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).

1: Magnetic Particles: Preparation, Properties and Applications: M. Ozaki. 2: Maghemite (gamma-Fe2O3): A Versatile Magnetic Colloidal Material C.J. Serna, M.P. Morales. 3: Dynamics of Adsorption and Oxidation of Organic Molecules on Illuminated Titanium Dioxide Particles Immersed in Water M.A. Blesa, R.J. Candal, S.A. Bilmes. 4: Colloidal Aggregation in Two-Dimensions A. Moncho-Jorda, F. Martinez-Lopez, M.A. Cabrerizo-Vilchez, R. Hidalgo Alvarez, M. Quesada-PMerez. 5: Kinetics of Particle and Protein Adsorption Z. Adamczyk.

Surface and Colloid Science

Mathematical Handbook for Scientists and Engineers

High resolution schemes for hyperbolic conservation laws

The aims of this paper are threefold: to increase the level of awareness within the shock-capturing community of the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very-high-resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.

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A Contribution to the Great Riemann Solver Debate

This text describes shock wave reflection phenomena from a phenomenological point of view Organized in five parts, the book covers an introduction to oblique shock wave reflection and the governing equations of the two- and three-shock theories; shock wave reflection in pseudo-steady flows; and reflection phenomena in steady flows and unsteady flows With regard to pseudo-steady, steady and unsteady flows, the possible types of specific reflections are described, criteria for their formation and termination are presented and their governing equations are solved analytically and graphically and compared with experimental results Modification of the governing equations by accounting for viscous and real gas effects are suggested In addition, unresolved problems are pointed out and ideas for future research are suggested The fifth part of the book constitutes a detailed source list of most of the scientific papers and reports which have been published in the subject area

Shock wave reflection phenomena

Handbook of shock waves

Shock-tube experiments were performed in order to verify recently developed theoretical models for the evolution of the shock-wave induced Richtmyer-Meshkov instability [Phys. Rev. Lett. 74, 534 (1995)]. Single-mode bubble and spike evolution and two-bubble interaction in both early and late nonlinear stages were investigated in a $M\ensuremath{\approx}1.3$ $\mathrm{Air}\ensuremath{-}\mathrm{to}\ensuremath{-}{\mathrm{SF}}_{6}$ shock-tube experiment. Experimental results for the single-mode and two-bubble cases, showing distinct bubble and spike evolution, were found to be in very good agreement with the theoretical model prediction as well as numerical simulations, verifying the key elements of the bubble-merger model used for the prediction of the multimode bubble and spike front evolution.

Study of Nonlinear Evolution of Single-Mode and Two-Bubble Interaction under Richtmyer-Meshkov Instability

The reflection of shock waves over straight reflecting surfaces in steady flows was investigated experimentally using the supersonic wind tunnel of Laboratoire d'Aerothermique du CNRS, Meudon, France. The results for a flow Mach number M0 = 4.96 contradict the state of the art regarding the regular [harr ] Mach reflection transition in steady flows. Not only was a hysteresis found to exist in this transition, but, unlike previous reports, regular reflection configurations were found to be stable in the dual-solution domain in which theoretically both regular and Mach reflection are possible.

Reconsideration of oblique shock wave reflections in steady flows. Part 1. Experimental investigation

An experimental and numerical systematic study of the growth of the Richtmyer–Meshkov instability-induced mixing following a re-shock is made, where the initial shock moves from the light fluid to the heavy one, over an incident Mach number range of 1.15–1.45. The evolution of the mixing zone following the re-shock is found to be independent of its amplitude at the time of the re-shock and to depend directly on the strength of the re-shock. A linear growth of the mixing zone with time following the passage of the re-shock and before the arrival of the reflected rarefaction wave is found. Moreover, when the mixing zone width is plotted as a function of the distance travelled, the growth slope is found to be independent of the re-shock strength. A comparison of the experimental results with direct numerical simulation calculations reveals that the linear growth rate of the mixing zone is the result of a bubble competition process.

Gabi Ben-Dor

Papers

Shock wave reflection phenomena

Handbook of shock waves

Study of Nonlinear Evolution of Single-Mode and Two-Bubble Interaction under Richtmyer-Meshkov Instability

Reconsideration of oblique shock wave reflections in steady flows. Part 1. Experimental investigation

Experimental and numerical investigation of the Richtmyer–Meshkov instability under re-shock conditions