Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time-series

We propose here a local exponential divergence plot which is capable of providing an alternative means of characterizing a complex time series. The suggested plot defines a time-dependent exponent and a ''plus'' exponent. Based on their changes with the embedding dimension and delay time, a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time, and the largest Lyapunov exponent has been obtained. When redefining the time-dependent exponent LAMBDA(k) curves on a series of shells, we have found that whether a linear envelope to the LAMBDA(k) curves exists can serve as a direct dynamical method of distinguishing chaos from noise.

Symmetry of chaotic attractors and kink-antikink structures in CMLs

In this paper the symmetries of coupled map lattices (CMLs) and their attractors are investigated by group and dynamical system theory, as well as numerical simulation, by means of which the kink-antikink patterns of CMLs in space-amplitude plots are discussed.

Local exponential divergence plot and optimal embedding of a chaotic time-series

we propose here a local exponential divergence plot which is capable of providing a new means of characterizing chaotic time series. The suggested plot defines a time dependent exponent LAMBDA and a ''plus'' exponent LAMBDA+ which serves as a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time and the largest Lyapunov exponent.

Two-time scales inner solutions and motion of a geostrophic vortex

Based on the authors' previous work, in this paper the systematical analyses on the motion and the inner solutions of a geostrophic vortex have been presented by means of thematched asymptotic expansion method with multiple time scales (S/gh001/2 and α S/gh001/2) and space scales. It has been shown that the leading inner solutions to the core structure in two-time scales analyses are identified with the results in normal one-time scale analyses. The time averages of the first-order solutions on short time variable τ are the same as the first-order solutions obtained in one normal time scale analyses. The geostrophic vortex induces an oscillatory motion in addition to moving with the background flow. The period, amplitude andthe deviation from the mean trajectory depend on the core structure and the initial conditions. The velocity of the motion of vortex center varies periodically and the time average of the velocity on short time variable τ is equal to the value of the local mean velocity.

Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

The dynamical process of a coronal transient associated with an eruptive prominence .2. Analytical solutions in finite regions

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Exact solutions to collisionless external gas flows

This paper presents exact density, velocity and temperature solutions for two problems of collisionless gas flows around a flat plate or a spherical object. At any point off the object, the local velocity distribution function consists of two pieces of Maxwellian distributions: one for the free stream which is characterized by free stream density, temperature and average velocity, n0, T0, U0; and the other is for the wall and it is characterized by density at wall and wall temperature, nw,Tw. Directly integrating the distribution functions leads to complex but exact flowfield solutions. To validate these solutions, we perform numerical simulations with the direct simulation Monte Carlo (DSMC) method. In general, the analytical and numerical results are virtually identical. The evaluation of these analytical solutions only requires less than one minute while the DSMC simulations require several days.

Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media

The coupled differential recurrence equations for the corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media are established in terms of the perturbation method. All the corrections (including the longitudinal field corrections) to the paraxial approximation solutions are presented in the weak-guidance approximation. As a concrete application, the first-order longitudinal field correction and the second-order transverse field correction to the paraxial approximation of a Gaussian beam propagating in a transversely quadratic refractive index medium are analytically investigated. (C) 1999 Optical Society of America [S0740-3232(99)00310-5].

Kinetic study of the 2-methyl-3-methoxy-4-phenylbutanoic acid produced by oxidation of microcystin in aqueous solutions

Microcystins (MCs) are a family of related cyclic hepatotoxic heptapeptides, of which more than 70 types have been identified. The chemically unique nature of the C20 beta-amino acid, (2S, 3S, 8S, 9S)-3-amino-9-methoxy-2,6,8-trimethyl-10-phenyldeca4,6-dienoic acid (Adda), portion of the MCs has been exploited to develop a strategy to analyze the entirety. Oxidation of MCs causes the cleavage of MC Adda to form 2-methyl-3-methoxy-4-phenylbutanoic acid (MMPB). In the present study, we investigated the kinetics of MMPB produced by oxidation of the most-often-studied MC variant, MC-LR (L = leucine, R = arginine), with permanganate-periodate. This investigation allowed insight regarding the influence of the reaction conditions (concentration of the reactants, temperature, and pH) on the conversion rate. The results indicated that the reaction was second order overall and first order with respect to both permanganate and MC-LR. The second-order rate constant ranged from 0.66 to 1.35 M/s at temperatures from 10 to 30 degrees C, and the activation energy was 24.44 kJ/mol. The rates of MMPB production can be accelerated through increasing reaction temperature and oxidant concentration, and sufficient periodate is necessary for the formation of MMPB. The initial reaction rate under alkaline and neutral conditions is higher than that under acidic conditions, but the former decreases faster than the latter except under weakly acidic conditions. These results provided new insight concerning selection of the permanganate-periodate concentration, pH, and temperature needed for the oxidation of MCs with a high and stable yield of MMPB.

Photodegradation of 2-naphthol in aqueous solutions in the presence of humic acid and ferric ions

In this work, the photodegradation of the carcinogenic pollutant 2-naphthol in aqueous solution containing Aldrich humic acid (HA) and ferric ions (Fe(III)) under 125 W and 250 W high pressure mercury lamp (HPML, lambda >= 365 nm) irradiation was investigated. The photooxidation efficiencies were dependent on the pH values, light intensities and Fe(III)/HA concentration in the water, with higher efficiency at pHs 3-4, and 50 mu mol l(-1) Fe(III) with 20 mg l(-1) HA under 250 W HPML. The initial rate of photooxidation increases with increasing, the initial concentration of 2-naphthol from 10 mu mol l(-1) to 100 mu mol l(-1), while do not change at 50 and 100 mu mol l(-1). However, higher removal efficiency of 2-naphthol is achieved at its lower initial concentration of 10 mu mol l(-1), and initial rate of photooxidation is 0.193 mu mol l(-1) min(-1). Dissolved oxygen (DO) plays an important role in the system containing Fe(III)-HA complexes in which Fenton and photo-Fenton reactions were enhanced in the environment. Hydroxyl radicals produced in HA solution with or without ferric ions were determined by using benzene as free radical scavenger and phenol as scavenging products proportional to hydroxyl radicals. By using UV-Vis and excited fluorescence spectrum techniques, the main photooxidation products, which have higher absorption in the region of 240-340 nm, were found, and the mechanisms for the oxidative degradation is proposed.