bluuebunny/crossref_metadata_2025 huggingface dataset:
Sexuality and Space
Authors: Elder Glen , Knopp Lawrence
Published: November 2020

. . . I have noticed with some dismay in recent years the appearance of tables representing various strange groups attending meetings of the Association of American Geographers. Marxist Geographers and Gay Geographers come to mind, and I wonder what next? Are we going to have a table of Whores in Geography, and Russian Communist Geography? . . . As for special tables, rooms and meeting times for such groups as Gay Geographers, we should flatly refuse any such groups the right to such representation. When engaging in their gay behavior they are not acting as geographers. . . . Our exclusion of such groups cannot be taken as a moralistic stand on the part of the Association, but simply as a professional one. It is not our business to support the Gay or the Street Walkers, or the Democrats or the Republicans. None of these groups, though they may have members or practitioners in geography, can be said to be geographers, per se. They should then not be permitted official or even associative status at our meetings. We have plenty to do in geography, and room for greater diversity of professional interest than almost any other society. There are, however, limits. We should confine our meetings to geography by geographers and for geographers. All others keep out. Carter (1977: 101–2) . . . In 1996, the Sexuality and Space Specialty Group (SSSG) came into being as a forum for addressing the sorts of sentiments expressed in the letter above, and for exploring the unquestioned heterosexuality of the geographical enterprise. While the sentiments expressed may seem extreme, they point to disciplinary resistances to certain lines of inquiry. The comments and the subsequent creation of the SSSG reveal how the topical contours of geography are, and always have been, politically negotiated. Until recently, sexuality research in geography had been considered especially out of place (see Valentine 1998; Chouinard and Grant 1995). Organized collectively under the aegis of the AAG, the SSSG represents considerable political will and work. Its presence underscores how marginalized groups can never take for granted their place in society, including the academy.
Urban Geography
Authors: Aitken Stuart , Mitchell Don
Published: November 2020

The study of urbanization processes and urban spaces is contentious and problematic. Different disciplines focus on different processes and ways of knowing, and urban life—its contexts and problems—is tugged and twisted in so many directions that it is difficult to know the appropriate questions to ask, let alone to articulate future research directions. Mayors and other city leaders are concerned about civic boosterism and the quality of life in their cities, planners try to manage competing claims on space and movement, and environmentalists grapple with degradation and equity, while economists conjure up more appropriate models of development and growth. The urban arena is a context for competing intellectual claims and traditions that at times converge on consensus but more often than not garner dissent. We forefront our appraisal of the subfield with a contention that guides most of what is to follow. The contention is important because it necessarily limits the kinds of research we talk about. We argue that with the emergence of a more sophisticated articulation of spatial theory in the last decade, geographers are now well positioned to say something important about the urban issues that are shaping the new millennium. This sea change occurred in the 1990s and now places many aspects of geographic research at the forefront of urban analysis. The articulation of spatial theory comes in large part from two sources: first, critical geography with its focus on the spatial construction of social life and, second, from emerging ideas about technology and space. It is not our intention to dismiss the importance of empirical and interpretative studies, which are discussed tangentially in relation to the central theoretical themes of the chapter. In this review, however, we emphasize the articulation of spatial theory as a significant development in urban geography as we enter the twenty-first century. We begin in the first main section by picking up where “The Urban Problematic” left off in Geography in America (1989). We describe the ways in which American geography is rising to the challenge of understanding the tremendous changes that are underway in cities and argue that the work of urban geographers focusing on the roles of space and scale is critical to understanding these changes.
Hazards
Authors: Montz Burrell E. , Cross John A.
Published: November 2020

In August of 1992, Hurricane Andrew battered south-eastern Florida, causing fifty-eight deaths, and more than $27 billion in property losses (National Climatic Data Center 1999). The following year, widespread flooding occurred within the Upper Mississippi River basin, inundating 5.3 million hectares during the worst flood to affect much of the region in this century. The Northridge earthquake (magnitude 6.7) led to sixty-one deaths and more than $20 billion in property damage and loss in 1994. A year later, Kobe, Japan, experienced a magnitude 6.9 earthquake. Despite massive efforts to prepare for such events, more than 6,000 lives were lost, and $150–200 billion in property damage was experienced. In 1998, Hurricane Mitch devastated Honduras, Nicaragua, and other parts of Central America. More than 5,600 people died in Honduras alone and approximately 70,000 homes were damaged. In Nicaragua, more than 850,000 people were affected, with approximately 2,860 deaths. Estimates of losses in agriculture, housing, transportation and other infrastructure are in excess of $1.3 billion dollars (United Nations Office for the Coordination of Humanitarian Affairs 1998). These are just a few, albeit particularly devastating, events that continued to focus our attention in the 1990s on hazards and disasters. The widespread news media coverage of these disaster events provided a backdrop for fictional portrayals as Hollywood rediscovered the disaster movie genre. With enhanced special effects and big-named stars, popular films such as Twister, Volcano, Dante’s Peak, Armageddon, Deep Impact, Titanic, and A Civil Action added a different slant to the media coverage of disasters and the public’s perception of hazards throughout the decade. The public’s interest and fascination in actual disasters also propelled several books to the bestseller list (Barry 1997; Junger 1997; Larson 1999). Both the fictional representations and the consequences of real disasters illustrate the shift in our understanding of the forces at work in such events. Some of the damage in Hurricane Andrew, for example, is attributed to inadequate enforcement of building standards. In Kobe, structures engineered to withstand seismic activity failed, prompting concern about just how safe infrastructure is in tectonically active areas. And Hurricane Mitch’s devastating toll cannot be explained solely by the storm. Decades of land abuse and a combination of social, political, and economic factors combined with the storm to cause the severe losses.
On Computable Numbers: Corrections and Critiques
Authors: Turing Alan , Post Emil
Published: November 2020

As is not uncommon in work of such complexity, there are a number of mistakes in ‘On Computable Numbers’. Turing corrected some of these in his short note 2.1, published in the Proceedings of the London Mathematical Society a few months after the original paper had appeared. The mathematician Emil L. Post’s critique of ‘On Computable Numbers’ was published in 1947 and formed part of Post’s paper ‘Recursive Unsolvability of a Problem of Thue’. Post is one of the major figures in the development of mathematical logic in the twentieth century, although his work did not gainwide recognition until after his death. (Born in 1897, Post died in the same year as Turing.) By 1936 Post had arrived independently at an analysis of computability substantially similar to Turing’s. Post’s ‘problem solver’ operated in a ‘symbol space’ consisting of ‘a two way infinite sequence of spaces or boxes’. A box admitted ‘of but two possible conditions, i.e., being empty or unmarked, and having a single mark in it, say a vertical stroke’. The problem solver worked in accordance with ‘a fixed unalterable set of directions’ and could perform the following ‘primitive acts’: determine whether the box at present occupied is marked or not; erase any mark in the box that is at present occupied; mark the box that is at present occupied if it is unmarked; move to the box to the right of the present position; move to the box to the left of the present position. Later, Post considerably extended certain of the ideas in Turing’s ‘Systems of Logic Based on Ordinals’, developing the important field now called degree theory. In his draft letter to Church, Turing responded to Post’s remarks concerning ‘Turing convention-machines’. It is doubtful whether Turing ever sent the letter. The approximate time of writing can be inferred from Turing’s opening remarks: Kleene’s review appeared in the issue of the Journal of Symbolic Logic dated September 1947 (12: 90–1) and Turing’s ‘Practical Forms of Type Theory’ appeared in the same journal in June 1948.
History of Hut 8 to December 1941 (1945)
Authors: Mahon Patrick
Published: November 2020

Patrick Mahon (A. P. Mahon) was born on 18 April 1921, the son of C. P. Mahon, Chief Cashier of the Bank of England from 1925 to 1930 and Comptroller from 1929 to 1932. From 1934 to 1939 he attended Marlborough College before going up to Clare College, Cambridge, in October 1939 to read Modern Languages. In July 1941, having achieved a First in both German and French in the Modern Languages Part II, he joined the Army, serving as a private (acting lancecorporal) in the Essex Regiment for several months before being sent to Bletchley. He joined Hut 8 in October 1941, and was its head from the autumn of 1944 until the end of the war. On his release from Bletchley in early 1946 he decided not to return to Cambridge to obtain his degree but instead joined the John Lewis Partnership group of department stores. John Spedan Lewis, founder of the company, was a friend of Hut 8 veteran Hugh Alexander, who effected the introduction. At John Lewis, where he spent his entire subsequent career, Mahon rapidly achieved promotion to director level, but his health deteriorated over a long period. He died on 13 April 1972. This chapter consists of approximately the first half of Mahon’s ‘The History of Hut Eight, 1939–1945’. Mahon’s typescript is dated June 1945 and was written at Hut 8. It remained secret until 1996, when a copy was released by the US government into the National Archives and Records Administration (NARA) in Washington, DC. Subsequently another copy was released by the British government into the Public Record Office at Kew. Mahon’s ‘History’ is published here for the first time. Mahon’s account is first-hand from October 1941. Mahon says, ‘for the early history I am indebted primarily to Turing, the first Head of Hut 8, and most of the early information is based on conversations I have had with him’.
Letter to Winston Churchill (1941)
Authors: Turing Alan , Welchman Gordon
Published: November 2020

During 1941, codebreaking at Bletchley Park was hindered by shortages of typists and unskilled staff. These shortages could have been easily rectified, but the codebreakers’ urgent requests were ignored by offcials in Whitehall. Going over the heads of those in command at GC & CS, Turing and his co-signatories wrote directly to the Prime Minister, Winston Churchill. On receiving the letter Churchill minuted his Chief of Staff, General Ismay: ‘action this day Make sure they have all they want on extreme priority and report to me that this had been done.’ It fell to Stuart Milner-Barry of Hut 6 to deliver the letter by hand to 10 Downing Street. In 1986, Milner-Barry recalled his trip to Whitehall: Why I was deputed to carry the letter to No. 10 I do not remember—at a guess, because I was the most readily expendable from the scene of action. What I do recall is arriving at Euston Station, hailing a taxi, and with a sense of total incredulity (can this really be happening?) inviting the driver to take me to 10 Downing Street. The taxi-driver never blinked an eyelid: without comment he directed himself to Whitehall. Arrived at the entrance to Downing Street, I was again surprised at the lack of formality: there was just a wooden barrier across the road, and one uniformed policeman who waved my driver on. At the door to No. 10 I paid off the taxi, rang the bell, was courteously ushered in, explained that I had an urgent letter which I was anxious to deliver to the Prime Minister personally, and was invited to wait. Of course I did not see the Prime Minister himself; but very shortly there appeared a dapper dark-suited figure of shortish stature whom I subsequently identified as Brigadier Harvie-Watt, Mr. Churchill’s PPS from 1941 to 1945. To him I again explained my errand; and while obviously and understandably puzzled as to who I might be and what this was all about, he took me sufficiently seriously to promise that he would without fail deliver the letter to the Prime Minister and stress its urgency.
Analytic program derivation in type theory
Authors: Mäenpää Petri
Published: November 2020

This work proposes a new method of deriving programs from their specifications in constructive type theory: the method of analysis-synthesis. It is new as a mathematical method only in the area of programming methodology, as it is modelled upon the most successful and widespread method in the history of exact sciences. The method of analysis-synthesis, also known as the method of analysis, was devised by Ancient Greek mathematicians for solving geometric construction problems with ruler and compass. Its most important subsequent elaboration is Descartes’s algebraic method of analysis, which pervades all exact sciences today. The present work expands this method further into one that aims at systematizing program derivation in a heuristically useful way, analogously to the way Descartes’s method systematized the solution of geometric and arithmetical problems. To illustrate the method, we derive the Boyer-Moore algorithm for finding an element that has a majority of occurrences in a given list. It turns out that solving programming problems need not be too different from solving mathematical problems in general. This point of view has been emphasized in particular by Martin-Löf (1982) and Dijkstra (1986). The idea of a logic of problem solving originates in Kolmogorov (1932). We aim to refine the analogy between programming and mathematical problem solving by investigating the mathematical method of analysis in the context of programming. The central idea of the analytic method, in modern terms, is to analyze the functional dependencies between the constituents of a geometric configuration. The aim is to determine how the sought constituents depend on the given ones. A Greek analysis starts by drawing a diagram with the sought constructions drawn on the given ones, in the relation required by the problem specification. Then the sought constituents of the configuration are determined in terms of the given ones. Analysis was the Greeks’ method of discovering solutions to problems. Their method of justification was synthesis, which cast analysis into standard deductive form. First it constructed the sought objects from the given ones, and then demonstrated that they relate as required to the given ones. In his Geometry, Descartes developed Greek geometric analysis-synthesis into the modern algebraic method of analysis.
Gene regulation and cell heredity
Authors: Maynard Smith John , Szathmary Eors
Published: November 2020

Two cellular mechanisms are essential for development. The first, gene regulation, makes it possible to switch on different genes in different cells, in response either to conditions external to the cell or to the activity of other genes within the cell. The second, cell heredity, ensures that these states of gene activity, once induced, can be stably transmitted through cell division, without the need for the continued presence of an external inducer. In this chapter, we describe how gene regulation and cell heredity are achieved in metazoans, and point to some similar mechanisms that are already present in prokaryotes. The central problem of gene regulation was posed, in a social context, by the scholastic Master Eckhardt: ‘Quis custodiet ipsos custodes?’ [Who regulates the regulators?] Clearly, the proposition that every gene needs a separate regulator gene leads to an infinite regress. There are various ways of resolving the paradox, which include one regulator controls several other genes, including regulators; one gene, even a regulator, is controlled by several other genes; and some genes may be both regulatory and structural. Plenty of examples are known for each case. It is also necessary that some genes be regulated by signals from outside the cell. The essential mechanism of gene regulation was discovered by Jacob & Monod (1961; Fig. 13.1) in E. coli. A regulatory gene codes for a protein, which, by binding to a specific regulatory sequence of another gene, alters the activity of that gene (negatively in the case originally described by Jacob & Monod, but the effect can also be positive). The regulation can be modified by a specific inducing molecule that alters the effect of the regulatory protein by binding to it allosterically. It is interesting that these two properties of regulatory proteins—that they can recognize specific regulatory sequences, and that their effectiveness can be altered by binding allosterically to inducers—are already present in prokaryotes. The complexity of multicellular eukaryotic development requires that an average gene be controlled by many others. Whereas regulatory elements in bacteria are usually simple switches, eukaryotes tend to have ‘smart’ genes, controlled by a complex of several regulatory proteins (Davidson, 1990; Beardsley, 1991).
Polymer characterization
Authors: Hosier Ian L. , Vaughan Alun S.
Published: November 2020

Polymer science is, of course, driven by the desire to produce new materials for new applications. The success of materials such as polyethylene, polypropylene, and polystyrene is such that these materials are manufactured on a huge scale and are indeed ubiquitous. There is still a massive drive to understand these materials and improve their properties in order to meet material requirements; however, increasingly polymers are being applied to a wide range of problems, and certainly in terms of developing new materials there is much more emphasis on control. Such control can be control of molecular weight, for example, the production of polymers with a highly narrow molecular weight distribution by anionic polymerization. The control of polymer architecture extends from block copolymers to other novel architectures such as ladder polymers and dendrimers. Cyclic systems can also be prepared, usually these are lower molecular weight systems, although these also might be expected to be the natural consequence of step-growth polymerization at high conversion. Polymers are used in a wide range of applications, as coatings, as adhesives, as engineering and structural materials, for packaging, and for clothing to name a few. A key feature of the success and versatility of these materials is that it is possible to build in properties by careful design of the (largely) organic molecules from which the chains are built up. For example, rigid aromatic molecules can be used to make high-strength fibres, the most highprofile example of this being Kevlar®; rigid molecules of this type are often made by simple step-growth polymerization and offer particular synthetic challenges as outlined in Chapter 4. There is now an increasing demand for highly specialized materials for use in for example optical and electronic applications and polymers have been singled out as having particular potential in this regard. For example, there is considerable interest in the development of polymers with targeted optical properties such as second-order optical nonlinearity, and in conducting polymers as electrode materials, as a route towards supercapacitors and as electroluminescent materials. Polymeric materials can also be used as an electrolyte in the design of compact batteries.
Controlled/‘living’ polymerization methods
Authors: Hayes Wayne , Rannard Steve
Published: November 2020

Chain-growth polymerizations such as free-radical polymerizations are characterized by four key processes:(i) initiation, (ii) propagation, (iii) chain transfer, and (iv) termination. If it is possible to minimize the contribution of chain transfer and termination during the polymerization, it is possible to achieve a level of control over the resulting polymer and achieve a predetermined number average molecular weight and a narrow molecular weight distribution (polydispersity). If such an ideal scenario can be created, the number of polymer chains that are produced is equal to the number of initiator groups; the polymerization will proceed until all of the monomer has been consumed and the polymer chain ends will remain active so that further addition of monomer will lead to continued polymerization. This type of polymerization was termed a ‘living’ polymerization by Szwarc in 1956 and represents one of the ultimate goals of synthetic polymer chemists. Flory determined that in the absence of termination, the number of propagating polymer chains must remain constant and that the rate of polymerization for each growing chain must be equal. In this situation, the number average degree of polymerization (DPn) and hence the molecular weight of the polymer can be predicted by simple consideration of the monomer to initiator ratio (see eqns (1) and (2), respectively). Several key criteria are used to elucidate the ‘living’ nature of a polymerization. For a polymerization to be considered ‘living’, the rate of initiation must exceed the rate of propagation. Therefore, all the propagating polymer chains are formed simultaneously and grow at the same rate. If this situation did not occur, the first chains formed would be longer than those initiated later and the molecular weight distribution of the propagating chains would broaden. In addition, an ideal ‘living’ or ‘immortal’ polymerization must not exhibit any termination of the propagating polymer chains over the lifetime of the reaction. Consequently, ‘living’ polymerizations are characterized by very narrow molecular weight distributions (Mw/Mn < 1.2).
Some examples of dendrimer synthesis
Authors: Tomalia Donald A.
Published: November 2020

Dendrimers are highly branched macromolecules with unique structural properties. They may be thought of as core–shell type macromolecules wherein they amplify their mass and terminal groups as a function of growth stages. These growth stages are referred to as generations (i.e. G= 0, 1, 2, . . .). They possess three key architectural features: (i) a core region; (ii) interior shell zones containing cascading tiers of branch cells (generations) with radial connectivity to the initiator core; and (iii) an exterior or surface region of terminal moieties attached to the outermost generation. With this architecture, a careful choice of building blocks and functional groups can provide control over shape, dimensions, density, polarity, reactivity, and solubility. One of the earlier dendrimers made, using a divergent strategy, is the Starburst® poly(amidoamine) (PAMAM) dendrimer family (Scheme 1). This method involved assembling repeat units to introduce branch cells around the initiator core through successive chemical reactions at the periphery of the growing macromolecule. The first step of PAMAM synthesis involves Michael addition of four moles of methyl acrylate to the nucleophilic ethylenediamine core. This leads to an electrophilic carbomethoxy surface, which is then allowed to react with an excess of 1,2-diaminoethane to give a nucleophilic surface at generation zero. Reiteration of these two steps now involves addition of 8 mol of methyl acrylate to give G = 0.5 (electrophilic, carbomethoxy surface). This is followed by amidation to return to a nucleophilic surface at G = 1.0. As a result of this reiterative branch cell assembly, it is apparent that these constructions follow systematic dendritic branching rules, with radial symmetry giving a well-defined three-dimensional geometry to the final dendritic product. In general, the placement of reactive functionalities on the exterior surface of the dendrimers allows introduction of a wide variety of terminal moieties. In alternate synthetic approaches, spacer groups have been deliberately introduced to relieve the steric hindrance in order to facilitate construction of the next generation. This may provide the possibility of enhancing interior cargo spaces for ‘guest–host’ type chemistry.
Probabilistic Directed Acyclic Graphs and Their Entropies
Authors: Grenander Ulf , Miller Michael I.
Published: November 2020

Probabilistic structures on the representations allow for expressing the variation of natural patterns. In this chapter the structure imposed through probabilistic directed graphs is studied. The essential probabilistic structure enforced through the directedness of the graphs is sites are conditionally independent of their nondescendants given their parents. The entropies and combinatorics of these processes are examined as well. Focus is given to the classical Markov chain and the branching process examples to illustrate the fundamentals of variability descriptions through probability and entropy.
Manifolds, Active Models, and Deformable Templates
Authors: Grenander Ulf , Miller Michael I.
Published: November 2020

To study shape we introduce manifolds and submanifolds examined in the continuum as the generators. Transformations are constructed which are built from the matrix groups and infinite products. This gives rise to many of the widely used structural models in image analysis often termed active models, essentially the deformable templates. These deformations are studied as both diffeomorphisms as well as immersions. A calculus is introduced based on transport theory for activating these deformable shapes by taking variations with respect to the matrix groups parameterizing them. Segmentation based on activating these manifolds is examined based on Gaussian random fields and variations with respect to the parameterizations.
Estimation on Metric Spaces with Photometric Variation
Authors: Grenander Ulf , Miller Michael I.
Published: November 2020

Model uncertainty comes in many forms. In this chapterweshall examine extensively the variable photometric model in which the underlying image field I(·) is modelled as an element of a Hilbert space I(·) ∈ H(φ) constructed via basis expansion {φi }. Inference involves both the pose and identity of the objects as well as the photometric intensity itself. This corresponds to making the template random, expanding the deformable template to include both the photometric variations and geometric variations.
Applications
Authors: Gautschi Walter
Published: November 2020

The connection between orthogonal polynomials and quadrature rules has already been elucidated in §1.4. The centerpieces were the Gaussian quadrature rule and its close relatives—the Gauss–Radau and Gauss–Lobatto rules (§1.4.2). There are, however, a number of further extensions of Gauss’s approach to numerical quadrature. Principal among them are Kronrod’s idea of extending an n-point Gauss rule to a (2n + 1)-point rule by inserting n + 1 additional nodes and choosing all weights in such a way as to maximize the degree of exactness (cf. Definition 1.44), and Turán’s extension of the Gauss quadrature rule allowing not only function values, but also derivative values, to appear in the quadrature sum. More recent extensions relate to the concept of accuracy, requiring exactness not only for polynomials of a certain degree, but also for rational functions with prescribed poles. Gauss quadrature can also be adapted to deal with Cauchy principal value integrals, and there are other applications of Gauss’s ideas, for example, in combination with Stieltjes’s procedure or the modified Chebyshev algorithm, to generate polynomials orthogonal on several intervals, or, in comnbination with Lanczos’s algorithm, to estimate matrix functionals. The present section is to discuss these questions in turn, with computational aspects foremost in our mind. We have previously seen in Chapter 2 how Gauss quadrature rules can be effectively employed in the context of computational methods; for example, in computing the absolute and relative condition numbers of moment maps (§2.1.5), or as a means of discretizing measures in the multiple-component discretization method for orthogonal polynomials (§2.2.5) and in Stieltjes-type methods for Sobolev orthogonal polynomials (§2.5.2). It is time now to discuss the actual computation of these, and related, quadrature rules.
Crystals and symmetry
Authors: Blow David
Published: November 2020

One of the fascinations of crystallography is the beautiful external appearance of crystals (Fig. 2.1), and the corresponding beauty of the atomic arrangements within them. At an early stage of studying a crystal, a crystallographer needs to analyse its underlying symmetry. This must be done because the crystallographic results must satisfy this symmetry and are constrained by it. It is needed to decide on the appropriate strategy for observation of X-ray scattering by the crystal. It is also essential to know the precise symmetry when interpreting the scattering data to obtain the crystal structure. The analysis of many crystal structures has been delayed because of mistakes in the symmetry assignment, and some have been incorrectly analysed. This chapter sets out to give an overview of crystal symmetry. It does not provide an exhaustive presentation. In particular, we shall concentrate on the symmetrical arrangements of chiral objects, in which mirror symmetry is forbidden. Much more detail about crystal symmetry can be found in many textbooks of crystallography, and a complete reference guide is provided in International Tables for Crystallography, Volume A (see Further Reading at the end of this chapter). An object is symmetrical if, after some operation has been carried out, the result is indistinguishable from the original object. Consider, for example, an equilateral triangle. If the triangle is rotated 120° about its centre, the resulting triangle is, in all respects, identical to the original triangle. This means that a second 120° rotation, producing a total rotation of 240°, also makes no change to the object. A third 120° rotation makes, of course, a 360° rotation, bringing the triangle back to its original orientation. So these rotations are called 3-fold rotation operations, and the equilateral triangle is said to possess 3-fold symmetry. The meaning of 3-fold symmetry is that the object may be rotated repeatedly by 360°/3 120° about its symmetry axis without changing it. Similarly 2-fold symmetry refers to rotation by 360°/2 180° and 6-fold symmetry refers to rotation by 60°. A left hand has no symmetry. Reflect it in a mirror and what you see looks like a right hand.
Waves
Authors: Blow David
Published: November 2020

In this very short chapter, some basic facts about waves are presented. Attached to this short chapter are several boxes which give the fundamental mathematical basis for understanding waves in a more quantitative fashion. There are many physical examples of waves. Waves in water are perhaps the most familiar example. A water wave is created by a disturbance in the height of the water surface. The amount by which the height of the water is disturbed by the wave is called its amplitude. Another important form of wave is sound, which is a variation of pressure in a gas or liquid (or of stress in a solid). But for our purposes the most important waves are electromagnetic waves, specifically X-rays, with wavelengths of an Ångström or so. Electromagnetic waves create a disturbance in both the electric field and the magnetic field: usually the wave is represented by its electric component. All these waves carry energy. The rate of energy transfer is called the intensity, and at a given wavelength the intensity is proportional to the square of the amplitude. Detectors of X-rays, discussed in Chapter 1, respond to the quantity of energy delivered by the beam, which is also proportional to the number of photons. The amplitude of any wave is thus proportional to the square root of its intensity. The most simple form of wave is a sinusoidal disturbance which moves forward at a fixed velocity. ‘Sinusoidal’ means shaped like a sine wave (Fig. 3.1). For reasons that will emerge, we will work more often with a cosine function, which is just the same shape as a sine wave, but which has its origin at a maximum point of the wave. A sinusoidal wave can be described by several properties: • the wavelength, which is the distance from one peak to the next; • the amplitude, which is the height of the wave peak above its mean level; • the phase, which specifies where the peak of the wave is, relative to an origin of measurement at the position x=0, and the time t =0; • the wave velocity, which is the velocity at which the wave advances along the propagation direction.
Isomorphous replacement
Authors: Blow David
Published: November 2020

In this chapter, we shall see how this historic observation created the first method for determining the atomic structure of proteins, a method which is still amongst the most important. As discussed in Chapters 1 and 3, detectors of X-rays measure the energy of light entering them. They are insensitive to the phase (Fig. 7.1). The energy of light in a diffracted beam is proportional to the square of its amplitude: all we can detect is the intensity of each diffracted wave. This applies to all available detectors of short-wavelength electromagnetic waves. In order to reconstruct the electron-density distribution ρ(x) from the observed scattering it is necessary to know the phase angle of the scattering associated with each Bragg reflection. The difficulty in determining the phase of a scattered wave is referred to as the phase problem, and the next three chapters present methods that are used to overcome it for macromolecular structure analysis. There is one situation where the phase problem is much simplified. If a structure has a centre of symmetry at the origin, all the waves that represent its Fourier transform are cosine-like (with maxima or minima at the origin), and the phases are 0° or 180°. This was presented in Chapter 4 for the one-dimensional case (see Figs 4.6 and 4.11), and applies in just the same way in two or three dimensions. All crystallographic structure determinations before 1940 dealt with centrosymmetric structures. This does not help us directly, because biological macromolecules are never centrosymmetric, and all phase angles are possible. Having said this, there are cases where crystals of biological materials have some reflections where phase is limited to 0° or 180°. These are usually reflections with at least one index zero, depending on the symmetry: for monoclinic crystals the h0l reflections are always in this category. More precise conditions are defined in Box 7.1. Figure 7.2 shows how a projection of a non-centrosymmetric structure along a 2-fold axis gives a centrosymmetric projection. Such a centrosymmetric projection requires a group of reflections to have phases of 0 or π.
Properties of Materials
Authors: Newnham Robert E.
Published: November 2020

Crystals are sometimes called 'Flowers of the Mineral Kingdom'. In addition to their great beauty, crystals and other textured materials are enormously useful in electronics, optics, acoustics and many other engineering applications. This richly illustrated text describes the underlying principles of crystal physics and chemistry, covering a wide range of topics and illustrating numerous applications in many fields of engineering using the most important materials today. Tensors, matrices, symmetry and structure-property relationships form the main subjects of the book. While tensors and matrices provide the mathematical framework for understanding anisotropy, on which the physical and chemical properties of crystals and textured materials often depend, atomistic arguments are also needed to quantify the property coefficients in various directions. The atomistic arguments are partly based on symmetry and partly on the basic physics and chemistry of materials. After introducing the point groups appropriate for single crystals, textured materials and ordered magnetic structures, the directional properties of many different materials are described: linear and nonlinear elasticity, piezoelectricity and electrostriction, magnetic phenomena, diffusion and other transport properties, and both primary and secondary ferroic behavior. With crystal optics (its roots in classical mineralogy) having become an important component of the information age, nonlinear optics is described along with the piexo-optics, magneto-optics, and analogous linear and nonlinear acoustic wave phenomena. Enantiomorphism, optical activity, and chemical anisotropy are discussed in the final chapters of the book.
Thermoelectricity
Authors: Newnham Robert E.
Published: November 2020

When two different metals are connected together in a circuit and the two junctions are held at different temperatures, five physical phenomena take place simultaneously. Thermal and electric currents flow in the circuit, giving rise to Joule heating and thermal conduction. The driving forces for these currents are three interrelated thermoelectric phenomena: the Seebeck Effect, the Peltier Effect, and the Thomson Effect. For commonly used thermocouples, a voltage is developed when the junctions are held at different temperatures. In practice, one junction is held at a constant temperature (often the melting point of ice), and the open circuit voltage is measured as a function of the temperature of the second junction. If the reference temperature is 0◦C, then the thermocouple voltage can be expressed as a power series. . . . V = αT + βT2 + γ T3 +· · · , . . . where T is the temperature in ◦C and the coefficients depend on the choice of metals. Data for Cu–Ni and Cu–Fe thermocouples are presented in Fig. 21.2 along with the governing equations. If the cold junction is at a temperature other than 0◦C, it is only necessary to add a constant term. From this it follows that dV/dT at one junction is independent of the temperature of the second junction.
Piezoresistance
Authors: Newnham Robert E.
Published: November 2020

Piezoresistivity, the change in electrical resistivity with mechanical stress, is commonly used to monitor static or slowly varying stresses and strains. The sensitivity of piezoresistive elements are often compared by means of a strain gage factor: G = Δ
Volcanic activity
Authors: Hallam Tony
Published: November 2020

Of all the geological phenomena that make an impression on the general public, volcanic eruptions must be the most spectacular. The sight of incandescent lava being spewed into the air or creeping down hillsides is a regular standby of television documentaries dealing with the natural world, and the invocation by Old Testament writers of fire and brimstone in their portraits of hell indicates how vivid is the image of volcanic activity that has persisted throughout recorded history. How significant, though, are erupting or exploding volcanoes as killers? Many years ago I paid a standard tourist visit to Pompeii and Herculaneum, the Roman towns destroyed by the eruption of Vesuvius in AD 79. I was duly impressed by the exhumed streets and buildings, but what caught my imagination most were the plaster casts from Pompeii of human beings found in recumbent or prone positions, or huddled against a wall, at the locations where they had been enveloped almost instantaneously by incandescent ash. These had been produced during the nineteenth-century excavations by a team of archaeologists led by an ingenious professor, who poured plaster of Paris down holes in the volcanic rock occupying the rooms of Roman villas. The rock was then removed. Good examples of these plaster casts can be seen in the Naples Museum, and picture postcards are freely available for tourists visiting the Bay of Naples area. They make disturbing mementi mori to send to your friends and relatives. It is not known how many died as a result of the Vesuvius eruptions: perhaps not too many, as most inhabitants had time to escape. This was not the case, though, with the eruption in 1902 of Mont Pelée in Martinique, during which no fewer than 30,000 inhabitants of St. Pierre – ‘the Paris of the West Indies’ – were killed as what is called a nuée ardente smothered the town. There were only two survivors. The term nuée ardente is normally translated as ‘glowing cloud’ or ‘glowing avalanche’, though some of the more frivolous students I have taught have preferred their own mistranslation: ‘ardent nudes’.
Fundamentals of Atomistic Simulations
Authors: Bulatov Vasily , Cai Wei
Published: November 2020

Fundamentally, materials derive their properties from the interaction between their constituent atoms. These basic interactions make the atoms assemble in a particular crystalline structure. The same interactions also define how the atoms prefer to arrange themselves in the dislocation core. Therefore, to understand the behavior of dislocations, it is necessary and sufficient to study the collective behavior of atoms in crystals populated by dislocations. This chapter introduces the basic methodology of atomistic simulations that will be applied to the studies of dislocations in the following chapters. Section 1 discusses the nature of interatomic interactions and introduces empirical models that describe these interactions with various degrees of accuracy. Section 2 introduces the significance of the Boltzmann distribution that describes statistical properties of a collection of interacting atoms in thermal equilibrium. This section sets the stage for a subsequent discussion of basic computational methods to be used throughout this book. Section 3 covers the methods for energy minimization. Sections 4 and 5 give a concise introduction to Monte Carlo and molecular dynamics methods. When put close together, atoms interact by exerting forces on each other. Depending on the atomic species, some interatomic interactions are relatively easy to describe, while others can be very complicated. This variability stems from the quantum mechanical motion and interaction of electrons [15, 16]. Henceforth, rigorous treatment of interatomic interactions should be based on a solution of Schrödinger’s equation for interacting electrons, which is usually referred to as the first principles or ab initio theory. Numerical calculations based on first principles are computationally very expensive and can only deal with a relatively small number of atoms. In the context of dislocation modelling, relevant behaviors often involve many thousands of atoms and can only be approached using much less sophisticated but more computationally efficient models. Even though we do not use it in this book, it is useful to bear in mind that the first principles theory provides a useful starting point for constructing approximate but efficient models that are needed to study large-scale problems involving many atoms.
More About Periodic Boundary Conditions
Authors: Bulatov Vasily , Cai Wei
Published: November 2020

We have already used periodic boundary conditions (PBC) for the static and dynamic simulations described in Chapters 2 and 3. There, PBC were applied along one or two directions of the simulation cell. Application of PBC in all three directions holds an important advantage when one’s goal is to examine the behavior in the bulk: under fully three-dimensional (3D) PBC, the simulated solid can be free of any surfaces. By comparison, the simulations discussed in the previous chapters all contained free surfaces or artificial interfaces in the directions where PBC were not applied. Full 3D PBC are easy to implement in an atomistic simulation through the use of scaled coordinates. However, there are important technical issues specific to simulations of lattice dislocations. First, a fully periodic simulation cell can accommodate only such dislocation arrangements whose net Burgers vector is zero. Thus, the minimal number of dislocations that can be introduced in a periodic supercell is two, i.e. a dislocation dipole. Two dislocations forming a dipole are bound to interact with each other, as well as with their periodic images. Associated with these interactions are additional strain, energy, and forces whose effects can “pollute” the calculated results. The good news is that, in most cases, the artifacts of PBC can be quantified through the use of linear elasticity theory so that physical properties of dislocations can be accurately extracted. Given the simplicity and robustness of PBC, the extrawork required to extract physical results is well worth it. This chapter describes how to evaluate and eliminate the artifacts that inevitably appear when 3D PBC are used for atomistic simulations of dislocations. In the following three sections, we show how to take full advantage of PBC when one wants to calculate the displacement field induced by a dislocation (Section 5.1), the dislocation’s core energy (Section 5.2) and Peierls stress (Section 5.3). The common theme for all three case studies is an attempt to construct a solution of the elasticity equations in a periodic domain by superimposing a periodic array of solutions of an infinite domain.
Kinetic Monte Carlo Method
Authors: Bulatov Vasily , Cai Wei
Published: November 2020

The PN model discussed in the preceding chapter is a continuum approach that requires some atomistic input to account for non-linear interactions in the dislocation core. In this chapter, we introduce yet another continuum model that uses atomistic input for a different purpose. The kinetic Monte Carlo (kMC) model does not consider any details of the core structure but instead focuses on dislocation motion on length and time scales far greater than those of the atomistic simulations. The model is especially effective for diamond-cubic semiconductors and other materials in which dislocation motion is too slow to be observed on the time scale of molecular dynamics simulations. The key idea of the kMC approach is to treat dislocation motion as a stochastic sequence of discrete rare events whose mechanisms and rates are computed within the framework of the transition state theory. Built around its unit mechanisms, the kMC model simulates dislocation motion and predicts dislocation velocity as a function of stress and temperature. This data then can be used to construct accurate mobility functions for dislocation dynamics simulations on still larger scales (Chapter 10). In this sense, kMC serves as a link between atomistic models and coarse-grained continuum models of dislocations. The kMC approach is most useful in situations where the system evolves through a stochastic sequence of events with only a few possible event types. The method has been used in a wide variety of applications other than dislocations. For example, the growth of solid thin films from vapor or in solution is known to proceed through attachment and diffusion of adatoms deposited on the surface. Based on a finite set of unit mechanisms of the motion of adatoms, kMC models accurately describe the kinetics of growth and the resulting morphology evolution of the epitaxial films [95, 96, 97]. Similar kMC models have been applied to dislocation motion in crystals with high lattice resistance, such as silicon. In these materials, dislocations consist of long straight segments interspersed with atomic-sized kinks, depicted schematically in Fig. 9.1(a) as short vertical segments. As was explained in Section 1.3, dislocation motion proceeds through nucleation and migration of kink pairs and can be described well by a kMC model.