Computation of the Morse Spectrum

The Morse spectrum is a limit set of Lyapunov exponents of periodic pseudo-trajectories. This notion is especially important in the case where a dynamical system has infinitely many periodic trajectories of large period. A method for estimating the Morse spectrum was suggested by the first author in J. Math. Anal. Appl., 252 (2000). This method is based on ideas of symbolic dynamics which reduces the study of a dynamical system to the study of a certain graph, called a symbolic image. Within the framework of this method, the computation of the Morse spectrum is connected with searching simple closed paths and extracting contours with suitable characteristics. However, under iterations of the symbolic image, the number of such paths sharply increases, which leads to huge expenses of memory and time. We suggest an algorithm for constructing contours with the maximal and minimal mean values. This algorithm is based on a special version of the simplex method. Numerical tests are also described. Bibliography: 13 titles. Illustrations: 3 figures.     

Allocating energy in a first-to-n match

This paper models a decision where a player must allocate limitedenergy over a contest of uncertain length. The motivating exampleis a squash match where one of the players is not as fit asthe other. Should a player's energy be concentrated in the earlygames of the match? Should it be spread evenly over all possiblegames? Or should it be conserved for the end of the match? Wemodel this as a decision problem where, in each game, the decision-makermust determine how much energy to expend. We assume that thereare only a small number of discrete energy choices for eachgame and that the more energy the decision-maker expends, themore likely he is to win that game. We solve for the optimaldecision with dynamic programming. With only two possible energychoices for each game, we show that it does not matter how energyis expended. In the case where there are three or more energychoices, we show how to take advantage of the structure of theproblem to determine the optimal sequence of decisions. As forpractical advice, the model suggests that when the decision-makerfalls behind in a match, he ought to switch to a more conservativeapproach by dividing his remaining energy evenly among all thepossible remaining games. Received 14 May 2003. Revised 5 January 2004.     

Numerical Modeling of Solitons in a Low Birefringent Optical Fiber

A numerical investigation, based on the split-step Fourier transform algorithm of all optical switching of solitons in a low birefringent optical fiber is presented. The numerical algorithm is described in detail. This revised version was published online in August 2006 with corrections to the Cover Date.     

Laser spectroscopic investigation of a new precursor-type polyparaphenylenevinylene

Optical, structural and morphological properties of thin films of polyparaphenylenevinylene (PPV) formed by an alkyl sulfinyl precursor route have been studied. Thin films were fabricated on an optical glass and on quartz glass either by spin-coating of the precursor solution or by layer-by-layer deposition using Langmuir–Blodgett technique. PPV precursor films were also spin-coated on gold-coated glass in order to study thin-film optical parameters by surface plasmon spectroscopy. We have been successful in forming about 40 precursor mono layers on quartz glass by Langmuir–Blodgett technique using optimized surface pressure and dipping conditions. After thermal conversion of the precursor layers good quality fluorescent PPV films of yellow colour have been obtained. Optical characterization of the films was carried out by linear absorption and emission spectroscopy, ellipsometry, and surface plasmon spectroscopy. Structural and morphological studies on the thin films were carried out by using X-ray scattering and atomic force microscopy. Wave-guided travelling-wave laser action has been achieved in a PPV film on quartz glass. The sample was transversally pumped with picosecond laser pulses (wavelength 347.15 nm, duration 35 ps). Laser emission occurred at 550 nm for pump pulse energy densities above .     

Dynamics and crystal chemistry of tellurites. II. Composition- and temperature-dependence of the Raman spectra of x(Tl2O)+(1−x) Te2O glasses: evidence for a phase separation?

Immiscibility effects are suggested to be inherent in tellurite glasses with weak (low valence) cations. This hypothesis is used to explain the structural evolution of the x(Tl₂O)+(1−x)Te₂O glass system as a function of the x value and during temperature-induced crystallisation processes. The results of Raman measurements support the hypothesis.     

Intercomparison of retrieval codes used for the analysis of high-resolution, ground-based FTIR measurements

A rigorous and systematic intercomparison of codes used for the retrieval of trace gas profiles from high-resolution ground-based solar absorption FTIR measurements is presented for the first time. Spectra were analyzed with the two widely used independent, retrieval codes: SFIT2 and PROFFIT9. Vertical profiles of O₃, HNO₃, HDO, and N₂O were derived from the same set of typical observed spectra. Analysis of O₃ was improved by using updated line parameters. It is shown that profiles and total column amounts are in excellent agreement, when similar constraints are applied, and that the resolution kernel matrices are also consistent. Owing to the limited altitude resolution of ground-based observations, the impact of the constraints on the solution is not negligible. It is shown that the results are also compatible for independently chosen constraints. Perspectives for refined constraints are discussed. It can be concluded that the error budget introduced by the radiative transfer code and the retrieval algorithm on total columns deduced from high-resolution ground-based solar FTIR spectra is below 1%.     

Improved convergence of a non-perturbative semi-classical pressure broadening model

It is shown that by including the second term of Magnus expansion, improved convergence can be achieved for the non-perturbative pressure broadening formalism proposed by Neilson and Gordon (J. Chem. Phys. 58 (1973) 4131). The present method was applied to the line broadening calculations of CO in a bath of Ar.     

Optical absorption of lithium metal vapor at high temperatures

Experimental results are reported for a unique spectroscopic device called the Plasma Spectroscopy Cell. Optical absorption of lithium metal vapor was observed at high density and temperature. Absorption spectra are analyzed using theoretical calculations of absorption cross sections for lithium-helium interactions, and singlet and triplet state transitions of diatomic lithium in the visible spectral range. This is believed to be the most complex example yet calculated in which absolute bound-bound, bound-free, free-bound, and free-free contributions for all possible optically allowed transitions are all included, in quite respectable agreement with experiment.     

Equilibrium States in the Quadruple–Kerr Solution

The extended quadruple–Kerr metric is used to consider equilibrium states of four collinear Kerr particles. We explain our previous failure to solve numerically the full set of the balance equations, and we derive a self–consistent system of the axis conditions leading to the equilibrium of all four constituents which can be black holes or hyperextreme objects. The equilibrium configurations obtained in this paper exhibit similar features with those occurring in the systems of two Kerr particles, for instance, the balance of four Kerr black holes with positive masses does not seem possible. Equilibrium states of two identical compound Kerr objects are also discussed.