correlations and isolation of flow and non-flow contributions to particle correlations in gold-gold collisions. The work also investigates long-range longitudinal correlations in small systems of deuteron-gold collisions. The former is related to the hydrodynamic transport properties of the quark-gluon plasma created in gold-gold collisions. The latter pertains to the question whether hydrodynamics is applicable to small systems, such as deuteron-gold collisions, and whether the quark-gluon plasma can be formed in those small-system collisions. The work presented in this thesis was conducted with the STAR experiment at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory, where the center-of-mass energy of both collision systems was a factor of 100 larger than the rest mass of the colliding nuclei. The results contained in this thesis are highly relevant to our quest for deeper understanding of quantum chromodynamics. The results obtained challenge the interpretation of previous works from several other experiments on small systems, and provoke a fresh look at the physics of hydrodynamics and particle correlations pertinent to high energy nuclear collisions.

This book provides novel insights into two fundamental subjects in solid mechanics: virtual work and shape change. The author explains how the principle of virtual work represents a tool for analysis of the mechanical effects of the evolution of the shape of a system, how it can be applied to observations and experiments, and how it may be adapted to produce predictive theories of numerous phenomena. The book is divided into three parts. The first relates the principle of virtual work to what we observe with our eyes, the second demonstrates its flexibility on the basis of many examples, and the third applies the principle to predict the motion of solids with large deformations. Examples of both usual and unusual shape changes are presented, and equations of motion, some of which are entirely new, are derived for smooth and non-smooth motions associated with, for instance, systems of disks, systems of balls, classical and non-classical small deformation theories, systems involving volume and surface damage, systems with interactions at a distance (e.g., solids reinforced by fibers), systems involving porosity, collisions, and fracturing of solids.

This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. From the mathematical perspective, causal fermion systems provide a general framework for describing and analyzing non-smooth geometries and "quantum geometries". The dynamics is described by a novel variational principle, called the causal action principle. In addition to the basics, the book provides all the necessary mathematical background and explains how the causal action principle gives rise to the interactions of the standard model plus gravity on the level of second-quantized fermionic fields coupled to classical bosonic fields. The focus is on getting a mathematically sound connection between causal fermion systems and physical systems in Minkowski space. The book is intended for graduate students entering the field, and is furthermore a valuable reference work for researchers in quantum field theory and quantum gravity.

This book investigates collisions occurring in the motion of solids, in the motion of fluids but also in the motion of pedestrians in crowds. The duration of these presented collisions is short compared to the whole duration of the motion: they are assumed instantaneous. The innovative concept demonstrated in this book is that a system made of two solids, is deformable because their relative position changes. The definition of the velocities of deformation of the system introduced in the classical developments of mechanics, the principle of the virtual work and the laws of thermodynamics, allows a large range of applications such as crowd motions, debris flow motions, and shape memory alloys motions. The set of the applications is even larger: social sciences and mechanics are unified to predict the motion of crowds with application to transport management and to evacuation of theaters management.

This volume is designed as an introductory text and reference book for graduate students, researchers and practitioners in the fields of astronomy, astrodynamics, satellite systems, space sciences and astrophysics. The purpose of the book is to emphasize the similarities between celestial mechanics and astrodynamics, and to present recent advances in these two fields so that the reader can understand the inter-relations and mutual influences. The juxtaposition of celestial mechanics and astrodynamics is a unique approach that is expected to be a refreshing attempt to discuss both the mechanics of space flight and the dynamics of celestial objects. "Celestial Mechanics and Astrodynamics: Theory and Practice" also presents the main challenges and future prospects for the two fields in an elaborate, comprehensive and rigorous manner. The book presents homogenous and fluent discussions of the key problems, rendering a portrayal of recent advances in the field together with some basic concepts and essential infrastructure in orbital mechanics. The text contains introductory material followed by a gradual development of ideas interweaved to yield a coherent presentation of advanced topics.

Ship optimization design is critical to the preliminary design of a ship. With the rapid development of computer technology, the simulation-based design (SBD) technique has been introduced into the field of ship design. Typical SBD consists of three parts: geometric reconstruction; CFD numerical simulation; and optimization. In the context of ship design, these are used to alter the shape of the ship, evaluate the objective function and to assess the hull form space respectively. As such, the SBD technique opens up new opportunities and paves the way for a new method for optimal ship design. This book discusses the problem of optimizing ship's hulls, highlighting the key technologies of ship optimization design and presenting a series of hull-form optimization platforms. It includes several improved approaches and novel ideas with significant potential in this field

This thesis focuses on the manipulation of sound properties by artificial materials. It elaborates on the fundamental design of acoustic metasurfaces and metastructures as the extension of metamaterials, and their functionality in the manipulation of sound properties. A broad and comprehensive guideline of designing acoustic metasurfaces and metastructures is also provided. Based on the proposed subwavelength metasurfaces and the metastructures with a simplified layout, multiple potential applications are demonstrated. This thesis will appeal to acoustic engineers and researchers who are interested in designing acoustic artificial structures.

This book provides analytical solutions to a number of classical problems in transport processes, i.e. in fluid mechanics, heat and mass transfer. Expanding computing power and more efficient numerical methods have increased the importance of computational tools. However, the interpretation of these results is often difficult and the computational results need to be tested against the analytical results, making analytical solutions a valuable commodity. Furthermore, analytical solutions for transport processes provide a much deeper understanding of the physical phenomena involved in a given process than do corresponding numerical solutions. Though this book primarily addresses the needs of researchers and practitioners, it may also be beneficial for graduate students just entering the field.

This book presents a selection of the best papers from the HEaRT 2015 conference, held in Lisbon, Portugal, which provided a valuable forum for engineers and architects, researchers and educators to exchange views and findings concerning the technological history, construction features and seismic behavior of historical timber-framed walls in the Mediterranean countries. The topics covered are wide ranging and include historical aspects and examples of the use of timber-framed construction systems in response to earthquakes, such as the gaiola system in Portugal and the Bourbon system in southern Italy; interpretation of the response of timber-framed walls to seismic actions based on calculations and experimental tests; assessment of the effectiveness of repair and strengthening techniques, e.g., using aramid fiber wires or sheets; and modelling analyses. In addition, on the basis of case studies, a methodology is presented that is applicable to diagnosis, strengthening and improvement of seismic performance and is compatible with modern theoretical principles and conservation criteria. It is hoped that, by contributing to the knowledge of this construction technique, the book will help to promote conservation of this important component of Europe's architectural heritage.

This book, on the general topic of hydroaerodynamics, investigates a number of exciting applications in this field, addressing specifically issues that allow seemingly paradoxical issues to be dealt with. The first part is devoted to the study of channel flows, in particular the lateral flow of a viscous and viscous-plastic liquid in a ring channel formed by coaxial cylinders. Specifically, the problem of dissipation of mechanical energy in channel flows of highly viscous liquids is addressed and solved. Furthermore, the mechanism leading to hydrodynamic erosion in intra-field pipelines (known as "channelized effect") is identified. Subsequently, a theory for channel flows with mass transfer through porous walls is developed. In the second part, viscous liquid free flows (jets) are investigated. In particular, a dispersion law for turbulent flow is derived and the existence of dynamic invariance in wake flows of variable density is demonstrated. The third part presents new insights from both theoretical and experimental research into concentrated vortex structure formation and development. The conditions for the existence of Taylor-Goertler vortices are determined and the mechanism for their formation is described. Last but not least, the theory of vortex rings, a particularly interesting problem in hydroaerodynamics, is introduced in the last section of this book. Care has been taken, when selecting original theoretical problems of interest, to make the link with related topics in the published literature. At the same time, all experimental research described in this book is given a meaningful physical interpretation and corroborated by suitable theoretical models and computations.

This improved and updated second edition covers the theory, development, and design of electro-acoustic transducers for underwater applications. This highly regarded text discusses the basics of piezoelectric and magnetostrictive transducers that are currently being used as well as promising new designs. It presents the basic acoustics as well as the specific acoustics data needed in transducer design and evaluation. A broad range of designs of projectors and hydrophones are described in detail along with methods of modeling, evaluation, and measurement. Analysis of projector and hydrophone transducer arrays, including the effects of mutual radiation impedance and numerical models for elements and arrays, are also covered. The book includes new advances in transducer design and transducer materials and has been completely reorganized to be suitable for use as a textbook, as well as a reference or handbook. The new edition contains corrections to the first edition, end-of-chapter exercises, and solutions to selected exercises. Each chapter includes a short introduction, end-of-chapter summary, and an extensive reference list offering the reader more detailed information and historical context. A glossary of key terms is also included at the end.

This book presents the signal processing algorithms that have been developed to process the signals acquired by a spherical microphone array. Spherical microphone arrays can be used to capture the sound field in three dimensions and have received significant interest from researchers and audio engineers. Algorithms for spherical array processing are different to corresponding algorithms already known in the literature of linear and planar arrays because the spherical geometry can be exploited to great beneficial effect. The authors aim to advance the field of spherical array processing by helping those new to the field to study it efficiently and from a single source, as well as by offering a way for more experienced researchers and engineers to consolidate their understanding, adding either or both of breadth and depth. The level of the presentation corresponds to graduate studies at MSc and PhD level. This book begins with a presentation of some of the essential mathematical and physical theory relevant to spherical microphone arrays, and of an acoustic impulse response simulation method, which can be used to comprehensively evaluate spherical array processing algorithms in reverberant environments. The chapter on acoustic parameter estimation describes the way in which useful descriptions of acoustic scenes can be parameterized, and the signal processing algorithms that can be used to estimate the parameter values using spherical microphone arrays. Subsequent chapters exploit these parameters including in particular measures of direction-of-arrival and of diffuseness of a sound field. The array processing algorithms are then classified into two main classes, each described in a separate chapter. These are signal-dependent and signal-independent beamforming algorithms. Although signal-dependent beamforming algorithms are in theory able to provide better performance compared to the signal-independent algorithms, they are currently rarely used in practice. The main reason for this is that the statistical information required by these algorithms is difficult to estimate. In a subsequent chapter it is shown how the estimated acoustic parameters can be used in the design of signal-dependent beamforming algorithms. This final step closes, at least in part, the gap between theory and practice.

A new title in the Manchester Physics Series, this introductory text emphasises physical principles behind classical mechanics and relativity. It assumes little in the way of prior knowledge, introducing relevant mathematics and carefully developing it within a physics context. Designed to provide a logical development of the subject, the book is divided into four sections, introductory material on dynamics, and special relativity, which is then followed by more advanced coverage of dynamics and special relativity. Each chapter includes problems ranging in difficulty from simple to challenging with solutions for solving problems. Includes solutions for solving problems Numerous worked examples included throughout the book Mathematics is carefully explained and developed within a physics environment Sensitive to topics that can appear daunting or confusing

Ring polymers are one of the last big mysteries in polymer physics, and this thesis tackles the problem of describing their behaviour when interacting in dense solutions and with complex environments and reports key findings that help shed light on these complex issues. The systems investigated are not restricted to artificial polymer systems, but also cover biologically inspired ensembles, contributing to the broad applicability and interest of the conclusions reached. One of the most remarkable findings is the unambiguous evidence that rings inter-penetrate when in dense solutions; here this behaviour is shown to lead to the emergence of a glassy state solely driven by the topology of the constituents. This novel glassy state is unconventional in its nature and, thanks to its universal properties inherited from polymer physics, will attract the attention of a wide range of physicists in the years to come.

This thesis presents a method for reliably and robustly producing samples of amyloid- (A ) by capturing them at various stages of aggregation, as well as the results of subsequent imaging with various atomic force microscopy (AFM) methods, all of which add value to the data gathered by collecting information on the peptide's nanomechanical, elastic, thermal or spectroscopical properties. Amyloid- (A ) undergoes a hierarchy of aggregation following a structural transition, making it an ideal subject of study using scanning probe microscopy (SPM), dynamic light scattering (DLS) and other physical techniques. By imaging samples of A with Ultrasonic Force Microscopy, a detailed substructure to the morphology is revealed, which correlates well with the most advanced cryo-EM work. Early stage work in the area of thermal and spectroscopical AFM is also presented, and indicates the promise these techniques may hold for imaging sensitive and complex biological materials. This thesis demonstrates that physical techniques can be highly complementary when studying the aggregation of amyloid peptides, and allow the detection of subtle differences in their aggregation processes.

This thesis presents an accurate and advanced numerical methodology to remedy difficulties such as direct numerical simulation of magnetohydrodynamic (MHD) flow in computational fluid dynamics (CFD), grid generation processes in tokamak fusion facilities, and the coupling between the surface tension force and Lorentz force in the metallurgical industry. In addition, on the basis of the numerical platform it establishes, it also investigates selected interesting topics, e.g. single bubble motion under the influence of either vertical or horizontal magnetic fields. Furthermore, it confirms the relation between the bubble's path instability and wake instability, and observes the anisotropic (isotropic) effect of the vertical (horizontal) magnetic field on the vortex structures, which determines the dynamic behavior of the rising bubble. The direct numerical simulation of magnetohydrodynamic (MHD) flows has proven difficult in the field of computational fluid dynamic (CFD) research, because it not only concerns the coupling of the equations governing the electromagnetic field and the fluid motion, but also calls for suitable numerical methods for computing the electromagnetic field. In tokamak fusion facilities, where the MHD effect is significant and the flow domain is complex, the process of grid generation requires considerable time and effort. Moreover, in the metallurgical industry, where multiphase MHD flows are usually encountered, the coupling between the surface tension force and Lorentz force adds to the difficulty of deriving direct numerical simulations.

This book provides a concise introduction to soft matter modelling. It offers an up-to-date review of continuum mechanical description of soft and biological materials from the basics to the latest scientific materials. It includes multi-physics descriptions, such as chemo-, thermo-, electro- mechanical coupling. It derives from a graduate course at Technion that has been established in recent years. It presents original explanations for some standard materials and features elaborated examples on all topics throughout the text. PowerPoint lecture notes can be provided to instructors.

New finite elements are needed as well in research as in industry environments for thedevelopment of virtual prediction techniques. The design and implementation of novel finiteelements for specific purposes is a tedious and time consuming task, especially for nonlinearformulations. The automation of this process can help to speed up this processconsiderably since the generation of the final computer code can be accelerated by order ofseveral magnitudes.This book provides the reader with the required knowledge needed to employ modernautomatic tools like AceGen within solid mechanics in a successful way. It covers the rangefrom the theoretical background, algorithmic treatments to many different applications. Thebook is written for advanced students in the engineering field and for researchers ineducational and industrial environments.

This book focuses on the study of heavy quarkonium production at high-energy colliders as a useful tool to explain both the perturbative and non-perturbative aspects of quantum choromodynamics. It provides the first comprehensive comparison between the theory and recent experiments and clarifies some longstanding puzzles in the heavy quarkonium production mechanism. In addition, it describes in detail a new framework for implementing precise computations of the physical observables in quantum field theories based on recently developed techniques. It can be used to simulate the complicated collider environment of the Large Hadron Collider at the Conseil Europeen pour la Recherche Nucleaire (CERN). Its accomplishment implies that the Monte Carlo simulations for high-energy physics experiments have reached the limits of precision. It offers readers a wealth of valuable information on the relevant techniques.