30 research outputs found
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