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In Chapter 7, the basic ideas of the Monte Carlo method are presented and demonstrated on two types of problems, the Ising model and simulations of atomic systems. In Chapter 8, applications to molecular systems, including polymers and biomolecules, are discussed. The Ising model does not really fit into the theme of Chapter 7, which is included in the part of the text focused on atomic and molecular scale simulations. The Ising model really belongs in the current chapter, which focuses on the use of the Monte Carlo method to simulate models of materials behavior at the mesoscale. However, the Ising model is just too good an example of the Metropolis Monte Carlo method, so we included it in Chapter 7. Consider its natural home, however, here.
There are many types of Monte Carlo applications that have been developed to model material properties and response. We shall examine only one of them in detail, the Q-state Potts model as applied to grain growth. Not only has the Potts model had wide applicability and impact in materials research, it reflects most of the issues faced in any mesoscale modeling based on the Monte Carlo method.
With the development of inexpensive, yet very fast, computers and the availability of software for many applications, computational modeling and simulation of materials has moved from being entirely in the hands of specialists to being accessible to those who use modeling not as their principal activity, but as an adjunct to their primary interests. With that change in accessibility of materials modeling and simulation come exciting new opportunities for using computational modeling to greatly advance the development and refinement of materials and materials processing.
The goal of this text is not to make experts – there are entire books on subjects that are treated in a few pages here. The text is, by design, introductory and we leave out many, if not most, details about implementation. We will present the key features and possibilities of computational materials science and engineering and discuss how to use them to advance the discovery, development, and application of materials.
MODELING AND SIMULATION
Before we start discussing materials modeling and simulation, it is appropriate to consider those words a bit more carefully. What do we mean by a “model” or a “simulation”? How are they different? Not to be overly pedantic, but it may help our discussion if we are a bit more precise in our definitions of these terms.
The traditional style of legal writing is the product of many influences. Some influences are constant, some are sporadic. They rarely exist in isolation; usually, many operate together. This chapter reviews the main influences on traditional legal drafting, namely:
familiarity and habit – the security that comes from adopting forms and words that have been used before and seem to be effective
conservatism in the legal profession, allied to the common law tradition of precedent
fear of negligence claims
the means of production
pressures to conform to professional norms
the desire to avoid ambiguity
the mixture of languages from which the law derives its vocabulary
payment by length of document
payment by time
the litigious environment of legal practice.
Some of these influences, such as the mixture of languages and payment by length of document, are largely historical, with little direct effect today. Others, however, remain pervasive.
The stylistic hallmarks of traditional legal drafting are apparent in many types of document. Some of the best (or worst) examples are leases – their dense prose and ‘torrential’ style intimidate even the hardiest reader. Other documents exhibiting a similar style include conveyances, wills, trust deeds, insurance policies, mortgages and shipping documents. The common thread pervading them all is tradition, going back hundreds of years. This tradition is so powerful that it has been impervious to reform through the centuries and continues to resist reform even today, when change might be thought an easy option. A tradition so persistent merits detailed scrutiny.
In the previous chapter we highlighted some judicial attitudes about the use of plain language in law. Of course, those attitudes were not formed in a vacuum, but rather in the context of a general trend towards the use of plain language in statutes and legal documents – the plain-language ‘movement’. In earlier editions of this book we detailed the early steps in that movement. In this edition, for reasons of space, we omit that discussion. However, the movement continues apace in many countries – including in non-English-speaking countries – and is now well documented. The movement arose out of the perceived benefits in using plain language in legal writing. In this chapter we consider some of those benefits.
The meaning of ‘plain English’
We begin with a point of terminology: what do we mean by ‘plain English’ in the context of legal writing? Proponents of the modern style of legal drafting use various terms to describe it, including ‘modern English’ and ‘standard English’. The term that has achieved the most widespread use is ‘plain English’. Some explanations of this term are:
The ‘practice of writing…in a clear and simple style’.
The ‘idiomatic and grammatical use of English that most effectively presents ideas to the reader’.
A ‘flexible and efficient writing style that readers can understand in one reading. It combines clear, concise expression, an effective structure and good document design.’
4.3 Perhaps the word plain is unfortunate. It suggests a kindergarten style of language – one which patronises adult readers. This leads some lawyers to consider ‘plain English’ to be inappropriate for law. They assume that it denotes an oversimplified ‘Dick and Jane’ style a form of language shorn of beauty, stripped of vocabulary, truncated in form, and deficient in style. This, however, is a misunderstanding of the true nature of plain English. As the Law Reform Commission of Victoria pointed out in its 1986 discussion paper Legislation, Legal Rights and Plain English, ‘plain English’ is a full, adult version of the language. To avoid any pejorative overtones in ‘plain English’, in this book we sometimes use the term ‘modern, standard English’.
Suppose we have an object under some prescribed load (i.e., an applied force).We can describe how the object will deform in response to that load with the results of elasticity theory. For the purposes of this textbook, we will restrict the discussion to the regime of small displacements, in which we can use a linear version of elasticity theory. The fundamental assumptions of linear elasticity are that (1) the displacements (strains) are small and (2) there are linear relationships between the strains and their associated stresses (we define stress and strain hereinafter). The assumption of linear elasticity is reasonable for many applications and is used extensively in structural analysis.
We note that there is a further restriction to linear elasticity. The applied stress must be low enough so that yielding does not occur, i.e., so that the material does not undergo permanent deformation. Consider a thin metal rod, for example. If one applies a small force to the rod, it deforms but springs back to its original state when the force is removed. If you keep increasing the force, eventually the rod bends and does not return to the original state when the force is removed. That deformation is caused by the movement of linear defects called dislocations, which are described in Appendix B.5.We also describe a basic model of plastic deformation in terms of dislocation motion in that section. Later in this chapter, in Appendix H.5, we discuss the relationship between elastic and plastic strain.
This chapter introduces some basic concepts used in the computations in this text. It is not a programming guide, as each software system has its own language and defined functions. We discuss some general methodologies that are common among programming languages and that crop up in a number of the methods in this text, for example the calculation of random numbers. We also discuss a few numerical methods. Specific implementations of the various methods are presented online at http://www.cambridge.org/lesar.
SOME BASIC CONCEPTS
Computers are discrete and thus all problems, whether discrete or continuous in space or time, must be converted to discrete methods on a computer. The requirement of having discrete methods presents challenges and guides the development of most of the models seen in this text. Some methods, such as molecular dynamics in Chapter 6, may be continuous in one dimension (space), but are solved with discrete time steps. Others, such as the Potts model of grain growth in Chapter 10, are discrete in both space and time.
RANDOM-NUMBER GENERATORS
A common need in essentially all of the methods discussed in this text is for random numbers. It is in many ways odd to discuss random numbers when talking about computers, which are precise and anything but random. Algorithms have been developed, however, that yield series of numbers that look random, at least relative to certain statistical measures of randomness. These algorithms are generally referred to as random-number generators. The challenge is that generators are not all of the same quality.
In Chapter 7 we introduced the Monte Carlo method, with the focus being on calculating equilibrium properties based on sampling of the degrees of freedom in a Hamiltonian (energy) function. In this chapter, the focus is on the Monte Carlo method applied to rates. We shall see that for certain classes of problems, we can find an association between the Monte Carlo “time” and actual time, opening the door to a new class of simulation methods that can model time-dependent processes at time scales far beyond what is possible with standard molecular dynamics.
The fundamental input to the kinetic Monte Carlo method is a list of possible events such as a jump from one site to another in a diffusion problem, a chemical reaction, etc. Associated with each event will be a rate, which will be related to a probability that the event will occur. An understanding of rates is thus very important, so in Appendix G.8 we give a brief review of kinetic rate theory.
A number of researchers independently developed what has come to be known as the kinetic Monte Carlo method. The N-fold way as a methodology for accelerating the simulations of the Ising model is probably the first example [38], which will be discussed in Chapter 10. Voter introduced a similar approach as a way to study the dynamics of cluster diffusion on surfaces [327]. We will discuss his calculation later in this chapter as one of two examples of the complexities, and limitations, of the kinetic Monte Carlo approach.
THE KINETIC MONTE CARLO METHOD
Consider a system whose properties are dominated by thermally activated processes, such as diffusion.
Language and Gender is an introduction to the study of the relation between gender and language use, written by two leading experts in the field. This new edition, thoroughly updated and restructured, brings out more strongly an emphasis on practice and change, while retaining the broad scope of its predecessor and its accessible introductions which explain the key concepts in a non-technical way. The authors integrate issues of sexuality more thoroughly into the discussion, exploring more diverse gendered and sexual identities and practices. The core emphasis is on change, both in linguistic resources and their use and in gender and sexual ideologies and personae. This book explores how change often involves conflict and competing norms, both social and linguistic. Drawing on their own extensive research, as well as other key literature, the authors argue that the connections between language and gender are deep yet fluid, and arise in social practice.
Since publication of the seventh edition of this seminal text, personal injury law has witnessed momentous changes. A major overhaul of the social security system began in 2012 and the Equality Act 2010 significantly modifies anti-discrimination law and its impact on the disabled. But perhaps the most important legal developments have affected the financing and conduct of personal injury claiming and the operation of the claims-management industry. This new edition takes account of all this activity while setting it into a wider and longer perspective. Complaints that Britain is a 'compensation culture' and that the tort system is out of control are explained and assessed and options for further change are explored. Through the turmoil and controversy, the tort system remains a central feature of the legal and social landscape. The book's enduring central argument for its radical reform remains as compelling as ever.
This book is a modern pedagogic introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods, the quantum theory of scalar and spinor fields, and then of gauge fields, is developed. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a brief survey of 'topological' objects in field theory and, new to this edition, a chapter devoted to supersymmetry.
Emphasising essential methods and universal principles, this textbook provides everything students need to understand the basics of simulating materials behaviour. All the key topics are covered from electronic structure methods to microstructural evolution, appendices provide crucial background material, and a wealth of practical resources are available online to complete the teaching package. Modelling is examined at a broad range of scales, from the atomic to the mesoscale, providing students with a solid foundation for future study and research. Detailed, accessible explanations of the fundamental equations underpinning materials modelling are presented, including a full chapter summarising essential mathematical background. Extensive appendices, including essential background on classical and quantum mechanics, electrostatics, statistical thermodynamics and linear elasticity, provide the background necessary to fully engage with the fundamentals of computational modelling. Exercises, worked examples, computer codes and discussions of practical implementations methods are all provided online giving students the hands-on experience they need.
More often than not, the issues that policy workers deal with on a daily basis are highly complex. While much in the theoretical literature (such as the idea of rational decision making discussed in Chapter 1 or theories concerning policy analysis and policy instruments as discussed in Chapter 4) suggests that clarity and certainty should characterise the policy development process, in reality determining the ‘right’ policy response from the vast array of available choices, with access to imperfect information and disparate community views, can be a daunting task.
In recent years the demand has been for ‘evidence-based policy’, which raises questions about what kinds of evidence exist and how it is best uncovered for the purposes of informing public policy. One possible implication of the term ‘evidence-based policy’ is that the contested and uncertain policy process discussed throughout this book can be rendered objective and certain. However, as will be discussed below, while there is no doubt that the collection and analysis of information has the potential to improve the advice provided to policy makers, there is no obligation on policy makers to heed such advice.
You change your laws so fast and without inquiring after results past or present that it is all experiment, seesaw, doctrinaire; a shuttlecock between battledores.
(Florence Nightingale, letter to Sir Francis Galton, 7 February 1891 cited in McDonald 2003).
No policy should ever be implemented and then ignored. Evaluation is a crucial element of good policy work. Done well, it produces specific advice about the future development – or abandonment – of a particular approach to solving a policy problem. Evaluation can be defined as the process of judging the merit or success of an initiative, that is, an ‘ex post assessment of the strengths and weaknesses of public programs and projects’ (Bovens, ’t Hart & Kuipers 2006: 319). Factors considered in policy evaluation include the merit and value of content, administration, output, and effects of policy (Vedung 2006: 397). Evaluation allows policy makers and managers to assess the impacts, benefits, and failings of a policy or program, to suggest improvements, and to make decisions on its ongoing viability or worth (see Nagel 2002; Rossi, Lipsey & Freeman 2003).
In order to make informed decisions, evaluators need the right information. Evaluation therefore involves collecting or collating evidence, including theoretical evidence, that will enable the results of an initiative to be compared with its stated objectives. In order to facilitate good evaluation, the intended goals of a policy need to be clear, and it is therefore necessary for ministers to state clearly at the outset what they hope to achieve from a given policy.
The work of policy analysis and development is varied and multifaceted. It is rare that any one person, or even any one organisation, is responsible for the identification of a particular problem, the generation of an original solution, the development of a specific proposal and the creation of the necessary support required to see a new policy implemented. These multiple layers of ‘policy making’ allow for a wide range of individuals and organisations to participate in the policy process. While the skills and knowledge required to contribute to different elements of the process may differ, an awareness of other participants is likely to be of use to all involved, if only to ensure that they develop the necessary relationships to ensure that their contribution is supported by others.
This chapter builds on the typology developed in Chapter 5 in order to provide an overview of the actual roles of those involved in ‘doing policy’. In Chapter 5 the abstract roles of policy researcher, policy promoter, policy designer and policy gatekeeper were discussed, but in practice such jobs are never advertised and few in the policy community would identify themselves as performing only one of those functions. In this chapter we describe the actual work of some of the main policy occupations, such as politician, adviser and academic, and in doing so highlight the variety of roles that can be played by individuals in each of those positions.
Policy is where ideas meet action. That is why policy makers need to grapple with both theory and practice. This book provides the foundation upon which students and practitioners alike can analyse the policy process as it is and create the policy process that there should be.
Sarah Maddison and Richard Denniss both have extensive experience not just in researching and teaching the policy process, but also in participating in it, and this breadth of experience defines the approach taken throughout this book. While some chapters are more about theory and others focus more on practice, both elements are interwoven throughout. The book exposes students to the big ideas about policy, but never steers them too far away from the need to develop policy in the real world.
This second edition has been extensively updated and is based on new examples and new evidence. It now includes a chapter dedicated to the task of policy evaluation and is linked to a new website with up-to-date case studies, chapter summaries, links to additional sources, and a flashcard glossary.
Anyone interested in politics needs to understand how political decisions are made. Behind what we hear described as ‘policy’ on the nightly news and what we read about in the newspaper is a complex process involving a range of players with competing interests, facing an array of pressures. These players may be inside or outside of government, and inside or outside of the bureaucracy. They may come from industry, the not-for-profit non-government sector, unions, professional bodies or from academia. Understanding the way these players interact, what drives and informs them, how they think, and what they do, helps us all to understand and interpret the policies that these complex relationships eventually produce: policies that have implications for each of us in our daily lives. Policy determines where roads are built, how many nurses work in a hospital, what fees you pay at university, how much tax we pay, the price of child care and so on and so on. Policy goes beyond measures of efficiency, effectiveness and political feasibility, with demonstrable effects on citizenship, justice, discourse and democracy (Ingram & Schneider 2006: 169). Almost every aspect of our lives is touched by policy. If we understand how policy is made we have greater capacity to participate in that process, to have our voices heard and to influence decisions. This book will provide students of policy with both a theoretical understanding of public policy and an introduction to some of the real-world challenges and skills involved in working in a range of policy roles.