On the effective diffusion in the Sierpiński carpet

Aguilar-Madera, Carlos G.; Herrera-Hernández, E. C.; Espinosa-Paredes, Gilberto; Carrillo, Jorge A. Briones

doi:10.1007/s10596-020-10016-z

Cited by 2 publications

(1 citation statement)

References 38 publications

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“…The investigation of effective diffusion in disordered and fractal media (such as gel or suspensions) remains unsolved. , To explain this phenomenon, several theoretical and experimental breakthroughs have been proposed. The Sierpiski carpet (similar to other fractal structures) is one of the most prominent fractal shapes used to analyze diffusion .…”

Section: Simulation and Frapmentioning

confidence: 99%

Fluorescence Recovery after Photobleaching in Colloidal Science: Introduction and Application

Moud

2022

ACS Biomater. Sci. Eng.

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FRAP (fluorescence recovery after photo bleaching) is a method for determining diffusion in material science. In industrial applications such as medications, foods, Medtech, hygiene, and textiles, the diffusion process has a substantial influence on the overall qualities of goods. All these complex and heterogeneous systems have diffusion-based processes at the local level. FRAP is a fluorescence-based approach for detecting diffusion; in this method, a high-intensity laser is made for a brief period and then applied to the samples, bleaching the fluorescent chemical inside the region, which is subsequently filled up by natural diffusion. This brief Review will focus on the existing research on employing FRAP to measure colloidal system heterogeneity and explore diffusion into complicated structures. This description of FRAP will be followed by a discussion of how FRAP is intended to be used in colloidal science. When constructing the current Review, the most recent publications were reviewed for this assessment. Because of the large number of FRAP articles in colloidal research, there is currently a dearth of knowledge regarding the growth of FRAP’s significance to colloidal science. Colloids make up only 2% of FRAP papers, according to ISI Web of Knowledge.

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Section: Simulation and Frapmentioning

confidence: 99%

Fluorescence Recovery after Photobleaching in Colloidal Science: Introduction and Application

Moud

2022

ACS Biomater. Sci. Eng.

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A Brief Survey of Paradigmatic Fractals from a Topological Perspective

Ortíz

Martínez-Cruz

et al. 2023

Fractal Fract

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The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a fractal dimension D which exceeds the topological dimension d. In this regard, we point out that the constitutive inequality D>d can have either a geometric or topological origin, or both. The main topological features of fractals are their connectedness, connectivity, ramification, and loopiness. We argue that these features can be specified by six basic dimension numbers which are generally independent from each other. However, for many kinds of fractals, the number of independent dimensions may be reduced due to the peculiarities of specific kinds of fractals. Accordingly, we survey the paradigmatic fractals from a topological perspective. Some challenging points are outlined.

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On the effective diffusion in the Sierpiński carpet

Cited by 2 publications

References 38 publications

Fluorescence Recovery after Photobleaching in Colloidal Science: Introduction and Application

Fluorescence Recovery after Photobleaching in Colloidal Science: Introduction and Application

A Brief Survey of Paradigmatic Fractals from a Topological Perspective

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