Phase dynamics of a detuned single-mode laser

We report measurements on the phase dynamics of a detuned single mode laser which has in the past shown correspondence to the complex Lorenz equation. The corresponding ranges of periodic pulsing, of detuned chaos and of windows within the chaotic domain are investigated.Invited paper     

Structure of fullerene-containing soot at different formation stages of arc discharge vaporization of graphite

Electron microscopy is used in a study of nanoclusters of the carbon soot deposited on a probe in different areas of arc discharge during graphite vaporization under conditions favorable for fullerene synthesis. It is found that the spatial network of soot nanoclusters consists of alternating regions of higher density or associates of carbon particles. Two types of nanoclusters have been identified with the correlation radii of the associates equal to 0.6–0.8 and 1.6–2.2 nm, respectively. Type I nanoclusters are dominant in the soot microparticles, and their structure shows practically no variations with increasing separation r of the soot collector from the discharge axis over the range of distances studied, r=1–9 cm. The effective radius R ₀ of the “elementary” particles making up the associates in the soot nanoclusters of Type I calculated with the use of scaling relationships is 0.15–0.17 nm and is close to the gas-kinetic radius of carbon atoms. Type II nanoclusters have been identified in soot collected at r>3 cm. Values of R ₀ calculated in this case are 0.6–0.9 nm and decrease with increasing r, which indicates the presence of fullerene molecules in these nanocluster associates.     

An isoperimetric inequality for the Heisenberg groups

We show that the Heisenberg groups of dimension five and higher, considered as Riemannian manifolds, satisfy a quadratic isoperimetric inequality. (This means that each loop of length L bounds a disk of area ~ L ².) This implies several important results about isoperimetric inequalities for discrete groups that act either on or on complex hyperbolic space, and provides interesting examples in geometric group theory. The proof consists of explicit construction of a disk spanning each loop in . Submitted: April 1997, Final version: November 1997     

Higher order radiative corrections to the QED Compton events at HERA

We estimate the higher order QED corrections to the QED Compton events at HERA employing the leading logarithmic approximation to all orders in α. The Compton events are events of the typee+p→e′+γ+ Hadrons, wheree′ and γ have nearly balancedp _T .     

Growth and magnetic characterization of YBCO films

Summary Epitaxial films of YBa₂Cu₃O_7−x were depositedin situ on LaAlO₃ substrates using single-target 90° off-axis sputtering. The films were characterized by magnetization measurements (M vs. T, H), applying the field parallel toc-axis. The observed differences in theT _c andJ _c values are attributed to the different oxygen content in the superconducting films. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

How should one define a (weak) crystal?

We compare two proposals for the study of positional long-range order: one in terms of the spectrum of the translation operator, the other in terms of the Fourier spectrum. We point out that only the first one allows for the consideration of molecular, as opposed to atomic, (weakly) periodic structures. We illustrate this point on the Thue-Morse system.     

All-fibre optical system for exciting and detecting the vibration of silicon microresonator sensors

An all-fibre optical system for optical interrogation and detection of the vibrations of a silicon microresonator is reported. Metal-coated silicon microresonators are excited by intensity modulated laser light delivered through an optical fibre, while the vibration of the resonators is detected by an optical fibre interferometer. Measurements have shown that an average optical power of 10 μW is sufficient to maintain the flexural vibration of the resonator. When the resonator is used as a pressure sensor, its resonant frequency changes from 62 kHz to 130 kHz as the pressure varies from -0°6 bar to 1 bar (gauge). A silicon resonator with 700 nm aluminium coating functions as a temperature sensor, showing a frequency shift from 262 kHz to 251 kHz when the temperature changes from 25 °C to 80 °C.     

Hamiltonian circle actions on symplectic manifolds and the signature

Let M be a symplectic manifold with a Hamiltonian circle action with isolated fixed points. We prove that σ (M) = b₀(M) − b₂(M) + b₄(M) − b₆(M) + … where σ (M) is the signature of M and b_i(M) is the ith Betti number of M.