Diffusion-limited-aggregation model

The authors [10] used the considered above physical model for dimethyldial-lylammoniumchloride (DMDAACh) radical polymerization [1] description. As it was shown in work [8], the radical polymerization of DMDAACh was simulated by the diffusion-limited aggregation model according to mechanism cluster-cluster. This means, that the indicated process is realized by small macromolecular coils merging into larger ones. This treatment allows to simirlate DMDAACh polymerization as the Eq. (2) with the Eq. (4) or (6) depending on the space type, in which it is realized. In this case the value pA can be determined as follows [10] ... 

The fractal approach was also used to investigate adsorption and desorption mechanisms of water vapor on active carbons that were derived from coconut shell, coal, coke and pitch fiber featuring a wide range of BET specific surface areas [78]. A values were measured for the water clusters adsorbed on primary carbon centers. Values ranging from 1.64 to 1.67 implied a diffusion-limited aggregation model on a pore wall plane, whereas higher A values (up to 1.86), measured at a relative pressure X = 0.95, implied the formation of water clusters that were partly merged vertically to the walls. 

Ferreira Jr, S.C. Effects of the screening breakdown in the diffusion-limited aggregation model. Eur. Phys. J. 42, 263 (2004)... 

Fig. 6. Domain shape obtained by computer simulation with the diffusion limited aggregation model (a), in comparison with experimental observation following a pressure jump (b).

More than 20 years ago, Matsushita et al. observed macroscopic patterns of electrodeposit at a liquid/air interface [46,47]. Since the morphology of the deposit was quite similar to those generated by a computer model known as diffusion-limited aggregation (D LA) [48], this finding has attracted a lot of attention from the point of view of morphogenesis in Laplacian fields. Normally, thin cells with quasi 2D geometries are used in experiments, instead of the use of liquid/air or liquid/liquid interfaces, in order to reduce the effect of convection. 

CA in which many filled cells execute a random walk but never interact with one another, cannot give rise to stable pattern formation since the cells will move at random forever. However, if cells can interact when they meet, so that one diffusing cell is allowed to stick to another, stable structures can be created. These structures illustrate the modeling of diffusion-limited aggregation (DLA), which is of interest in studies of crystal formation, precipitation, and the electrochemical formation of solids. 

Parkinson, J., Kadler, K. E., and Brass, A. (1995). Simple physical model of collagen fibrillogenesis based on diffusion-limited aggregation./. Mol. Biol. 247, 823-831. 

The mathematical model called diffusion-limited aggregation (DLA) was introduced by Witten and Sander in 1981 [46]. The model starts with a particle at the origin of a lattice. Another particle is allowed to walk at random (simulating Brownian motion) until it arrives at a site adjacent to the seed particle. At each time step, the traveling particle moves from one site to... 

Diffusion-limited aggregation of particles results in a fractal object. Growth processes that are apparendy disordered also form fractal objects (30). Sol—gel particle growth has also been modeled using fractal concepts (3,20). The nature of fractals requires that they be invariant with scale, ie, the fractal must look similar regardless of the level of detail chosen. The second requirement for mass fractals is that their density decreases with size. Thus, the fractal model overcomes the problem of increasing density of the classical models of gelation, yet retains many of its desirable features. The mass of a fractal, Af, is related to the fractal dimension and its size or radius, R, by equationS ... 

Hadjipanayis GC, Siegel RW (1994) Nanophase Materials Synthesis-Properties-Apphcations. NATO ASI Series 260. Kluwer Academic Publ, Dordrecht, The Netherlands Halsey TC (2000) Diffusion-limited aggregation A model for pattern formation. Phys Today, Nov 2000, p 36-41... 

The dendrite growth process may be described on the basis of cluster growth model of diffusion-limited aggregation (DLA) and fractal concepts in surface growth [83, 85],... 

I Jury, M and H. Fliihler. 1995. Modeling solute leaching in soils by diffusion-limited aggregation Basic concepts and application to conservative solutes. Water Resour. Res. 31 2443-2452. 

Two models of aggregation result in fractal distributions of uniform particles. In the Diffusion-Limited Aggregatioij ) model, particles are launched one at a time from random positions on an infinitely distant horizon and travel by random walks... 

As the treatment [31 ] was obtained within the frameworks of a more general model of diffusion-limited aggregation, its correspondence to the experimental data indicated unequivocally, such that aggregation processes in these systems were controlled by diffusion. Therefore, let us consider briefly the nanofiller particle diffusion. Statistical walkers diffusion constant can be determined with the aid of the equation as in what follows [31] ... 

Simulated models random walk without crossover (RWCO), diffusion-limited aggregation of particle-cluster (DLA-P-Cl) and cluster-cluster (DLA-Cl-Cl) types. Flory s critical parameter ... 

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