Diffusion Limited Aggregation Algorithm Research Articles

Research on the Model Improvement of a DLA Fractal River Network

Computer simulations are introduced into the river dynamics field to provide a basis for studying fractal river networks. This paper improved on the defects of particle aggregation and growth methods in the standard diffusion-limited aggregation (DLA) model and proposed a fractal algorithm for simulating the evolution of the river network. To correct these defects, this model used watershed geomorphology as the entry point and analyzed the characteristics of runoff classification, aspect probability and contour lines. Thus, the unit-gradient growth calculation method, anisotropic Brownian motion and other related parameter optimization mechanisms (such as probability-position and step size) were established. In addition, the 2D fractal river network was simulated under different conditions. These simulations calculated the bifurcation ratio of the rendering based on Horton's law, and its value was bounded between the values of natural river channels (3 ~ 5). The standard DLA algorithm was used for simulation, but the bifurcation ratio (±5.2) of the aggregate was higher than the value of the natural river network. Therefore, the improved model can reflect the structural characteristics of the river network more realistically based on quantitative indicators. The evolution mechanism of the natural watershed was evaluated by the cyber-physical systems theory, providing a model base to study the growth and evolution of river networks. The fractal dimension of the water system fitted with each simulated subgraph was based on the box counting method. The value boundary was between 1.457 and 1.747, providing a division standard for the development degree of the watershed geomorphology. Further, according to the relationship between the number of particles and the fractal dimension, the sensitivity test of the model was also analyzed and evaluated, and its sensitivity coefficient gradually increased from 2.75 to 8.38 based on a suitable data-set, which will make the predicted watershed water system closer to its development level. Finally, use of the improved DLA model was suggested for modeling river networks.

Lift Off and Breakage of the Structure of Fractal - Like Aggregate

A new mathematical model of aggregate of N identical spherical particles is proposed. Model is able to simulate aggregates with different flexibility. Mutual forces in normal direction between primary particles are described by spring-mass system with parameters related to the material properties. The flexibility of aggregate structure is controlled by harmonic interaction functions. Developed model was used to study the lift-off phenomenon of aggregates in the fluid. Simulation were performed for numerically generated few population of fractal-like aggregates by Diffusion Limited Aggregation algorithm (DLA), which differ with number of primary particles in aggregate’s structure and fractal dimension. Numerical results show that aggregates with more open morphology with fractal dimension in the range of Df = 1.6 - 1.8 are lifted-off easier, compared to aggregates with compacted structure. The effectiveness of the lift off is enhanced by the deformation of the aggregate caused by the flexibility of its structure.

Ultraviolet scattering properties of alumina particle clusters at three phase states in aircraft plume

We simulate the clusters of alumina particles using the parallel diffusion limited aggregation algorithm (DLA), and solve the scattering matrixes of the alumina particles in different phase states (alpha phase, gamma phase and liquid) through the multiple sphere T matrix method in UV. The effect of the number of monomers, fractal dimension and incident wavelength to the scattering phase function of the clusters of alumina particles is discussed. The results show that the different of the number of monomers, fractal dimensions and incident wavelengths have significant effect on the scattering properties of the clustered alumina particle. The researchers used to make the alumina particle equivalent to the alpha phase spherical particle, but it is too simplistic. We compare the scattering phase functions of the equivalent volume sphere (EVS), the equivalent surface sphere (ESS) and the clusters of alumina particles in three kinds of phase states. The results show that the backward scattering would be overestimated if the alumina particle is equivalent to the alpha phase spherical particle. Accurate phase function calculation in different phase states is very helpful to study the radiation propagation characteristics of aircraft plume.

Aggregation and dendritic growth in a magnetic granular system

We experimentally study the aggregation of non-Brownian paramagnetic beads in a vibrofluidized system induced by an external magnetic dipole. A dendritic growth is observed in real time, particle by particle, and with the naked eye. Two aggregation stages are observed, where tip, tip-split and side-branching growths are differentiated. We found clusters morphologically similar to those generated by a diffusion limited aggregation algorithm (DLA). However, in our case, due to the finite range of the magnetic field, the clusters reach a finite size and their structures exhibit different rates of aggregation. These are revealed by the existence of two different scaling relations of the mass with the gyration radius, and the nature of the radial mass distribution function. The structures of the clusters are fractal objects with an effective mass fractal dimension of around 1.8. We found that an exponential function describes the aggregation phenomenon as a function of time. This exponential behavior is independent of the final state of the morphology (shape and length) of the agglomerates.

English

The formation mechanism of the growth of bacterial colony is studied by comparing the formation of the bacteria with the patterns obtained by Monte Carlo simulations using the diffusion limited aggregation algorithm. For this purpose, the morphological changes of the growing patterns are controlled by a sticking probability parameter, α, which represents the trajectories of the particles joining to the growing colonies, the complex reactions, and biological dynamics such as concentration of nutrient, temperature, and humidity in the growing environment. Specially, the sticking probability parameter is related to the biological activation and irreversible growth of the bacteria via growth energy for the mobility in the environment and perimeters of the colonies. Morphologies of the aggregation of the bacterial colonies have irregular, fractal, and compact structures. In this study, first, fractal dimensions are assessed for simulations and the real systems. The density of bacteria as ρ in region defined by circle of radius r centered at initial dropping seed from center through the perimeter is computed by using scaling method.  Second, critical exponents of patterns are calculated.  As a function of r, ρ reaches the asymptotic ρ0 (α) following power-law `r = r0 + Ar­­­ – g with universal exponents γ = 0.47 for α = 1. The value of the main density for the bacterial patterns has ρ0 ~ α – β, where β = 0.32 according to the scaling theory. Finally, the results obtained are found in good agreement with the experiments and can be useful for the researchers studying about bacterial colonization patterns.   Key words: Monte Carlo simulation, diffusion limited aggregation, sticking probability parameter, critical exponent, bacterial colony formation.

The single scattering properties of the aerosol particles as aggregated spheres

The light scattering and absorption properties of anthropogenic aerosol particles such as soot aggregates are complicated in the temporal and spatial distribution, which introduce uncertainty of radiative forcing on global climate change. In order to study the single scattering properties of anthorpogenic aerosol particles, the structures of these aerosols such as soot paticles and soot-containing mixtures with the sulfate or organic matter, are simulated using the parallel diffusion limited aggregation algorithm (DLA) based on the transmission electron microscope images (TEM). Then, the single scattering properties of randomly oriented aerosols, such as scattering matrix, single scattering albedo (SSA), and asymmetry parameter (AP), are computed using the superposition T-matrix method. The comparisons of the single scattering properties of these specific types of clusters with different morphological and chemical factors such as fractal parameters, aspect ratio, monomer radius, mixture mode and refractive index, indicate that these different impact factors can respectively generate the significant influences on the single scattering properties of these aerosols. The results show that aspect ratio of circumscribed shape has relatively small effect on single scattering properties, for both differences of SSA and AP are less than 0.1. However, mixture modes of soot clusters with larger sulfate particles have remarkably important effects on the scattering and absorption properties of aggregated spheres, and SSA of those soot-containing mixtures are increased in proportion to the ratio of larger weakly absorbing attachments. Therefore, these complex aerosols come from man made pollution cannot be neglected in the aerosol retrievals. The study of the single scattering properties on these kinds of aggregated spheres is important and helpful in remote sensing observations and atmospheric radiation balance computations.

Measuring neuronal branching patterns using model-based approach

Neurons have complex branching systems which allow them to communicate with thousands of other neurons. Thus understanding neuronal geometry is clearly important for determining connectivity within the network and how this shapes neuronal function. One of the difficulties in uncovering relationships between neuronal shape and its function is the problem of quantifying complex neuronal geometry. Even by using multiple measures such as: dendritic length, distribution of segments, direction of branches, etc, a description of three dimensional neuronal embedding remains incomplete. To help alleviate this problem, here we propose a new measure, a shape diffusiveness index (SDI), to quantify spatial relations between branches at the local and global scale. It was shown that growth of neuronal trees can be modeled by using diffusion limited aggregation (DLA) process. By measuring “how easy” it is to reproduce the analyzed shape by using the DLA algorithm it can be measured how “diffusive” is that shape. Intuitively, “diffusiveness” measures how tree-like is a given shape. For example shapes like an oak tree will have high values of SDI. This measure is capturing an important feature of dendritic tree geometry, which is difficult to assess with other measures. This approach also presents a paradigm shift from well-defined deterministic measures to model-based measures, which estimate how well a model with specific properties can account for features of analyzed shape.

Centric diatom morphogenesis: a model based on a DLA algorithm investigating the potential role of microtubules

Diatoms are single-celled algae which possess characteristic rigid cell walls (frustules) composed of amorphous silica. Frustule formation occurs within a specialised organelle termed the silica deposition vesicle (SDV). During diatom morphogenesis, silica particles are transported to the SDV by silica transport vesicles. Once released within the SDV, the particles are then thought to diffuse until they encounter part of the growing aggregate upon which they adhere. The particles may then undergo a further period of surface relocalisation (sintering) which leads to a smoothing of the surface. A number of computer simulations based on a modified diffusion-limited aggregation (DLA) algorithm, have been undertaken to investigate the potential role of microtubules (which are known to be associated with the periphery of the SDV) in localising deposition of new siliceous material. Based on our findings, we present a new model of diatom morphogenesis which is able to account for many morphological features of diatoms including the influence of environmental effects such as changes in pH and salinity, and the formation of a regular branched pattern.

Growth model of Au films on Ru (001)

In an attempt to find generic features of the fractal growth of Au films deposited on Ru (001), a simple simulation model based on irreversible diffusion-limited aggregation (DLA) is discussed. Highly irregular two-dimensional dendritic islands of Au particles that gradually grow on a larger host lattice of Ru particles and have fractal dimension d f≈1.70 each, are generated via a multiple ad-hoc version of the DLA algorithm for single aggregates. Annealing effects on the island morphology are reproduced assuming different sticking probabilities at nearest-neighbour lattice sites of Au films on Ru(001). Using simulation data, growth of islands is described in analogy to diffusion-limited, precipitate growth with a soft impingement of precipities. This leads one to analyse thin film island growth kinetics in such fractal systems and to predict a main peak in the scattering intensity patterns due to inter-island interference.