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).

저작근 근전도에 관한 정상교합자와 ii급 부정교합자의 비교 연구

Microencapsulated healing agents that possess adequate strength, long shelf-life and excellent bonding to the host material are required for self-healing materials. Urea-formaldehyde microcapsules containing dicyclopentadiene were prepared by in situ polymerization in an oil-in-water emulsion that meet these requirements for self-healing epoxy. Microcapsules of 10-1000 microm in diameter were produced by appropriate selection of agitation rate in the range of 200-2000 rpm. A linear relation exists between log(mean diameter) and log(agitation rate). Surface morphology and shell wall thickness were investigated by optical and electron microscopy. Microcapsules are composed of a smooth 160-220 nm inner membrane and a rough, porous outer surface of agglomerated urea-formaldehyde nanoparticles. Surface morphology is influenced by pH of the reacting emulsion and interfacial surface area at the core-water interface. High yields (80-90%) of a free flowing powder of spherical microcapsules were produced with a fill content of 83-92 wt% as determined by CHN analysis.

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In situ poly(urea-formaldehyde) microencapsulation of dicyclopentadiene

Microencapsulated dicyclopentadiene (DCPD) healing agent and Grubbs' Ru catalyst are incorporated into an epoxy matrix to produce a polymer composite capable of self-healing. The fracture toughness and healing efficiency of this composite are measured using a tapered double-cantilever beam (TDCB) specimen. Both the virgin and healed fracture toughness depend strongly on the size and concentration of microcapsules added to the epoxy. Fracture of the neat epoxy is brittle, exhibiting a mirror fracture surface. Addition of DCPD-filled urea-formaldehyde (UF) microcapsules yields up to 127% increase in fracture toughness and induces a change in the fracture plane morphology to hackle markings. The fracture toughness of epoxy with embedded microcapsules is much greater than epoxy samples with similar concentrations of silica microspheres or solid UF polymer particles. The increased toughening associated with fluid-filled microcapsules is attributed to increased hackle markings as well as subsurface microcracking not observed for solid particle fillers. Overall the embedded microcapsules provide two independent effects: the increase in virgin fracture toughness from general toughening and the ability to self-heal the virgin fracture event.

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Microcapsule induced toughening in a self-healing polymer composite

▪ Abstract The recent progress in three-dimensional boundary-layer stability and transition is reviewed. The material focuses on the crossflow instability that leads to transition on swept wings and rotating disks. Following a brief overview of instability mechanisms and the crossflow problem, a summary of the important findings of the 1990s is given.

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Stability and transition of three-dimensional boundary layers

We consider the problem of nonlinear steady convection in a horizontal mushy layer rotating about a vertical axis. We analyse the stationary modes of convection in the form of two-dimensional oblique rolls and three-dimensional distorted patterns. Under a near-eutectic approximation and the limit of large far-field temperature, we determine the two- and three-dimensional solutions to the weakly nonlinear problem by using a perturbation technique, and the stability of these solutions is investigated with respect to arbitrary three-dimensional disturbances. The results of the analyses in a particular range of values of the amplitude of convection indicate in particular that, over most of the range of values of the parameters, subcritical convection in the form of down-hexagons with down-flow at the cell centres and up-flow at the cell boundaries can be preferred over up-hexagonal convection, where the convective flow is upward at the cell centres and downward at the cell boundaries

Nonlinear steady convection in rotating mushy layers

We consider the problem of nonlinear convection in horizontal mushy layers during the solidification of binary alloys We analyse the oscillatory modes of convection in the form of two- and three-dimensional travelling and standing waves Under a near-eutectic approximation and the limit of large far-field temperature, we determine the solutions to the nonlinear problem by using a perturbation technique, and the stability of two- and three-dimensional solutions in the form of simple travelling waves, general travelling waves and standing waves is investigated The results of the stability and the nonlinear analyses indicate that supercritical simple travelling rolls are stable over most of the studied range of parameter values, while supercritical standing rolls can be stable only over some small range of parameter values, where the simple travelling rolls are unstable The results of the investigation of the onset of plume convection and chimney formation leading to the occurrence of freckles in the alloy crystal indicate that the chimney of the plume can be generated internally or near the lower boundary of the mushy layer The roles of a Stefan number, a permeability parameter and a concentration ratio on the flow instability in both linear and nonlinear regimes are also determined

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On nonlinear convection in mushy layers Part 1. Oscillatory modes of convection

This paper presents part 2 of a study of nonlinear convection in horizontal mushy layers during the solidification of binary alloys. Part 1 dealt with only the oscillatory modes of convection (Riahi, J. Fluid Mech. vol. 467, 2002, pp. 331–359). In the present paper we consider the particular range of parameters where the critical values of the scaled Rayleigh number $R$ for the onset of oscillatory and stationary convection are close to each other, and we develop and analyse a nonlinear theory in such a parameter regime which takes into account those mixed stationary and oscillatory modes of convection with common wavenumber vectors. Under a near-eutectic approximation and in the limit of large far-field temperature, we first determine a number of weakly nonlinear solutions, and then the stability of these solutions is investigated. The most interesting result is the preference for a mixed solution composed of standing and stationary hexagonal modes over a relatively wide range of the parameter values and for $R$ just above its lowest subcritical value where convection is possible. Such a preferred solution has properties mostly in agreement with the experimental results due to Tait et al. ( Nature , vol. 359, 1992, pp. 406–408) in the sense that the flow is downward at the cell centres, upward at the cell boundaries and there is some tendency for channel formation at the cell nodes.

https://www.ideals.illinois.edu/bitstream/handle/2142/275/1007.pdf?sequence=1

Daniel N. Riahi

Papers

Nonlinear steady convection in rotating mushy layers

On nonlinear convection in mushy layers Part 1. Oscillatory modes of convection

On nonlinear convection in mushy layers. Part 2. Mixed oscillatory and stationary modes of convection

Flow Instabilities in a Horizontal Dendrite Layer Rotating about an Inclined Axis

On Stationary and Oscillatory Modes of Flow Instability in a Rotating Porous Layer during Alloy Solidification