Scale Relativity and Fractal Space-Time: Theory and Applications

Nottale, Laurent

doi:10.1007/s10699-010-9170-2

Cited by 53 publications

(52 citation statements)

References 91 publications

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“…where λ 1 and λ 2 are constants of integration. By setting λ 1 = 1 and λ 2 = Λ, with Λ, the well known cosmological constant [34], one obtains the following model…”

Section: C-reconstruction Of Cosmological Vacuum F (T ) Modelsmentioning

confidence: 99%

Cosmological study of autonomous dynamical systems in modified Tele-Parallel gravity

et al. 2019

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Cosmological approaches of autonomous dynamical system in the framework of f (T ) gravity are investigated in this paper. Our methods applied to flat Friedmann-Robertson-Walker equations in f (T ) gravity, consist to extract dynamical systems whose time-dependence is contained in a single parameter m depending on the Hubble rate of Universe and its second derivative. In our attempt to investigate the autonomous aspect of the dynamical systems reconstructed in both vacuum and nonvacuum f (T ) gravities, two values of the parameter m have been considered for our present analysis. In the so-called quasi-de Sitter inflationary era (m ≃ 0), the corresponding autonomous dynamical systems provide stable de Sitter attractors and unstable de Sitter fixed points. Especially in the vacuum f (T ) gravity, the approximate form of the f (T ) gravity near the stable and the unstable de Sitter fixed points has been performed. The matter dominated era case (m = − 9 2 ) leads to unstable fixed points confirming matter dominated era or not, and stable attractor fixed point describing dark energy dominated era. Another subtlety around the stable fixed point obtained at matter dominated case in the non-vacuum f (T ) gravity is when the dark energy dominated era is reached, at the same time, the radiation perfect fluid dominated succumbs.

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“…where λ 1 and λ 2 are constants of integration. By setting λ 1 = 1 and λ 2 = Λ, with Λ, the well known cosmological constant [34], one obtains the following model…”

Section: C-reconstruction Of Cosmological Vacuum F (T ) Modelsmentioning

confidence: 99%

Cosmological study of autonomous dynamical systems in modified Tele-Parallel gravity

et al. 2019

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“…The purpose of this retro-active force loop is to tune the form of oscillations to the form predicted by the theory [10], for oscillations of a generalized quantum wave packet.…”

Section: Discussionmentioning

confidence: 99%

“…According to our understanding of the basic concepts of the theory [10], such an artificial tuning is unnecessary in the case of a natural fractal geometry being present along with the presence of dynamic potentials driving the transfer processes. The latter involve oscillators of different sizes and scales.…”

Section: Discussionmentioning

confidence: 99%

Mechanically Assisted Low-Temperature Pyrolysis of Hydrocarbons

Alevanau¹,

Vyhoniailo²,

Kuznechik³

et al. 2018

EPE

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The focus of the study is experimental setups and conditions leading to pyrolysis (cracking) of such gaseous hydrocarbons as methane, mixed propane and butane, at the temperatures of the heater below 200˚C. The process was mechanically assisted by putting the substances being decomposed into a dynamic interaction with the fractal interfaces of cracks in titanium dioxide films, as well as in tin and bismuth alloy. During a trial, the alloy was periodically heated and cooled so that it changed its phase state, and fractal interfaces were created between its surface and the gases. The interaction of the gases with fractal surfaces of the alloy being produced by mechanical fracturing made it possible to obtain gas cracking even at the lower temperatures of the heater (150˚C). It should be noted that at this temperature, the heater couldn't melt the alloy in the heated volume with the gas.

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“…non quantum), we have other models, offering predictions and explanations. Connecting the different scales in nature (from quantum to cosmological) is a major challenge in physics, on which Scale Relativity (Nottale 2010) already made impressive progresses.…”

Section: Vidalmentioning

confidence: 99%