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

THE appearance of a treatise in English upon the mathematical theory of elasticity is an event the potential importance of which may be judged by the that the author, in his frequent suggestions for collateral reading, refers to only three such, those of Southwell, Timoshenko, and Love. In spirit and content Sokolnikoff}s book differs greatly from each and all of these. It may be described by a possible sub-title: “A pure mathematician surveys topics related to certain problems in the mathematical theory of elasticity”. It is symptomatic of the change in outlook of American mathematics over the past few decades. Mathematical Theory Of Elasticity Prof. I. S. Sokolnikoff with the collaboration of Asst. Prof. R. D. Speche. Pp. xi + 373. (New York and London: McGraw-Hill Book Co., Inc., 1946.) 22s. 6d.

Mathematical Theory Of Elasticity

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.

/pdf/a-contribution-to-the-great-riemann-solver-debate-54n7nbyg4g.pdf

A Contribution to the Great Riemann Solver Debate

Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

Recent studies that dealt with supersonic/hypersonic flows over various geometrical configurations, which resemble the shapes of supersonic/hypersonic intakes and vehicles, revealed that there were situations in which spatial and temporal oscillating pressure fields were established in steady flows. It was found that the oscillating pressure fields could reach extremely high-pressure peaks. Pressure peaks that were more than two orders of magnitude (even up to 500 times) larger than the ambient pressure were obtained in some of these studies. It is hypothesized that the oscillating pressure fields with the extremely high pressure peaks could cause sever structural damages to the surfaces of supersonic/hypersonic intakes and vehicles over which they are developed. Introduction A variety of hysteresis processes in the shock wave flow fields have been discovered in the past decade in the course of a comprehensive experimental, numerical and analytical study that was undertaken by the research group headed by Ben-Dor [1]. It was found, in the course of the investigation, that some of the flow fields were associated with oscillating pressure fields in which extremely high-pressure peaks were developed. Owing to the fact that the investigated geometries resemble geometries associated with supersonic/hypersonic intakes and vehicles it is hypothesized that the extremely high-pressure peaks could cause sever structural damages to the supersonic/hypersonic intakes and vehicles. For this reason, it has been decided to gather and present the various phenomena together. Present Study The flow fields that were associated with extremely high-pressure peaks were obtained in the case of shock-on-shock interactions over two general geometries: a curvilinear cone and a double wedge. The results in presented in the following. Shock-on-Shock Interaction of Conical Shock Waves over a Curvilinear Cone A schematic illustration of the geometrical set-up is shown in Fig. 1. A conical ring with a sharp leading edge and a curvilinear cone with a sharp nose are mounted along the same axis in a Materials Science Forum Online: 2004-09-15 ISSN: 1662-9752, Vols. 465-466, pp 123-130 doi:10.4028/www.scientific.net/MSF.465-466.123 © 2004 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific.net. (Semanticscholar.org-11/03/20,14:30:25) supersonic flow. The distance between the inlet of the conical ring and the tip (nose) of the curvilinear cone is S. The conical ring generates an incident converging conical shock wave, i1, and the curvilinear cone generates a diverging conical (curvilinear) shock wave, i2. These two conical shock waves interact. The resulting overall wave configuration could be either an overall regular reflection-oRR (Fig. 2a) or an overall Mach reflection-oMR (Fig. 2b) depending on the angle of interaction between the two conical shock waves. The oRR consists of an incident converging conical shock wave, i1, generated by the conical ring, a curvilinear diverging conical shock wave, i2, generated by the curvilinear cone, and two refracted shock waves, r1 and r2. The oMR consists of two Mach reflection wave configurations, which share a common Mach stem, m. Figure 2. Schematic illustration of the two wave configurations: (a) An overall regular reflection (oRR) wave configuration, (b) An overall Mach reflection (oMR). One of the ways for changing the angle of interaction between the two conical shock waves (i1 and i2) is to change the horizontal distance, S, between the conical ring and the curvilinear cone [1]. A numerical simulation of this process resulted in the overall multi-loop hysteresis, shown in Fig 3, in the ( ) m H , X -plane. The stable flow states, which were encountered when the curvilinear cone was shifted along the X = → 0 2 2 . and the reversed X = → 2 2 0 . paths were ABCDEFGHIJKLMNOPQ and QPRSMTKJUHGVEDWBA, respectively. These two different paths of stable flow states consist of two types of hysteresis loops: the major hysteresis loop, loop SNOPRS, which consists of both oMRs and oRRs for the same flow conditions, and the minor hysteresis loop (BCDWB, EFGVE, HIJUH and KLMTK), which consists of only oMRs that are associated with different flow patterns for the same flow conditions. A typical oRR wave configuration that is encountered along the major SNOPRS hysteresis loop is shown in Fig. 4 together with the pressure distribution that is associated with it. It is evidence from the pressure distribution that a pressure peak, which is about 145 times larger than the ambient pressure, i.e., about 14.5 MPa, is reached. Figure 1. Schematic illustration of the geometrical set-up used in the course of the present numerical study. Figure 124 Explosion, Shock Wave and Hypervelocity Phenomena in Materials

Shock wave induced extremely high oscillating pressure peaks

Shock waves having constant velocities with respect to an inertial frame of reference can be investigated using steady flow concepts by attaching a frame of reference to the shock wave. In such a frame of reference, the shock wave is stationary, and the entire flow field is known as either pseudo-stationary or pseudo-steady. The transformation, known as a Galilean transformation, is shown schematically in figure 2.1. In figure 2.1a a constant velocity shock wave, having a velocity of Vs, is propagating from left to right, towards a flow having a velocity Vj, and inducing behind it a flow velocity Vj. The velocities with respect to a frame of reference attached to the shock wave are shown in figure 2.1b. In this frame of reference the flow in state (i) propagates towards the stationary shock wave with the velocity Uj = Vs - Vj. Upon passing through the shock wave its velocity is reduced to u: = Vs - Vj. The velocity field shown in figure 2.1b is actually obtained from the velocity field shown in figure 2.1a by superimposing on it a velocity equal to the shock wave velocity but in the opposite direction. The flow field of figure 2.1b is pseudo-steady, and hence can be treated using the steady flow theory for oblique shock waves.

Shock Wave Reflections in Pseudo-Steady Flows

This study aims at understanding the phenomenon of shock reflection over different geometries of concave surfaces. Double cylindrical concave wedges are generated computationally by changing different geometrical parameters like the radii of the cylindrical surfaces and the initial wedge angle of the two surfaces. The study focuses on the effects of the change of the geometry of the concave surfaces and the incident shock wave Mach numbers on the overall behavior of shock wave reflections. The simulations are done for four different incident shock wave Mach numbers. The investigation of the geometrical effect reveals a number of interesting wave features starting from the early stage of the shock interaction and transition from transitioned regular reflection (TRR) over the first concave surface followed by complex shock reflections over the second concave surface. Two new behaviors of shock reflection are found over the second concave surface, which appear to depend on the initial wedge angle of the concave surfaces. First, an additional shock wave appears when the TRR over the first concave surface meets the incident shock wave on the second concave surface and eventually merges with the reflected wave. Second, the additional shock wave falls behind the incident one and penetrates the reflected wave over the second concave surface. Also, it was found that the difference between the transition wedge angles over the two concave surfaces increased as the incident shock wave Mach number increased. These findings indicate that the shock wave does have a characteristic to retain its memory.

Studying Shock Wave Reflections over Double Cylindrical Concave Wedge Reflectors

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