On a recursive method for the estimation of unknown parameters of partially observed chaotic systems

We investigate a recently proposed method for on-line parameter estimation and synchronization in chaotic systems. This novel technique has been shown effective to estimate a single unknown parameter of a primary chaotic system with known functional form that is only partially observed through a scalar time series. It works by periodically updating the parameter of interest in a secondary system, with the same functional form as the primary one but no explicit coupling between their dynamic variables, in order to minimize a suitably defined cost function. In this paper, we review the basics of the method, and investigate its robustness and new extensions. In particular, we study the performance of the novel technique in the presence of noise (either observational, i.e., an additive contamination of the observed time series, or dynamical, i.e., a random perturbation of the system dynamics) and when there is a mismatch between the primary and secondary systems. Numerical results, including comparisons with other techniques, are presented. Finally, we investigate the extension of the original method to perform the estimation of two unknown parameters and illustrate its effectiveness by means of computer simulations.     

New interpretations of XPS spectra of nickel metal and oxides

A current interpretation of XPS spectra of Ni metal assumes that the main 6 eV satellite is due to a two hole c3d⁹4s² (c is a core hole) final state effect. We report REELS observation in AES at low voltages of losses (plasmons and inter-band transitions) corresponding to the satellite structures in Ni metal 2p spectra. The satellite near 6 eV is attributed to a predominant surface plasmon loss. A current interpretation of Ni 2p spectra of oxides and other compounds is based on charge transfer assignments of the main peak at 854.6 eV and the broad satellite centred at around 861 eV to the cd⁹L and the unscreened cd⁸ final-state configurations, respectively (L is a ligand hole). Multiplet splittings have been shown to be necessary for assignment of Fe 2p and Cr 2p spectral profiles and chemical states. The assignments of Ni 2p states are re-examined with intra-atomic multiplet envelopes applied to Ni(OH)₂, NiOOH and NiO spectra. It is shown that the free ion multiplet envelopes for Ni²⁺ and Ni³⁺ simulate the main line and satellite structures for Ni(OH)₂ and NiOOH. Fitting the NiO Ni 2p spectral profile is not as straightforward as the hydroxide and oxyhydroxide. It may involve contributions from inter-atomic, non-local electronic coupling and screening effects with multiplet structures significantly different from the free ions as found for MnO. A scheme for fitting these spectra using multiplet envelopes is proposed.     

Pressure effects on the quadrupole coupling constant of 7Li in first stage lithium graphite

The pressure dependence of the experimental ⁷Li NMR spectra is reported for first stage lithium graphite (LiC₆) intercalation compound at temperatures T = 232 and 293 K. This experiment together with the presented point charge model calculation of the ⁷Li quadrupole coupling constant $\text{(}\text{e}{}^2\text{qQ}\text{h}\text{)}$ allows an unambiguous determination of the sign of e²qQ/h which is negative: $\text{e}{}^2\text{qQ}\text{h=-52 kHz}$ at p = 1 bar and T = 232 K. The averaged location of the electrons transferred from the Li intercalant to the graphite layers, as estimated in this study, is in excellent agreement with earlier theoretical energy-band calculations. The compressibility of LiC₆ in the c-direction is predicted to be k_c = 1.7 × 10^-12cm²dyn^-1, it agrees with estimates derived from the available phonon dispersion relations.     

The Fermi to Gamow-Teller mixing ratio of theβ + decay of52Mn and time-reversal invariance

To date, ten experimental measurements of the asymmetry parameter have been made for the positron decay of⁵²Mn. The Fermi to Gamow-Teller mixing ratioy can be deduced from such measurements and this quantity is important because the time-reversal violating amplitude is proportional toy/(1+y²). Our theoretical calculation using the Collective Model yieldsy=? 3.5×10^?4 for the deformation parameterβ=0.1 andy=? 4.6×10^?4 forβ=0.2. Such small values ofy are consistent with time-reversal invarisance.     

Asymptotic stability of the numerical solution for an integrodifferential reaction-diffusion system

This paper presents the study of the numerical solution of a reaction-diffusion system involving a reaction term of integral type arising from biological models. By means of a monotone approach we introduce upper and lower solutions and then we show the existence and the asymptotic behavior of nonnegative numerical solutions. To this end, we require the positivity of the numerical scheme and so we can use some properties of positive and M-matrices. Finally we give some sufficient conditions to verify the asymptotic stability of the numerical solution.     

Generalized fractional programming duality: A parametric approach

Using a parametric approach, duality is presented for a minimax fractional programming problem that involves several ratios in the objective function.The first author is thankful to Natural Science and Engineering Research Council of Canada for financial support through Grant A-5319, and the authors are thankful to the anonymous referees for useful suggestions.     

Highly polarized dithiafulvenes: synthesis and nonlinear optical properties

Push-pull dithiafulvenes with reduced bond length alternation (BLA) and high optical nonlinearities have been prepared. The interplay between the proaromaticity of the donor and the structural and optical properties of these merocyanines is discussed. The donor ability of dithiafulvenes can reach that of ferrocene or dialkylaminophenyl groups.     

The epitaxial sexiphenyl (0 0 1) monolayer on TiO2(1 1 0): A grazing incidence X-ray diffraction study

A para-sexiphenyl monolayer of near up-right standing molecules (nominal thickness of 30 Å) is investigated in-situ by X-ray diffraction using synchrotron radiation and ex-situ by atomic force microscopy. A terrace like morphology is observed, the step height between the terraces is approximately one molecular length. The monolayer terraces, larger than 20 μm in size, are extended along the [0 0 1] direction of the TiO₂(1 1 0) substrate i.e. along the Ti-O rows of the reconstructed substrate surface. The structure of the monolayer and its epitaxial relationship to the substrate is determined by grazing incidence X-ray diffraction. Extremely sharp diffraction peaks reveal high crystalline order within the monolayer, which was found to have the bulk structure of sexiphenyl. The monolayer terraces are epitaxially oriented with the (0 0 1) plane parallel to the substrate surface (out-of-plane order). Four epitaxial relationships are observed. This in-plane alignment is determined by the arrangement of the terminal phenyl rings of the sexiphenyl molecules parallel to the oxygen rows of the substrate.     

Electrospray deposition in vacuum

We have used the established technique of electrospray in developing a portable vacuum electrospray system which can deposit, in vacuo, dissolved molecules onto a sample which may then be analysed by UHV techniques. As an initial test of the system we have analysed silicon samples with an electrosprayed layer of poly(ethylene) oxide (PEO) using atomic force microscopy (AFM). The polymer forms different structures depending on the voltage applied to the emitter, and solution composition. The system is part of our ongoing effort to deposit other materials such as nanoparticles, and large dye molecules for developing molecular dye sensitised solar cells.