
This book presents a comprehensive overview of the foundations of singlemolecule studies, based on manipulation of the molecules and observation of these with fluorescent probes. It first discusses the forces present at the singlemolecule scale, the methods to manipulate them, and their pros and cons. It goes on to present an introduction to singlemolecule fluorescent studies based on a quantum description of absorption and emission of radiation due to Einstein. Various considerations in the study of single molecules are introduced (including signal to noise, nonradiative decay, triplet states, etc.) and some novel superresolution methods are sketched. The elastic and dynamic properties of polymers, their relation to experiments on DNA and RNA, and the structural transitions observed in those molecules upon stretching, twisting, and unzipping are presented. The use of these singlemolecule approaches for the investigation of DNA–protein interactions is highlighted via the study of DNA and RNA polymerases, helicases, and topoisomerases. Beyond the confirmation of expected mechanisms (e.g., the relaxation of DNA torsion by topoisomerases in quantized steps) and the discovery of unexpected ones (e.g., strandswitching by helicases, DNA scrunching by RNA polymerases, and chiral discrimination by bacterial topoII), these approaches have also fostered novel (third generation) sequencing technologies.

The technique of small angle solution scattering has been revolutionized in the last two decades. Exponential increases in computing power, parallel algorithm development, and the development of synchrotron, freeelectron Xray sources, and neutron sources, have combined to allow new classes of studies for biological specimens. These include timeresolved experiments in which functional motions of proteins are monitored on a picosecond timescale, and the first steps towards determining actual electron density fluctuations within particles. In addition, more traditional experiments involving the determination of size and shape, and contrast matching that isolate substructures such as nucleic acid, have become much more straightforward to carry out, and simultaneously require much less material. These new capabilities have sparked an upsurge of interest in solution scattering on the part of investigators in related disciplines. Thus, this book seeks to guide structural biologists to understand the basics of small angle solution scattering in both the Xray and neutron case, to appreciate its strengths, and to be cognizant of its limitations. It is also directed at those who have a general interest in its potential. The book focuses on three areas: theory, practical aspects and applications, and the potential of developing areas. It is an introduction and guide to the field but not a comprehensive treatment of all the potential applications.

The aim of this book is to provide new ideas for studying living matter by a simultaneous understanding of behavior from molecules to the cell, to the whole organism in the light of physical concepts. Indeed, forces guide most biological phenomena. In some cases these forces can be welldescribed and thus used to model a particular biological phenomenon. This is exemplified here by the study of membranes, where their shapes and curvatures can be modeled using a limited number of parameters that are measured experimentally. The growth of plants is another example where the combination of physics, biology and mathematics leads to a predictive model. The laws of thermodynamics are essential, as they dictate the behavior of proteins, or more generally biological molecules, in an aqueous environment. Integrated studies from the molecule to a larger scale need a combination of cuttingedge approaches, such as the use of new Xray sources, incell NMR, cryoelectron microscopy or singlemolecule microscopy. Some are described in dedicated chapters while others are mentioned in discussion of particular topics, such as the interactions between HIV and host cells which are being progressively deciphered thanks to recent developments in various types of microscopy. All the concepts and methods developed in this book are illustrated alongside three main biological questions: host–pathogen interactions, plant development and flowering and membrane processes. Through these examples, the book intends to highlight how integrated biology including physics and mathematics is a very powerful approach.

The book is a general text that shows how materials can contribute to solving problems facing nations in the 21st century. It is illustrated with diverse applications and highlights the potential of existing materials for everyday life, healthcare and the economies of nations. There are 13 chapters and a glossary of 500 materials with their descriptions, historical development, their use or potential use and a range of references. Specific areas include synthetic polymers (e.g. nylon), natural polymers (e.g. proteins, cellulose) and the role of materials in the development of digital computers and in healthcare. Solidstate lighting, energy supplies in the 21st century, disruptive technologies and intellectual property, in particular patents, are discussed. The book concludes by asking how the 21st century will be characterised. Will it be the Silicon Age, Genomic Age or New Polymer Age, as examples?

Aqueous foams are studied both as materials with many applications, and as model systems for fields ranging from metallurgy to mathematics to biology. They are complex fluids with unique and unusual properties, exemplified as much by their multiscale structure as by the dynamical processes through which they evolve and even their dual liquidlike and solidlike behaviour. In this book, readers can easily find clear, uptodate answers to their questions regarding the physical and physicochemical properties of aqueous foams, explained using current knowledge of their structure, their stability, and their rheology. Newcomers to the field will find descriptions of numerous applications of foams in daily life and in industrial processes, the definition of basic concepts, hundreds of figures, and simple experiments to perform at home. Those who want to proceed further will find updated references, exercises with solutions, appendices with experimental and numerical techniques, and boxed text with the further mathematical detail.

Turbojet and turbofan engines, rocket motors, road vehicles, aircraft, pumps, compressors, and turbines are examples of machines which require a knowledge of fluid mechanics for their design. The aim of this undergraduatelevel textbook is to introduce the physical concepts and conservation laws which underlie the subject of fluid mechanics and show how they can be applied to practical engineering problems. The first ten chapters are concerned with fluid properties, dimensional analysis, the pressure variation in a fluid at rest (hydrostatics) and the associated forces on submerged surfaces, the relationship between pressure and velocity in the absence of viscosity, and fluid flow through straight pipes and bends. The examples used to illustrate the application of this introductory material include the calculation of rocketmotor thrust, jetengine thrust, the reaction force required to restrain a pipe bend or junction, and the power generated by a hydraulic turbine. Compressiblegas flow is then dealt with, including flow through nozzles, normal and oblique shock waves, centred expansion fans, pipe flow with friction or wall heating, and flow through axialflow turbomachinery blading. The fundamental NavierStokes equations are then derived from first principles, and examples given of their application to pipe and channel flows and to boundary layers. The final chapter is concerned with turbulent flow. Throughout the book the importance of dimensions and dimensional analysis is stressed. A historical perspective is provided by an appendix which gives brief biographical information about those engineers and scientists whose names are associated with key developments in fluid mechanics.

This book, the first of a fourpart series on fluid dynamics, consists of four chapters on classical theory suitable for an introductory undergraduate course. Chapter 1 discusses the continuum hypothesis and introduces macroscopic functions. The forces acting inside a fluid are analysed, and the Navier–Stokes equations are derived for incompressible and compressible fluids. Chapter 2 studies the properties of flows represented by exact solutions of the Navier–Stokes equations, including Couette flow between two parallel plates, Hagen–Poiseuille flow through a pipe, and Kármán flow above an infinite rotating disk. Chapter 3 deals with inviscid incompressible flows, starting with a discussion of integrals of the Euler equations, the Bernoulli integral, and the Cauchy–Lagrange integral. Kelvin’s Circulation Theorem is proved, and used to identify physical situations where a flow can be treated as potential. Attention is principally directed at twodimensional potential flows. These can be described in terms of a complex potential, allowing the full power of the theory of functions of a complex variable to be used. The method of conformal mapping is introduced and used to study various flows, including flow past Joukovskii aerofoils. Chapter 4 introduces the elements of gasdynamics, describing compressible flows of a perfect gas, including supersonic flows. Particular attention is paid to the theory of characteristics, which is used, for example, to analyse Prandtl–Meyer flow over a body surface bend and a corner. Shock waves are discussed and the chapter concludes with analysis of unsteady flows, including the theory of blast waves.

In July 2009, many experts in the mathematical modelling of biological sciences gathered in Les Houches for a fourweek summer school on the mechanics and physics of biological systems. The goal of the school was to present to students and researchers an integrated view of new trends and challenges in physical and mathematical aspects of biomechanics. While the scope for such a topic was very wide, the summer school focused on problems where solid and fluid mechanics play a central role. The school covered both the general mathematical theory of mechanical biology in the context of continuum mechanics but also the specific modelling of particular systems in the biology of the cell, plants, microbes, and in physiology. The chapters in this book contain the lecture notes which are organized (as was the school) around five different main topics all connected by the common theme of continuum modelling for biological systems: biofluidics, biogels, biomechanics, biomembranes, and morphogenesis. These notes are not meant as a journal review of the topic but rather as a gentle tutorial introduction on the basic problematic in modelling biological systems from a mechanics perspective.

Many of the distinctive and useful phenomena of soft matter come from its interaction with interfaces. Examples are the peeling of a strip of adhesive tape or the coating of a surface or the curling of a fibre via capillary forces or the electrically driven ow along a microchannel, or the collapse of a porous sponge. These interfacial phenomena are distinct from the intrinsic behaviour of a soft material like a gel or a microemulsion. Yet many forms of interfacial phenomena can be understood via common principles valid for many forms of soft matter. Our goal in organizing this school was to give students a grasp of these common principles and their many ramifications and possibilities. The school comprised over fifty 90minute lectures over four weeks in July 2013. Four fourlecture courses by Howard Stone, Michael Cates, David Nelson, and L. Mahadevan served as an anchor for the program. A number of shorter courses and seminars rounded out the school.This volume presents lecture notes prepared by the speakers and submitted for publication after the school. The lectures are grouped under two main themes: Hydrodynamics and interfaces, and Soft matter.

The book is the second part in a series which describes fluid dynamics. The book introduces asymptotic methods, and their applications to fluid dynamics. It first discusses the mathematical aspects of the asymptotic theory. This is followed by an exposition of the results of inviscid flow theory, starting with subsonic flows past thin aerofoils. This includes unsteady flow theory and the analysis of separated flows. The book then considers supersonic flow past a thin aerofoil, where the linear approximation leads to the Ackeret formula for the pressure. It also discusses the secondorder Buzemann approximation, and the flow behaviour at large distances from the aerofoil. Then the properties of transonic and hypersonic flows are discussed in detail. The book concludes with a discussion of viscous lowReynoldsnumber flows. Two classical problems of the lowReynoldsnumber flow theory are considered: the flow past a sphere and the flow past a circular cylinder. In both cases the flow analysis leads to a difficulty, known as Stoke’s paradox. The book shows that this paradox can be resolved using the formalism of matched asymptotic expansions.

The name “random walk” for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of “Nature”. The same year, a similar problem was formulated by Albert Einstein in one of his Annus Mirabilis works. Even earlier problem was posed by Louis Bachelier in his thesis devoted to the theory of financial speculations in 1900. Nowadays theory of random walks was proved useful in physics and chemistry (diffusion, reactions, mixing in flows), economics, biology (from animal spread to motion of subcellular structures) and in many other disciplines. The random walk approach serves not only as a model of simple diffusion but of many complex sub‐ and superdiffusive transport processes as well. This book discusses main variants of the random walks and gives the most important mathematical tools for their theoretical description.

Xray scattering is a wellestablished technique in materials science. Several excellent textbooks exist in the field, typically written by physicists who use mathematics to make things clear. Often these books do not reach students and scientists in the field of soft matter (polymers, liquid crystals, colloids, and selfassembled organic systems), who usually have a chemicaloriented background with limited mathematics. Moreover, often these people like to know more about xray scattering as a technique to be used, but do not necessarily intend to become an expert. This volume is unique in trying to accommodate both points. The aim of the book is to explain basic principles and applications of xray scattering in a simple way. The intention is a paperback of limited size that people will like to have on hand rather than on a shelf. Second, it includes a large variety of examples of xray scattering of soft matter with, at the end of each chapter, a more elaborate case study. Third, the book contains a separate chapter on the different types of order/disorder in soft matter that play such an important role in modern selfassembling systems. Finally, the last chapter treats soft matter surfaces and thin film that are increasingly used in coatings and in many technological applications (liquid crystal displays, nanostructured block copolymer films). There is a niche for a book of this type that potentially addresses a large group of (soft matter) students and scientists.

This book provides an overview of fundamental methods and advanced topics associated with complex, especially biological, fluids. The contents are taken from a graduate level course taught to biomedical engineers, many of whom are math averse. Consequently the book is organized around gentle historical foundations and illustrative tabletop experiments to make for accessible reading. The book begins with derivations of fundamental equations, defined in the simplest terms possible, and adds embellishments one at a time to build toward the analysis of complex fluid dynamics an and introduction to spontaneous pattern formation. Topics covered include elastic surfaces, flow through elastic tubes, pulsatile flows, effects of entrances, branches, and bends, shearing flows, effects of increased Reynolds number, inviscid flows, rheology in complex fluids, statistical mechanics, diffusion, and selfassembly.

Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a nonnormal operator is studied using an example by Trefethen et al. The integrable models (KdV, Hasimoto’s vortex soliton) and their hamiltonian formalism are studied. Delving into deeper mathematics, geodesics on Lie groups are studied: first using the Lie algebra and then using Milnor’s approach to the curvature of the Lie group. Arnold’s deep idea that Euler’s equations are the geodesic equations on the diffeomorphism group is then explained and its curvature calculated. The next three chapters are an introduction to numerical methods: spectral methods based on Chebychev functions for ODEs, their application by Orszag to solve the Orr–Sommerfeld equation, finite difference methods for elementary PDEs, the Magnus formula and its application to geometric integrators for ODEs. Two appendices give an introduction to dynamical systems: Arnold’s cat map, homoclinic points, Smale’s horse shoe, Hausdorff dimension of the invariant set, Aref ’s example of chaotic advection. The last appendix introduces renormalization: Ising model on a Cayley tree and Feigenbaum’s theory of period doubling.

We present a comprehensive overview of microrheology, emphasizing the underlying theory, practical aspects of its implementation, and current applications to rheological studies in academic and industrial laboratories. Key methods and techniques are examined, including important considerations to be made with respect to the materials most amenable to microrheological characterization and pitfalls to avoid in measurements and analysis. The fundamental principles of all microrheology experiments are presented, including the nature of colloidal probes and their movement in fluids, soft solids, and viscoelastic materials. Microrheology is divided into two general areas, depending on whether the probe is driven into motion by thermal forces (passive), or by an external force (active). We present the theory and practice of passive microrheology, including an indepth examination of the Generalized StokesEinstein Relation (GSER). We carefully treat the assumptions that must be made for these techniques to work, and what happens when the underlying assumptions are violated. Experimental methods covered in detail include particle tracking microrheology, tracer particle microrheology using dynamic light scattering and diffusing wave spectroscopy, and laser tracking microrheology. Second, we discuss the theory and practice of active microrheology, focusing specifically on the potential and limitations of extending microrheology to measurements of nonlinear rheological properties, like yielding and shearthinning. Practical aspects of magnetic and optical tweezer measurements are preseted. Finally, we highlight important applications of microrheology, including measurements of gelation, degradation, highthroughput rheology, protein solution viscosities, and polymer dynamics.

The aim of this book is to understand networks and the basic principles of their structural organization and evolution. The ideas are presented in a clear and a pedagogical way. Special attention is given to real networks, both natural and artificial, including the Internet and the World Wide Web. Collected empirical data and numerous real applications of existing theories are discussed in detail, as well as the topical problems of communication and other networks.

This book presents a dynamic new approach to the physics of enzymes and DNA from the perspective of materials science. Unified around the concept of molecular deformability—how proteins and DNA stretch, fold, and change shape—the book describes the complex molecules of life from the innovative perspective of materials properties and dynamics, in contrast to structural or purely chemical approaches. It covers a wealth of topics, including nonlinear deformability of enzymes and DNA; the chemodynamic cycle of enzymes; supramolecular constructions with internal stress; nanorheology and viscoelasticity; and chemical kinetics, Brownian motion, and barrier crossing. Essential reading for researchers in materials science, engineering, and nanotechnology, the book also describes the landmark experiments that have established the materials properties and energy landscape of large biological molecules. The book gives graduate students a working knowledge of model building in statistical mechanics, making it an essential resource for tomorrow's experimentalists in this cuttingedge field. In addition, mathematical methods are introduced in the biomolecular context. The result is a generalized approach to mathematical problem solving that enables students to apply their findings more broadly.

Soft matter represents a collection of materials such as polymer, colloids, surfactants, and liquid crystals and their composites. These materials do not belong to conventional classes of materials (simple fluids or solids), but they are used extensively in our everyday life and in modern technology (in displays, device manufacturing, energysaving technology, biomedical applications, etc.). Soft matter consists of units much larger than atoms; their typical length is 0.01 μm–100 μm. This gives two characteristics to soft matter: large nonlinear response to external forces; and long relaxation time and slow dynamics. The aim of this book is to discuss the materials of such characteristics for undergraduate and graduate course students explaining basic physical concepts such as phase transition and Brownian motion. Attempts have been made to connect such physics to our experience in everyday life.

The human genome of three billion letters has been sequenced. So have the genomes of thousands of other organisms. With unprecedented resolution, modern technologies are allowing us to peek into the world of genes, biomolecules, and cells, and flooding us with data of immense complexity that we are just barely beginning to understand. A huge gap separates our knowledge of the components of a cell and what is known from our observations of its physiology. This book explores what has been done to close this gap of understanding between the realms of molecules and biological processes. It contains illustrative mechanisms and models of gene regulatory networks, DNA replication, the cell cycle, cell death, differentiation, cell senescence, and the abnormal state of cancer cells. The mechanisms are biomolecular in detail, and the models are mathematical in nature.

This is Part 3 of a book series on fluid dynamics. This is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture courses, and then progressing through more advanced material up to the level of modern research in the field. This book is devoted to highReynolds number flows. It begins by analysing the flows that can be described in the framework of Prandtl’s 1904 classical boundarylayer theory. These analyses include the Blasius boundary layer on a flat plate, the FalknerSkan solutions for the boundary layer on a wedge surface, and other applications of Prandtl’s theory. It then discusses separated flows, and considers first the socalled ‘selfinduced separation’ in supersonic flow that was studied in 1969 by Stewartson and Williams, as well as by Neiland, and led to the ‘tripledeck model’. It also presents Sychev’s 1972 theory of the boundarylayer separation in an incompressible fluid flow past a circular cylinder. It discusses the tripledeck flow near the trailing edge of a flat plate first investigated in 1969 by Stewartson and in 1970 by Messiter. It then considers the incipience of the separation at corner points of the body surface in subsonic and supersonic flows. It concludes by covering the Marginal Separation theory, which represents a special version of the tripledeck theory, and describes the formation and bursting of short separation bubbles at the leading edge of a thin aerofoil.