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).

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Geophysical fluid dynamics.

Journal of Physics A - Mathematical and General, Special Issue. SI Aug 11 2006 ?? Preface

A pressure sensor based on irregular microhump patterns has been proposed and developed. The devices show high sensitivity and broad operating pressure regime while comparing with regular micropattern devices. Finite element analysis (FEA) is utilized to confirm the sensing mechanism and predict the performance of the pressure sensor based on the microhump structures. Silicon carbide sandpaper is employed as the mold to develop polydimethylsiloxane (PDMS) microhump patterns with various sizes. The active layer of the piezoresistive pressure sensor is developed by spin coating PEDOT:PSS on top of the patterned PDMS. The devices show an averaged sensitivity as high as 851 kPa−1, broad operating pressure range (20 kPa), low operating power (100 nW), and fast response speed (6.7 kHz). Owing to their flexible properties, the devices are applied to human body motion sensing and radial artery pulse. These flexible high sensitivity devices show great potential in the next generation of smart sensors for robotics, real-time health monitoring, and biomedical applications.

High Sensitivity, Wearable, Piezoresistive Pressure Sensors Based on Irregular Microhump Structures and Its Applications in Body Motion Sensing

A class of periodic solutions of nonlinear envelope equations, e.g., the nonlinear Schrodinger equation (NLS), is expressed in terms of rational functions of elliptic functions. The Hirota bilinear transformation and theta functions are used to extend and generalize this class of solutions first reported for NLS earlier in the literature. In particular a higher order NLS and the Davey–Stewartson (DS) equations are treated. Doubly periodic standing waves solutions are obtained for both the DSI and DSII equations. A symbolic manipulation software is used to confirm the validity of the solutions independently.

/pdf/a-class-of-exact-periodic-solutions-of-nonlinear-envelope-2knnhck0rf.pdf

A class of exact, periodic solutions of nonlinear envelope equations

http://hub.hku.hk/bitstream/10722/48615/1/123463.pdf

Interactions of breathers and solitons in the extended Korteweg–de Vries equation

https://hub.hku.hk/bitstream/10722/226329/1/Content.pdf

Breathers and rogue waves for a third order nonlocal partial differential equation by a bilinear transformation

Rogue waves in fluid dynamics and optical waveguides are unexpectedly large displacements from a background state, and occur in the nonlinear Schrodinger equation with positive linear dispersion in the regime of positive cubic nonlinearity. Rogue waves of a derivative nonlinear Schrodinger equation are calculated in this work as a long-wave limit of a breather (a pulsating mode), and can occur in the regime of negative cubic nonlinearity if a sufficiently strong self-steepening nonlinearity is also present. This critical magnitude is shown to be precisely the threshold for the onset of modulation instabilities of the background plane wave, providing a strong piece of evidence regarding the connection between a rogue wave and modulation instability. The maximum amplitude of the rogue wave is three times that of the background plane wave, a result identical to that of the Peregrine breather in the classical nonlinear Schrodinger equation model. This amplification ratio and the resulting spectral broadening arising from modulation instability correlate with recent experimental results of water waves. Numerical simulations in the regime of marginal stability are described.

/pdf/rogue-wave-modes-for-a-derivative-nonlinear-schrodinger-3v6x0yczl8.pdf

Kwok Wing Chow

Papers

High Sensitivity, Wearable, Piezoresistive Pressure Sensors Based on Irregular Microhump Structures and Its Applications in Body Motion Sensing

A class of exact, periodic solutions of nonlinear envelope equations

Interactions of breathers and solitons in the extended Korteweg–de Vries equation

Breathers and rogue waves for a third order nonlocal partial differential equation by a bilinear transformation

Rogue wave modes for a derivative nonlinear Schrödinger model.