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).

第12次 아시아ㆍ太平洋 矯政局長會議 參加記

Microwave photonics with superconducting quantum circuits

心臓病診療プラクティス 16. 心不全を癒す

1 The Equations of Gas Dynamics 2 Magnetoplasma Dynamics 3 Waves in Magnetoplasmas 4 Magnetoplasma Stability 5 Transport in Magnetoplasmas 6 Extensions of Theory Bibliography Index

Physics of plasmas

A weakly driven pendulum cannot be strongly excited by a fixed frequency drive. The only way to strongly excite the pendulum is to use a drive whose frequency decreases with time. Feedback is often used to control the rate at which the frequency decreases. Feedback need not be employed, however; the drive frequency can simply be swept downwards. With this method, the drive strength must exceed a threshold proportional to the sweep rate raised to the 3/4 power. This threshold has been discovered only recently, and holds for a very broad class of driven nonlinear oscillators. The threshold may explain the abundance of 3:2 resonances and dearth of 2:1 resonances observed between the orbital periods of Neptune and the Plutinos (Pluto and many of the Kuiper Belt objects), and has been extensively investigated in the Diocotron system in pure-electron plasmas.

http://users.df.uba.ar/sgil/physics_paper_doc/papers_phys/ondas_optics/nonlinear_2k2pdf.pdf

Autoresonant (nonstationary) excitation of pendulums, Plutinos, plasmas, and other nonlinear oscillators

An electronic transmission line that contains an array of nonlinear elements (Josephson junctions) is studied theoretically. A continuous nonlinear wave equation describing the dynamics of the node flux along the transmission line is derived. It is shown that due to the nonlinearity of the system, a mixing process between four waves with different frequencies is possible. The mixing process can be utilized for amplification of weak signals due to the interaction with a strong pump wave. An analytical solution for the spatial evolution of the wave amplitudes is derived, and found to be in excellent agreement with the results of numerical computations. Simulations of realistic parameters show that the power gain can exceed 20 dB over a bandwidth of more than 2 GHz.

Parametric amplification in Josephson junction embedded transmission lines

The propagation of a cold relativistic electron beam in a free electron laser with an axial guide magnetic field is considered. The possibility of several steady‐state helical trajectories for the electrons is shown, and the stability against perturbations and accessibility of such steady states is considered. Necessary and sufficient conditions for the stability are derived and indicate the importance of the transition region at the entrance of the laser. Possible modes of operation of the laser in different steady‐state regimes are suggested and illustrated by numerical examples.

Electron beam dynamics in combined guide and pump magnetic fields for free electron laser applications

A classical mechanism is proposed for the many-photon ionization of Rydberg atoms in a quasimonochromatic oscillating electric field with an amplitude smaller than the stochasticity threshold. The mechanism is based on the dynamic autoresonance between the slowly varying frequency of the oscillating field and the Keplerian frequency (or one of its harmonics) of atomic electrons. It is shown that a large fraction of an initial ensemble of atoms can be efficiently excited by this coherent mechanism and then ionized via the stochastic instability.

Strong autoresonance excitation of Rydberg atoms: The Rydberg accelerator.

We report on the autoresonant (nonlinear phase locking) manipulation of the diocotron mode in a non-neutral plasma. Autoresonance is a very general phenomena in driven nonlinear oscillator and wave systems, and allows us to control the amplitude of a nonlinear wave without the use of feedback. These are the first controlled laboratory studies of autoresonance in a collective plasma system.

Lazar Friedland

Papers

Autoresonant (nonstationary) excitation of pendulums, Plutinos, plasmas, and other nonlinear oscillators

Parametric amplification in Josephson junction embedded transmission lines

Electron beam dynamics in combined guide and pump magnetic fields for free electron laser applications

Strong autoresonance excitation of Rydberg atoms: The Rydberg accelerator.

Autoresonant (Nonstationary) Excitation of the Diocotron Mode in Non-neutral Plasmas