A Numerical Study for the Relationship between Natural Manganese Dendrites and DLA Patterns

2016 ◽  
Vol 71 (3) ◽  
pp. 225-234
Author(s):  
Tugba Ozbey ◽  
Mehmet Bayirli
Keyword(s):  
Critical Exponent ◽  
Numerical Study ◽  
Formation Mechanisms ◽  
Diffusion Limited Aggregation ◽  
Density Correlation ◽  
Diffusion Limited ◽  
Crystalline Anisotropy ◽  
The Relationship ◽  
Good Agreement ◽  
Dla Model

AbstractThe formation mechanisms and the origin of manganese dendrites on the magnesite ore have been under discussion. The growth process of the manganese dendrites is statistically studied by comparing them to aggregations obtained according to the diffusion limited aggregation (DLA) model via Monte Carlo simulations. In this case, ten manganese dendrite patterns changing from the least dense to the densest aggregations on the surface are separately selected to determine the relationship between real and simulated patterns. The sticking parameter is ranged from 0.05≤t≤1. The density–density correlation functions C(r) (their critical exponent A), fractal dimension Df, critical exponent α, and critical exponent β pertaining to the root mean square (rms) thickness have been computed for both the ten manganese dendrites and the simulated aggregations representing them. The results indicate that manganese dendrites may be determined with the general DLA model. Analyses of manganese dendrites, both scaling and simulations, suggest the growth mechanism for the macroscopic expression of crystalline anisotropy for the dendritic patterns. These results are in good agreement with the values in other literature and can be helpful in comparing natural and simulated aggregations (both dendritic and compact deposits).

DIFFUSION-LIMITED AGGREGATION IN LAMINAR FLOWS

2003 ◽  
Vol 14 (09) ◽  
pp. 1171-1182 ◽  
Author(s):  
R. M. H. MERKS ◽  
A. G. HOEKSTRA ◽  
J. A. KAANDORP ◽  
P. M. A. SLOOT
Keyword(s):  
Flow Direction ◽  
Cluster Structure ◽  
Three Dimensional ◽  
Laminar Flows ◽  
Diffusion Field ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Advection Diffusion ◽  
Multiple Particles ◽  
Dla Model

In the diffusion-limited aggregation (DLA) model, pioneered by Witten and Sander (Phys. Rev. Lett.47, 1400 (1981)), diffusing particles irreversibly attach to a growing cluster which is initiated with a single solid seed. This process generates clusters with a branched morphology. Advection–diffusion-limited aggregation (ADLA) is a straightforward extension to this model, where the transport of the aggregating particles not only depends on diffusion, but also on a fluid flow. The authors studying two-dimensional and three-dimensional ADLA in laminar flows reported that clusters grow preferentially against the flow direction. The internal structure of the clusters was mostly reported to remain unaffected, except by Kaandorp et al. (Phys. Rev. Lett.77, 2328 (1996)) who found compact clusters "as the flow becomes more important". In the present paper we present three-dimensional simulations of ADLA. We did not find significant effects of low Reynolds-number advection on the cluster structure. The contradicting results by Kaandorp et al. (1996) were recovered only when the relaxation into equilibrium of the advection–diffusion field was too slow, in combination with the synchronous addition of multiple particles.

Fractal Diffusion Limited Aggregation of Soot Particles Based on Fuzzy Membership Functions

2019 ◽  
Vol 29 (05) ◽  
pp. 1950073 ◽  
Author(s):  
Jie Sun ◽  
Wei Qiao ◽  
Shuai Liu
Keyword(s):  
Fuzzy Systems ◽  
Soot Particle ◽  
Membership Functions ◽  
Engine Emissions ◽  
Diffusion Limited Aggregation ◽  
Soot Particles ◽  
Fuzzy Membership Functions ◽  
Diffusion Limited ◽  
Particle Aggregates ◽  
Dla Model

In this paper, the membership function in fuzzy systems is used in the Diffusion Limited Aggregation (DLA) model to investigate the fractal diffusion of soot particles from diesel engine emissions. The transformation of the morphology of soot particle aggregates and the control of fractal diffusion of soot particles are investigated by analyzing the nonlinear relationship between the motion steps and angles of diffusing particles. The simulation results demonstrate that the morphology of the aggregates varies from loose to compact by changing the particles’ motion steps and angles in membership functions. Meanwhile, the Ballistic Aggregation (BA)-like aggregates are obtained. Furthermore, the control of the morphology of soot particle aggregates is realized, which makes the settlement of the aggregates become easier. This will provide a reference for further understanding the growth mechanism of soot particle diffusion and enhancing the purification technology of the soot particles.

Thin film growth by single and multi-center DLA model: Fractal analysis

2021 ◽  
pp. 2150162
Author(s):  
Xun Zhou ◽  
Min Zhang ◽  
Chaoyong Deng
Keyword(s):  
Fractal Analysis ◽  
Film Growth ◽  
Growth Direction ◽  
Diffusion Limited Aggregation ◽  
Fractal Growth ◽  
Diffusion Limited ◽  
Internal Interaction ◽  
One Step ◽  
Dla Model ◽  
Number Of Particles

A modified Diffusion Limited Aggregation (DLA) model has been established for single and multi-center fractal growth. Number of particles [Formula: see text], size of one step [Formula: see text], deposition probability [Formula: see text], growth direction, and interaction effect are had been take into consideration for fractal analysis. In addition, the effect of internal interaction in multi-center growth have been taken into consideration. Fractal growth morphology shows strong boundary and interaction effects.

Insights into the Formation Process of the Retinal Vasculature

Fractals ◽  
1997 ◽  
Vol 05 (04) ◽  
pp. 615-624 ◽  
Author(s):  
S. Kyriacos ◽  
F. Nekka ◽  
L. Cartilier ◽  
P. Vico
Keyword(s):  
Structural Characteristic ◽  
Fractal Analysis ◽  
Formation Process ◽  
Natural Sciences ◽  
Retinal Vasculature ◽  
Formation Processes ◽  
Diffusion Limited Aggregation ◽  
Theoretical Approaches ◽  
Diffusion Limited ◽  
Dla Model

Growth phenomena have been studied extensively in natural sciences. This interest has been renewed since the introduction of the fractal concept. In an attempt to understand the origin of irregular phenomena, several computer models and theoretical approaches have recently been developed. Studies using fractal analysis of the retinovasculature have proposed diffusion-limited aggregation (DLA) one of the most popular models to explain the formation of the retina. A deeper investigation of the physiological laws ruling the development of the retinovasculature has, however, revealed static and dynamic discrepancies with DLA, leading to rejection of the DLA model, and reopening the debate. In light of comparison of the two formation processes and of the absence of a DLA structural characteristic in retinovasculature, we discuss the validity of some previously proposed models.

CONTACT PROCESS ON FRACTAL CLUSTERS SIMULATED BY GENERALIZED DIFFUSION-LIMITED AGGREGATION (g-DLA) MODEL

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050137
Author(s):  
ASHWINI V. MAHAJAN ◽  
ABHAY V. LIMAYE ◽  
ARUN G. BANPURKAR ◽  
PRASHANT M. GADE
Keyword(s):  
Nearest Neighbor ◽  
Local Density ◽  
Contact Process ◽  
Universality Class ◽  
Active Phase ◽  
Diffusion Limited Aggregation ◽  
Remote Areas ◽  
Fractal Clusters ◽  
Diffusion Limited ◽  
Dla Model

The spread of infectious disease, virus epidemic, fashion, religion and rumors is strongly affected by the nearest neighbor hence underlying morphologies of the colonies are crucial. Likewise, the morphology of naturally grown patterns ranges from fractal to compact with lacunarity. We analyze the contact process on the fractal clusters simulated by generalized Diffusion-limited Aggregation (g-DLA) model. In g-DLA model, randomly walking particle is added to the cluster with sticking probability [Formula: see text] depending on the local density of occupied sites in the neighborhood of radius [Formula: see text] from the center of active site. It takes values [Formula: see text], [Formula: see text] and [Formula: see text] ([Formula: see text]) for highly dense, moderately dense and sparsely occupied regions, respectively. The corresponding morphology varies from fractal to compact as [Formula: see text] varies from [Formula: see text] to [Formula: see text]. Interestingly, the contact process on the g-DLA clusters shows clear transition from active phase to absorbing phase and the exponent values fall between 1-d and 2-d in directed percolation (DP) universality class. The local persistence exponents at transition are studied and are found to be much smaller than that for 1-d and 2-d DP cases. We conjecture that infection in the fractal cluster does not easily reach far-flung or remote areas at the periphery of the cluster.

Study on fractal and island growth processes of thin films with a modified DLA model

2019 ◽  
Vol 33 (35) ◽  
pp. 1950441
Author(s):  
Min Zhang ◽  
Xun Zhou ◽  
Chaoyong Deng
Keyword(s):  
Particle Number ◽  
Three Dimensional ◽  
Transformation Process ◽  
Island Growth ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Number Formula ◽  
Dla Model ◽  
2D To 3D ◽  
Number Of Particles

A modified diffusion-limited aggregation (DLA) model for two-dimensional (2D), three-dimensional (3D) fractal growth and 3D island growth was established based on the DLA model in this paper. The number of particles [Formula: see text] and the size of the box size [Formula: see text] (related to side length [Formula: see text]), which are related to film thickness, are considered in the study. The simulation results are a good reflection of the actual experimental results. The results show that the particle number and simulation box size can affect the fractal morphology and fractal dimension of the film, and also the 2D to 3D transformation. In addition, the critical particle number [Formula: see text] and the critical box size [Formula: see text] during the transformation process are also given.

Numerical Study of Turbulent Flows Through a Circular Duct With a Rotating Fan

2009 ◽  
Author(s):  
Gaurav Rajwade ◽  
Jie Cui
Keyword(s):  
Turbulent Flows ◽  
Numerical Study ◽  
Pressure Rise ◽  
Flow Conditions ◽  
Circular Duct ◽  
Flow Information ◽  
Computational Fluid Dynamics Cfd ◽  
Air Circulation ◽  
The Relationship ◽  
Good Agreement

A fan is an important part for air circulation in household appliances and automobiles. In this research an attempt has been made to extract the flow information using the Computational Fluid Dynamics (CFD) technique. The numerical results were found for a case with a stationary fan inside the duct and the data obtained were in good agreement with the experiment. The evolution of velocity profiles at various axial locations for different flow conditions were also studied in this research. The numerical method was then extended to the cases with a rotating fan. A proof-of-concept run was also successfully carried out to showe the relationship between air flow rate in the duct and the corresponding pressure rise.

DIFFUSION-LIMITED AGGREGATION DRIVEN BY OPTIMAL TRANSPORTATION

Fractals ◽  
2010 ◽  
Vol 18 (02) ◽  
pp. 247-253 ◽  
Author(s):  
QINGLAN XIA ◽  
DOUGLAS UNGER
Keyword(s):  
Transition Point ◽  
Full Range ◽  
Phase Transition Point ◽  
Optimal Transportation ◽  
Transport Cost ◽  
Diffusion Limited Aggregation ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Final Cluster ◽  
Dla Model

In this article, we combine the DLA model of Witten and Sander with ideas from ramified optimal transportation. We propose a modification of the DLA model in which the probability of sticking is inversely proportional to the additional transport cost from the point to the root. We used a family of cost functions parameterized by a parameter α as studied in ramified optimal transportation. α < 0 promotes growth near the root whereas α > 0 promotes growth at the tips of the cluster. α = 0 is a phase transition point and corresponds to standard DLA. What makes this model interesting is that when α is negative enough (e.g. α < -2) the final cluster is an one-dimensional curve. On the other hand, when α is positive enough (e.g. α > 2) we get a nearly two dimensional disk. Thus our model encompasses the full range of fractal dimension from 1 to 2.

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

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