ArticleEuropean biophysics journal : EBJ2015
Fractal model of anomalous diffusion.
Article in European biophysics journal : EBJ, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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7 citing papers in PubMed.
- Subdiffusion from competition between multi-exponential friction memory and energy barriers.The European physical journal. E, Soft matter · 2025Article
- Scale invariance in a nonvibrating magnetic granular system.Scientific reports · 2020Article
- Particle Mobility Analysis Using Deep Learning and the Moment Scaling Spectrum.Scientific reports · 2019Article
- Extensions and solutions for nonlinear diffusion equations and random walks.Proceedings. Mathematical, physical, and engineering sciences · 2019Article
- Diffusion on Middle-Entropy (Basel, Switzerland) · 2018Article
- Fractal analysis of lateral movement in biomembranes.European biophysics journal : EBJ · 2018Article
- Fractional calculus in pharmacokinetics.Journal of pharmacokinetics and pharmacodynamics · 2018Article
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1 author.
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Abstract
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
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