Classical and quantal aspects of resonant normal forms

The Birkhoff-Gustavson normal form is employed to study separately chaos and resonances in a system with two degrees of freedom. In the integrable regime, tunnelling effects are appreciable when the nearest level spacings show oscillations. Tunnelling among states in the libration and rotation tori regions is also observed. The regularity of avoided crossings due to tunnelling indicates a collective effect and is associated with an isolated resonance. The spectral fluctuations also show a strong level correlation. The Husimi distribution, on the other hand, is insensitive to avoided crossings. An integrable approximation to the overlap of resonances is obtained and a theoretical description is given for an isolated cubic resonance plus a complex orbit. In the non-integrable regime chaos is stronger after overlapping and preferentially at low energies.

Carbon monoxide oxidation over platinum: Stable, oscillatory and quasi-chaotic regimes

We model the heterogeneously catalyzed oxidation of CO over a Pt surface. A phase diagram analysis is used to probe the several steady state regimes and their stability. We incorporate an experimentally observed 'slow' sub-oxide kinetic step, thereby generalizing a previously presented model. In agreement with experimental data, stable, oscillatory and quasi-chaotic regimes are obtained. Furthermore, the inclusion of the sub-oxide step yields a relaxation oscillation regime. © 1998 Elsevier Science B.V. All rights reserved.

Deformed Gaussian orthogonal ensemble and the statistical fluctuations in the spectra of the quartic oscillator

The nearest-neighbor spacing distributions proposed by four models, namely, the Berry-Robnik, Caurier-Grammaticos-Ramani, Lenz-Haake, and the deformed Gaussian orthogonal ensemble, as well as the ansatz by Brody, are applied to the transition between chaos and order that occurs in the isotropic quartic oscillator. The advantages and disadvantages of these five descriptions are discussed. In addition, the results of a simple extension of the expression for the Dyson-Mehta statistic Δ3 are compared with those of a more popular one, usually associated with the Berry-Robnik formalism. ©1999 The American Physical Society.

Coherent atomic oscillations and resonances between coupled Bose-Einstein condensates with time-dependent trapping potential

The atomic tunneling between two tunnel-coupled Bose-Einstein condensates (BECs) in a double-well time-dependent trap was studied. For the slowly varying trap, synchronization of oscillations of the trap with oscillations of the relative population was predicted. Using the Melnikov approach, the appearance of the chaotic oscillations in the tunneling phenomena between the condensates was confirmed.

Chaotic oscillation in an attractive Bose-Einstein condensate under an impulsive force

The chaotic oscillation in an attractive Bose-Einstein condensate (BEC) under an impulsive force was discussed using mean-field Gross-Pitaevskii (GP) equation. It was found that sustained chaotic oscillation resulted in a BEC under the action of an impulsive force generated by suddenly changing the interatomic scattering length or the harmonic oscillator trapping potential. The analysis suggested that the final state interatomic attraction played an important role in the generation of the chaotic dynamics.

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

Electrocatalytic and voltammetric determination of sulfhydryl compounds through iron nitroprusside modified graphite paste electrode

Iron nitroprusside Fe(II)NP was incorporated into a carbon paste electrode and the electrochemical studies were performed with cyclic voltammetry. The cyclic voltammogram of Fe(II)NP exhibits two redox couple with formal potential (E0')1 = 0.24 e (E0')2 = 0.85 V vs SCE attributed to Fe(II)/Fe(II) and Fe (II)(CN)5NO/Fe(III)(CN)5NO, respectively. The redox couple with (E0')2 = 0.85 V presents an electrocatalytic response for sulfhydryl compounds. The electrocatalytic oxidation of sulfhydryl compounds by the mediator has been used for the determination of L-cysteine and N-acetylcysteine. The modified graphite paste electrode gives a linear range from 9.2 x 10-4-2.0 x 10-2;; 9.6 x 10-4-1.4 x 10-2mol L-1 for the determination of L-cysteine and N-acetylcysteine, respectively, with detection limit of 1.9 x 10-4 mol L-1;; 1.5 x 10 -4 mol L-1 and relative standard desviations ± 5% and 1.5 x 10-3 mol L-1 ± 4% (n=3). The amperometric sensitivities are 0.024 and 0.027 μA/μmol L-1 for L-cysteine and N-acetylcysteine, respectively. The application of this electrode was tested and a commercial pharmaceutical product (Fluimucil) has been determined.

Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management

The investigation of the dynamics of a discrete soliton in an array of Bose-Einstein condensates under the action of a periodically time-modulated atomic scattering length [Feshbach-resonance management (FRM)] was discussed. The slow and rapid modulations, in comparison with the tunneling frequency were considered. An averaged equation, which was a generalized discrete nonlinear Schrödinger equation, including higher-order effective nonlinearities and intersite nonlinear interactions was derived in the case of the rapid modulation. It was demonstrated that the modulations of sufficient strength results in splitting of the soliton by direct simulations.

Tuning of fuzzy inference systems through unconstrained optimization techniques

This paper presents a new methodology for the adjustment of fuzzy inference systems. A novel approach, which uses unconstrained optimization techniques, is developed in order to adjust the free parameters of the fuzzy inference system, such as its intrinsic parameters of the membership function and the weights of the inference rules. This methodology is interesting, not only for the results presented and obtained through computer simulations, but also for its generality concerning to the kind of fuzzy inference system used. Therefore, this methodology is expandable either to the Mandani architecture or also to that suggested by Takagi-Sugeno. The validation of the presented methodology is accomplished through an estimation of time series. More specifically, the Mackey-Glass chaotic time series estimation is used for the validation of the proposed methodology.

Local dimension and finite time prediction in coupled map lattices

Forecasting, for obvious reasons, often become the most important goal to be achieved. For spatially extended systems (e.g. atmospheric system) where the local nonlinearities lead to the most unpredictable chaotic evolution, it is highly desirable to have a simple diagnostic tool to identify regions of predictable behaviour. In this paper, we discuss the use of the bred vector (BV) dimension, a recently introduced statistics, to identify the regimes where a finite time forecast is feasible. Using the tools from dynamical systems theory and Bayesian modelling, we show the finite time predictability in two-dimensional coupled map lattices in the regions of low BV dimension. © Indian Academy of Sciences.

Preconcentration and determination of mercury(II) at a chemically modified electrode containing 3-(2-thioimidazolyl)propyl silica gel

A mercury-sensitive chemically modified graphite paste electrode was constructed by incorporating modified silica gel into a conventional graphite paste electrode. The functional group attached to the (3-chloropropyl) silica gel surface was 2-mercaptoimidazole, giving a new product denoted by 3-(2-thioimidazolyl)propyl silica gel, which is able to complex mercury ions. Mercury was chemically adsorbed on the modified graphite paste electrode containing 3-(2-thioimidazolyl)propyl silica (TIPSG GPE) by immersion in a Hg(II) solution, and the resultant surface was characterized by cyclic and differential pulse anodic stripping voltammetry. One cathodic peak at 0.1 V and other anodic peak at 0.34 V were observed on scanning the potential from -0.1 to 0.8 V (0.01 M KNO3; ν = 2.0 mV s-1 νs. Ag/AgCl). The anodic peak at 0.34 V show an excellent sensitivity for Hg(II) ions in the presence of several foreign ions. A calibration graph covering the concentration range from 0.02 to 2 mg L-1 was obtained. The detection limit was estimated to be 5 μg L-1. The precision for six determinations of 0.05 and 0.26 mg L-1 Hg(II) was 3.0 and 2.5% (relative standard deviation), respectively. The method can be used to determine the concentration of mercury(II) in natural waters contaminated by this metal. 2005 © The Japan Society for Analytical Chemistry.

Optimal linear and nonlinear control design for chaotic systems

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Rössler system and the Duffing oscillator are provided to show the effectiveness of this method. Copyright © 2005 by ASME.

Preparation of a silica gel modified with 2-amino-1,3,4-thiadiazole for adsorption of metal ions and electroanalytical application

Silica gel with a specific area of 382 m2 g-1 and an average pore diameter of 60 Å was chemically modified with 2-amino-1,3,4-thiadiazole, for the purpose of selective adsorption of heavy metals ions and possible use as a chemically modified carbon paste electrode (CMCPE). The following properties of this functionalized silica gel are discussed: selective adsorption of heavy metal ions measured by batch and chromatographic column techniques, and utilization as preconcentration agent in a chemically modified carbon paste electrode (CMCPE) for determination of mercury(II). The chemical selectivity of this functional group and the selectivity of voltammetry were combined for preconcentration and determination. ©2006 Sociedade Brasileira de Química.

Scaling properties of the fermi-ulam accelerator model

The chaotic low energy region (chaotic sea) of the Fermi-Ulam accelerator model is discussed within a scaling framework near the integrable to non-integrable transition. Scaling results for the average quantities (velocity, roughness, energy etc.) of the simplified version of the model are reviewed and it is shown that, for small oscillation amplitude of the moving wall, they can be described by scaling functions with the same characteristic exponents. New numerical results for the complete model are presented. The chaotic sea is also characterized by its Lyapunov exponents.

The feigenbaumes δ for a high dissipative bouncing ball model

We have studied a dissipative version of a one-dimensional Fermi accelerator model. The dynamics of the model is described in terms of a two-dimensional, nonlinear area-contracting map. The dissipation is introduced via inelastic collisions of the particle with the walls and we consider the dynamics in the regime of high dissipation. For such a regime, the model exhibits a route to chaos known as period doubling and we obtain a constant along the bifurcations so called the Feigenbaum's number 8.