Concentration Influence on Diffusion Limited Cluster Aggregation

1994 ◽  
Vol 367 ◽  
Author(s):  
ST.C. Pencea ◽  
M. Dumitrascu
Keyword(s):  
Brownian Motion ◽  
Fractal Dimensions ◽  
Simple Random Walk ◽  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Dimensional Lattice ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Diffusion Limited ◽  
Diffusion Limited Cluster Aggregation

AbstractDiffusion-limited cluster aggregation has been simulated on a square two dimensional lattice. In order to simulate the brownian motion, we used both the algorithm proposed initially by Kolb et all. and a new algorithm intermediary between a simple random walk and the ballistic model.The simulation was performed for many values of the concentration, from 1 to 50%. By using a box-counting algorithm one has calculated the fractal dimensions of the obtained clusters. Its increasing vs. concentration has been pointed out. The results were compared with those of the classical diffusion-limited aggregation (DLA).

Simulation of Fractal-Like Crystal Growth

1991 ◽  
Vol 46 (1-2) ◽  
pp. 203-205
Author(s):  
Attila Felinger ◽  
Jänos Liszi
Keyword(s):  
Crystal Growth ◽  
Fractal Dimensions ◽  
Stochastic Method ◽  
Square Lattice ◽  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Equilibrium Crystallization ◽  
Diffusion Limited ◽  
Large Clusters ◽  
Small Clusters

AbstractNon-equilibrium crystallization was simulated on a two dimensional square lattice. Several clusters were grown simultaneously by using the model of diffusion limited aggregation. The growing process was reversible, i.e. dissolution of particles from the boundary of any cluster was made possible. The rate of growth and dissolution was determined by a stochastic method. The simulation resulted in an aggregate pattern having a few large and several small clusters. The fractal dimensions of the large clusters were found in the range of D = 1.62-1.72.

The Simulation of the Two-Dimensional Ising Model on the Creutz Cellular Automaton for the Fractals Obtained by Using the Model of Diffusion-Limited Aggregation

2010 ◽  
Vol 65 (8-9) ◽  
pp. 705-710 ◽  
Author(s):  
Ziya Merdan ◽  
Mehmet Bayirli ◽  
Mustafa Kemal Ozturk
Keyword(s):  
Cellular Automaton ◽  
Finite Size ◽  
Fractal Dimensions ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Linear Dimensions ◽  
Creutz Cellular Automaton ◽  
Good Agreement

The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for the lattice with L = 80, 120, and 160. The values of the fractal dimensions are compared with the results of former studies. As increasing the linear dimensions they are in good agreement with those. The fractals obtained by using the model of DLA are simulated on the Creutz cellular automaton by using a two-bit demon. The values computed for the critical temperature and the static critical exponents within the framework of the finite-size scaling theory are in agreement with the results of other simulations and theoretical values

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

Aggregation Characteristics of Cu and Ag Nanoparticles in Presence of Starch as the Polymer Stabilizer

2010 ◽  
Vol 123-125 ◽  
pp. 615-618 ◽  
Author(s):  
Indrajit Sinha ◽  
Manjeet Singh ◽  
Rajiv Kumar Mandal
Keyword(s):  
Small Molecule ◽  
Ag Nanoparticles ◽  
Growth Models ◽  
Chemical Reduction ◽  
Cluster Aggregation ◽  
Diffusion Limited ◽  
X Ray Scattering ◽  
Polymer Stabilizer ◽  
Aqueous Conditions ◽  
Diffusion Limited Cluster Aggregation

This presentation deals with the aggregation characteristics of Cu and Ag nanoparticles in presence of starch as the polymer stabilizer. Uncontrolled aggregation of the destabilized nanoparticles offers problem for applications based on surface plasmon activity. Polymer or small molecule surfactants are used to control nature of aggregation of nanoparticles produced by chemical reduction synthesis routes. Different growth models such as diffusion limited cluster aggregation (DLCA), reaction limited cluster aggregation (RLCA) proposed to explain the formation of fractal colloidal aggregates do not account for aggregate formation in presence of polymer or small molecule surfactants. We shall be discussing the role of starch on the aggregation characteristics of copper and silver nanoparticles formed by chemical reduction in aqueous conditions. The effect of NaOH concentration and consequently the pH on such aggregation kinetics during such synthesis is delineated. We use small angle x-ray scattering (SAXS) to quantitatively understand different aspects of aggregation behavior.

scholarly journals Diamond aggregation

2010 ◽  
Vol 149 (2) ◽  
pp. 351-372
Author(s):  
WOUTER KAGER ◽  
LIONEL LEVINE
Keyword(s):  
Random Walk ◽  
Growth Model ◽  
Power Law ◽  
Simple Random Walk ◽  
Internal Diffusion ◽  
Diffusion Limited Aggregation ◽  
Directional Bias ◽  
Model Based ◽  
Diffusion Limited ◽  
Logarithmic Fluctuations

AbstractInternal diffusion-limited aggregation is a growth model based on random walk in ℤd. We study how the shape of the aggregate depends on the law of the underlying walk, focusing on a family of walks in ℤ2 for which the limiting shape is a diamond. Certain of these walks—those with a directional bias toward the origin—have at most logarithmic fluctuations around the limiting shape. This contrasts with the simple random walk, where the limiting shape is a disk and the best known bound on the fluctuations, due to Lawler, is a power law. Our walks enjoy a uniform layering property which simplifies many of the proofs.

Two-dimensional fractal growth by diffusion limited aggregation of copper

1989 ◽  
Vol 140 (4) ◽  
pp. 193-196 ◽  
Author(s):  
A.S. Paranjpe ◽  
Sandhya Bhakay-Tamhane ◽  
M.B. Vasan
Keyword(s):  
Two Dimensional ◽  
Diffusion Limited Aggregation ◽  
Fractal Growth ◽  
Diffusion Limited

Morphogenesis of the bone marrow: fractal structures and diffusion- limited growth

Blood ◽  
1996 ◽  
Vol 87 (12) ◽  
pp. 5027-5031 ◽  
Author(s):  
F Naeim ◽  
F Moatamed ◽  
M Sahimi
Keyword(s):  
Bone Marrow ◽  
Spatial Organization ◽  
Fractal Dimensions ◽  
Fractal Structures ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Morphometric Analyses ◽  
Cellular Area ◽  
Pathologic Processes

Bone marrow (BM) provides a particular spatial organization that allows interaction between its various components. Characterization of the spatial patterns in the BM and understanding the mechanisms that give rise to them may play a role in better understanding of the BM pathologic processes. Morphometric analyses were performed in BM biopsy samples from 30 patients (16 men and 14 women) with an average age of 46 years, ranging from 17 to 77 years. The biopsies were obtained during the course of patient care to rule out BM involvement in a variety of hematologic disorders before or after therapy. Three different, but structurally interrelated, parameters were measured: (A) cellular area, (B) nuclear area, and (C) cell numbers. All three methods, in all cases, showed that the spatial structure of the BM is fractal. The average values of the fractal dimensions (Df) were 1.7 +/- 0.08, 1.64 +/- 0.1, and 1.69 +/- 0.04 for categories A, B, and C, respectively. The overall value of Df for the cellularity in the range of 40% to 60% was about 1.67 +/- 0.09. Fractal dimensions of 1.6 to 1.7 represent configurations that correspond to two-dimensional diffusion limited aggregation structures, suggesting that the structural configuration of hematopoietic cells is dependent on the diffusion of regulatory cytokines in the BM.

scholarly journals Projection of compact fractal sets: application to diffusion-limited and cluster-cluster aggregates

2008 ◽  
Vol 15 (4) ◽  
pp. 695-699 ◽  
Author(s):  
F. Maggi
Keyword(s):  
Fractal Dimension ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Cohesive Sediment ◽  
Mathematical Approach ◽  
Two Dimensional ◽  
Atmospheric Sciences ◽  
Practical Applications ◽  
Fractal Sets ◽  
Diffusion Limited

Abstract. The need to assess the three-dimensional fractal dimension of fractal aggregates from the fractal dimension of two-dimensional projections is very frequent in geophysics, soil, and atmospheric sciences. However, a generally valid approach to relate the two- and three-dimensional fractal dimensions is missing, thus questioning the accuracy of the method used until now in practical applications. A mathematical approach developed for application to suspended aggregates made of cohesive sediment is investigated and applied here more generally to Diffusion-Limited Aggregates (DLA) and Cluster-Cluster Aggregates (CCA), showing higher accuracy in determining the three-dimensional fractal dimension compared to the method currently used.

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