2009AIP conference proceedingsRequires access

The Study of the Discrete Quasi-Multifractal Process

А. И. Саичев, Vladimir Filimonov, Massimo Macucci, Giovanni Basso

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Abstract

This work is dedicated to the study of the multifractal diffusion process, constructed using Quasi‐Multifractal Model. In contrast to other works, a multifractal spectrum, determining properties, is calculated using statistical processing of realizations of the process, where realizations were obtained by numerical simulation of the sampled model. Presented results of numerical simulations showed presence of 3 significantly different modes of quasi‐multifractal processes, which we called “monofractal” “tempered multifractal” and “strongly multifractal.” The “temporal” and “spectral” differences of these modes are also discussed.

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What this paper is about

This work is dedicated to the study of the multifractal diffusion process, constructed using Quasi‐Multifractal Model. In contrast to other works, a multifractal spectrum, determining properties, is calculated using statistical processing of realizations of the process, where realizations were obtained by numerical simulation of the sampled model. Presented results of numerical simulations showed presence of 3 significantly different modes of quasi‐multifractal processes, which we called “monofractal” “tempered multifractal” and “strongly multifractal.” The “temporal” and “spectral” differences of these modes are also discussed.

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Available abstract

This work is dedicated to the study of the multifractal diffusion process, constructed using Quasi‐Multifractal Model. In contrast to other works, a multifractal spectrum, determining properties, is calculated using statistical processing of realizations of the process, where realizations were obtained by numerical simulation of the sampled model. Presented results of numerical simulations showed presence of 3 significantly different modes of quasi‐multifractal processes, which we called “monofractal” “tempered multifractal” and “strongly multifractal.” The “temporal” and “spectral” differences of these modes are also discussed.

Key concepts: Multifractal system, Statistical physics, Fractal, Process (computing), Stochastic process, Mathematics, Spectrum (functional analysis), Diffusion

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