A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Readers' resposes versus reader-response theories : An empirical study

This study examines both theoretically an empirically how well the theories of Norman Holland, David Bleich, Wolfgang Iser and Stanley Fish can explain readers' interpretations of literary texts. The theoretical analysis concentrates on their views on language from the point of view of Wittgenstein's Philosophical Investigations. This analysis shows that many of the assumptions related to language in these theories are problematic. The empirical data show that readers often form very similar interpretations. Thus the study challenges the common assumption that literary interpretations tend to be idiosyncratic. The empirical data consists of freely worded written answers to questions on three short stories. The interpretations were made by 27 Finnish university students. Some of the questions addressed issues that were discussed in large parts of the texts, some referred to issues that were mentioned only in passing or implied. The short stories were "The Witch à la Mode" by D. H. Lawrence, "Rain in the Heart" by Peter Taylor and "The Hitchhiking Game" by Milan Kundera. According to Fish, readers create both the formal features of a text and their interpretation of it according to an interpretive strategy. People who agree form an interpretive community. However, a typical answer usually contains ideas repeated by several readers as well as observations not mentioned by anyone else. Therefore it is very difficult to determine which readers belong to the same interpretive community. Moreover, readers with opposing opinions often seem to pay attention to the same textual features and even acknowledge the possibility of an opposing interpretation; therefore they do not seem to create the formal features of the text in different ways. Iser suggests that an interpretation emerges from the interaction between the text and the reader when the reader determines the implications of the text and in this way fills the "gaps" in the text. Iser believes that the text guides the reader, but as he also believes that meaning is on a level beyond words, he cannot explain how the text directs the reader. The similarity in the interpretations and the fact that the agreement is strongest when related to issues that are discussed broadly in the text do, however, support his assumption that readers are guided by the text. In Bleich's view, all interpretations have personal motives and each person has an idiosyncratic language system. The situation where a person learns a word determines the most important meaning it has for that person. In order to uncover the personal etymologies of words, Bleich asks his readers to associate freely on the basis of a text and note down all the personal memories and feelings that the reading experience evokes. Bleich's theory of the idiosyncratic language system seems to rely on a misconceived notion of the role that ostensive definitions have in language use. The readers' responses show that spontaneous associations to personal life seem to colour the readers' interpretations, but such instances are rather rare. According to Holland, an interpretation reflects the reader's identity theme. Language use is regulated by shared rules, but everyone follows the rules in his or her own way. Words mean different things to different people. The problem with this view is that if there is any basis for language use, it seems to be the shared way of following linguistic rules. Wittgenstein suggests that our understanding of words is related to the shared ways of using words and our understanding of human behaviour. This view seems to give better grounds for understanding similarity and differences in literary interpretations than the theories of Holland, Bleich, Fish and Iser.

Renormalisation of the Fayet-Illiopoulos term in supersymmetric spontaneously broken U( 1) gauge theories

It is shown that the Fayet-Illiopoulos D term in N= 1 supersymmetric spontaneously broken U( 1) gauge theories may get one-loop corrections, even when trace U( 1) charges are zero. However, these corrections are only logarithmically divergent and hence do not affect the naturalness of the theory.

Double-Edged Imitation : Theories and Practices of Pastiche in Literature

This study concentrates on the contested concept of pastiche in literary studies. It offers the first detailed examination of the history of the concept from its origins in the seventeenth century to the present, showing how pastiche emerged as a critical concept in interaction with the emerging conception of authorial originality and the copyright laws protecting it. One of the key results of this investigation is the contextualisation of the postmodern debate on pastiche. Even though postmodern critics often emphasise the radical novelty of pastiche, they in fact resuscitate older positions and arguments without necessarily reflecting on their historical conditions. This historical background is then used to analyse the distinction between the primarily French conception of pastiche as the imitation of style and the postmodern notion of it as the compilation of different elements. The latter s vagueness and inclusiveness detracts from its value as a critical concept. The study thus concentrates on the notion of stylistic pastiche, challenging the widespread prejudice that it is merely an indication of lack of talent. Because it is multiply based on repetition, pastiche is in fact a highly ambiguous or double-edged practice that calls into question the distinction between repetition and original, thereby undermining the received notion of individual unique authorship as a fundamental aesthetic value. Pastiche does not, however, constitute a radical upheaval of the basic assumptions on which the present institution of literature relies, since, in order to mark its difference, pastiche always refers to a source outside itself against which its difference is measured. Finally, the theoretical analysis of pastiche is applied to literary works. The pastiches written by Marcel Proust demonstrate how it can become an integral part of a writer s poetics: imitation of style is shown to provide Proust with a way of exploring the role of style as a connecting point between inner vision and reality. The pastiches of the Sherlock Holmes stories by Michael Dibdin, Nicholas Meyer and the duo Adrian Conan Doyle and John Dickson Carr illustrate the functions of pastiche within a genre detective fiction that is itself fundamentally repetitive. A.S. Byatt s Possession and D.M. Thomas s Charlotte use Victorian pastiches to investigate the conditions of literary creation in the age of postmodern suspicion of creativity and individuality. The study thus argues that the concept of pastiche has valuable insights to offer to literary criticism and theory, and that literary pastiches, though often dismissed in reviews and criticism, are a particularly interesting object of study precisely because of their characteristic ambiguity.

Spontaneous symmetry breaking in twisted noncommutative quantum theories

We analyze aspects of symmetry breaking for Moyal spacetimes within a quantization scheme which preserves the twisted Poincare´ symmetry. Towards this purpose, we develop the Lehmann-Symanzik- Zimmermann (LSZ) approach for Moyal spacetimes. The latter gives a formula for scattering amplitudes on these spacetimes which can be obtained from the corresponding ones on the commutative spacetime. This formula applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone’s theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

The two-dimensional,q-state (q>4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.

Application of various viscosity theories to the viscosity data of methyl methacrylate-acrylonitrile random copolymersstar

Values of Ko, Flory constant related to unperturbed dimensions, are evaluated for methyl methacrylate-acrylonitrile random copolymers using Flory-Fox, Kurata-Stockmayer and Inagaki-Ptitsyn methods and compared with the Ko values obtained by Stockmayer-Fixman method. Ko values are seen to be less in solvents which have large a (Mark-Houwink exponent) values. A correlation between Ko and a is developed to arrive at a more reliable estimate of Ko for this copolymer system.

Renormalisation of the Fayet-Illiopoulos term in supersymmetric spontaneously broken U( 1) gauge theories

It is shown that the Fayet-Illiopoulos D term in N= 1 supersymmetric spontaneously broken U( 1) gauge theories may get one-loop corrections, even when trace U( 1) charges are zero. However, these corrections are only logarithmically divergent and hence do not affect the naturalness of the theory.

Comparison of Elasticity, Shell Core, and Sandwich Shell Theories

The problem of an infinite circular sandwich shell subjected to an a\isymmetric radial line load is investigated using three-dimensional elasticity theory, shell core method, and sandwich shell theory due to Fulton and Schmidt. A comparison of the stresses and displacements with an exact elasticity solution is carried out for various shell parameters in order to clearly bring out the limitations of sandwich shell theories of Fulton and Schmidt as well as the shell core solution.

Cancellation of quadratically divergent mass corrections in globally supersymmetric spontaneously broken gauge theories

The one-loop quadratically divergent mass corrections in globally supersymmetric gauge theories with spontaneously broken abelian and non-abelian gauge symmetry are studied. Quadratically divergent mass corrections are found to persist in an abelian model with an ABJ anomaly. However, additional supermultiplets necessary to cancel the ABJ anomaly, turn out to be sufficient to eliminate the quadratic divergences as well, rendering the theory natural. Quadratic divergences are shown to vanish also in the case of an anomaly free model with spontaneously broken non-abelian gauge symmetry.

An analysis of theories of search and search behavior

Theories of search and search behavior can be used to glean insights and generate hypotheses about how people interact with retrieval systems. This paper examines three such theories, the long standing Information Foraging Theory, along with the more recently proposed Search Economic Theory and the Interactive Probability Ranking Principle. Our goal is to develop a model for ad-hoc topic retrieval using each approach, all within a common framework, in order to (1) determine what predictions each approach makes about search behavior, and (2) show the relationships, equivalences and differences between the approaches. While each approach takes a different perspective on modeling searcher interactions, we show that under certain assumptions, they lead to similar hypotheses regarding search behavior. Moreover, we show that the models are complementary to each other, but operate at different levels (i.e., sessions, patches and situations). We further show how the differences between the approaches lead to new insights into the theories and new models. This contribution will not only lead to further theoretical developments, but also enables practitioners to employ one of the three equivalent models depending on the data available.

Magnetic superconductors: Model theories and experimental properties of rare-earth compounds

Superconducting and magnetically long-range ordered states were believed to be mutually exclusive phenomena. The discovery of rare-earth compounds in recent years, which exhibit both superconductivity and magnetic ordering (ferromagnetic, antiferromagnetic or sinusoidal), has led to considerable theoretical and experimental work on such systems. In the present article, we give a review of various theoretical models and important experimental results. In the theoretical sections, we start with the Abrikosov-Gorkov pair breaking theory for dilute alloys and discuss its improvement in the work of Müller-Hartmann and Zittartz. Then, in the context of magnetic superconductors, various microscopic theories that have been advanced are presented. These predict re-entrant behaviour in some systems (ferromagnetic superconductors) and coexistence regions in others (particularly antiferromagnetic superconductors). Following this, phenomenological generalized Ginzburg-Landau theories for two kinds of orders (superconducting and magnetic) are presented. A section dealing with renormalization group analysis of phase diagrams in magnetic superconductors is given. In experimental sections, the properties of each rare-earth compounds (ternary as well as some tetranery) are reviewed. These involve susceptibility, heat capacity, resistivity, upper critical field, neutron scattering and magnetic resonance measurements. The anomalous behaviour of the upper critical field of antiferromagnetic superconductors near the Néel temperature is discussed both in theory sections and experimental section for various systems.