Visualizing the log-periodic pattern before crashes

We present a method for visualizing the pattern which we believe to be a precursor signature of financial crashes (or ruptures). The log-periodicity of the pattern is investigated through the envelope function technique. Three periods of the Dow Jones Industrial Average (DJIA) are investigated: 1982-1987, 1992-1997 and 1993-1998. The presence of a rupture in the end of 1998 is outlined from data taken before the end of August 1998. Received 15 October 1998 and Received in final form 19 November 1998     

Superradiant laser: First-order phase transition and non-stationary regime

We solve the superradiant laser model in two limiting cases. First the stationary low-pumping regime is considered where a first-order phase transition in the semiclassical solution occurs. This discontinuity is smeared out in the quantum regime. Second, we solve the model in the non-stationary regime where we find a temporally periodic solution. For a certain parameter range well-separated pulses may occur. Received: 19 June 1998 / Accepted: 19 October 1998     

Quantum derivation of the excess noise factor in lasers with non-orthogonal eigenmodes

By generalizing recently obtained results we calculate the excess noise factor (Petermann factor) for a laser system with non-orthogonal eigenmodes. The quantum consistency of the calculation is shown through the explicit conservation of input-output commutation rules. As a result of the calculation, the excess noise in the lasing mode is shown to depend on the laser gain below threshold, and on the noise analysis frequency below and above threshold. Received: 27 October 1998 / Received in final form: 11 March 1999     

Spectral Properties of Uperpositions of Ornstein-Uhlenbeck Type Processes

Stationary processes with prescribed one-dimensional marginal laws and long-range dependence are constructed. The asymptotic properties of the spectral densities are studied. The possibility of Mittag-Leffler decay in the autocorrelation function of superpositions of Ornstein-Uhlenbeck type processes is proved. AMS 2000 Subject Classification Primary 60E07, 60G10, 60G18 Secondary 62M10, 62P05 Supported by the Danish National Research Foundation and EPSRC grant RCMT091. Partially supported by the ARC grants DP 0345577, DP0559807 and EPSRC grant RCMT091.     

Noise in porous silicon structures in air and in conditions of gas adsorption

Low-frequency noise, in the range 1–500 Hz, is measured at room temperature in samples of Au/PS/SCS/Al structure with a layer of porous silicon. Numerical values of the Hooge parameter α_H are estimated and the dependence of α_H on the composition of the gaseous environment, where the sample is placed, is determined. Possible reasons of observed high values of α_H for the samples in air and of the increase in α_H in conditions of gas adsorption are discussed. Introducing of carbon oxide in air changes the shape of spectrum.     

Laser Stabilisation for the Measurement of Thermal Noise

In order to measure the thermal noise of a mirror suspended in a vacuum it is necessary for the length measurement error due to intensity and frequency noise of the probe laser to be reduced below the thermal noise level. Here we report on an experiment to reduce the frequency and intensity noise of a 40mW Nd:YAG laser for this purpose. The frequency is stabilised using the standard reflection locking technique. To stabilise the laser intensity a technique which uses the properties of an in loop light field has been developed. This technique is capable of suppressing the intensity noise below the shot noise limit without reducing the useful laser power. A servo based on this technique has been designed and tested. The experimental results indicate that the laser noise can be reduced to a level which will allow a displacement sensitivity of 1.5 × 10^-19m/ Hz for the detection of thermal noise in a frequency band of 10 to 500Hz.     

Optimization over Spaces of Discontinuous 2D Functions

The existence of solution for optimization problems over a space of discontinuous 2D functions is addressed. The main result relies on the choice of a suitable topology making the feasible set compact. Application to image segmentation and/or identification problems is considered and robustness of the solution is discussed.     

A Noise Temperature Analysis of the Electrical Degradation of Thin Nanostructured Films

Thermal noise measurements at proper biasing conditions are shown to represent a powerful tool for the characterization of the homogeneity of thin nanostructured films and their adhesion to the substrate. By modeling a thin-film as a two-dimensional random resistor network, we introduce a new type of excess-noise arising from local sources of Nyquist noise due to the presence of defective regions. The dishomogeneous Joule heating of the film is responsible for a thermal and electrical instability which is efficiently described by using a biased percolation model. The results of our simulations show that the Nyquist excess-noise temperature should provide a sensitive and non-destructive indicator of the packing density and of the quality of heat contact to the substrate of nanostructured films with grain size in the range 10–500 nm.     

High temperature (T>300 K) light emitting diodes for 8–12 μm spectral range

Contrary to conventional light emitting diodes for visible and very near infrared utilizing interband (ω>E_g) luminescence, the longer infrared emitting diodes (LIREDs) we describe here utilize intraband (ω<E_g) electron transitions and emit beyond the fundamental absorption range of the material used. Made of indirect band gap semiconductors (like Ge, Si) and, therefore, free from the Auger recombination impact, LIREDs efficiently operate at higher temperatures (T>300 K) in the longer wavelength atmospheric window (8–12 μm). Electrically modulated power emitted is comparable to that for black body sources whereas shorter rise–fall times are due to recombination processes (200 μs) and not dependent on pixel thermal mass and thermal conduction. LIREDs can be made of different semiconductor structures provided the controllable modulation of free carrier concentration in the device base is achieved. The main parameters of Ge based LIREDs under injection mode are reported.