Synchronization of periodic self-oscillations by common noise

We consider the effect of external noise on the stability properties of self-oscillations. A stochastic equation for the phase is derived at the limit of weak noise (in the appropriate sense). The stationary probability-density distribution is used for an analytic calculation of the Lyapunov exponent. We show that the exponent is always negative for the small noise level, which corresponds to synchronization of self-oscillations.     

Laser lineshape effects on cavity-enhanced absorption spectroscopy signals

The quantitative effects of laser lineshape on signals from cavity-enhanced absorption spectroscopy (CEAS) and integrated cavity output spectroscopy (ICOS) experiments are examined. The governing equations for CEAS signals including the laser lineshape are derived. Approximations under which the laser lineshape may be neglected or replaced with an effective lineshape are presented. It is shown that the laser lineshape effects may be parameterized with two dimensionless variables: the laser linewidth normalized by the absorption linewidth, and the peak sample absorbance normalized by the mirror loss. In terms of the dimensionless variables, we simulate CEAS and ICOS signals and the absorbances inferred from them. The simulation results provide a useful tool for CEAS and ICOS practitioners to gauge the importance of laser lineshape effects in specific experiments. Simulations are performed for the four combinations of Gaussian and Lorentzian lineshapes for the laser and the absorption. PACS 42.62.Fi; 78.40.-q; 32.70.Jz     

A new model for a mode-locked semiconductor laser

We consider a new model for passive mode locking in a semiconductor laser comprising a set of delay differential equations. Bifurcations leading to the appearance and break-up of the mode-locking regime are studied numerically.     

Characterisation of adsorbed layers on sulphide minerals by photoelectron spectroscopy

The systems galena/2-mercaptobenzothiazole (MBT) and pyrite/MBT have been studied using synchrotron radiation excited photoelectron spectroscopy (SRXPS). The chemisorption of MBT and the multilayer formation of 2,2′-dithiobis(benzothiazole) (BBTD) are evidenced by additional structures, observed beside the substrate signals, in the S2p-spectra of cleaved mineral surfaces after adsorption of MBT. The amount of the complex remains constant at concentrations as high as 10^–5 mol/L whereas the amount of BBTD increases. From the dependence of the adsorbate intensities on the excitation energy the conclusion can be drawn that an overlayer of BBTD on a chemisorbed layer of MBT is formed. The very weak adsorption of MBT on pyrite in alkaline solutions may explain the selective flotation of galena from pyrite in alkaline media.     

A Miura of the Painlevé I Equation and Its Discrete Analogs

We present Miura transformations for the continuous and several discrete Painlev\'e I equations. In the case of the continuous P_I, we use the Hamiltonian formulation of the Painlev\'e equations and show that there exists a Miura transformation between P_I and the binomial, second degree, equation of Cosgrove SD_V. In the case of the discrete P_I's we obtain two different kinds of Miuras. One kind relates a d-P_I to some other d-P_I while the other leads to discrete four-point equations which are the discrete analogs of the derivative of Cosgrove's equation SD_V.     

Numerical modeling of a XeCl laser excited by microwave discharge

12 , 169 (1987). Reasonably good agreements in the peak output power and laser efficiency have been achieved. Model calculations also predict that an efficiency as high as 2.7% can be obtained once the conditions of the above-mentioned experiments have been optimized. From the consideration that the skin depth effectively limits the absorption length of the microwave pumping and hence the excitable volume, it is concluded that high input power densities (>2 MW/cm³) and higher gas pressures (between 3 and 10 atm) are the preferable conditions to achieve higher efficiency. Preliminary calculations on CCl₄ containing XeCl gas mixtures show that improvement in laser efficiency by several folds may be achieved as a result of the higher intrinsic efficiency of excimer formation. Received: 23 September 1996 / Revised version: 25 March 1997     

Determination of the largest lyapunov index for short chaotic time sequences in self-oscillating chemical reactions

A method was developed for the determination of largest Lyapunov index for short chaotic time sequences with allowance for the presence of noise in the response of the system. For this purpose a simple unidimensional representation modelling the dynamics of irregular self-oscillations was investigated. Conditions were found for adequate determination of the largest Lyapunov index from the noise-distorted signals. The results were used to obtain the largest Lyapunov index for the Belousov—Zhabotinskii reaction taking place in an ideal-mixing closed reactor and in a constant-mixing flow-type reactor. Institute of Organic Chemistry, National Academy of Sciences of Ukraine. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 33, No. 3, pp. 136–142, May–June, 1997.