Chemistry in the market place

This book is an expanded version of the first edition of Chemistry in the Market Place. It is a work of high seriousness but its 'flavour' is perhaps best captured in the words of its author as he describes the circumstances of its beginnings: {u2018}over three glasses of cool, artificially coloured, artificially foam stabilised, enzyme clarified, preserved, gassed, amber fluid{u2019} two colleagues and he came to realise that consumers needed some {u2018}real{u2019} chemistry, chemistry that would help them to make sense of the arguments that rage about various aspects of consumer products, particularly those of safety and efficacy. The thrust of the book is towards the product and the chemistry needed to understand it, rather than towards chemistry illustrated by the product. Its scope is wide and includes chemistry in the laundry, the kitchen, the garden, the boudoir, the medicine chest. It also deals with motor cars, the accidental poisoning of children, and carcinogens. It is extensively illustrated with plates, figures, and tables, and contains practical experiments for its users. The book will be welcomed by high school, college and adult education lecturers who are interested in creating courses in consumer chemistry. Concerned consumers will also benefit greatly from the information the work contains, regardless of their knowledge of chemistry. Home economics teachers will find that it forms a perfect complement to their existing texts. It is, in short, an important, practical, hook on a highly significant subject

Order and Frustration in Chiral Liquid Crystals

This paper reviews the complex ordered structures induced by chirality in liquid crystals. In general, chirality favors a twist in the orientation of liquid-crystal molecules. In some cases, as in the cholesteric phase, this favored twist can be achieved without any defects. More often, the favored twist competes with applied electric or magnetic fields or with geometric constraints, leading to frustration. In response to this frustration, the system develops ordered structures with periodic arrays of defects. The simplest example of such a structure is the lattice of domains and domain walls in a cholesteric phase under a magnetic field. More complex examples include defect structures formed in two-dimensional films of chiral liquid crystals. The same considerations of chirality and defects apply to three-dimensional structures, such as the twist-grain-boundary and moire phases.Comment: 39 pages, RevTeX, 14 included eps figure

Tilt Texture Domains on a Membrane and Chirality induced Budding

We study the equilibrium conformations of a lipid domain on a planar fluid membrane where the domain is decorated by a vector field representing the tilt of the stiff fatty acid chains of the lipid molecules, while the surrounding membrane is fluid and structureless. The inclusion of chirality in the bulk of the domain induces a novel budding of the membrane, which preempts the budding induced by a decrease in interfacial tension.Comment: 5 pages, 3 figure

Fingering Instability of Dislocations and Related Defects

We identify a fundamental morphological instability of mobile dislocations in crystals and related line defects. A positive gradient in the local driving force along the direction of defect motion destabilizes long-wavelength vibrational modes, producing a ``fingering'' pattern. The minimum unstable wavelength scales as the inverse square root of the force gradient. We demonstrate the instability's onset in simulations of a screw dislocation in Al (via molecular dynamics) and of a vortex in a 3-d XY ``rotator'' model.Comment: 4 pages, 3 figure

Dynamics of Ordering in Alloys with Modulated Phases

This paper presents a theoretical model for studying the dynamics of ordering in alloys which exhibit modulated phases. The model is different from the standard time-dependent Ginzburg-Landau description of the evolution of a non-conserved order parameter and resembles the Swift-Hohenberg model. The early-stage growth kinetics is analyzed and compared to the Cahn-Hilliard theory of continuous ordering. The effects of non-linearities on the growth kinetics are discussed qualitatively and it is shown that the presence of an underlying elastic lattice introduces qualitatively new effects. A lattice Hamiltonian capable of describing these effects and suitable for carrying out simulations of the growth kinetics is also constructed.Comment: 18 pages, 3 figures (postscript files appended), Brandeis-BC9

Causal categories: relativistically interacting processes

A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a `causal category'. We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics.Comment: 43 pages, lots of figure

Correlating matched-filter model for analysis and optimisation of neural networks

A new formalism is described for modelling neural networks by means of which a clear physical understanding of the network behaviour can be gained. In essence, the neural net is represented by an equivalent network of matched filters which is then analysed by standard correlation techniques. The procedure is demonstrated on the synchronous Little-Hopfield network. It is shown how the ability of this network to discriminate between stored binary, bipolar codes is optimised if the stored codes are chosen to be orthogonal. However, such a choice will not often be possible and so a new neural network architecture is proposed which enables the same discrimination to be obtained for arbitrary stored codes. The most efficient convergence of the synchronous Little-Hopfield net is obtained when the neurons are connected to themselves with a weight equal to the number of stored codes. The processing gain is presented for this case. The paper goes on to show how this modelling technique can be extended to analyse the behaviour of both hard and soft neural threshold responses and a novel time-dependent threshold response is described

Avalanches in Breakdown and Fracture Processes

We investigate the breakdown of disordered networks under the action of an increasing external---mechanical or electrical---force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by scaling laws, and the estimated values of the exponents are consistent with those found in mean-field theory. The breakdown point is characterized by a discontinuity in the macroscopic properties of the material, such as conductivity or elasticity, indicative of a first order transition. The scaling laws suggest an analogy with the behavior expected in spinodal nucleation.Comment: 15 pages, 12 figures, submitted to Phys. Rev. E, corrected typo in authors name, no changes to the pape

Generalised quantum weakest preconditions

Generalisation of the quantum weakest precondition result of D'Hondt and Panangaden is presented. In particular the most general notion of quantum predicate as positive operator valued measure (POVM) is introduced. The previously known quantum weakest precondition result has been extended to cover the case of POVM playing the role of a quantum predicate. Additionally, our result is valid in infinite dimension case and also holds for a quantum programs defined as a positive but not necessary completely positive transformations of a quantum states.Comment: 7 pages, no figures, added references, changed conten