bluuebunny/crossref_metadata_2025_split huggingface dataset:
An Adaptive CFD Solver for Time-Dependent Environmental Flow Problems
Authors: Berzins M , Gaskell P H , Sleigh A , Speares W , Tomlin A , Ware J M 
Published: November 2023

Abstract
This paper will describe the application of the SPRINT2D unstructured mesh finite volume code to time-dependent environmental problems and show that the combination of space and time adaptivity makes it possible to gain greater insight into CFD problems. The code has been written through a joint Shell Research Ltd (Thornton Research Centre) and Leeds University (School of Computer Studies) Research programme. The key feature of the software is that applications codes may be written which are based on a toolkit of robust numerical routines. The paper outlines some of these routines and shows how they have been applied to two example problems. Sections 2 and 3 describe the finite volume discretization scheme and the mesh generation and adaptivity routines for unstructured triangular meshes. Section 4 covers the method of lines time integration approach using a range of explicit and implicit time integration methods for both stiff and nonstiff o.d.e.s. A simple spatial error estimate is used to adapt the mesh, and controlled in conjunction with the time error to balance the two errors. Sections 5 and 6 describe the numerical examples while Section 7 contains a summary and outlines an extension of the approach to three dimensional problems.
An Efficient Relaxation Method for a Centred Navier-Stokes Solver
Authors: Corre B , Khalfallah K , Lerat A 
Published: November 2023

Abstract
An implicit unsteady scheme of Lax-Wendroff type was developed in ([5]-[10]) to solve the Euler and Navier-Stokes equations; its internal dissipation is very low but just sufficient to compute accurate solutions of steady aerodynamic problems without using any artificial viscosity or upwinding. Practical calculations yielded very satisfactory results in terms of accuracy (see [6),(10)). These results were obtained by using an approximate spatial factorization of the implicit stage. Recently, the efficiency of the 2D and 3D Euler solver was greatly improved by applying some line relaxation method ([2), (7)). The aim of this paper is to study a similar method for viscous problems. The structure of the original Navier-Stokes solver does not allow a direct extension of the relaxation method to the viscous case. Therefore a new hybrid scheme has been developed : it offers features well suited for an efficient relaxation - basically diagonal dominance - and meanwhile preserves the solution accuracy thanks to a low numerical dissipation in the viscous zone.
Interaction laws and domain decomposition
Authors: Boer B F A de , Veldman A E P 
Published: November 2023

Abstract
With the advent of parallel computers the concept of domain decomposition has become increasingly popular. In the aerodynamic community this concept has been used ever since the ‘discovery’ of the boundary layer by Prandtl in 1904. He divided the flow field in two regions: a thin viscous shear layer and an external region with inviscid flow. The communication between these regions takes place in terms of pressure distribution and displacement thickness. The pressure is closely related to the external streamwise velocity Ue, which in terms of a streamfunction ψ can be written as ue= ∂ ψ/ ∂n is normal to the shear layer). The displacement thickness is immediately related to the streamfunction ψ itself. Hence we recognize, what is nowadays called, a domain-decomposition method with Dirichlet-Neumann coupling.
A TVD Flow Algorithm for FAME
Authors: Onslow S H , Peshkin D A 
Published: November 2023

Abstract
The challenge of generating computational meshes for complex three-dimensional configurations has been the subject of many years work at DRA Farnborough. One approach pursued has been that of using composite, overlapping meshes. Following this approach, the configuration to be meshed is divided into a number of elementary geometric features and then each feature is given its own mesh. The method used is called Feature Associated Mesh Embedding (FAME), and has proved capable of providing high quality meshes for realistic aircraft configurations.
Discrete Mathematics and its Application to Ecology
Authors: Maini Philip 
Published: November 2023

Abstract
In this chapter we will illustrate how simple mathematical ideas can be used to understand how a population grows. We first consider the well-known problem which generates the Fibonacci sequence. Consider a population of rabbits. Suppose that every pair of rabbits can reproduce only twice, when they are one and two-months old, and that each time they produce exactly one new pair of rabbits. Assume that all newborn rabbits survive. The problem here is to see if we can predict how many newborn rabbits there will be in a certain generation given an initial newborn rabbit population.
Toward the twentieth century: from ancient optics to relativity theory
Authors: Pais Abraham 
Published: November 2023

Abstract
The year was 1903. The Wright brothers had launched the first successful manned airplane flight. Henry Ford had founded his motor company. The first Tour de France had been run and the first World Series in baseball had been played (Boston beat Pittsburgh). Paul Gauguin and Camille Pissarro had died, and Pablo Picasso was in his blue period. Copenhagen had its first Social Democratic mayor and its first motorized taxicab. Niels R yberg Finsen had become the first Dane to win a Nobel Prize, in medicine.
How Bohr secured his permanent base of operations
Authors: Pais Abraham 
Published: November 2023

Abstract
The contributions which mark out Planck, Einstein, and Bohr as the founders of the quantum theory are now in place. Planck’s on blackbody radiation (5g) and Einstein’s on the light-quantum and on heat capacities ((5h) and (Sc)) have been sketched only lightly; Bohr’s on atomic structure has been dealt with in much more detail, as befits this book.
Toward the edge of physics in the Bohr style, and a bit beyond
Authors: Pais Abraham 
Published: November 2023

Abstract
The first international physics conference after World War II was held from 22 to 27 July 1946 at the Cavendish Laboratory. Its themes were ‘Fundamental particles and low temperatures’. In the preface to the proceedings one reads: ‘The subject of Fundamental Particles is nowadays so wide that the arrangement of the programme was not easy.’ The opening address was given by Bohr. It is entitled ‘Problems of elementary particle physics’.
In which Bohr moves full steam into his later years
Authors: Pais Abraham 
Published: November 2023

Abstract
As the curtain rises for the final act, we see Bohr at age 60, still holding centre stage, still in full vigor, still running up steps two at a time.Bohr has now reached the zenith of his influence. He has become a public figure of the first rank, he and Margrethe often being called Denmark’s second royal family. High dignitaries visit his home. From Denmark, the king and queen, cabinet ministers, and ambassadors come for dinner.
Epilog
Authors: Pais Abraham 
Published: November 2023

Abstract
Physicists and other friends, young and old, sent expressions of sorrow and sympathy to Margrethe Bohr and her family.* So did dignitaries from various parts of the world.President Kennedy wrote to Mrs Bohr: ‘I am deeply saddened by Professor Bohr’s death. American scientists, indeed all American citizens who knew doctor Bohr’s name and his great contributions, have respected and venerated him for more than two generations ... We are forever indebted to him for the scientific inspiration he brought along on his many visits to the United States, and especially for his great contribution to the atomic center at Los Alamos.
Introduction
Authors: Barbour A D , Holst Lars , Janson Svante 
Published: November 2023

Abstract
One of the oldest limit theorems of probability is the Poisson ‘law of small numbers’. In its simplest form, it states that the binomial distribution Bi (n,p) converges to the Poisson distribution Po(λ) as n→; ∞, if p =λ/n for some λ&gt; 0, as was proved by Poisson (1837), pp. 205–207. The first person to have appreciated its use in the statistical analysis of rare events seems to have been von Bortkewitsch (1898), who emphasized that statistical methods were not only applicable to data consisting of large numbers, even though normal approximation might no longer be appropriate. His analysis of the numbers of Prussian soldiers killed each year as a result of being kicked by horses has proved particularly memorable, although it was only one of several sets of data that he considered. What is more important is that he showed that the Poisson distribution fitted the data very closely, by tabulating the expected and observed frequencies and by comparing the sample variance with the sample mean.
Independent and dissociated terms
Authors: Barbour A D , Holst Lars , Janson Svante 
Published: November 2023

Abstract
When approximating the distribution of a sum W of independent indicator random variables (Iα, α ∈ Γ), there are many methods available. The simple formula for the characteristic function allows Fourier inversion and complex analytic techniques to be brought into play directly, or as applied by Kerstan (1964). Alternatively, the use of these techniques in an operator framework, as in Le Cam (1960) and Deheuvels and Pfeifer (1988), brings excellent results. That the Stein–Chen method also works well in this context is hardly surprising—independence is mathematically a very powerful tool—but, in view of the many competing possibilities, it is perhaps not to be expected that dramatically better results can be proved.
Measurement, Regression, and Calibration
Authors: Brown Philip J 
Published: November 2023

Abstract
The book starts with a range of examples and develops techniques progressively, starting with standard least squares prediction of a single variable from another and moving onto shrinkage techniques for multiple variables. Chapters 6 and 7 refer mostly to methods that have been specifically developed for spectroscopy. The other chapters are quite general in their applicability. Likelihood and Bayesian inference features strongly, the latter allowing flexible analysis of a wide range of multivariate regression problems. The last chapter presents some Bayesian approaches to pattern recognition. For teaching purposes instructors may find particular chapters sufficiently self contained to recommend in isolation as reference or reading material. For example chapter 4 gives an in depth development of a range of shrinkage techniques. including partial least squares regression, ridge regression and principal components regression; together with discussion of the recently proposed continuum regression. Chapter 8 on pattern recognition may also be of us by itself in courses on multivariate analysis and Bayesian Statistics.
Simple linear regression
Authors: Brown Philip J 
Published: November 2023

Abstract
Suppose a single random variable Y is such that for a given value of another variable X = x, the conditional expectation is linear in x :
Here Y might be some measure of lung function and x the cumulative exposure to asbestos dust for a building worker. We may note that x may not be the originally measured variable, it may rather be some function of it; the same applies to Y. What is required is that linearity of conditional expectation holds for the calculated variables, and that in obtaining a measurement pair (xi,Yi) on each of n workers, uncorrelated errors Ei, with constant variance, add to eqn (2.1) to give the random observation Yi, so that
Regularized multiple regression
Authors: Brown Philip J 
Published: November 2023

Abstract
The Gauss-Markov theorem lends considerable weight to the use of least-squares as a method of fitting a linear parametric model. It provides ‘best’ estimators. It does, however, have a very restricted notion of what is best. Firstly it confines attention to estimators linear in the response Y. Secondly it looks only at unbiased estimators. Thirdly it minimizes mean-squared error, that is, it is concerned with expected squared error or quadratic loss: in the scalar case it uses is as an estimator of θ. Even retaining quadratic loss, there may be estimators which are either biased or non-linear in Y or both, which have an average performance far better than least-squares over much of the relevant parameter space. Such estimators may be introduced in a variety of ways. They are often thought to be particularly apt when the model matrix, X, becomes singular or rather near to singular. They are sometimes called regularized estimators and at other times shrinkage estimators, due to the reduced length of the estimated regression parameter vector compared to that of least-squares. The term regularized emanates from the method of regularization in approximation theory literature. Introducing a Lagrange multiplier, λ., this amounts to minimization of or its Hilbert space generalization. Their use as estimators or predictors comprises a large literature; a much smaller literature addresses wider inferential questions. In the model (3.7) assumed here, where columns of X have mean zero, generally, as in standard least-squares estimation.
Regression on curves
Authors: Brown Philip J 
Published: November 2023

Abstract
This chapter extends the discussion of regression modelling to the situation where the set of explanatory variables is indexed by a variate, frequency, or time, and when plotted as in Fig. 1.5 each set of explanatory variables forms a discretized curve. These variables essentially form some sub-sampled sequence of a continuous random process, so that there is an order to the variables and often the sub-sampling will be at equally spaced intervals of the underlying continuous variate (frequency or time). The number, q, typically here large, of explanatory random variables, will be denoted Y(q) = (Y1, Y2, ..., Yq,) and will be used to predict the response or interest variable, here univariate and denoted as X. Training data are available for which both the interest variable and the explanatory variables are observed on n specimens. In this chapter we assume that the data may be viewed as obtained at random so that we are in the random or natural calibration case as opposed to the more problematic controlled calibration where the interest variable has been strictly designed in the training data. In effect the calibration paradigm just reduces to standard regression prediction except that we have reversed the roles of X and Y. As in Chapter 4, the number q of explanatory variables may be very much larger than the number of observations, and there is a high degree of indeterminacy in fitting linear models. The detergent example described in Section 6.9 has n=l2 and q = 43 extracted frequencies, but had the full set of frequencies been used q would be 1168, leading to the full set of 12 Y(q) shown in Fig. 1.5. In this example component 2 of Table 1.4 serves as the twelve X-observations for calibration.
Non-linearity and selection
Authors: Brown Philip J 
Published: November 2023

Abstract
All the models so far considered have been linear in the unknown parameters. This allows the fitting of models non-linear in the measured variables, but at the expense of consequent non-linearity in prediction after controlled calibration. In this chapter we address these non-linear models, both from the viewpoint of exploring the extra complexities that arise and of reviewing methods for avoiding them. In particular variable selection techniques can be used to pick variables for which a linear model holds. This can be particularly advantageous in relating spectra to composition in that the spectral curve measured at a large number of wavelengths embodies a considerable degree of redundancy, and wavelengths may be selected at which the model relating absorbance to composition is quite linear. At other wavelengths which are avoided the relationship may be far from linear. We start in Section 7.2 by offering some diagnostics for detecting non-linearity and interaction and illustrate these on the sugars data described in Example 1.6. Then methods of variable selection are reviewed and illustrated on the same data as well as the detergent data of Example 1.5. Finally, properties of non-linear models relating to possible multimodality of inference are explored in Section 7.10. The earlier sections of the chapter focus on near-IR spectral data but the issues are quite general.
Pattern recognition
Authors: Brown Philip J 
Published: November 2023

Abstract
This chapter explores the use of Bayes theorem in simple applications of pattern recognition and identification. The main development that follows is of discrimination between p multivariate normal populations. This introductory section concludes with two examples on updating evidence in applications of medical screening and of forensic science. In the training data the p populations are identified by p dummy variables, 1 for the presence of that population, 0 for absence. For each observation in the training data these constitute the x-variables corresponding to q-variate Y. Once a linear relationship between x and Y is established, in future it is desired to predict the x (population of origin) from an observed q-vector Z (the future Y). This is classical discrimination, and directly parallels the calibration paradigm of the rest of this book. In particular, recall the direct link between the regression of Y on x and that of x on Y of Section 5.5. This algebraic link does not depend on whether x is a random variable. In particular there is the well-known two-population result that linear discrimination as developed by Fisher can be reproduced by regression of the dummy variable, which identifies the population of origin, on the q variates. However, there is one special feature here: the x-variables are identifiers of the population and not continuous variates. It is therefore desirable and possible to further give the probability that the future Z derives from each of the p populations.
Experimental strategies
Authors: Atkinson A C , Doney A N 
Published: November 2023

Abstract
We are mainly concerned with experiments where the purpose is to elucidate the behaviour of a system by fitting an approximating function or model. The distinction is with experiments where the prime interest is in estimating differences, or other contrasts, in yield between units receiving separate treatments. Often the approximating function will be a low-order polynomial. But, as in Chapter 18, the models may sometimes be non-linear functions representing knowledge of the mechanism of the system under study. There are several advantages to summarizing and interpreting the results of an experiment through a fitted model.
Models and least squares
Authors: Atkinson A C , Doney A N 
Published: November 2023

Abstract
The plots in Chapter 4 illustrate some of the forms of relationship between an m-dimensional factor x and the true response η (x), which will often be written as η (x, β), to stress dependence on a vector of p unknown parameters β. For a first-order model p = m +1. Measurements of η (x) are subject to error, giving observations y. Often the experimental error is additive and the model for the observations is
Mixture experiments
Authors: Atkinson A C , Doney A N 
Published: November 2023

Abstract
We shall chiefly consider the case when the remaining factors, if any, do not vary during the experiment. Then (12.1) defines the q components of a mixture. In mixture experiments the response will depend only on the proportions of the components in the mixture, for example an alloy, but not on the total amount. Experiments of this kind occur frequently in such areas as chemistry, medicine, and agriculture. An extensive survey of mixture experiments is given by Cornell (1990).
Experiments with both qualitative and quantitative factors
Authors: Atkinson A C , Doney A N 
Published: November 2023

Abstract
This chapter is concerned with the design of experiments when the response depends on both qualitative and quantitative factors. In the chemical industry the yield of a process might depend not only on the quantitative factors temperature and pressure, but also on such qualitative factors as the batch of raw material and the type of reactor. Likewise, an antibiotic might be given orally or by an injection, a qualitative factor with two levels. The composition and dosage of the antibiotic could be the quantitative factors.
Blocking response surface designs
Authors: Atkinson A C , Doney A N 
Published: November 2023

Abstract
This chapter, like Chapter 13, is concerned with the design of experiments when the response depends on both qualitative and quantitative factors. For the exact designs of Chapter 13 the number of trials at each level of the qualitative factor is determined by the search algorithm. However, if the qualitative factor corresponds to a blocking variable there may be a specified, and possibly non-constant, number of trials at each level of the qualitative factor. Examples include the number of plots in a field in an agricultural field trial and the number of runs on a chemical plant that can be obtained from a single batch of raw material.
Restricted design regions
Authors: Atkinson A C , Doney A N 
Published: November 2023

Abstract
A major advantage of a general theory such as that of optimum experimental design is the provision of methods for the solution of non-standard problems. In this chapter we illustrate this consequence of the theory through the construction of designs for non-standard design regions. For response surface models these are regions which are neither cubical nor spherical and so are not covered by the results of Chapter 11. For mixture designs, the non-standard regions depart from the simplex for which designs were derived in Chapter 12. A description of a variety of non-standard design problems is given by Snee (1985). His major theme is the usefulness of the computer in the design and conduct of a wide variety of experiments. One area of application is the construction of D-optimum designs for irregular experimental regions. He gives seven examples of such regions and discusses desirable properties of designs, but does not calculate the D-optimum designs. The examples giving rise to non-standard regions are listed briefly below before we consider four examples in more detail.
Clustering from the Perspective of Combinatorial Data Analysis
Authors: Arabie Phipps , Huber Lawrence J . 
Published: November 2023

Abstract
Perhaps the most well-developed and commonly used form of combinatorial data analysis is clustering, which we might characterize as those methods concerned in some way with the identification of homogeneous groups of objects, based on whatever data are available. The literature of cluster analysis is enormous and precludes our giving much space to applications; fortunately, the Classification Society of North America publishes an annual bibliography, Classification Literature Automated Search Service, based on citations to “classic” articles and books as compiled by the Institute for Scientific Information. The target articles being cited are drawn largely from the periodicals’ literature of clustering and multidimensional scaling; after considerable winnowing, 876 citations were given for 1992 (Volume 21; Day, 1992).