1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the problem of synchronization consists of modeling each member of the population as a phase oscillator. In this review, synchronization is analyzed in one of the most representative models of coupled phase oscillators, the Kuramoto model. A rigorous mathematical treatment, specific numerical methods, and many variations and extensions of the original model that have appeared in the last few years are presented. Relevant applications of the model in different contexts are also included.

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The Kuramoto model: A simple paradigm for synchronization phenomena

: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

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Nonlinear Time Series Analysis.

▪ AbstractThe coexistence in the deep ocean of a finite, stable stratification, a strong meridional overturning circulation, and mesoscale eddies raises complex questions concerning the circulation energetics. In particular, small-scale mixing processes are necessary to resupply the potential energy removed in the interior by the overturning and eddy-generating process. A number of lines of evidence, none complete, suggest that the oceanic general circulation, far from being a heat engine, is almost wholly governed by the forcing of the wind field and secondarily by deep water tides. In detail however, the budget of mechanical energy input into the ocean is poorly constrained. The now inescapable conclusion that over most of the ocean significant “vertical” mixing is confined to topographically complex boundary areas implies a potentially radically different interior circulation than is possible with uniform mixing. Whether ocean circulation models, either simple box or full numerical ones, neither explic...

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Vertical mixing, energy, and the general circulation of the oceans

The archetypal feature of a viscoplastic fluid is its yield stress: If the material is not sufficiently stressed, it behaves like a solid, but once the yield stress is exceeded, the material flows like a fluid. Such behavior characterizes materials common in industries such as petroleum and chemical processing, cosmetics, and food processing and in geophysical fluid dynamics. The most common idealization of a viscoplastic fluid is the Bingham model, which has been widely used to rationalize experimental data, even though it is a crude oversimplification of true rheological behavior. The popularity of the model is in its apparent simplicity. Despite this, the sudden transition between solid-like behavior and flow introduces significant complications into the dynamics, which, as a result, has resisted much analysis. Over recent decades, theoretical developments, both analytical and computational, have provided a better understanding of the effect of the yield stress. Simultaneously, greater insight into the material behavior of real fluids has been afforded by advances in rheometry. These developments have primed us for a better understanding of the various applications in the natural and engineering sciences.

Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics

An experimental investigation is conducted into the collapse of granular columns inside rectangular channels. The final shape is documented for slumps inside relatively wide channels, and for collapses inside much narrower slots. In both cases, the collapse is initiated by withdrawing a swinging gate or sliding door, and the flow remains fairly two-dimensional. Four different granular media are used; the properties of the materials vary significantly, notably in their angles of friction for basal sliding and internal deformation. If ). In all cases, the numerical constant of proportionality in these scaling relations shows clear material dependence. In wide slots, there is no obvious universal scaling behaviour of the final profile, but such a behaviour is evident in narrow slots. The experimental results are compared with theoretical results based on a shallow granular-flow model. The qualitative behaviour of the slump in the wide slot is reproduced by the theoretical model. However, there is qualitative disagreement between theory and the experiments in the narrow slot because of the occurrence of secondary surface avalanching.

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Granular collapse in two dimensions

Thin-layer theory is developed for Bingham plastic fluids; the specific case of a fluid flowing down an inclined plane is considered. In contrast to previous work it is indicated how the Bingham model leads directly to a self-consistent thin-layer theory; this does not rely upon adopting a bi-viscous approximation. The theory describes the fluid in terms of regions of fully plastic flow bounded by a `fake' yield surface. Above this fake yield surface are `pseudo-plugs' – regions in which the leading-order equations predict a plug, but which are seen to be weakly yielded at higher order.

A consistent thin-layer theory for Bingham plastics

Calculations are presented of the rate of energy conversion of the barotropic tide into internal gravity waves above topography on the ocean floor. The ocean is treated as infinitely deep, and the topography consists of periodic obstructions; a Green function method is used to construct the scattered wavefield. The calculations extend the previous results of Balmforth et al. for subcritical topography (wherein waves propagate along rays whose slopes exceed that of the topography everywhere), by allowing the obstacles to be arbitrarily steep or supercritical (so waves propagate at shallower angles than the topographic slopes and are scattered both up and down). A complicated pattern is found for the dependence of energy conversion on e, the ratio of maximum topographic slope to wave slope, and the ratio of obstacle amplitude and separation. This results from a sequence of constructive and destructive interferences between scattered waves that has implications for computing tidal conversion rates for the global ocean.

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Tidal Conversion by Supercritical Topography

It is not currently known what excites solar five-minute oscillations. Of the two most plausible possibilities, thermal overstability and stochastic excitation by turbulent convection, the single most important discriminating factor is the intrinsic stability of the pulsation modes. In view of this fact, the problem of the linear stability of model solar envelopes is addressed. A time-dependent, non-local mixing-length prescription is employed for convection, and the Eddington approximation to radiative transfer. The calculations reveal that low-degree acoustic modes are damped. Moreover, the theoretical damping rates compare well with measurements of solar oscillation line widths. Turbulent pressure fluctuations play a critical role in stabilizing the pulsations

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Neil Balmforth

Papers

Yielding to Stress: Recent Developments in Viscoplastic Fluid Mechanics

Granular collapse in two dimensions

A consistent thin-layer theory for Bingham plastics

Tidal Conversion by Supercritical Topography

Solar pulsational stability – I. Pulsation-mode thermodynamics