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分形和多重分形方法在环境污染中的应用。

Fractal and multifractal approach to environmental pollution.

机构信息

Dipartimento di Fisica Nucleare e Teorica, Università degli Studi di Pavia, Via A. Bassi 6, 1-27100, Pavia, Italy.

出版信息

Environ Sci Pollut Res Int. 1997;4(2):91-8. doi: 10.1007/BF02986286.

DOI:10.1007/BF02986286
PMID:19005790
Abstract

A few case studies will be presented involving both radioactive and chemical pollution at small, medium, and large space-time scales. Reported are recent advances in the field of environmental pollution involving the use of fractals and multifractals. The mathematical tools proposed here may offer new perspectives for investigating many of the problems of nonlinear variability which commonly arise when dealing with pollutants, such as the presence of outliers and the sparseness of the sampling networks. They may also lead to a simplification of the models adopted for studying natural phenomena, thanks to a scaling approach. Finally, they may provide parameters whose values are directly related to the nonlinear dynamics involved in the pollutant distribution in the environment which, in turn, may be relevant for computer simulation and epidemiological or risk assessment purposes.

摘要

将呈现一些涉及小、中、大时空尺度的放射性和化学污染的案例研究。报告了涉及分形和多重分形应用的环境污染领域的最新进展。这里提出的数学工具可能为研究污染物出现的离群值和采样网络稀疏等常见非线性变化问题提供新的视角。由于采用了缩放方法,它们也可能简化用于研究自然现象的模型。最后,它们可以提供与环境中污染物分布所涉及的非线性动力学直接相关的值,这可能有助于计算机模拟以及流行病学或风险评估目的。

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本文引用的文献

1
Functional box-counting and multiple elliptical dimensions in rain.雨的功能盒计数和多个椭圆维度。
Science. 1987 Feb 27;235(4792):1036-8. doi: 10.1126/science.235.4792.1036.
2
Fractal measures and their singularities: The characterization of strange sets.分形测度及其奇点:奇异集的刻画
Phys Rev A Gen Phys. 1986 Feb;33(2):1141-1151. doi: 10.1103/physreva.33.1141.
3
Modelling the Chernobyl radioactive fallout (II): A multifractal approach in some European countries.切尔诺贝利放射性沉降物建模(II):一些欧洲国家的多重分形方法。
Chemosphere. 1996 Dec;33(12):2359-71. doi: 10.1016/s0045-6535(96)00320-7.