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.

scholarly journals One-dimensional long-range diffusion-limited aggregation I

2016 ◽  
Vol 44 (5) ◽  
pp. 3546-3579 ◽  
Author(s):  
Gideon Amir ◽  
Omer Angel ◽  
Itai Benjamini ◽  
Gady Kozma
Keyword(s):  
Long Range ◽  
Diffusion Limited Aggregation ◽  
One Dimensional ◽  
Diffusion Limited

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.

The Geometry of Dla: Different Aspects of the Departure from Self-Similarity

1994 ◽  
Vol 367 ◽  
Author(s):  
B.B. Mandelbrot ◽  
A. Vespignani ◽  
H. Kaufman
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Properties ◽  
Finite Size ◽  
Scaling Behavior ◽  
Self Similarity ◽  
Diffusion Limited Aggregation ◽  
One Dimensional ◽  
Diffusion Limited ◽  
Large Numbers ◽  
The One

AbstractIn order to understand better the morphology and the asymptotic behavior in Diffusion Limited Aggregation (DLA), we studied a large numbers of very large off-lattice circular clusters. We inspected both dynamical and geometric asymptotic properties, namely the moments of the particle's sticking distances and the scaling behavior of the transverse growth crosscuts, i.e., the one dimensional cuts by circles. The emerging picture for radial DLA departs from simple self-similarity for any finite size. It corresponds qualitatively to the scenario of infinite drift starting from the familiar five armed shape for small sizes and proceeding to an increasingly tight multi-armed shape. We show quantitatively how the lacunarity of circular clusters becomes increasingly “compact” with size. Finally, we find agreement among transverse cuts dimensions for clusters grown in different geometries, suggesting that the question of universality is best addressed on the crosscut.

scholarly journals Single-particle entanglement of the entanglement Hamiltonian eigenmodes

2018 ◽  
Vol 33 (16) ◽  
pp. 1850085 ◽  
Author(s):  
Mohammad Pouranvari
Keyword(s):  
Phase Transition ◽  
Single Particle ◽  
Transition Point ◽  
Numerical Study ◽  
Entanglement Entropy ◽  
Phase Transition Point ◽  
Free Fermion ◽  
Phase Detection ◽  
One Dimensional ◽  
Free Fermion Model

Single-particle entanglement entropy (SPEE) is calculated for entanglement Hamiltonian eigenmode in a one-dimensional free fermion model that undergoes a delocalized–localized phase transition. In this numerical study, we show that SPEE of entanglement Hamiltonian eigenmode has the same behavior as SPEE of Hamiltonian eigenmode at the Fermi level: as we go from delocalized phase toward localized phase, SPEE of both modes decrease in the same manner. Furthermore, fluctuations of SPEE of entanglement Hamiltonian eigenmode — which can be obtained through the calculation of moments of SPEE — signature very sharply the phase transition point. These two modes are also compared by calculation of single-particle Rényi entropy (SPRE). We show that SPEE and SPRE of entanglement Hamiltonian eigenmode can be used as phase detection parameters.

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