bluuebunny/crossref_metadata_2025 huggingface dataset:
Nematic Rubber Elasticity
Authors: Warner M , Terentjev E M
Published: November 2023

Nematic networks can be highly rubbery, that is capable of large extensions and com-posed of molecules with liquid-like mobility. The difference between nematic and clas-sical elastomers is principally only that of molecular shape anisotropy induced by the liquid crystalline order. The simplest description of nematic rubber elasticity is essen-tially an extension of classical molecular rubber elasticity, reviewed in Chapter 3. We shall accordingly call it a 'neo-classical' theory of rubber elasticity, referring to the identity of approach. It will be introduced in this chapter and its richness explored in subsequent chapters of this book. This chapter will conclude with simple illustrations of the neo-classical free energy not involving rotations of the director and complex strains. Already remarkable phenomena arise, for instance we describe spontaneous thermal distortion, optical distortions, complex thermal history and relaxation, the Landau the-ory of transitions and the influence of mechanical stress on thermal effects. The nematic rubber elastic free energy is simple, even if the thermo-mechanical history has been complex. Readers unconcerned about the details of how this is so should omit Sect. 6.3, marked :j:, only reading its main conclusion which is stated in its opening paragraph.
Soft Elasticity
Authors: Warner M , Terentjev E M
Published: November 2023

The new element is that changing the director orientation allows a significant reduction in the elastic energy. The first example, Sect. 6.7, was the nematic-mechanical instability seen by Mitchell where the director jumps discontinuously to allow the rubbery network to accommodate the imposed strain. More generally, the director rotates in a continuous fashion. In this chapter we initially illustrate the role of rotation by discussing the relative rotation coupling constant D1(briefly mentioned in Sect. 2.8). The analogous coupling D2 of symmetric network strains to relative rotations is also discussed here. We then address the singular nematic rotational response to strains and the apparent liquid-like mechanical response (low storage moduli) observed for some strain geometries. We call this effect ‘soft elasticity’. Section 6.7 sketched some deformations that apparently cost little or no energy, provided the director changed. Experiments confirm it is indeed nematic rotations that make the new elasticity possible.
Smectic Elastomers
Authors: Warner M , Terentjev E M
Published: November 2023

Smectic elastomers and gels are permanently crosslinked networks of polymers that spontaneously form smectic or lamellar phases. They are as common as nematic networks. From the symmetry point of view there is a great variety of possible phases, combining one-dimensional layered order with various degrees of structure and alignment of mesogenic groups. We shall first consider the most simple smectic order, appropriately called ‘smectic A’ or lamellar Lαa phase, where the molecular anisotropy is coaxial with the layer normal. In other words, the nematic director (which is the principal axis of uniaxial optical birefringence) is locked perpendicular to the smectic layers.
Environmental Exposure Assessment
Authors: Nieuwenhuijsen Mark , Brunekreef Bert
Published: November 2023

Nowadays, health risks associated with environmental exposures are generally small; therefore, exposure assessment needs to be of a high quality to detect a risk when there truly is a risk. Part of the exposure assessment process is to optimize exposure estimates with the aim to detect possible risk and optimize the exposure–response relationship. This can be achieved, for example, by optimizing the distribution of the variance of the exposure estimates [1]. Exposure assessment in environmental epidemiological studies should, and has frequently, made use of both temporal and spatial variability in environ- mental and exposure levels to optimize the estimates, and determining the main sources of variance in each is one of the important aspects of the assessment.
Measurement Error Consequences And Design Issues
Authors: Armstrong Ben
Published: November 2023

This chapter is concerned with the effects that inaccuracy in data, particularly exposure data (including misclassification of exposure) has on results of epidemiological studies. Readers may be aware that such error impacts adversely on studies, but may not be aware just in what way.
Special Study Designs And Analyses In Environmental Epidemiology
Authors: Nieuwenhuijsen Mark
Published: November 2023

This chapter deals with more special designs in environmental epidemiology. A number of these designs are data intensive (time-series, spatial epidemiology and cluster analyses) and use specific statistical methods. These studies generally rely on routinely collected environmental or health data and have a history of statistical method development. The time-series studies specifically make use of temporal variability in both environmental and health data to examine any relationship, while spatial epidemiological studies specifically make use of spatial variability in environmental and health data.
Stakeholder And Participant Involvement
Authors: Rojas Primitivo , Neutra Raymond
Published: November 2023

Environmental epidemiology studies range from analyses of existing data, which involves no contact with study subjects, to sample surveys involving a few percent of a dispersed population where there is not a ‘natural community’ to involve, to disease registry or case control studies where an association of diseased persons may form a community, to particular geographical communities which experience unexplained disease clusters or unusual hazard exposures. For all of these studies there are potential policy implications of the results, and each type of study has different types of potential for stakeholder involvement.
Ethics And Environmental Epidemiology
Authors: Soskolne Colin
Published: November 2023

Epidemiologists, as with other professionals, are paying increasing attention to the topic of ethics; that is, the norms of professional conduct. This is partly because publicly funded enterprises and agencies–many of which employ epidemiologists–need to be held accountable for the activities of their members. This said, it was only recently, in the mid-1980s, that epidemiologists introduced the discussion and consideration of ethics to their profession [1]. Environmental epidemiologists formally acknowledged this topic through the International Society for Environmental Epidemiology (ISEE), which stimulated discussion of ethical issues when it established its Standing Committee on Ethics and Philosophy in 1991.
Using Integrated Assessment To Analyze And Forecast The Future Effects Of Global Environmental Change
Authors: Martens Pim , Huynen Maud
Published: November 2023

Global environmental changes are a manifestation of a larger pattern of change in the scale and intensity of human affairs. Global climate change is one of the most widely discussed of these global environmental changes. In 1996, the UN Intergovernmental Panel on Climate Change (IPCC) concluded that human-made changes in the global atmosphere were probably already beginning to change world climate [1]. During 1997 and 1998, global temperatures reached their highest levels since record keeping began in the mid-nineteenth century. Overall, ten of the twelve hottest years of the twentieth century occurred after 1988.
The Role And Limits Of Epidemiology In Policy Arguments
Authors: Neutra Raymond
Published: November 2023

For the purposes of this chapter, ‘environmental health policy arguments’ is taken to refer to arguments related to decisions about ongoing practices with regard to the physical and chemical environment that are likely to affect rates of disability, disease and death in the human population. This chapter will focus on ways that etiological epidemiology enters into the policy process. The many ways that descriptive epidemiology can be used to inform policy will not be covered here, for it has been admirably discussed elsewhere [1].
Selecting the items
Authors: Streiner David L , Norman Geoffrey R
Published: November 2023

Except for scales that are aimed at a selected group whose educational level is known, the usual rule of thumb is that the scale should not require reading skills beyond that of a 12-year-old. This may seem unduly low, but many people who are high-school graduates are unable to comprehend material much above this level. Many ways have been proposed to assess the reading level required to understand written material. Some methods, like the ‘cloze’ technique (Taylor 1957), eliminate every nth word to see at what point meaning disappears; the easier the material, the more words can be removed and accurately ‘filled in’ by the reader. Other methods are based on the number of syllables in each word or the number of words in each sentence (e.g. Flesch 1948; Fry 1968). However, these procedures can be laborious and time- consuming, and others may require up to 300 words of text (e.g. McLaughlin 1969). These are usually inappropriate for scales or questionnaires, where each item is an independent passage, and meaning may depend on one key word.
Validity
Authors: Streiner David L , Norman Geoffrey R
Published: November 2023

In the previous chapters, we examined various aspects of reliability; that is, how reproducible the results of a scale are under different conditions. This is a necessary step in establishing the usefulness of a measure, but it is not sufficient. The next step is to determine if the scale is measuring what we think it is; that is, the scale’s validity. To illustrate the difference, imagine that we are trying to develop a new index to measure the degree of headache pain. We find that patients get the same score when they are tested on two different occasions, that different interviewers get similar results when assessing the same patient, and so on; in other words, the index is reliable. However, we still have no proof that differences in the total score reflect the degree of headache pain: the scale may be measuring pain from other sources; or it may be tapping factors entirely unrelated to pain, such as depression or the tendency to complain of bodily ailments. In this chapter, we will examine how to determine if we can draw valid conclusions from the scale.
Methods of administration
Authors: Streiner David L , Norman Geoffrey R
Published: November 2023

Having developed the questionnaire, the next problem is how to administer it. This is an issue which not only affects costs and response rates but, as we shall see, may influence which questions can be asked and in what format. The three methods commonly used to administer questionnaires are: face-to-face interviews, over the telephone, and by mail.
Ethical considerations
Authors: Streiner David L , Norman Geoffrey R
Published: November 2023

Initially, the major focus of the professional organizations was on establishing standards for the tests themselves. In 1895, the American Psychological Association (APA) began looking at the feasibility of standardizing ‘mental’ and physical tests (Novick 1981).
Nanofabrication
Authors: Jones Richard A L
Published: November 2023

I do not Jike to think of myself as old, but, in the time it has taken me to grow up, an industry which dominates our world has itself grown to maturity from virtually nothing. That industry is of course the personal computer industry, and the technology on which it is based, in its modern form, is the integrated circuit. When I was fourteen or so, I was being taught to do calculations with a strange analogue device called a slide rule, while one of the richest and most cosmopolitan of my fellow pupils amazed the rest of the class with his new, and very expensive, pocket electronic calculator. By the time that I had left school, I had seen my first personal computer, though of course such devices were far too new-fangled to play any part in my undergraduate education (I went to a very ancient and conservative university). During the time I did my Ph.D., IBM launched their Personal Computer, bringing corporate respectability to what had previously been the domain of hobbyists, and pretty much every aspect of the modern world changed for ever.
Making soft machines
Authors: Jones Richard A L
Published: November 2023

Successful scientists are just as aware of the power of an image as any advertiser or marketer. The image that has, more than any other, defined the promise of nanotechnology was made in 1989 by Don Eigler; appropriately it depicted the logo of a company—IBM—picked out in individual xenon atoms (see figure 5. 1 ). To make the image, individual atoms were moved across a surface into place using a scanning tunnelling microscope, an instrument that was invented in IBM. Enthusiastic disciples of extreme nanotechnology have seized on this image as proof that their goal—the manufacture of nanoscale machines an atom at a time—is now in sight. I think this is wrong. These experiments are a magnificent technical achievement, and they have allowed scientists to study some fascinating new physics. But they are not a step on the path to the development of true nanoscale machines, because they encourage us to think about making these machines in ways that do not take into account how different physics is at these very small scales. It is all too easy to visualise a cantilever that picks up an atom and sets it in its place as being just like a robot arm that picks up some component in a car factory and bolts it onto the engine. This kind of analogy between the macroworld and the nanoworld is both seductive and dangerous. Thinking about nanoscale design in this way leads to the risk that our designs will not work.
Electrophysiology and brain imaging of biological motion
Authors: Puce Aina , Perrett David
Published: November 2023

The movements of the faces and bodies of other conspecifics provide stimuli of considerable interest to the social primate. Studies of single cells, field potential recordings and functional neuroimaging data indicate that specialized visual mechanisms exist in the superior temporal sulcus (STS) of both human and non-human primates that produce selective neural responses to moving natural images of faces and bodies. STS mechanisms also process simplified displays of biological motion involving point lights marking the limb articulations of animate bodies and geometrical shapes whose motion simulates purposeful behaviour. Facial movements such as deviations in eye gaze, important for gauging an individual’s social attention, and mouth movements, indicative of potential utterances, generate particularly robust neural responses that differentiate between movement types.
A Unifying Computational Framework for Motor Control and Social Interaction
Authors: Wolpert Daniel M , Doya Kenji , Kawato Mitsuo
Published: November 2023

Recent empirical studies have implicated the use of the motor system during action observation, imitation and social interaction. In this paper, we explore the computational parallels between the processes that occur in motor control and in action observation, imitation, social interaction and theory of mind. In particular, we examine the extent to which motor commands acting on the body can be equated with communicative signals acting on other people and suggest that computational solutions for motor control may have been extended to the domain of social interaction.
Critical assessment of economic evaluation
Authors: Drummond Michael E , Sculpher Mark J , Torrance George W , O’Brien Bernie J , Stoddart Greg L
Published: November 2023

Those who receive or read an economic evaluation are often faced with the difficult task of assessing study results. The question that readers of evaluations are most likely to ask themselves is’Are these results useful to me in my setting?’ The answer to this question is determined by the answers to the following specific questions.
Cost analysis
Authors: Drummond Michael E , Sculpher Mark J , Torrance George W , O’Brien Bernie J , Stoddart Greg L
Published: November 2023

The analysis of the comparative costs of alternative treatments or health care programmes is common to all forms of economic evaluation and therefore most of the methodological issues discussed in this chapter are likely to be of relevance to all analyses. Although many of the issues surrounding costing are context specific and the analyst’s options are often limited by the availability of data, it is possible to give some general guidance. Three particularly thorny issues, the treatment of overhead costs (techniques for allocating shared overhead costs to individual projects), the allowance for differential timing of costs (the techniques of discounting and annuitization of capital expenditure), and the role and estimation of productivity costs will be discussed in some detail. However, the chapter begins by covering some of the basic questions that an evaluator might have when embarking on a costing study in the health field.
Cost-utility analysis
Authors: Drummond Michael E , Sculpher Mark J , Torrance George W , O’Brien Bernie J , Stoddart Greg L
Published: November 2023

Cost-utility analysis (CUA) is a form of evaluation that focuses particular attention on the quality of the health outcome produced or forgone by health programmes or treatments. It has many similarities to cost-effectiveness analysis {CEA), and thus all the points discussed in Chapter 4 on cost analysis and many of those discussed in Chapter 5 on CEA also apply here. The first section of this chapter reviews some of the general issues the analyst would need to consider when undertaking a CUA. Later sections discuss particular issues in more detail.
Vocal expression of affect
Authors: Juslin Patrik N , Scherer Klaus R
Published: November 2023

Imagine yourself sitting in a cafeteria. Suddenly, you can overhear another person’s conversation without being able to see the person in question. Within a few seconds of hearing that person’s voice, you are able to infer the person’s gender (a female), age (a young woman), and perhaps even her origin (from the south), social status (upper class), and physical health (having a cold). All this you can tell from hearing her voice, even though you are unable to understand the verbal contents of her conversation.
Introduction to the Mathematical Theory of Compressible Flow
Authors: Novotný A , Straškraba I
Published: November 2023

This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to focus on various modules of the material, either in part or more fully. Chapters include detailed heuristic arguments providing motivation for technical aspects that are rigorously presented later on in the text; for instance, the existence theory for steady and unsteady Navier-Stokes equations of isentropic compressible flow, and two-by-two systems of Euler equations in one space dimension. These parts are presented in a textbook style with auxiliary material in supporting sections and appendices. The book includes a rich index and extensive bibliography, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of compressible flow, as well as in the book itself.
Weak Solutions For Nonsteady Navier–Stokes Equations Of Compressible Barotropic Flow
Authors: Novotný A , Straškraba I
Published: November 2023

This chapter is devoted to the weak solvability of nonstationary compressible Navier–Stokes equations in the barotropic regime, and to the investigation of some of their qualitative properties. In Section 7.1 we formulate the problem in bounded and exterior domains with homogenous Dirichlet boundary conditions and state the main results. In the next section (Section 7.2), we study the continuity with respect to time of the linear momentum and of the total energy. The main ideas to prove existence and the main difficulties of the proof are explained in Section 7.3. Then, in Section 7.4 we introduce the chain of approximations which we use to solve the original problem. Section
Foundations of Modern Cosmology
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

Recent discoveries in astronomy, especially those made with data collected by satellites such as the Hubble Space Telescope and the Wilkinson Microwave Anisotropy Probe, have revolutionized the science of cosmology. These new observations offer the possibility that some long-standing mysteries in cosmology might be answered, including such fundamental questions as the ultimate fate of the universe. Foundations of modern cosmology provides an accessible, thorough and descriptive introduction to the physical basis for modern cosmological theory, from the big bang to a distant future dominated by dark energy. This second edition includes the latest observational results and provides the detailed background material necessary to understand their implications, with a focus on the specific model supported by these observations, the concordance model. Consistent with the book’s title, emphasis is given to the scientific framework for cosmology, particularly the basics concepts of physics that underlie modern theories of relativity and cosmology; the importance of data and observations is stressed throughout. The book sketches the historical background of cosmology, and provides a review of the relevant basic physics and astronomy. After this introduction, both special and general relativity are treated, before proceeding to an in-depth discussion of the big bang theory and physics of the early universe. The book includes current research areas, including dark matter and structure formation, dark energy, the inflationary universe, and quantum cosmology.
Lighting the Worlds
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

Humanity contemplates the cosmos from the restricted vantage point of a small planet near the edge of an out-of-the-way galaxy. How it is that we can learn anything at all about so vast a thing as the universe? The universe is more than its contents alone; the physical laws that govern the interactions among objects tell us the properties of the cosmos. From the smallest elementary particles to the largest galaxy cluster, the rules of the universe leave their mark.
Infinite Space and Absolute Time
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

What is the universe? If the universe is everything, can there be anything beyond it? Where do we fit into the universe? How was the universe created? What will be its eventual fate? With all the complexity that we see immediately around us, how can we hope to understand something so intricate on even larger scales? Such questions have been asked for as long as we have any traces of human thoughts. The answers that have been imagined have been profound, or philosophical, or fanciful, or stern; but until the development of modern science, the explanations offered had less to do with the way the universe was, than the way humans imagined it might be. The universe remained mysterious and ineffable.
Modeling the Universe
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

Two major developments, Hubble’s observations and Einstein’s theory of general relativity, moved the subject of cosmology out of the realm of the mainly philosophical and firmly into the arena of science. Now the task of developing an actual model of a dynamic universe lies before us. While at first glance it may seem an impossible undertaking, we are aided by the adoption of the cosmological principle. This is an enormous simplification, for it implies that the metric which describes space and time, and specifies their evolution, must be the Robertson–Walker metric.
The Early Universe
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

The recognition that the universe is expanding leads naturally to the question of its origins. From what might the universe have expanded? What might the universe have been like when it was much smaller? What does “smaller” mean for a universe? Within the standard models, a straightforward projection to earlier time leads to the conclusion that the universe was once much denser and more compact than it is today. Indeed, taking this to its ultimate limit, the universe was infinitely dense at that cosmic time when the scale factor R was zero.
A Message from the Big Bang
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

When the Sun sets the night sky darkens, lit up only here and there by points of lights we now know to be distant suns. But why is the sky dark at night? The sky is bright during the day because the Sun is so close, and therefore its light fills the sky when it is visible; at night, conversely, it might be argued that the distant stars cannot brighten the sky. But this argument is inadequate, a fact which Kepler was one of the first to recognize. If the universe is infinite, and contains an infinite number of stars that live forever, then every line of sight must end on a star. It is true that a star’s light diminishes as the square of the distance, but the volume of space sampled increases by exactly the same factor as distance becomes greater.
Knots and Surfaces
Authors: Gilbert N D , Porter T
Published: November 2023

The main theme of this book is the mathematical theory of knots and its interaction with the theory of surfaces and of group presentations. Beginning with a simple diagrammatic approach to the study of knots, reflecting the artistic and geometric appeal of interlaced forms, Knots and Surfaces takes the reader through recent advances in our understanding to areas of current research. Topics included are straightforward introductions to topological spaces, surfaces, the fundamental group, graphs, free groups, and group presentations. These topics combine into a coherent and highly developed theory to explore and explain the accessible and intuitive problems of knots and surfaces. Both as an introduction to several areas of prime importance to the development of pure mathematics today, and as an account of pure mathematics in action in an unusual context, this book presents novel challenges to students and other interested readers.
Topological spaces
Authors: Gilbert N D , Porter T
Published: November 2023

The purpose of this chapter is to provide the theoretical background for a rigorous discussion of knots and surfaces, against which the vaguely expressed ideas lying behind our previous discussion can be made precise. The central notion is that of a topological space. The precision that topological spaces bring to the ideas of continuity and nearness is, of course, essential to any proper treatment of knots and surfaces. Moreover, topological ideas will prove crucial in the development of more sophisticated invariants in later chapters. Since our interest in topological spaces stems from specific applications that we already have in mind, we make no attempt to give a comprehensive account of even the basic theory of topological spaces here. There are several textbooks that do the job well, and we mention Armstrong (1983) and Brown (1988) as providing suitable further reading.
Presentations of groups
Authors: Gilbert N D , Porter T
Published: November 2023

We need group theory so as to be able to handle some of the deeper invariants of knots, in particular the group of a knot. We might expect the type of group theory needed would be fairly limited and somewhat specialized. However, the overall process translating geometric problems into algebraic ones is very much two way-algebra pervades the topology and vice versa-so quite a lot of group theory turns out to have implications in topology, whilst the topology can provide new methods and insights in group theory. Attempts to compartmentalize mathematics fail; there are too many important links joining apparently distinct branches. There is an underlying and all-pervading logical structure that is difficult to pin down and to see clearly, but which is none the less there behind all of mathematics.
Van Kampen’s theorem
Authors: Gilbert N D , Porter T
Published: November 2023

In this chapter we will examine the statement and proof of the Van Kampen theorem. If you glance forward to where this theorem is stated in full and in detail, you may wonder why such an apparently technical theorem is needed. Complicated theorems occur at numerous places within mathematics courses at this level and students often ask themselves why such theorems are deemed necessary. Again it is often the case that the lecturers have used the results explicitly or implicitly so many times in research projects that it becomes selfevident to them that these theorems are important and hence it can be extremely difficult to explain their importance to someone meeting them for the first time. With the Van Kampen theorem, we are lucky. We have been developing the theory of the fundamental group and if we pause to take stock of our present knowledge (and ignorance), it should become clearer why theorems of the Van Kampen type are needed. An even closer look will suggest what it should say and will also give us a sketch proof. Writing out a formal proof is another matter and will be dealt with later on; the first priorities are to guess what the result will say (before we meet its detailed statement), to see why the result is true and why certain technical restrictions are necessary; the details of the formal proof are (initially) somewhat less important. Once you understand the idea of the proof the details can be seen merely as the ‘justification of the obvious’.
Rank-1 rules-the method of good lattice points
Authors: Sloan I H , Joe S
Published: November 2023

In this chapter we look at rank-1 rules, which are rules of the form where z is an s-dimensional integer vector having no factor in common with N. Such rules were first introduced by Korobov (1959), Bahvalov (1959), and Hlawka (1962). They are often referred to as number-theoretic rules since their accuracy is related to the number-theoretic properties of N and the components of z (for example, see Korobov 1963 or Hua and Wang 1981).
Lattice rules of higher rank-a first look
Authors: Sloan I H , Joe S
Published: November 2023

In this chapter we begin the quantitative study of lattice rules of higher rank. In Chapters 2 and 3 we looked at the structure of lattice rules and at their representations as multiple sums. Now we turn to the question of how good such rules might be.
Maximal rank lattice rules
Authors: Sloan I H , Joe S
Published: November 2023

In this chapter we look at lattice rules that have the maximal rank s. We meet a simple characterization of maximal rank rules, and show that some maximal rank rules yield outstandingly attractive error bounds. Later in this book we shall see that maximal rank rules have other attributes that make them attractive in computational algorithms.
Practical implementation of lattice rules
Authors: Sloan I H , Joe S
Published: November 2023

In previous chapters we have been mainly concerned with the theoretical properties of lattice rules. Now in this chapter we turn to practical matters. We recall that Chapter 6 gave theoretical grounds for believing that it would be advantageous to use lattice rules of maximal rank.
Surface properties: electronic
Authors: Prutton M
Published: November 2023

The earlier chapters have concentrated upon the techniques required to obtain information about what kind of atoms are present at a surface and where they are situated. As the need for other techniques arises they will be discussed, but now attention will be turned towards the ways in which the properties of surfaces can be related to their composition and structure. The calculation of the electronic states at a surface is bound to be more complex than the corresponding calculation for electrons inside a solid. The latter is complicated enough, because the least tightly bound electrons are free to move in the periodic potential established by the arrangement of nuclei and tightly bound electrons the ion cores. Furthermore, the moving electrons repel each other because of their negative charges. Thus, Schrodinger’s equation has to be solved for a many-body periodic potential. This is rarely analytically possible. Various approximations are sought whose complexity depends upon the physical property being described and the precision needed to compare this property with experimental measurements. Free electron theory treats the periodic arrangement of positively charged ion cores in a crystal as a smeared out, generally attractive, potential for the gas of free electrons.
Surface properties: atomic motion
Authors: Prutton M
Published: November 2023

Up to this point the discussion of both methods and properties has been in terms of rigid lattices of atoms or molecules. In practice, of course, the atoms are in motion, and this motion should be included in a treatment of any properties it may affect. In this chapter the atomic vibrations at a surface will be discussed, as they reveal themselves in the temperature dependence of the intensity of a LEED pattern and in special features in electron-loss spectra. More extreme atomic motions occurring during the melting of a surface and during the motion of an adatom across it will also be outlined. It is well known that there is a fall in the intensity of the beams in an X-ray diffraction experiment (using a bulk single crystal) as the crystal temperature is raised. At the same time the intensity in the diffuse background of the diffraction pattern becomes higher. The simplest explanation of these observations is that the individual atoms of the crystal are vibrating independently about their equilibrium positions and, as a result, the exact Bragg conditions is not met. This is because scattered waves from the rigid lattice that were adding up in phase now have phase differences fluctuating with time due to the motion of the scatterers.
The Gauss Linking Number in Quantum Gravity
Authors: Gambini Rodolfo , Pullin Jorge
Published: November 2023

We show that the exponential of the Gauss (self-)linking number of a knot is a solution of the Wheeler-DeWitt equation in loop space with a cosmological constant. Using this fact, it is straightforward to prove that the second coefficient of the Jones polynomial is a solution of the Wheeler-DeWitt equation in loop space with no cosmological constant. We perform calculations from scratch, starting from the connection representation and give details of the proof. Implications for the possibility of generation of other solutions are also discussed.
Oxford Studies In Probability 4
Authors: Petrov Valentin V
Published: November 2023

This book is devoted to limit theorems and probability inequalities for sums of independent random variables. It includes limit theorems on convergence to infinitely divisible distributions, the central limit theorem with rates of convergence, the weak and strong law of large numbers, the law of the iterated logarithm, and also many inequalities for sums of an arbitrary number of random variables. The aim of the book is two-fold. First, the book can be a basis for a course in probability for graduate or advanced undergraduate students. Second, the book can serve as a reference formulations of many (mostly recent) results which are usually inaccessible in book form. These supplements border on the basic text and make it possible for the reader to look at the frontier of modern investigations.
Weak limit theorems: convergence to infinitely divisible distributions
Authors: Petrov Valentin V
Published: November 2023

Consider a sequence of series of random variables that are independent within each series. Suppose k. oo as n oo. We set ourselves the task of finding all the limit distributions for sums of the form as n -> oo.
Weak limit theorems: the central limit theorem and the weak law of large numbers
Authors: Petrov Valentin V
Published: November 2023

In Chapter 3 we studied the conditions under which the distributions of sums of independent random variables will converge to a limit distribution. We were interested in the weak convergence of distributions; the corresponding limit theorems are called the weak limit theorems, contrary to the strong limit theorems making use of the convergence almost surely. The necessary and sufficient conditions were found for the weak convergence of distributions of sums of independent random variables to a given infinitely divisible distribution. These conditions are quite complicated but are very helpful when we are looking for simpler conditions of convergence to a prescribed infinitely divisible distribution such as a normal, a degenerate, or a Poisson distribution.
Strong limit theorems: the strong law of large numbers
Authors: Petrov Valentin V
Published: November 2023

The second part of this lemma was found by Erdös and Renyi. In a traditional formulation of the Borel-Cantelli lemma the condition of pairwise independence is replaced by the stronger condition of the mutual independence of the events A1, ... , An for every n.
The Transmission Problem Revisited
Authors: Dassios George , Kleinman Ralph
Published: November 2023

In this chapter we present another derivation of the low frequency expansions for transmission problems. In contrast to the problems involving impenetrable scatters, the existence of fields in v- in transmission problems enables an alternate derivation of low frequency expansions employing volume integrals over v-. In many respects the procedure for determining the coefficients in low frequency expansions is simpler than that based entirely on boundary integrals. In acoustics the lossless case was treated in Dassios (1977) and the lossy case was considered in Dassios (1989b) but not in the explicit form presented here. The development in acoustics and electromagnetics has not appeared in the literature, while the material on elasticity is based on the work of Kiriaki and Polyzos (1988).
Rayleigh Scattering
Authors: Dassios George , Kleinman Ralph
Published: November 2023

In this chapter we particularize the general results of Chapters 3 and 4 to the first nontrivial terms in the low frequency expansions known as Rayleigh approximations or Rayleigh terms of both the near and the far fields. Also included are the leading terms in the scattering cross sections. These results are given for general shapes in terms of the potential functions to which they have been reduced in Chapters 3 and 4. For acoustics and electromagnetics, most of the material in this chapter refers to results obtained in the 1960s and the 1970s by a number of researchers such as D. S. Jones, R. E. Kleinman, T. B. A. Senior, V. Twersky, J. Van Bladel and many others. The corresponding material in elasticity was developed in the 1980s by G. Dassios, K. Kiriaki, D. Polyzos and others.
The Ellipsoid
Authors: Dassios George , Kleinman Ralph
Published: November 2023

In this chapter we present explicit results for low frequency scattering by a triaxial ellipsoid with semi-axes  a  1 > a  2 > a  3 > 0. Results for rotationally symmetric ellipsoids are easily obtained by setting a  2 = a  3 (prolate spheroid) or a  1 = a  2 (oblate spheroid). Results for the sphere may be recovered by a limiting process from either a prolate or an oblate setting, but this is not always a trivial calculation due to the occurrence of indeterminate forms. No such difficulties occur in the reduction of ellipsoids to spheroids.
Spin Precession and Spin Depolarization
Authors: Karlsson Erik b.
Published: November 2023

The major part of this book will deal with techniques and experimental results from DPAC and μSR, which are methods based on the observation of the spin precession and spin relaxation of nuclei and positive muons respectively. This chapter includes general equations of spin motion common to NMR and EPR spectroscopies as well as to the methods of interest here, some useful analogies between NMR, DPACt and μSR, and a discussion of the number of probe spins necessary to record useful spectra with each of these methods. Since both DPAC and μSR signals are detected by radiation emitted from probe nuclei or particles which themselves are radioactive, there will also be a discussion of how these radiations are detected most efficiently with a view to extracting maximum information on the solid state systems probed.
Defects in Metals
Authors: Karlsson Erik b.
Published: November 2023

Isolated impurity atoms in an otherwise perfect metallic crystal form point defects in the crystals. Heavy atoms enter the host metal lattices substitutionally, and the point symmetry at such sites is the same as that for the host atoms. The EFGs at the nuclei of impurity atoms depend on the local electronic structure around these centres as well as on the symmetry and distances to the charged ion cores in the host crystal. Therefore data on EFGs contain implicit information on the electronic structure of the point defects. EFGs at point defects cannot be straightforwardly predicted from the parameters determined in a usual band-structure calculation, since such a calculation would require a detailed knowledge of the wave functions in the vicinity of the impurity atom. A theoretical approach based on a simulation of the ‘impurity plus nearest host metal atoms’ by a sufficiently large molecular cluster is a more appropriate basis for predictions of impurity EFGs and has been attempted in a few cases (Lindgren 1986). However, most of the comparison between experimental data and theory is still at a much less ambitious level. Since the experimental data are of fairly high accuracy, they can be said to form a future resource for testing electronic structure calculations for impurities in metals-a topic of considerable interest for materials science.
Semiconductors
Authors: Karlsson Erik b.
Published: November 2023

The physics of semiconductors is a vast field, rich in physical phenomena and extremely fertile when it comes to technical applications. The methods discussed here represent an almost vanishing fraction of the total number of works on semiconductors; however, they can be said to observe some of the phenomena from a new and different point of view and therefore provide interesting complementary information. PAC and μ.SR spectroscopies have both contributed: the first mainly as a tool to study the existence and geometry of certain defect centres under specified annealing conditions, and the second mainly as a way to mimic H impurities in Si, Ge, and 111-V (GaAs-type), II-VI (CdTe-type), and I-VII (CuCl-type) semiconductors. Both methods have also been used to observe changes in the properties of such defect centres under different p- or n-doping conditions.
Hydrogen and Hydrogen-like Impurities in Metals
Authors: Karlsson Erik b.
Published: November 2023

In Chapter 8 the properties of hydrogen-like impurities and their interaction with heavier trace elements in Si were discussed in some detail. The physics of hydrogen impurities in metals is essentially different: they do not form paramagnetic centres, they are much more mobile (and are sometimes described as a lattice gas filling the metallic lattice at higher concentrations), and as a consequence of the mobility they are easily trapped by other fixed defects in a metallic solid.
Quantum Diffusion of Light Interstitial Particles
Authors: Karlsson Erik b.
Published: November 2023

In the introduction to Chapter 9, as well as in the examples discussed earlier, we have referred to a set of potential wells for hydrogen and positive muons provided by the different interstitial sites. Between these wells there are potential barriers which the particles must overcome during diffusion. The activation energies quoted in the examples are a rough measure of the heights of these barriers.
The Quantum Theory Of Potential Scattering
Authors: Fröbrich P , Lipperheide R
Published: November 2023

Potential scattering is the scattering of two collision partners whose mutual interaction is described by a static potential. This potential depends in general on the structure of the collision partners, in particular, on their size and shape (usually taken as spherical), but once the potential is specified and the centre-of-mass motion is separated out, the scattering problem in the remaining relative coordinate reduces to the description of the motion of a point-particle with a mass equal to the reduced mass of the two collision partners in the static field of the interaction potential. Only elastic scattering can be described in this way.
Semiclassical Scattering
Authors: Fröbrich P , Lipperheide R
Published: November 2023

Although the nuclear scattering systems are so small that their quantitative description must generally be based on quantum theory, it is often found that a classical treatment is quite adequate. In fact, it was the application of purely classical laws of motion to the scattering of a-partidcs which led Rutherford to the discovery of the nucleus in 1911, years before the corresponding quantum laws had been formulated. Therefore, the question arises whether quantum scattering theory can be formulated in such a way that the connection with classical mechanics is uncovered; and whether one may then define conditions under which the quantum expressions can be approximately written in terms of purely classical quantities. This is indeed the case. The corresponding approximation is the semiclassical approximation. The condition under which it is valid is essentially that the wavelength characterizing the scattering wave function is small compared with the relevant dimensions of the scattering system.
The Wave-Optical Description Of Potential Scattering
Authors: Fröbrich P , Lipperheide R
Published: November 2023

In the preceding chapter we have discussed the semiclassical approximation to quantum scattering theory, where the dynamics is described in terms of classical trajectories. By analytic continuation of these trajectories into the complex plane the treatment has even been extended to the scattering by complex, i.e. absorptive, potentials.
Deep-inelastic collisions. Phenomena and theory
Authors: Fröbrich P , Lipperheide R
Published: November 2023

So far we have been concerned with direct and compound-nucleus reactions. We shall now consider another type of reaction, the dissipative or deep-inelastic collisions (DIC), which display features of both of the former. Deep-inelastic collisions are special to heavy ions, and are the more pronounced the heavier the collision partners. They can be described in classical terms, and generally take place at intermediate impact parameters. For large impact parameters they go over into the direct or quasi-elastic reactions, and for small impact parameters into fusion.
How to Give an LDS Formulation for a Logic
Authors: Gabbay Dov M
Published: November 2023

This chapter is concerned with the problem of how to give an LDS formulation into a traditionally presented logic. Given a logical system presented to us as a Hilbert system or as a Gentzen system or via tableaux or possibly via some algebraic semantics, we want to present it as an LDS system with a suitable algebra of labels. We realise there may be more than one way of doing it. We have to be more clear in what we mean by ‘presenting it’.
A General Theory of Structured Consequence Relations
Authors: Gabbay Dov M
Published: November 2023

In previous chapters we introduced a systematic framework where the logical units are labelled formulas (of the form t : A, where tis a term in some algebra) and where the logical rules are rules for manipulating both formulas and their labels. The intuition behind LDS is that in t : A, A carries declarative information and the label t, represents further information of a different nature which we do not want to ‘code’ into A. It turns out that many monotonic, non-monotonic and probabilistic systems can be presented as LDS systems. An LDS database Δ is a constellation of labelled formulas with additional structure on the labels.