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Fractal Fract
Special Issues
Advances in Multiparticle Fractal Aggregation
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Advances in Multiparticle Fractal Aggregation

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (1 February 2023) | Viewed by 7530

Special Issue Editors

Dr. Oleksandr Tomchuk

E-Mail Website
Guest Editor
Faculty of Physics, Taras Shevchenko National University of Kyiv, 03127 Kyiv, Ukraine
Interests: physics of liquid state; fractal aggregation; neutron scattering; scattering theory; small-angle scattering and reflectometry; nanocarbon; magnetic colloids; nanostructured materials for biomedical purposes; polydispersity effects
Dr. Mikhail Avdeev

E-Mail Website
Guest Editor
Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
Interests: scattering of thermal neutrons; small-angle neutron and X-ray scattering; neutron reflectometry; thin film characterization and diagnostics; nanostructured/nanocomposite materials; colloids at interfaces; dispersive nanosystems; magnetic fluids; carbon nanostructures; bio-active dispersions; electrochemical interfaces

Special Issue Information

Dear Colleagues,

Nowadays, nanostructured materials have become widespread, the specific physicochemical properties of nanoparticles incorporated into a solid or liquid matrix able to significantly improve performance. However, the aggregation of these particles at the nanoscale can lead to a change in the physicochemical characteristics of the system and, as a consequence, to a decrease in beneficial effects or, conversely, to their improvement, where, in this case, aggregation often has a non-compact fractal character. A self-similar structure with a dimension of less than three entails effects that manifest themselves in a special way in macroscopic parameters, such as a specific surface area, viscosity, etc., with similar phenomena able to be observed in polymeric or related biological systems. Therefore, the monitoring and control of aggregation are the cornerstones of modern nanotechnology, and, as such, a crucial role in the scientific research of such systems is played by the problems of modeling fractal clusters, which significantly help in the data description of experimental and computational methods.

Therefore, fractals and fractional orders provide modern tools for the field of particle aggregation. This Special Issue focuses on the “Advances in Multiparticle Fractal Aggregation”. We invite you to submit comprehensive original research papers and review articles, the topics of interest including, but not limited to:

  • The application of fractal methods in the study of natural and technological systems with aggregation;
  • Multiparticle aggregation mechanisms;
  • Modeling fractal aggregates;
  • Neutron, light and X-ray scattering by fractals;
  • Atomic force and electron microscopy of irregular structures;
  • Dimension-dependent physical–chemical properties;
  • Self-similar structure of colloids;
  • Fractal aggregates in polymer systems;
  • Fractally packed biological objects;
  • Sol–gel synthesis.

Dr. Oleksandr Tomchuk
Dr. Mikhail Avdeev
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractal clusters
  • multiparticle aggregation
  • modeling fractal aggregates
  • fractional surfaces
  • fractal analyses
  • scale-invariant structure
  • powders
  • suspensions
  • nanocomposites
  • polymer systems
  • small-angle scattering
  • microscopy methods
  • molecular dynamics
  • Monte Carlo simulation
  • population balance equations

Published Papers (4 papers)

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Research

24 pages, 2499 KiB  
Article
An Intelligent Model for Supercapacitors with a Graphene-Based Fractal Electrode to Investigate the Cyclic Voltammetry
by Nida Kati and Ferhat Ucar
Fractal Fract. 2023, 7(3), 218; https://doi.org/10.3390/fractalfract7030218 - 26 Feb 2023
Cited by 2 | Viewed by 1748
Abstract
The aim of this study was to investigate the performance measurement of supercapacitors using the electrochemical properties of cyclic voltammetry (CV). The use of CV is crucial in evaluating the electrochemical performance of supercapacitors and determining the surface area of the catalyst with [...] Read more.
The aim of this study was to investigate the performance measurement of supercapacitors using the electrochemical properties of cyclic voltammetry (CV). The use of CV is crucial in evaluating the electrochemical performance of supercapacitors and determining the surface area of the catalyst with regard to the fractal properties of the electrode. The study specifically focused on the CV behavior of a supercapacitor formed by a cobalt-doped ceria/reduced graphene oxide (Co-CeO2/rGO) fractal nanocomposite, and its assessment was conducted using a machine learning (ML) model with the enhanced XGBoost. The model was trained using an experimental open-source dataset. The results showed that the proposed XGBoost model had a superior ability to predict the CV behavior of the supercapacitor, with nearly perfect results for the MAE, RMSE, and R-squared metrics, which are effective at evaluating the performance of regression models. With the successful design of the proposed intelligent prediction model, the study is expected to provide valuable insights into forming novel nanocomposite forms with high accuracy and minimal need for experiments. Full article
(This article belongs to the Special Issue Advances in Multiparticle Fractal Aggregation)
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12 pages, 718 KiB  
Article
Effective Fractal Dimension at 2d-3d Crossover
by Alexander V. Chalyi
Fractal Fract. 2022, 6(12), 739; https://doi.org/10.3390/fractalfract6120739 - 14 Dec 2022
Viewed by 1348
Abstract
This article is aimed at reviewing and studying the effects of the 2d-3d crossover on the effective fractal and spatial dimensions, as well as on the critical exponents of the physical properties of bulk and bounded systems at criticality. Here we consider the [...] Read more.
This article is aimed at reviewing and studying the effects of the 2d-3d crossover on the effective fractal and spatial dimensions, as well as on the critical exponents of the physical properties of bulk and bounded systems at criticality. Here we consider the following problems: (1) the two types of dimensional crossovers and the concept of the universality classes; (2) a smooth 2d-3d crossover and the calculation of the effective fractal and spatial dimensions, as well as the effective critical indices; (3) the fractal dimension, its connection with the random mean square order-parameter fluctuations and a new phase formation; (4) the fractal nuclei of a new phase and the medical consequences of carcinogenesis and nucleation isomorphism. Full article
(This article belongs to the Special Issue Advances in Multiparticle Fractal Aggregation)
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19 pages, 4141 KiB  
Article
Investigation of the Relationship between the 2D and 3D Box-Counting Fractal Properties and Power Law Fractal Properties of Aggregates
by Rui Wang, Abhinandan Kumar Singh, Subash Reddy Kolan and Evangelos Tsotsas
Fractal Fract. 2022, 6(12), 728; https://doi.org/10.3390/fractalfract6120728 - 9 Dec 2022
Cited by 3 | Viewed by 1726
Abstract
The fractal dimension Df has been widely used to describe the structural and morphological characteristics of aggregates. Box-counting (BC) and power law (PL) are the most common methods to calculate the fractal dimension of aggregates. However, the prefactor k, as another [...] Read more.
The fractal dimension Df has been widely used to describe the structural and morphological characteristics of aggregates. Box-counting (BC) and power law (PL) are the most common methods to calculate the fractal dimension of aggregates. However, the prefactor k, as another important fractal property, has received less attention. Furthermore, there is no relevant research about the BC prefactor (kBC). This work applied a tunable aggregation model to generate a series of three-dimensional aggregates with different input parameters (power law fractal properties: Df,PL and kPL, and the number of primary particles NP). Then, a projection method is applied to obtain the 2D information of the generated aggregates. The fractal properties (kBC and Df,BC) of the generated aggregates are estimated by both, for 2D and 3D BC methods. Next, the relationships between the box-counting fractal properties and power law fractal properties are investigated. Notably, 2D information is easier achieved than 3D data in real processes, especially for aggregates made of nanoparticles. Therefore, correlations between 3D BC and 3D PL fractal properties with 2D BC properties are of potentially high importance and established in the present work. Finally, a comparison of these correlations with a previous one (not considering k) is performed, and comparison results show that the new correlations are more accurate. Full article
(This article belongs to the Special Issue Advances in Multiparticle Fractal Aggregation)
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18 pages, 1334 KiB  
Article
On the Link between the Langevin Equation and the Coagulation Kernels of Suspended Nanoparticles
by José Morán
Fractal Fract. 2022, 6(9), 529; https://doi.org/10.3390/fractalfract6090529 - 18 Sep 2022
Cited by 2 | Viewed by 1793
Abstract
The ability of the Langevin equation to predict coagulation kernels in the transition regime (ranging from ballistic to diffusive) is not commonly discussed in the literature, and previous numerical works are lacking a theoretical justification. This work contributes to the conversation to gain [...] Read more.
The ability of the Langevin equation to predict coagulation kernels in the transition regime (ranging from ballistic to diffusive) is not commonly discussed in the literature, and previous numerical works are lacking a theoretical justification. This work contributes to the conversation to gain better understanding on how the trajectories of suspended particles determine their collision frequency. The fundamental link between the Langevin equation and coagulation kernels based on a simple approximation of the former is discussed. The proposed approximation is compared to a fractal model from the literature. In addition, a new, simple expression for determining the coagulation kernels in the transition regime is proposed. The new expression is in good agreement with existing methods such as the flux-matching approach proposed by Fuchs. The new model predicts an asymptotic limit for the kinetics of coagulation in the transition regime. Full article
(This article belongs to the Special Issue Advances in Multiparticle Fractal Aggregation)
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