bluuebunny/crossref_metadata_2025_split huggingface dataset:
Bonding of sp-valent metals
Authors: Pettifor D G 
Published: November 2023

Abstract
A metal is often pictured as a gas of free electrons into which has been immersed a lattice of positive ions. The metallic bond is, therefore, thought of as having no directional character in contrast to saturated covalent bonds with their hybrid orbitals resistant to bond bending. The metal atoms behave like hard spheres that are held together by the all-pervasive electron glue, taking close-packed structures such as fee, bee, or hep. Unlike valence compounds with their restrictive requirement of electron-pair bonding between neighbouring sites, metals can form alloys over a wide range of composition, atoms of one type replacing those of another with comparative ease within the electron gas. We will see in this chapter that this conventional view of the metallic bond is indeed an excellent description of sp-valent metals such as sodium, magnesium, and aluminium. We will begin, therefore, by linking the world of small molecules and extended solids together by applying the jellium model to a study of cohesion in atomic clusters. We will find that it predicts special stability for alkali metal clusters containing magic numbers of atoms that correspond to electronic shell closings. However, as we have already seen in Chapter 2, jellium is only in equilibrium at one specific electron density. The underlying ionic lattice is required for differentiating between the elements and predicting the properties of the sp-valent metals. The influence of a periodic crystalline potential on the electronic structure is introduced through the one-dimensional Kronig-Penney model that illustrates all the essential features of band theory. The key concept of the pseudopotential is presented in order to account for the well-known but surprising fact that the free-electron gas is only very weakly perturbed by the ionic lattice. This allows us to develop a quantitative nearly free electron (NFE) model of the metallic bond that is entirely consistent with the usual picture of a metal as a gas of free electrons into which has been immersed a lattice of positive ions.
Structure of sp-valent metals
Authors: Pettifor D G 
Published: November 2023

Abstract
The description of the metallic bond in the previous chapter assumed that the free-electron gas remained homogeneously distributed as the pseudopotential lattice of ion cores was immersed within it. In practice, of course, the free electrons will respond to screen the ion cores, thereby leading to a modulation of the electron density. This modulated electron density then acts in turn on the underlying ionic lattice to give rise to a structuredependent contribution in the total energy. We will see in this chapter that this small structurally dependent contribution to the binding energy can be evaluated quantitatively using second-order perturbation theory within the nearly free electron (NFE) approximation.
Diffuse Neutron Scattering From Crystalline Materials
Authors: Nield Victoria M , Keen David A 
Published: November 2023

Abstract
The present book is an accessible, comprehensive guide to diffuse neutron scattering, an important technique for studying structural disorder in materials. The text takes the reader through theoretical, computational and experimental developments in the subject and describes in detail its application to a number of structural disorder problems. These include the more traditional subjects of substitutional disorder in alloys and orientational disorder in molecular systems as well as the more recent studies of superionic and framework materials. Particular emphasis is placed on recent refinement methods for data interpretation which are compared with established computer simulation techniques and analytical approaches. The book collects disparate themes into one unique volume, written as an introduction to the method for graduate scientists. It will be a valuable reference text for any crystallographer keen to understand and apply modern interpretative techniques to diffuse scattering data.
Introduction
Authors: Nield Victoria M , Keen David A 
Published: November 2023

Abstract
Diffuse scattering occurs from all crystalline materials at all temperatures. It arises from any temporary or permanent breakdown of space group symmetry, and so contains information on the deviations from the average structure. Information on all the different types of disorder in crystalline solids is present, and interpretation of the diffuse scattering is necessary for a detailed understanding of local structural information.
Computer simulation and modelling
Authors: Nield Victoria M , Keen David A 
Published: November 2023

Abstract
It is becoming increasingly common for scientists to adopt computer simulation methods to investigate crystalline systems. This is principally for two reasons, both of which are essentially pragmatic. First, scientists are more likely to be investigating far more complex materials, including those materials which display disorder. It is often not possible to apply established theoretical descriptions to such systems analytically and, as has been shown in Chapter 3, it very quickly becomes a complex task to describe the interactions between atoms or spins rigorously as the material becomes increasingly disordered. Even model systems which can be described very simply may be difficult to solve exactly. Computer simulations have sometimes been termed ‘computer experiments’ and in some senses they are just that: the computer contains a well defined small system which is constrained to obey specific interactions and from which physical properties of the system are ‘measured’ using thermodynamic principles or other appropriate averaging. However computer simulations have another role since they can also be used to bridge the gap between what can be expressed theoretically and what can be measured experimentally. They can be used to check the validity of approximations made when developing theoretical expressions by applying them to systems of real interest. They also allow the scientist to ‘see’ the effect of analytical parameters in terms of ‘real’ atom positions and correlations. This is especially true in the case of structural disorder where a more complete picture may be obtained from a computer simulation than from an analytical treatment relying on a number of possibly inappropriate approximations.
Alloys and other binary materials
Authors: Nield Victoria M , Keen David A 
Published: November 2023

Abstract
In the previous chapters we have built up our understanding of the experimental and theoretical methods applicable to alloys and binary systems. In the present chapter we review a wide selection of studies on these materials. These are largely neutron scattering studies, taken from the recent literature. However, where appropriate, X-ray studies which supplement the neutron work, or are in some sense novel or ground breaking, have been included. Space has not allowed a significant amount of detail to be included on the background to the studies, and the interested reader is referred to the original papers for further insight.
Green-Function Methods
Authors: Davison Sydney G , Stęślicka Maria 
Published: November 2023

Abstract
Of all the methods discussed so far, none is as mathematically sophisticated and elegant as the Green-function (GF) ones to be described here in their various forms. Because these techniques are both powerful and versatile, it is important to master them, despite their more abstract formalism, which tends to make them somewhat more difficult to understand. The great advantage of GF techniques is that they provide direct access to the density of states (DOS) to which many physical properties are related. For example, the intensity of photoemission from solids is proportional to the DOS. Indeed, most spectroscopic yields are linked to the initial DOS. Other properties, such as bond order (Phillips 1969), can also be related to the GF.
Elastic Scattering of Ions by Atoms
Authors: Bransden B H , McDowell M R C 
Published: November 2023

Abstract
In this chapter a short account of the theory of ion atom elastic scattering will be given on the assumption that the interaction between two atoms (or ions) A and B can be represented by a real central energy-independent potential W(R), where R = RA R8 is the position vector of A relative to B. This model can be applied to describe the relative motion of A and B approximately even if the collision is inelastic (capture, excitation, or ionization), provided the impact energy is large compared with changes in the internal electronic energies of the atoms. This is usually the case when the impact energy is of the order of 100 eV or greater.
Charge Exchange at Very Low Energies the Perturbed Stationary State Model
Authors: Bransden B H , McDowell M R C 
Published: November 2023

Abstract
In this chapter we shall discuss charge exchange at energies for which the relative velocity of the colliding ions is very small compared with typical orbital velocities of the pseudomolecule composed of the active electron moving in the field of the ionic cores A and 8. A natural choice of basis functions in a coupled channel model for such a collision is a set of adiabatic molecular orbitals, modified by suitable translation factors as in equations (3.99). The coupled equations, determining the channel wave functions using the coordinate set (s, R) where R is the vector joining A to 8 and s is the position vector of the electron relative to C, the centre of mass of A and B, are then of the form (3.93), the overlap and potential matrix elements being defined by the expressions (3.91) and (3.94). In the perturbed stationary state model, which in the past was employed for the majority of calculations at very low energies, the translation factors which allow for the change in translational motion of the electron on capture are neglected completely. This model, originally developed by Massey and Smith (1933) is described in Section 4.1. At very low energies the number of significant partial waves is limited and a partial-wave expansion of the coupled equations is indicated.
Many-Electron Systems
Authors: Bransden B H , McDowell M R C 
Published: November 2023

Abstract
As we have already noted in Sections 4.7 and 5.9, the coupled channel methods developed in Chapter 3 for quasi-one-electron systems can be generalized, in principle, for systems with any number of electrons. The basis functions can be adiabatic molecular wave functions which diagonalize the electronic Hamiltonian, or atomic functions (and pseudostates) which diagonalize the unperturbed atomic Hamiltonians in the different arrangements. In the former case all the interactions including the electronelectron interaction are taken into account and in the latter all the internal interactions in the separate atoms are allowed for in the basis. Calculating such basis functions for a many-electron system with sufficient accuracy is already a demanding task; nevertheless there have been a growing number of investigations of two-electron or quasi-two-electron systems, some of which have been illustrated in Chapter 6. To some extent, the difficulties of constructing many-particle molecular wave functions can be overcome by using a basis in which electron electron correlation is absent. Correlation can then be taken into account when forming the coupled equations. This approach, which is due to Hare] and Salin, will be discussed below. Apart from the calculation of basis functions, the computational effort required to treat two-electron systems can be very great, compared with one-electron systems, for several reasons. For example, the elements of the interaction matrix become more difficult to compute. In particular, with an atomic basis composed of travelling Slater orbitals the computation of the matrix elements of the electron-electron interaction are particularly time consuming. If specifically two-electron processes are important, for example double capture, double excitation or ionization, simultaneous capture and excitation, or simultaneous capture and ionization, the size of the basis required to represent the two-electron wave function is much greater than that required for one-electron systems.
Pseudo-equilibrium replica analysis
Authors: Coolen A C C 
Published: November 2023

Abstract
The first serious attempt in literature at solving an MG model using statistical mechanical techniques dealt with the simplest case of having fake and inconsistent market histories, i.e. with ζ = 1 in equation (2.2) and with equation (2.4) describing fake history statistics, two strategies per agent (i.e. S = 2), and additive decision noise (2.12). It employed a strategy that had in the past proved effective in the study of non-equilibrium neural network models. The idea is to find a Lyapunov function H(q) for the MG process, with q = (q 1 ,..., qN), which would allow one to determine the stationary state properties via an analysis of the minima of H(q).
The overall bid distribution
Authors: Coolen A C C 
Published: November 2023

Abstract
At this stage we make a small detour. Rather than introducing and analyzing new MG versions, we pause briefiy and return to the intriguing simulation data on the overall bid statistics as shown for instance in Figs 1.2 (for the on-line MG with true market history) and 1.11 (for the online MG with ‘fake’ market history).
MG versions with new types of phase transitions
Authors: Coolen A C C 
Published: November 2023

Abstract
The generating functional method allows us for N →∞ to reduce the problem of solving the original coupled and disordered N -agent process to that of solving a stochastic and non-Markovian ‘effective single-agent’ equation, without disorder. So far our strategy in analyzing this single-agent equation has been to first look for ergodic states, described by TTI stationary solutions, with finte susceptibility χ. We assumed that, if such a solution exists (which was found to be true in each of the MG versions studied so far, for sufficiently large α), given time, the system will forget its initial conditions and approach this particular stationary state. Numerical simulations have so far confirmed this assumed scenario. The predictions for the persistent observables of the MG, as well as for the location of the point where this particular solution should break down (marked by a divergence of χ) and the resulting phase diagrams, agreed perfectly with our experimental observations.
Theory of stationary random processes
Authors: Diggle Peter J 
Published: November 2023

Abstract
We begin this chapter by recalling some notation and definitions from Chapters 1 and 2. A random function is a set of random variables {Y(t)}, in which the time-index, t can assume any real value. The trend of {Y(t)} is the non-random function µ(t) = E[Y(t)].
Forecasting
Authors: Diggle Peter J 
Published: November 2023

Abstract
Before discussing specific forecasting methods, we make the point that forecasting involves extrapolation in the presence of random variation, and as such is bound to be difficult in practice. The difficulties are threefold. Firstly, we need to be confident that the mechanisms generating the historical data will continue to apply in the future. Secondly, even if we can assume a stable generating mechanism, we need to express this mechanism in the form of a statistical model for the data. The difficulty here is that different models may fit the historical data equally well, yet give quite different predictions of the future. Thirdly, even supposing we have identified the correct statistical model, the statistical uncertainty inherent in any estimates of the model parameters will be magnified as predictions are made progressively further into the future.
Simplified and two-stage quasi-likelihood estimators
Authors: Hutton J E , Ogunyemi, O T , Nelson Paul I 
Published: November 2023

Abstract
Properties of a quasi-likelihood estimator are typically obtained from an expansion of the quasi-likelihood in which the remainder term is asymptotically negligible. The remainder term, however, can be very difficult to control in some important applications, especially in models where both the mean and variance depend on the unknown parameter. In such cases we propose a modified quasi-likelihood based on the use of a simplified covariance matrix. Conditions for the consistency and asymptotic normality of the resulting estimators are developed. We illustrate this approach with a branching process with immigration model and present a simulation study of the small sample behaviour of the estimators.
Making use of a regression model for inferences about a finite population mean
Authors: Mantel H 
Published: November 2023

Abstract
Godambe and Thompson (1986) define and develop simultaneous optimal estimation of super-population and finite-population parameters based on a super-population model and a survey-sampling design. However, we may be interested in estimating a finite population mean that has no direct relationship to the finite-population parameter of Godambc and Thompson’s theory. In this paper we extend the super-population model in such a way that there is a direct relationship between the finite-population mean and the finite¬ population parameter. The resulting estimator of the finite-population mean is compared to the generalized regression estimator.
The glim language
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl 
Published: November 2023

Abstract
This chapter outlines the basic components of the GLIM language and introduces the general syntax and mode of use of the package. GLIM statements are composed of characters from the GLIM character set, which is listed in the Reference Guide [13.1]. Essentially, this consists of upper- and lower-case letters, digits, and a range of operators and brackets which will be introduced in the relevant chapters of the User Guide. Lower-case letters are treated as equivalent to the corresponding upper-case letters in statements when they are interpreted by the GLIM program, except in strings when the case is retained. The character ‘@’ is used in fault messages to indicate an invalid input character.
File handling and utilities
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl 
Published: November 2023

Abstract
GLIM has facilities for inputting statements and data from external files and similarly output can be directed to a file to provide hard copy output. These are accessed via secondary input and secondary output channels. Certain channels are automatically available to the user. One of these is for the transcript file which, by default, is a copy of everything that appears on the screen during an interactive session, including both input and output. Another is for the journal file which is a record of the GLIM statements input by the user during a session. This can be ‘replayed’ to reproduce a GLIM session. The user has control over what should be automatically stored in these files (see [4.3.1]). A third file which is available for input by the user is the macro library. This contains tried and tested macros which provide a valuable extension to the facilities available in GLIM [Appendix A]. There are also facilities for the user to save (to a dump file) the GLIM session in its current state and subsequently restart it at a later time, thus allowing an analysis to be spread over more than one session.
The Theory of Generalized Linear Models
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl 
Published: November 2023

Abstract
In Chapter IO it was observed that the standard (univariate) statistical models can be thought of as being special cases of a more general structure, called a generalized linear model (GLM). This chapter introduces the underlying theory behind a GLIM analysis by defining more rigorously what is meant by a generalized linear model (GLM) and by outlining the algorithmic basis of the model fitting procedures of GLIM.
The PASS Facility
Authors: Swan Tony , Gilchrist Robert , Bradley Malcolm , Clarke Mike , Green Peter , Reese Allan , Hinde John , Stalewski Andrew , O’brien Carl 
Published: November 2023

Abstract
Execution of a PASS statement causes the keyword or integer, the values of the list of vector(s)/scalar(s), and the elements of the macro to be passed to the FORTRAN subroutine PASS. As distributed in the standard release of GLIM, the body of subroutine PASS includes some routines for illustrative purposes. It is anticipated, though, that the user may wish to supply their own body for PASS, which will perform certain operations on the input parameters that are not available (or not easily available) via the standard GLIM directives. This note explains how this may be achieved.
Inverse Natural Exponential Families on Jr
Authors: Seshadri V 
Published: November 2023

Abstract
Recall that in Chapter 1, Section 1.4 we promised an explanation of the term ‘inverse’ appearing in the inverse Gaussian distribution. We shall now offer an explanation and justification of this usage by introducing the concept of inverse pairs of distributions (measures) and natural exponential families on R The ideas were defined in Letac (1986b) who coined the term ‘reciprocity’ in true Gallic style (note that the French usage of the terms ‘reciproque’ and ‘inverse’ corrspond exactly to the terms ‘inverse’ and ‘reciprocal’ just another instance of inversion), in an attempt to provide significant examples of inverse variates first introduced in his terse one-page paper by Tweedie (1945).
Statistical Properties
Authors: Seshadri V 
Published: November 2023

Abstract
The numerous distributional properties discussed in Chapter 2 and the important role played by the inverse Gaussian law in the study of exponential families motivate a survey of the development of statistical methods of in ference based on this law. The usefulness of this law in applied work has had a modest beginning with the estimation methods of Schrodinger, and the pioneering works of Halphen and Tweedie. We review some basic statistical theory and methodology concerned with this law. We shall, however, desist from analysing data sets, focusing attention only on theoretical issues. The reader is assumed to be familiar with a reasonably good background of mathematical statistics.
Norms of redress
Authors: Richard DeRidder , Kumar Rashmi , Schruijer Sandra G L 
Published: November 2023

Abstract
The issue we will address in this chapter is related to the second finding. Are the relatively positive reactions to the other group member’s norm violation due to the respondents’ desire to convey a positive impression of themselves on the investigator? This would mean that the reactions subjects gave in the questionnaires were biased by social desirability. It could also be, and this is the argument we will elaborate in this chapter, that their responses stemmed from shared opinions about the most appropriate reactions in instances where norm violation by one group may trigger a conflict. In other words, it will be argued, and studied empirically, that in groups, such as Hindus and Muslims, certain ‘norms of redress’ exist that stipulate how group members should react in situations in which another group starts a possible escalation of negative intergroup behaviour by violating a norm.