Speeding up of microstructure reconstruction: I. Application to labyrinth patterns

Recently, entropic descriptors based the Monte Carlo hybrid reconstruction of the microstructure of a binary/greyscale pattern has been proposed (Piasecki 2011 Proc. R. Soc. A 467 806). We try to speed up this method applied in this instance to the reconstruction of a binary labyrinth target. Instead of a random configuration, we propose to start with a suitable synthetic pattern created by cellular automaton. The occurrence of the characteristic attributes of the target is the key factor for reducing the computational cost that can be measured by the total number of MC steps required. For the same set of basic parameters, we investigated the following simulation scenarios: the biased/random alternately mixed #2m approach, the strictly biased #2b and the random/partially biased #2rp one. The series of 25 runs were performed for each scenario. To maintain comparable accuracy of the reconstructions, during the final stages the only selection procedure we used was the biased one. This allowed us to make the consistent comparison of the first three scenarios. The purely random #2r approach of low efficiency was included only for completeness of the approaches. Finally, for the conditions established, the best single reconstruction and the best average tolerance value among all the scenarios were given by the mixed #2m method, which was also the fastest one. The slightly slower the alternative #2b and #2rp variants provided comparable but less satisfactory results.Comment: 11 pages, 3 figures, 2 tables, published versio

On modeling of growth processes driven by velocity fluctuations

In the classical theory of diffusion limited growth, it is assumed that the concentration field of solution is described by the standard diffusion equation. It means that particles of the solution undergo a random walk described by the Wiener process. In turn, it means that the velocity of particles is a stochastic process being Gaussian white noise. In consequence, the velocity–velocity correlation function is the Dirac -function and velocity correlation time is zero. In many cases such modeling is insufficient and one should consider models in which velocity is correlated in space and/or time. The question is whether correlations of velocity can change the kinetics of growth, in particular, whether the long-time asymptotics of the growth kinetics displays the power-law time dependence with the classical exponent 1/2. How to model such processes is a subject of this paper