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Publication

Lorenz Type Behaviors Associated To Fractal-Non-Fractal Transition In The Dynamics Of The Complex Systems

Maria-Alexandra Paun
2019
Journal Articles

Abstract

In the framework of Fractal Theory of Motion for the Scale Relativity Theory with arbitrary and constant fractal dimensions, dynamics in complex systems associated to the fractal-non-fractal transition are analyzed. Working with the assumption that these dynamics are described by means of fractal curves, Lorenz type behaviors become "operational" through a Galerkin method. Then Rayleigh and Prandtl effective numbers are specified both by means of classical kinetic coefficients and scale resolution while the dynamics variables act as the limit of a family of mathematical functions, non-differentiable for non-null scale resolution.

Official source

https://infoscience.epfl.ch/entities/publication/8b50dbff-1521-47e3-8fc0-2b686e8357df

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Maria-Alexandra Paun
2019
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/8b50dbff-1521-47e3-8fc0-2b686e8357df

About this result

Related concepts (27)

Fractal

In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar.

Fractal curve

A fractal curve is, loosely, a mathematical curve whose shape retains the same general pattern of irregularity, regardless of how high it is magnified, that is, its graph takes the form of a fractal. In general, fractal curves are nowhere rectifiable curves — that is, they do not have finite length — and every subarc longer than a single point has infinite length. A famous example is the boundary of the Mandelbrot set. Fractal curves and fractal patterns are widespread, in nature, found in such places as broccoli, snowflakes, feet of geckos, frost crystals, and lightning bolts.

Fractal dimension

In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern. A fractal pattern changes with the scale at which it is measured. It is also a measure of the space-filling capacity of a pattern, and it tells how a fractal scales differently, in a fractal (non-integer) dimension. The main idea of "fractured" dimensions has a long history in mathematics, but the term itself was brought to the fore by Benoit Mandelbrot based on his 1967 paper on self-similarity in which he discussed fractional dimensions.

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