There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

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

The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

Dynamics and stability of thin liquid films

Quantum plasmonics is an exciting subbranch of nanoplasmonics where the laws of quantum theory are used to describe light–matter interactions on the nanoscale. Plasmonic materials allow extreme subdiffraction confinement of (quantum or classical) light to regions so small that the quantization of both light and matter may be necessary for an accurate description. State-of-the-art experiments now allow us to probe these regimes and push existing theories to the limits which opens up the possibilities of exploring the nature of many-body collective oscillations as well as developing new plasmonic devices, which use the particle quality of light and the wave quality of matter, and have a wealth of potential applications in sensing, lasing, and quantum computing. This merging of fundamental condensed matter theory with application-rich electromagnetism (and a splash of quantum optics thrown in) gives rise to a fascinating area of modern physics that is still very much in its infancy. In this review, we discuss and compare the key models and experiments used to explore how the quantum nature of electrons impacts plasmonics in the context of quantum size corrections of localized plasmons and quantum tunneling between nanoparticle dimers. We also look at some of the remarkable experiments that are revealing the quantum nature of surface plasmon polaritons.

Quantum Plasmonics

An asymptotic procedure based upon a two-scale approach is developed for wave propagation in a doubly periodic inhomogeneous medium with a characteristic length scale of microstructure far less than that of the macrostructure. In periodic media, there are frequencies for which standing waves, periodic with the period or double period of the cell, on the microscale emerge. These frequencies do not belong to the low-frequency range of validity covered by the classical homogenization theory, which motivates our use of the term ‘high-frequency homogenization’ when perturbing about these standing waves. The resulting long-wave equations are deduced only explicitly dependent upon the macroscale, with the microscale represented by integral quantities. These equations accurately reproduce the behaviour of the Bloch mode spectrum near the edges of the Brillouin zone, hence yielding an explicit way for homogenizing periodic media in the vicinity of ‘cell resonances’. The similarity of such model equations to high-frequency long wavelength asymptotics, for homogeneous acoustic and elastic waveguides, valid in the vicinities of thickness resonances is emphasized. Several illustrative examples are considered and show the efficacy of the developed techniques.

/pdf/high-frequency-homogenization-for-periodic-media-45rz5yixos.pdf

High-frequency homogenization for periodic media

Critical concepts from three different fields, elasticity, plasmonics and metamaterials, are brought together to design a metasurface at the geophysical scale, the resonant metawedge, to control seismic Rayleigh waves. Made of spatially graded vertical subwavelength resonators on an elastic substrate, the metawedge can either mode convert incident surface Rayleigh waves into bulk elastic shear waves or reflect the Rayleigh waves creating a "seismic rainbow" effect analogous to the optical rainbow for electromagnetic metasurfaces. Time-domain spectral element simulations demonstrate the broadband efficacy of the metawedge in mode conversion while an analytical model is developed to accurately describe and predict the seismic rainbow effect; allowing the metawedge to be designed without the need for extensive parametric studies and simulations. The efficiency of the resonant metawedge shows that large-scale mechanical metamaterials are feasible, will have application, and that the time is ripe for considering many optical devices in the seismic and geophysical context.

/pdf/a-seismic-metamaterial-the-resonant-metawedge-u1ge71yqw5.pdf

A seismic metamaterial: The resonant metawedge.

Preface.- 1 Fundamentals of acoustic metamaterials.- 2 Locally resonant structures for low frequency surface acoustic band gap applications.- 3 Band-gap properties of prestressed structures.- 4 Ultrasound transmission through periodically perforated plates.- 5 Novel Ultrasound Imaging Applications.- 6 Subwavelength focussing in metamaterials using far field time reversal.- 7 Anisotropic metamaterials for transformation acoustics and imaging.- 8 Transformation Acoustics.- 9 Acoustic Cloaking Via Homogenization.- 10 Acoustic Cloaking with Plasmonic Shells.- 11 Cloaking Liquid Surface Waves and Plasmon Polaritons.- 12 Transformation elastodynamics and active exterior acoustic cloaking.

Richard V. Craster

Papers

Dynamics and stability of thin liquid films

Quantum Plasmonics

High-frequency homogenization for periodic media

A seismic metamaterial: The resonant metawedge.

Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking