ON THE DETERMINATION OF THE STOCHASTICITY THRESHOLD OF INVARIANT CURVES

We consider the problem of determining the stochasticity transition value in nearly-integrable mappings. We perform explicitly a canonical transformation, which conjugates the original mapping to an integrable one, up to a given order in the perturbing parameter. Then we derive a numerical evidence of the existence of an invariant curve associated with the transformed system and, correspondingly, to the original one. In the second part of the paper we implement a numerical method due to M. Hénon [Hénon] for the computation of the rotation number corresponding to a given initial condition. Following an idea of Laskar et al. [1992] and Laskar [1993], we determine with high accuracy the critical breakdown threshold of invariant curves for standard-mapping like systems which allows not only to test Hénon's method but also to compare our analytical results with an accurate numerical one. An application is also made about the accuracy of the leap frog method.

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DETERMINATION OF THE FREQUENCY VECTOR IN THE FOUR-DIMENSIONAL STANDARD MAPPING

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127496000941 ◽

1996 ◽

Vol 06 (08) ◽

pp. 1579-1585 ◽

Cited By ~ 3

Author(s):

ALESSANDRA CELLETTI ◽

CLAUDE FROESCHLÉ ◽

ELENA LEGA

Keyword(s):

Initial Conditions ◽

Numerical Technique ◽

Chaotic Regime ◽

Frequency Vector ◽

Two Dimensional ◽

Breakdown Threshold ◽

Onset Of Chaos ◽

Standard Mapping ◽

Dimensional Mapping

Different numerical methods, for the computation of frequency versus initial conditions in the four-dimensional standard mapping, are proposed. The first method relies on the analytic properties of invariant rotational tori. A purely numerical technique was derived from an extension of a method suggested by M. Hénon for the two-dimensional mapping. A refinement of the last technique can be obtained implementing the frequency analysis introduced by J. Laskar. These methods agree up to some values of the coupling and perturbing parameters, close to the breakdown threshold for the onset of chaos. The transition to the chaotic regime is further confirmed by the computation of Lyapunov exponents and by suitable slice projections of the original mapping.

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Determination of rate constants of redox reactions of second order from current-less potential-time curves by a simplified graphical-numerical method

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19831358 ◽

1983 ◽

Vol 48 (5) ◽

pp. 1358-1367 ◽

Cited By ~ 4

Author(s):

Antonín Tockstein ◽

František Skopal

Keyword(s):

Numerical Method ◽

Explicit Form ◽

Rate Constant ◽

Optimization Algorithm ◽

Rate Constants ◽

Redox Reactions ◽

Second Order ◽

Wide Region ◽

Recurrent Formula

A method for constructing curves is proposed that are linear in a wide region and from whose slopes it is possible to determine the rate constant, if a parameter, θ, is calculated numerically from a rapidly converging recurrent formula or from its explicit form. The values of rate constants and parameter θ thus simply found are compared with those found by an optimization algorithm on a computer; the deviations do not exceed ±10%.

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The Degree of Oxidation of Graphene Oxide

Nanomaterials ◽

10.3390/nano11030560 ◽

2021 ◽

Vol 11 (3) ◽

pp. 560

Author(s):

Alexandra Carvalho ◽

Mariana C. F. Costa ◽

Valeria S. Marangoni ◽

Pei Rou Ng ◽

Thi Le Hang Nguyen ◽

...

Keyword(s):

Graphene Oxide ◽

Ab Initio ◽

State Of The Art ◽

High Accuracy ◽

Precise Determination ◽

Photoemission Spectroscopy ◽

Pristine Graphene ◽

X Ray ◽

Degree Of Oxidation

We show that the degree of oxidation of graphene oxide (GO) can be obtained by using a combination of state-of-the-art ab initio computational modeling and X-ray photoemission spectroscopy (XPS). We show that the shift of the XPS C1s peak relative to pristine graphene, ΔEC1s, can be described with high accuracy by ΔEC1s=A(cO−cl)2+E0, where c0 is the oxygen concentration, A=52.3 eV, cl=0.122, and E0=1.22 eV. Our results demonstrate a precise determination of the oxygen content of GO samples.

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Numerical investigation of double-diffusive convection in rectangular cavities with different aspect ratio I: High-accuracy numerical method

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.05.002 ◽

2021 ◽

Vol 94 ◽

pp. 155-169

Author(s):

Jian-Qing Yang ◽

Bing-Xin Zhao

Keyword(s):

Aspect Ratio ◽

Numerical Method ◽

Numerical Investigation ◽

High Accuracy ◽

Double Diffusive Convection ◽

Diffusive Convection ◽

Double Diffusive

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A hybrid analytical-numerical method based on Isogeometric Analysis for determination of time varying gear mesh stiffness

Mechanism and Machine Theory ◽

10.1016/j.mechmachtheory.2021.104291 ◽

2021 ◽

Vol 160 ◽

pp. 104291

Author(s):

Andreas Beinstingel ◽

Michael Keller ◽

Michael Heider ◽

Burkhard Pinnekamp ◽

Steffen Marburg

Keyword(s):

Numerical Method ◽

Isogeometric Analysis ◽

Time Varying ◽

Mesh Stiffness ◽

Gear Mesh ◽

Gear Mesh Stiffness

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Electrochemical device based on nonspecific DNAzyme for the high-accuracy determination of Ca2+ with Pb2+ interference

Bioelectrochemistry ◽

10.1016/j.bioelechem.2020.107732 ◽

2020 ◽

pp. 107732

Author(s):

Hui Wang ◽

Qingyao Luo ◽

Yiguang Zhao ◽

Xuemei Nan ◽

Fan Zhang ◽

...

Keyword(s):

High Accuracy ◽

Electrochemical Device ◽

Accuracy Determination

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Based on Atomic Spectrometry for the Determination of Titanium Element in Molten Steel

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.622-623.1528 ◽

2012 ◽

Vol 622-623 ◽

pp. 1528-1531

Author(s):

Cui Hong Ma ◽

Wei Qiang Zhang

Keyword(s):

Molten Steel ◽

Emission Spectroscopy ◽

Atomic Emission ◽

Lag Time ◽

High Accuracy ◽

Atomic Spectrometry ◽

Atomic Emission Spectrometry ◽

Emission Spectrometry ◽

Important Significance

Atomic emission spectrometry with high accuracy, short lag time, and low detection limit, it has been widely applied in various fields. The application of atomic emission spectrometry in the converter steelmaking process has an important significance to improve the smelting of speed and steel quality. This article describes the principle of atomic emission spectroscopy (AES) analysis. Spectra obtained by the experimental for qualitative analysis, detected molten steel containing titanium element.

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An Efficient Galerkin BEM to Compute High Acoustic Eigenfrequencies

Journal of Vibration and Acoustics ◽

10.1115/1.3085894 ◽

2009 ◽

Vol 131 (3) ◽

Cited By ~ 9

Author(s):

Mario Durán ◽

Jean-Claude Nédélec ◽

Sebastián Ossandón

Keyword(s):

Numerical Method ◽

Integral Equations ◽

High Frequency ◽

High Accuracy ◽

Integral Representations ◽

Stability And Convergence ◽

Symmetric Matrices ◽

Frequency Interval ◽

Numerical Treatment ◽

The Stability

An efficient numerical method, using integral equations, is developed to calculate precisely the acoustic eigenfrequencies and their associated eigenvectors, located in a given high frequency interval. It is currently known that the real symmetric matrices are well adapted to numerical treatment. However, we show that this is not the case when using integral representations to determine with high accuracy the spectrum of elliptic, and other related operators. Functions are evaluated only in the boundary of the domain, so very fine discretizations may be chosen to obtain high eigenfrequencies. We discuss the stability and convergence of the proposed method. Finally we show some examples.

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