The Romans gradually, whether by military action or diplomacy, eroded the power of the successor-states to Alexander's vast empire until they fell under Roman control either by conquest or by testamentary disposition, the latter in the case of the Pergamene kingdom, willed to Rome when Attalus III died without heir in 133, or Cyrene, bequeathed to Rome by Apion in 96. The last to survive were the Ptolemaic kingdoms of Cyprus and Egypt, ruled, after the death in 80 of Alexander II, by Ptolemy XII Auletes and his brother, both sons of Ptolemy IX by an unknown Greek concubine. After much controversy over an alleged will of Alexander II bequeathing his realms to Rome, in early 59, through massive bribery, Auletes was finally able to procure the senate's recognition of his title to the throne and status as “friend and ally” of the Roman people. That did not stop the Romans, however, from acting on another provision of the will of Alexander II by annexing Cyprus (leading to the suicide of Ptolemy of Cyprus) and using the fresh revenue to subsidize the corn dole for the urban plebs.

In Alexandria the annexation of Cyprus and increased taxation required to pay off the monarch's bribes to Roman powerbrokers provoked widespread riots, during which Ptolemy escaped clandestinely and made his way to Rome, where he received hospitality in Pompey's Alban villa and began to lobby for his own restoration. The Romans who had lent money to the king were, of course, in favor in order to protect their investment, but there was disagreement over the commander best suited to the mission, Pompey, Crassus and P. Cornelius Lentulus Spinther (cos. 57) all being candidates. In the meantime word reached Alexandria of Ptolemy's escape and residence in Rome.

The relation of C.’s extant speeches to those he actually delivered in court has been much discussed. The following is a brief survey of the evidence and its implications (the second actio of Verres’ trial, the defense of Milo and the Second Philippic are special cases, the first and third never delivered, the second heavily revised for publication).

C. rarely delivered his speeches from a manuscript, and when he or another speaker did so, the fact might draw comment and/or explanation. Ordinarily he would write out in advance the beginning of the speech and some critical points and have the rest worked out in his mind (Quint. Inst. 10.7.1). Such rough notes for his speeches, the commentarii, remained among his papers at his death and were published by Tiro in at least thirteen books (Diomedes GL I 368.28). Both Asconius and Quintilian were familiar with them but make no mention of any divergence between the commentarii and the delivered speeches (Asc. 87.10 C; Quint. loc. cit. and 4.1.69). The one direct piece of evidence bearing upon the relation of the oral and written versions of the speeches is provided by Cornelius Nepos, who reports that C.’s speech Pro Cornelio was delivered in “almost the same words” as the published version.

The first tribunal de ui at Rome was enacted by the consul Q. Lutatius Catulus in 78 as a tool for suppressing the revolt led by his colleague M. Aemilius Lepidus; it was evidently a quaestio extraordinaria rather than a permanent institution. M. Caelius Rufus was charged under the lex Plautia de ui, which was probably enacted in 70 by the plebeian tribune M. Plautius Silvanus (MRR II 128), the man who also introduced the lex Plautia de reditu Lepidanorum; possibly the lex de ui was a concession to those who feared new unrest if the exiles were allowed to return. Certainly the lex Plautia de ui was in effect by 63, since in that year Catiline was prosecuted under it (TLRR 223). Perhaps Plautius proposed this legislation, rather than rely on the existing quaestio maiestatis, since the latter was better adapted to prosecuting the ringleaders of armed violence than the rank and file. The lex Plautia outlawed any act of violence that was directed contra rem publicam and established a standing court (quaestio perpetua) to hear relevant charges; it also provided that that court meet daily, even during festivals (dies festi), and that its cases receive priority over other pending trials.

This is not the place for a full biography of Clodia Metelli, but since C. presents her as his main antagonist in this speech, it is worth considering briefly who she was and what rôle she played in this trial. A daughter of Ap. Claudius Pulcher (cos. 79), she was probably born by 93; she was married, possibly by 79, to Q. Metellus Celer (cos. 60). Of her three brothers, Appius achieved the consulate (54), Gaius the praetorship (56), Publius the tribunate of the plebs (58) and aedileship (56). She also had two sisters, though the order of their births is unclear. In any case, both of her sisters also married consuls: one married L. Licinius Lucullus (cos. 74); the other, Claudia Tertia, married Q. Marcius Rex (cos. 68). Clodia herself was widowed by the sudden death of her husband in 59 (see further on §§59–60). She is known to have possessed three properties, a house on the Palatine, gardens on the Tiber and a house at Baiae. There is no reference to her dated later than 44.

The date of publication of Cael. has been controversial since Norden argued that it remained unpublished during C.’s lifetime because the Council of Luca of mid-April interfered with any plans for publication; hence it was edited posthumously from his papers with “doublets” remaining in the text as traces of C.’s improvisation during delivery. But the “doublets,” i.e. reprise of topics previously mooted (§28 ∼ §§41–3 and §38 and §§48–50), can be otherwise explained; and C. heard of the Council of Luca only ca. 25 April; even if he drew immediate conclusions from that information, in view of the speed with which he could work, the prior writing up and circulation of the speech is not excluded. As a general rule it is probably true that C. wrote up and circulated quickly the forensic speeches that he meant to publish. Crawford points out that a desire to memorialize “the devastating attack on the Clodii” would have argued for immediate publication; indeed the speech shows the wounds of the exile still raw (§§32, 50).

The phase-field method is a thermodynamics-based approach most often employed to model phase changes and evolving microstructures in materials. It is a mesoscopic method, in which the variables may be abstract non-conserved quantities measuring whether a system is in a given phase (e.g., solid, liquid, etc.) or a conserved quantity, such as a concentration. Interfaces are described by the smooth variation of those quantities from one phase to another and are diffuse, not sharp.

The phase-field method is increasingly being used in materials science and engineering because of its flexibility and utility. We discuss the basic method here, but researchers are continually creating new features and new approaches within the basic phase-field framework.

We first introduce the basic mathematical formalism, followed by some simple examples of the phase field in one and two dimensions. Implementation of the phase field requires some new computational methods, which will be discussed in the regular text and an appendix. Finally, we will discuss some applications of the phase-field method in materials research.

CONSERVED AND NON-CONSERVED ORDER PARAMETERS

In phase-field modeling, the state of a system is described by a function of position and time. This function could be a specific property of the system such as concentration or it could be a parameter that indicates what phase the system is in, e.g., solid or liquid. This function is generally referred to as an order parameter.

The behavior of a material can be related to the types of bonding between the atoms, whether it be metallic, covalent, ionic, etc. That bonding represents the distribution of electrons around the nuclei. Covalent bonds have a localized electronic distribution between atoms and are generally strong and directional. Materials with strongly covalent bonds include important semiconductors, such as silicon, gallium, and diamond. Metallic systems, in contrast, may have a degree of directionality to their bonding, but the dominant feature is a delocalized sea of electrons. Ionic bonds are dominated by the strong electrostatic interactions between the ions. Fundamentally, the properties of each material start with its bonding.

A fundamental description of bonding requires a calculation of the electronic distributions. The class of methods that yield such information are called electronic structure methods. In this chapter, we shall briefly review the basics of these methods, pointing out their inherent approximations. There are numerous books devoted to the fundamental theories behind these methods – embodied in quantum mechanics – as well as many texts devoted to electronic structure methods themselves [167, 219, 251, 254]. We can at best give a brief guide to this topic needed for discussions later in the text and as well as for a basis for understanding and evaluating this fascinating field.

Not so many years ago, practitioners of electronic structure calculations typically used homegrown computer codes, which often required heroic efforts on the parts of the programmers.

Engineered designs are generally based on the use of a constrained, and fixed, set of materials. Because materials development is slow, the role of the materials engineer is generally one of materials selection, i.e., choosing a material from a restricted list to fit a specific need in a product design process. Traditionally, the optimal material was a balance between best meeting the product performance goals and minimizing the cost of the material. In recent years, an increased focus has been on the life cycle of the material, with an eye towards recycling and reuse.

The selection of the best material for an application begins with an understanding of the properties needed for the design as well as a way to display and access the properties of candidate materials. If the design is based on a single criterion for the material, such as density, for example, then the choice of a material is usually pretty simple. If multiple criteria must be met, then a way to compare multiple properties of a set of materials with each other is needed. A common way to do that is through an “Ashby plot”, a scatter plot that displays one or more properties of many materials or classes of materials [13, 14]. For example, suppose one needs a material that is both stiff and light. Stiffness is measured in Young's modulus, while knowing the density of a material will enable one to pick the lightest material for a specific volume.

In this chapter, we discuss how to extend the methods introduced in the previous chapters from atomic to macromolecular systems. The basic ideas are the same, but there are additional complexities that arise from the molecular shapes. The simulation of molecular systems, especially polymeric and biological materials, is a very active field and we barely touch the surface here. For more information, please see the texts in the Suggested reading section.

After a review of the basic properties of macromolecules, the chapter continues with a discussion of some of the common approaches to model the interaction between the molecules, followed by descriptions of how molecular dynamics and Monte Carlo methods can be applied to molecular systems. When discussing systems of large molecules, such as polymers or proteins, however, it becomes challenging to include the full complexity of the molecules within a calculation. Thus, various models that approximate the physics have been developed. The chapter ends with a discussion of some of these approximate methods.

INTRODUCTION

Polymers (macromolecules) are large molecules made up of long chains of monomer units. In some biological molecules, the number of monomers (N) can be quite high, e.g., in DNA N ˜ 108 in some cases. In other systems, N can be of the order of a few hundred. The identity of the monomer units defines the overall properties of the polymer – DNA and RNA are made up of nucleotides, proteins are made up of amino acids, etc.

Overview

Legal drafters seek to give effective written expression to instructions from clients. The skills needed to undertake that task are sometimes formidable. And the skills are exercised in a context where the ultimate arbiters of meaning are not the clients or the drafters, but the courts. This is not to say that drafters should write defensively, tailoring words and concepts for the judge alone. On the contrary, they must write for their clients, who are the readers and users of the documents. But they must also appreciate that a document may end up before a judge, and so must strive to ensure that the judge will interpret their draft as they (the drafters) intended. This, therefore, means that competent drafters must understand the principles which courts apply when interpreting legal documents – the so-called ‘principles of interpretation’.

This chapter examines the ways in which judges interpret legal documents. It begins by reviewing cases where judges have decried aspects of the ‘traditional’ style of legal drafting. Our purpose in this section is to emphasise that traditional legal drafting has no inherent superiority over the modern, plainer style which we recommend in this book.