Mass Fractal Dimension Research Articles

Microreactor for the characterization of zeolite hydrothermal synthesis by small angle X-ray scattering (SAXS)

During zeolite synthesis, exploring the growth of nanoparticles is crucial for studying the crystallization mechanism. Synchrotron radiation small angle X-ray scattering (SAXS) is a powerful technique for the in-situ characterization of zeolite crystallization. Herein, a microreactor was developed for use at the Beijing Synchrotron Radiation Facility (BSRF) to achieve the in-situ SAXS characterization of the nucleation and growth of zeolite crystallization. The results show that the fractal structure convert from surface fractal during induction nucleation to mass fractal during crystal growth. The surface fractal dimension first fluctuated slightly and increased rapidly, while the mass fractal dimension gradually increased, reflecting the particle growth. This work provides important information for further exploring zeolite crystallization.

Swarming Transition in Super-Diffusive Self-Propelled Particles.

A super-diffusive Vicsek model is introduced in this paper that incorporates Levy flights with exponent α. The inclusion of this feature leads to an increase in the fluctuations of the order parameter, ultimately resulting in the disorder phase becoming more dominant as α increases. The study finds that for α values close to two, the order-disorder transition is of the first order, while for small enough values of α, it shows degrees of similarities with the second-order phase transitions. The article formulates a mean field theory based on the growth of the swarmed clusters that accounts for the decrease in the transition point as α increases. The simulation results show that the order parameter exponent β, correlation length exponent ν, and susceptibility exponent γ remain constant when α is altered, satisfying a hyperscaling relation. The same happens for the mass fractal dimension, information dimension, and correlation dimension when α is far from two. The study reveals that the fractal dimension of the external perimeter of connected self-similar clusters conforms to the fractal dimension of Fortuin-Kasteleyn clusters of the two-dimensional Q=2 Potts (Ising) model. The critical exponents linked to the distribution function of global observables vary when α changes.

Dispersion Performances of Naphthalimides Doped in Dual Temperature- and pH-Sensitive Poly (N-Isopropylacrylamide-co-acrylic Acid) Shell Assembled with Vinyl-Modified Mesoporous SiO2 Core for Fluorescence Cell Imaging.

Developing effective intelligent nanocarriers is highly desirable for fluorescence imaging and therapeutic applications but remains challenging. Using a vinyl-grafted BMMs (bimodal mesoporous SiO2 materials) as a core and PAN ((2-aminoethyl)-6-(dimethylamino)-1H-benzo[de]isoquinoline-1,3(2H)-dione))-dispersed dual pH/thermal-sensitive poly(N-isopropylacrylamide-co-acrylic acid) as a shell, PAN@BMMs with strong fluorescence and good dispersibility were prepared. Their mesoporous features and physicochemical properties were extensively characterized via XRD patterns, N2 adsorption-desorption analysis, SEM/TEM images, TGA profiles, and FT-IR spectra. In particular, their mass fractal dimension (dm) features based on SAXS patterns combined with fluorescence spectra were successfully obtained to evaluate the uniformity of the fluorescence dispersions, showing that the dm values increased from 2.49 to 2.70 with an increase of the AN-additive amount from 0.05 to 1%, along with the red shifting of their fluorescent emission wavelength from 471 to 488 nm. The composite (PAN@BMMs-I-0.1) presented a densification trend and a slight decrease in peak (490 nm) intensity during the shrinking process. Its fluorescent decay profiles confirmed two fluorescence lifetimes of 3.59 and 10.62 ns. The low cytotoxicity obtained via in vitro cell survival assay and the efficient green imaging performed via HeLa cell internalization suggested that the smart PAN@BMM composites are potential carriers for in vivo imaging and therapy.

Melting of fractal snowflakes: Experiments and modeling

Numerical simulations of snow accretion on aircraft or weather phenomena require an accurate prediction of the melting of snowflakes. In the present study, an experimental setup for the investigation of snowflake melting is presented, which utilizes an acoustic levitator holding a snowflake in a warm airflow. Based on the experimental findings, a theoretical model for the melting process is developed. This theoretical model takes into account that the generated liquid water is driven into the porous ice structure by capillary forces and does not accumulate at the outer surface of the snowflake. This enables the use of a mass–size relationship in form of a power law, which is common in atmospheric sciences. The model prediction of the evolution of the maximum dimension during melting agrees well with the experiments. Moreover, the snowflake melting durations are also estimated well, if an accurate value is available for the particle mass fractal dimension, i.e., the exponent in the mass–size power law.

Anomalous small-angle X-ray scattering analyses on hierarchical structures of rubber-filler systems.

The hierarchical structures of poly(styrene-ran-butadiene) (SBR) rubber/carbon black (CB) systems vulcanized with sulfur and ZnO have been clarified using anomalous small-angle X-ray scattering (ASAXS) near the Zn absorption edge. In the case of SBR/CB systems vulcanized with peroxide, it has been found previously that the hierarchical structures formed by CB consist of aggregates of primary particles and agglomerates of those aggregates with mass-fractal dimensions. However, to date the hierarchical structures in SBR/CB systems vulcanized with sulfur and ZnO have not been well investigated, despite being commonly used. This is because the strong scattering contrast of Zn prevents the quantitative analyses of the hierarchical structures of CB using X-ray scattering. In this study, the effects of Zn on the scattering intensity were eliminated and the structure factors of CB in SBR/CB systems were obtained using the ASAXS method. By extrapolating to the zero volume fraction of CB, the particle structure factor of the CB aggregates was estimated and it was found that the CB aggregates consist of closely packed CB primary particles. The presence of large particles of ZnO and particles of ZnS on the order of 10 nm in size is confirmed.

Evaluation of Soil-Water Characteristic Curves for Different Textural Soils Using Fractal Analysis

The soil-water characteristic curve (SWCC) is an essential tool to determine hydraulic and mechanical properties of unsaturated soils. As an inherent influencing factor, soil texture controls the characteristics of SWCCs. Fractal theory can quantitatively describe the physical characteristics of soil. This study used particle size distribution data and water content data contained in the UNSODA2.0 database to explore the fractal characteristics of 12 soil types with different textures under different matrix suctions. The SWCC fractal model was adopted to characterize the hydraulic properties of soil with various soil textures. The findings revealed that the mass fractal dimensions of particles from these 12 different soil types significantly differed and were closely related to the clay content. Fractal dimension increased with increasing clay content. The fractal dimension established a good relationship between soil structure and hydraulic properties. Fractal analysis can be used to determine the connection between physical properties and soil hydraulic parameters. The estimated results of the SWCC fractal model indicated that it had a good performance regarding the description of SWCCs for the 12 soil textures. The soil structure could be described through fractal dimensions, which can effectively indicate soil hydraulic characteristics. The estimated fractal dimension of this model could be obtained by particle size distribution. Furthermore, using the SWCC fractal model, we found that the SWCC of coarse textured soil changed sharply in the low suction stage and its residual water content was small, and the SWCC of fine textured soil changed gently with a large residual water content. The water retention capacity followed the order clay > silty clay > sandy clay > clay loam > silty clay loam > sandy clay loam > loam > silt loam > sandy loam > silt > loamy sand > sand.

Dispersion Performances and Fluorescent Behaviors of Naphthalic Anhydride Doped in Poly(acrylic acid) Frameworks for pH-Sensitive Ibuprofen Delivery via Fractal Evolution.

The pH-responsive fluorescent P(1,8-naphthalic anhydride (NA)-acrylic acid (AA)) matrix was successfully prepared by a doping method using poly(acrylic acid) (PAA) as a pH-sensitive polymer and NA as a fluorescent tracer. The fluorescent behaviors of the used NA dispersed in PAA frameworks were demonstrated based on fractal features combined with various characterizations, such as small-angle X-ray scattering (SAXS) patterns, photoluminescence (PL) spectra, scanning electron microscope (SEM) images, thermogravimetry (TG) profiles, Fourier transform infrared (FT-IR) spectroscopy, and time-resolved decays. The effects of NA-doping on the representative fluorescent P(NA-AA) were investigated, in which the fluorescent performance of the doped NA was emphasized. The results indicated that aggregated clusters of the doped NA were gradually serious with an increase in NA doping amount or extension of NA doping time, accompanied by an increase in mass fractal dimension (Dm) values. Meanwhile, the doped NA presented stable fluorescent properties during the swelling-shrinking process of PAA. Ibuprofen (IBU) was used as a model drug, and fractal evolutions of the obtained P(NA-AA) along with the drug loading and releasing behaviors were evaluated via SAXS patterns, in which the drug-loaded P(NA-AA) presented surface fractal (Ds) characteristics, while the Dm value varied from 2.94 to 2.58 during sustained drug-release in pH 2.0, indicating occurrences of its structural transformation from dense to loose with extension of IBU-releasing time. Finally, the cytotoxicity and cellular uptake behaviors of the obtained P(NA-AA) were preliminarily explored. These demonstrations revealed that the resultant P(NA-AA) should be a potential intelligent-responsive drug carrier for targeted delivery.

Removing starch granule-associated surface lipids affects structure of heat-moisture treated hull-less barley starch

The effects of starch granule-associated surface lipids removal on hull-less barley starch structure formed by heat-moisture treatment were investigated. Removing surface lipids made the peak at 2θ of 13° disappear and resulted in higher lamellar peak intensity after harsh treatment and a lower reduction in mass fractal dimension (from 2.49 to 2.43) and radius of gyration (from 24.3 to 24.0) when temperature increased from 100 to 120 °C at 20 % moisture. Treatment at 25 % moisture and 120 °C decreased relative crystallinity (from 15.73 % to 7.43 %) and Gaussian peak area (from 646.7 to 137.7) of native starch, and decreased relative crystallinity (from 14.24 % to 12.56 %) and Gaussian peak area (from 604.1 to 539.6) for starch without surface lipids. Different trends of change in lamellar thickness, linear crystallinity, peak temperatures, and enthalpy of gelatinization were observed among modified starches with increasing temperature and/or moisture content. These results demonstrate that removing surface lipids changes structure of heat-moisture treated starch.

Characterization of Fragility in Silica-Based Ionogels

The present study examines the ionic conductivity and transport properties for ionic liquids confined within mesoporous materials. The fragility index was determined for several samples with varying microstructures and used to characterize performance as a pseudosolid electrolyte. The degree of microstructure complexity was characterized via the mass fractal dimension, which correlates with the fragility index in the pore size domain studied. We demonstrate for the materials studied here that the presence of the microporous matrix serves to inhibit ion mobility, and as the complexity of the matrix increases, the fragility index also increases, leading to lower conductivity materials. The microstructural features influencing conductivity were examined using Archie’s law when assuming the matrix conductivity to be negligible. This type of analysis, previously validated for rock matrices, has now been extended to pseudosolid electrolyte materials. The results indicate that ionogel samples can approach the conductivity of the unconfined ionic liquid. These conclusions are applicable to a variety of pseudosolid electrolyte systems and have important implications for the design of electrochemical devices.

Study on Energy Density Distribution and Mass Fractal of Deep Saturated Coal Samples under Uniaxial Stepwise High Stressed Loading and Unloading Path

The geostress in deep coal roadway is high and affected by mining frequently; under the influence of water-rock interaction, the bearing capacity of coal continues to deteriorate. Based on the characteristics of short water absorption process and low moisture content of deep coal samples in this experiment, the threshold range of quantitative division of water absorption stage of coal samples is given, and the structural characteristics of deep coal samples that are more susceptible to cracks are analyzed. The actual loading process is simulated through uniaxial stepwise high stressed loading and unloading experiments, the gradual development of cracks was the root cause of instability of coal, and saturated water mainly aggravates the instability process through these cracks; the stepwise high stressed loading and unloading path makes cracks more likely to occur in the sample. After each level of loading and unloading, the average stiffness is approximately linear trend degradation. By calculating the energy density of deep coal samples in each stage before the peak, the change of energy density indexes between saturated and dried samples is different from relative shallow samples, and the energy density indexes do not decrease but increases instead. However, the proportion of each energy is generally positive and inverted “U”-type distribution. The change trend of plastic energy in proportion to dissipation energy can be used as the judgment feature of coal sample instability. The instability of deep coal samples is mainly caused by the gradual dissipation of plastic energy to generate cracks and divided into fragments with large and long edge, resulting in low mass fractal dimension. In engineering practice, the loading times should be reduced and the suitable pressure grouting should be conducted timely to delay the deterioration process of crack development in deep water-bearing coal under high stress disturbance.

Structural heterogeneity of soil clods: Correlating Weibull parameters to fracture surface topography

Planes of weakness (i.e. cracks) existing in the soil matrix propagate, creating fracture surfaces and fragmenting the clod into smaller clods. The cracking process defines the fracture topography (i.e., roughness) that control many processes from flow exchange between macropore and matrix to local carbon storage and turnover. To date, useful relations between the surface topography of fractures and hydro-mechanical soil properties are missing because of technical and conceptual limitations. The objective was to test the assumption that the Weibull modulus of clod tensile strength can be related to the surface topography of fractures that resulted from the breakage of standardized soil clods. For carrying out standardized indirect tensile strength tests, a tension testing machine was constructed to prompt and monitor aggregate rupture. A total of 280 clods of 4 size-classes from two contrasting soils were considered. Clods were from the finer-textured Bt horizon of a Haplic Luvisol and the coarser-textured C horizon with lower amount of organic compounds of a Haplic Regosol. The natural clods were standardized in a cylindrical shape, in order to capture differences in the structural heterogeneity in terms of particle binding forces and porosity quantified by the Weibull modulus (m) of tensile strength. The stronger hierarchical organisation of the structure was quantified by smaller values of m (Bt: 3.1 vs C: 3.6) and the mass fractal dimension (Bt: 2.93 vs C: 2.98), and by higher values of the friability (m−1) (Bt: 0.14 vs C: 0.06). From these results, the random forest ensemble learning algorithm showed that the spatial heterogeneity of the organo-mineral pore coating (O-M) (shape factor of frequency distribution Bt: 0.58 vs C: 0.69), and not the organic carbon content (OC) (Bt: 0.48 vs C: 0.1 %), was the most important variable for predicting tensile strength (importance O-M: 0.21 vs OC: 0.09). Furthermore, the greater the spatial heterogeneity of the clod (m values ca. 1.4 for Bt) the lower the fracture surface roughness (ca. 1.8 µm2 µm−2) when compared to a more homogeneous clod (m values ca. 3.6, fracture surface roughness ca. 2.7 µm2 µm−2 for C). According to the random forest ensemble learning algorithm, porosity was the most important variable (variable importance 0.95) for predicting the rupture surface roughness followed by the spatial heterogeneity of the organo-mineral pore coatings, water content, and soil texture. Fracture surface roughness decreased when increasing porosity or decreasing the shape factor of the frequency distribution of organo-mineral coatings. Results confirmed that the Weibull modulus of clod tensile strength can be related with clod fracture surface roughness resulting from standardized clod breakage tests. This sheds light on the Weibull modulus as a distinct macro property for linking soil hydraulic and mechanical properties. This is of special importance in the parameterization of coupled models that combine the spatial heterogeneity of soil physical properties with the effects of hydrostatic forces on the soil structure.

Fractal Characteristics of Deep Shales in Southern China by Small-Angle Neutron Scattering and Low-Pressure Nitrogen Adsorption

The occurrence and flow of shale gas are substantially impacted by nanopore structures. The fractal dimension provides a new way to explore the pore structures of shale reservoirs. In this study, eight deep shale samples from Longmaxi Formation to Wufeng Formation in Southern Sichuan were selected to perform a series of analysis tests, which consisted of small-angle neutron scattering, low-pressure nitrogen adsorption, XRD diffraction, and large-scale scanning electron microscopy splicing. The elements that influence the shale fractal dimension were discussed from two levels of mineral composition and pore structures, and the relationship between the mass fractal dimension and surface fractal dimension was focused on during a comparative analysis. The results revealed that the deep shale samples both had mass fractal characteristics and surface fractal characteristics. The mass fractal dimension ranged from 2.499 to 2.991, whereas the surface fractal dimension ranged from 2.814 to 2.831. The mass fractal dimension was negatively correlated with the surface fractal dimension. The mass fractal dimension and the surface fractal dimension are controlled by organic matter pores, and their development degree significantly affects the fractal dimension. The mass fractal dimension increases with the decrease of a specific surface area and pore volume and increases with the increase of the average pore diameter. The permeability and surface fractal dimension are negatively correlated, but no significant correlation exists between the permeability and mass fractal dimension, and the internal reason is the dual control effect of organic matter on shale pores. This study comprehensively analyses the mass fractal characteristics and surface fractal characteristics, which helps in a better understanding of the pore structure and development characteristics of shale gas reservoirs.

Multi-scale structures and physicochemical properties of waxy starches from different botanical origins

The multi-scale structures and physicochemical relationships of three different types of waxy starches (maize, tapioca, and potato) were investigated. The maize and tapioca starches exhibited A-type crystalline polymorph compared to potato starch (B-type). The WMS showed higher amorphous content (5.56 %) than other waxy starches. The WTS exhibited a low tendency of retrogradation with its high fa (DP 6–12) and low fb3 (DP ≥ 37) proportion of chains. Double helix content of WPS was observed highest with a high pasting viscosity (952.3 BU). Low fa (DP 6–12) and high fb3 (DP ≥ 37) chain proportions of the WPS retrograded easily. The compactness of the semi-crystalline aggregation structure influenced the retrogradation properties of waxy starches with a positive correlation. Furthermore, the peak viscosity of pastes was correlated with the proportion of fb3 (DP ≥ 37) chains, mass fractal dimension, and double helix content. The results provide guidance to design the application of waxy starches in the production of clean-labels.

An improved pore-solid fractal model for predicting coastal saline soil hydraulic properties based on changepoints determined by genetic algorithm-support vector regression

Coastal soil is an important reserve land resource. The accurate prediction of soil hydraulic properties plays an important role in understanding the improvement of soil properties after reclamation in coastal areas. With the development of modern mathematical theory, the pore-solid fractal (PSF) model has become an important basis for simulating soil hydraulic properties. The accuracy of PSF model depends on the accurate acquisition of changepoints and fractal dimensions. Previous studies have found that micro-CT scanning combined with image processing could accurately obtain fractal dimensions. However, we still need soil water retention data to determine changepoints, which greatly limits the application of fractal models for estimating soil hydraulic properties. In this case, we determined the relationship between changepoints and soil physical and chemical properties and established a genetic algorithm-support vector regression (GA-SVR) model to predict changepoints. Then an improved PSF model was adopted to predict soil water retention curve in coastal areas of Jiangsu Province based on image processing. The results showed that soil physical and chemical properties changed the soil water movement and changepoints by affecting soil pore distribution. In coastal saline soil, four parameters (BD, silt, EC, SOM) were selected to predict changepoints. The mass fractal dimension (Dm) was mainly influenced by the porosity and the heterogeneity of pore space. The porosity, pore diameter and specific surface area were the determining factors of DS value. Reclamation activities in coastal reclamation area changed Dm value but had no clear effect on DS value. By combining predicted changepoints, measured water content at the suction of changepoints and fractal dimensions, the accuracy of the PSF model had been greatly improved.

Fractal Characteristics of the Seepage Erosion Process in Porous Soil

Seepage-induced erosion in porous soil has always been a major concern in the field of geofluids. Various fractal models have been built to theoretically investigate the porosity and permeability coefficient. However, the seepage erosion process (i.e., incubation, formation, evolution, and destruction) in porous soil is not clearly demonstrated to clarify the seepage fractal characteristics. In this paper, a series of hydraulic tests were performed to reveal the mass fractal characteristics of sandy gravels, coarse-grained sands, and fine-grained sands in the seepage erosion process. The results show that the mass fractal dimension was appropriate to describe the cumulative mass distribution of particles, the complexity of pore networks, and the dynamic changes of the seepage erosion process. Moreover, the scale-invariant interval, as an essential precondition for the accurate calculation of the mass fractal dimension, was to some extent affected by the average grain size and the fine content of porous soil. In particular, the changing trend of porosity and permeability coefficient with the mass fractal dimension was demonstrated in the seepage erosion process. Both porosity and permeability coefficients indicated an increasing trend as the development of seepage erosion. However, the mass fractal dimension gradually decreased due to the removal of fine particles induced by seepage flow water. Research findings will not only provide a new perspective on the seepage erosion mechanism but also predict the development of the seepage erosion process in engineering practice.

Pressure transient analysis for multi-wing fractured vertical well in coalbed methane reservoir based on fractal geometry and fractional calculus

In this paper, a semi-analytical mathematical model of pressure transient analysis (PTA) for multi-wing fractured vertical well (MWFV) in coalbed methane (CBM) reservoir is proposed, which considers the complexity of porous media by fractal geometry, the anomalous diffusion based on fractional calculus and the stress sensitivity represented by the exponential expression. Then through line source theory, dimensionless transformation, Pedrosa transformation, and other methods, the solution of the bottom hole pressure is obtained. At last, the PTA curve is presented by the Stehfest inversion method, and seven flowing regimes are identified. It can be observed that after introducing fractal geometry and fractional calculus, the PTA curve is quite different from the traditional curve in the slope of the derivative curve. The influences of related parameters are discussed, including mass fractal dimension, anomalous diffusion coefficient, number of hydraulic fractures, fracture angle, and stress sensitivity factor. Relevant results can provide better guidance to understand the CBM production performance in MWFV.

Effects of Biogas Slurry on Crop Yield, Physicochemical Properties and Aggregation Characteristics of Lime Concretion Soil in Wheat–Maize Rotation in the North China Plain

Biogas slurry is a potential sustainable substitute for chemical fertilizers and a soil amendment to restore soil organic matter depletion and structural deterioration. The effects of substituting biogas slurry for chemical fertilizer on a lime concretion soil in the North China Plain were investigated. A field experiment examined the consequences of applying different proportions (0, 25, 50, 75 and 100%) of biogas slurry, while maintaining the same total nitrogen supply, over a period of 5 years. We determined effects on crop yield (winter wheat/summer maize rotation), soil physiochemical properties and aggregation characteristics (using dry- and wet-sieving) in the last experimental year. All fertilizer treatments increased crop yield relative to a control. 50% substitution by biogas slurry gave the highest yield of wheat and maize. Increasing substitution progressively increased soil pH, water holding capacity, organic matter content, total nitrogen content, available phosphorus and potassium contents and C/N ratio; conversely, bulk density declined. Soil aggregate size distribution and stability were improved to varying degrees by biogas slurry substitution, in comparison with chemical fertilizer application alone and unamended control; optimal values for macro-aggregate mass proportion, fractal dimension and percentage of aggregate destruction were achieved with 50% substitution, coinciding with the highest crop yield. Lime concretion black soil was readily amenable to improvement by biogas slurry application, while maintaining optimal crop yields. Its use should be a priority for environmentally coordinated crop production and animal husbandry in this region.

Mass fractal dimension from 2D microscopy images via an aggregation model with variable compactness.

Microscopy-image analysis provides precious information on size and structure of colloidal aggregates and agglomerates. The structure of colloids is often characterized using the mass fractal dimension , which is different from the two-dimensional (2D) fractal dimension that can be computed from microscopy images. In this work, we propose to use a recent morphological aggregation model to find a relationship between 2D image fractal dimension and 3D mass fractal dimension of aggregates and agglomerates. Our case study is represented by scanning transmission electron microscopy images of boehmite colloidal suspensions. The behaviour of the computed at different acid and base concentration shows a fair agreement with the results of small angle x-ray scattering and with the literature, enabling to use the versus relationship to study the impact of the composition of the colloidal suspension on the density of colloidal aggregates andagglomerates.

A fractal physics-based data-driven model for water-flooding reservoir (FlowNet-fractal)

This paper proposed a fractal physics-based data-driven framework for reservoir simulation (name as FlowNet-fractal) by integrating physics-based data-driven model with fractal theory. FlowNet-fractal enables fast history matching and production prediction of water flooding reservoirs by considering the fractal characteristics of reservoir permeability and porosity. Details of FlowNet-fractal calculation were given with an oil-water two-phase flow example. In the FlowNet-fractal, transmissibility, control pore volumes (PVs), fractal mass dimension and fractal index were separately defined in each one-dimensional connection element to map reservoir properties, which more specifically reflected reservoir heterogeneity than the traditional FlowNet method. In this paper, an example of simple heterogeneous reservoir model and two actual water-flooding reservoir cases with different scales were given. The calculation results showed that the FlowNet-fractal method outperformed the FlowNet method in both the convergence speed and the accuracy of history matching. Moreover, the heterogeneity of the reservoir model was also defined by the inversed fractal mass dimension and the fractal index. • An integrated fractal-physics-based data-driven model and fractal theory are proposed in this research as the FlowNet-fractal framework for reservoir simulation. • The FlowNet-fractal approach beats the FlowNet method in terms of computing correctness, convergence speed, and historical matching effect. • Using the fractal mass dimension and fractal index, FlowNet-fractal may not only highlight reservoir heterogeneity but also significantly boost calculation rate.

Modification of the RLA model for presenting a cluster system of a composite material with a fractal filler structure

The paper proposes a modification of the diffusion-limited aggregation model to study the properties of a cluster system. A computational experiment to determine the mutual influence of the sticking probability and the volume concentration of particles on the formation of fractal clusters in a cluster system was carried out in accordance with the second-order orthogonal central compositional plan (OCCP). As a result of a computational experiment in accordance with the OCCP, an equation was obtained for the dependence of the mass fractal dimension of clusters on the volume of particle concentration and the probability of adhesion of diffusing particles and cluster particles in the adhesion zone. This dependence was obtained in a range of volume concentration of particles from 2 to 5 % and the probability of adhesion of diffusing particles and particles of clusters in the adhesion zone from 0.2 to 1.