arXiv subjects

W. Olchawa

Publications and source records attributed to W. Olchawa.

12 recordsLinked to original sources

arXiv2024

A modified cellular automaton using activation and inhibition regions geometrically compatible with biaxial anisotropy

Young's cellular automaton, recently applied to study the spatiotemporal evolution of binary patterns for favorable/hostile environments, has now been modified from a different point of view. In this model, each differentiated cell (DC) produces two diffusing morphogens: a short-range activator and a long-range inhibitor. Their combination creates the so-called local 'w' field. Undifferentiated cells (UCs) are passive. The question arises how to adapt it to modelling patterning processes in anisotropic substrates with a biaxial dependence of the morphogen diffusion rate. We use activation/inhibition regions with appropriate shape geometry defined by the so-called deformation parameter p. We complement this model by adding a physically reasonable transition zone with controlled local field slope. The patterning process uses the morphogenetic field W calculated separately for each cell, which is the sum of the 'w' values generated by all regional DCs surrounding the cell. It acts as a chemical signal determining the next state of the cell. We also introduce a threshold W* defining the required absolute chemical signal strength. The state of each cell can change depending on the rules for W and W*. This improves the stability of the model evolution and extends its applications. Using two pairs of two-point orthogonal correlation functions, we reveal their directional sensitivity to changes in biaxial anisotropy. Finally, we illustrate the general two-parameter dependence of the average final DC concentration on the geometry of the activation/inhibition regions and on the value of the long-range inhibitor. This facilitates the recognition of characteristic features of the evolution of DC concentration in our model.

cond-mat.stat-mech↗

arXiv2020

A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions

The main goal of our research is to develop an effective method with a wide range of applications for the statistical reconstruction of heterogeneous microstructures with compact inclusions of any shape, such as highly irregular grains. The devised approach uses multi-scale extended entropic descriptors (ED) that quantify the degree of spatial non-uniformity of configurations of finite-sized objects. This technique is an innovative development of previously elaborated entropy methods for statistical reconstruction. Here, we discuss the two-dimensional case, but this method can be generalized into three dimensions. At the first stage, the developed procedure creates a set of black synthetic clusters that serve as surrogate inclusions. The clusters have the same individual areas and interfaces as their target counterparts, but random shapes. Then, from a given number of easy-to-generate synthetic cluster configurations, we choose the one with the lowest value of the cost function defined by us using extended ED. At the second stage, we make a significant change in the standard technique of simulated annealing (SA). Instead of swapping pixels of different phases, we randomly move each of the selected synthetic clusters. To demonstrate the accuracy of the method, we reconstruct and analyze two-phase microstructures with irregular inclusions of silica in rubber matrix as well as stones in cement paste. The results show that the two-stage reconstruction (TSR) method provides convincing realizations for these complex microstructures. The advantages of TSR include the ease of obtaining synthetic microstructures, very low computational costs, and satisfactory mapping in the statistical context of inclusion shapes. Finally, its simplicity should greatly facilitate independent applications.

cs.CE↗

arXiv2018

Sensitivity to initial conditions in an extended activator-inhibitor model for the formation of patterns

Despite simplicity, the synchronous cellular automaton [D.A. Young, Math. Biosci. 72, 51 (1984)] enables reconstructing basic features of patterns of skin. Our extended model allows studying the formatting of patterns and their temporal evolution also on the favourable and hostile environments. As a result, the impact of different types of an environment is accounted for the dynamics of patterns formation. The process is based on two diffusible morphogens, the short-range activator and the long-range inhibitor, produced by differentiated cells (DCs) represented as black pixels. For a neutral environment, the extended model reduces to the original one. However, even the reduced model is statistically sensitive to a type of the initial distribution of DCs. To compare the impact of the uniform random distribution of DCs (R-system) and the non-uniform distribution in the form of random Gaussian-clusters (G-system), we chose inhibitor as the control parameter. To our surprise, in the neutral environment, for the chosen inhibitor-value that ensures stable final patterns, the average size of final G-populations is lower than in the R-case. In turn, when we consider the favourable environment, the relatively bigger shift toward higher final concentrations of DCs appears in the G. Thus, in the suitably favourable environment, this order can be reversed. Furthermore, the different critical values of the control parameter for the R and the G suggest some dissimilarities in temporal evolution of both systems. In particular, within the proper ranges of the critical values, their oscillatory behaviours are different. The respective temporal evolutions are illustrated by a few examples.

q-bio.CB↗

arXiv2018

Statistical Reconstruction of Microstructures Using Entropic Descriptors

We report a multiscale approach of broad applicability to stochastic reconstruction of multiphase materials, including porous ones. The approach devised uses an optimization method, such as the simulated annealing (SA) and the so-called entropic descriptors (EDs). For a binary pattern, they quantify spatial inhomogeneity or statistical complexity at discrete length-scales. The EDs extract dissimilar structural information to that given by two-point correlation functions (CFs). Within the SA, we use an appropriate cost function consisting of EDs or comprised of EDs and CFs. It was found that the stochastic reconstruction is computationally efficient when we begin with a preliminary synthetic configuration having in part desirable features. Another option is low-cost approximate reconstructing of the entire multiphase medium beyond the SA technique. The information included in the target ED-curve was utilized for this purpose. For a given volume fraction the low-cost trial microstructures can be generated in two ways. In the first one, applied to ceramics and carbonate samples, the interpenetrating spheres generate a number of trial configurations. In the second one, with phase-EDs, here used to the sandstone sample, the overlapping superspheres do it. Both methods use a radius determined from the EDs-linked two-exponent power-law. However, the supersphere deformation parameter allows controlling of the spatial inhomogeneity of prototypical microstructures. At last, even for a hypothetical ED-curve (under reasonable assumptions), the specific microstructure can be found, if it is realizable for a given volume fraction. In general, the EDs-based methods offer a compromise between computational efficiency and the accuracy of reconstructions.

cond-mat.mtrl-sci↗

arXiv2017

Controlling spatial inhomogeneity in prototypical multiphase microstructures

A wide variety of real random composites can be studied by means of prototypes of multiphase microstructures with a controllable spatial inhomogeneity. To create them, we propose a versatile model of randomly overlapping super-spheres of a given radius and deformed in their shape by the parameter p. With the help of the so-called decomposable entropic measure, a clear dependence of the phase inhomogeneity degree on the values of the parameter p is found. Thus, a leading trend in changes of the phase inhomogeneity can be forecast. It makes searching for possible structure/property relations easier. For the chosen values of p, examples of two and three-phase prototypical microstructures show how the phase inhomogeneity degree evolves at different length scales. The approach can also be applied to preparing the optimal starting configurations in reconstructing real materials.

cond-mat.mtrl-sci↗

arXiv2017

Low-cost approximate reconstructing of heterogeneous microstructures

We propose an approximate reconstruction of random heterogeneous microstructures using the two-exponent power-law (TEPL). This rule originates from the entropic descriptor (ED) that is a multi-scale measure of spatial inhomogeneity for a given microstructure. A digitized target sample is a cube of linear size L in voxels. Then, a number of trial configurations can be generated by a model of overlapping spheres of a fixed radius, which are randomly distributed on a regular lattice. The TEPL describes the averaged maximum of the ED as a function of the phase concentration and the radius. Thus, it can be used to determine the radius. The suggested approach is tested on surrogate samples of ceramic and carbonate. In each of the cases, fifty low-cost trials provided a few good enough candidates to a selection of the optimal reconstruction. When a better accuracy is planned, the final reconstructions can serve as the starting configurations. Then, the resulting reconstructions should be competitive indeed to those starting with random configurations.

cond-mat.stat-mech↗

arXiv2015

Entropic descriptor based reconstruction of three-dimensional porous microstructures using a single cross-section

The simple entropic method to statistical reconstructing of heterogeneous three-dimensional media from a single two-dimensional image is briefly reported. We apply the entropic descriptor quantifying spatial inhomogeneity that depends on length scale. The multiscale reconstructing procedure is boosted when we start from the synthetic 3D configuration. It is randomly generated with the overlapping spheres of a radius depending on the structure considered. In our scenario, the simulated annealing terminates when all assigned temperature loops are completed. Thus, the quality of the results for different samples can be fairly compared. The reliable 3D reconstructions of porous sandstone, ceramics and carbonate samples are obtained. They suggest the entropic method is a promising approach, which offers a kind of compromise between the computational efficiency and the accuracy of the statistical reconstructions. Furthermore, this approach is versatile enough to be extended for any multiphase medium.

cond-mat.stat-mech↗

arXiv2015

On multi-scale percolation behaviour of the effective conductivity for the lattice model with interacting particles

Recently, the effective medium approach using 2x2 basic cluster of model lattice sites to predict the conductivity of interacting droplets has been presented by Hattori et al. To make a step aside from pure applications, we have studied earlier a multi-scale percolation, employing any kxk basic cluster for non-interacting particles. Here, with interactions included, we examine in what way they alter the percolation threshold for any cluster case. We found that at a fixed length scale k the interaction reduces the range of shifts of the percolation threshold. To determine the critical concentrations, the simplified model is used. It diminishes the number of local conductivities into two main ones. In the presence of a dominance of the repulsive interaction over the thermal energy, the exact percolation thresholds at scales k=2 and 3 can be obtained from analytical formulas. Furthermore, by a simple reasoning, we obtain the limiting threshold formula for odd k. When k>>1, the odd-even difference becomes negligible. Hence, the 0.75 is the highest possible value of the threshold.

cond-mat.stat-mech↗

arXiv2015

Pressure Shift and Gravitational Red Shift of Balmer Lines in White Dwarfs. Rediscussion

The Stark-induced shift and asymmetry, the so-called pressure shift (PS) of $H_α$ and $H_β$ Balmer lines in spectra of DA white dwarfs (WDs), as masking effects in measurements of the gravitational red shift in WDs, have been examined in detail. The results are compared with our earlier ones from before a quarter of a century (Grabowski et al. 1987, hereafter ApJ'87; Madej and Grabowski 1990). In these earlier papers, as a dominant constituent of the Balmer-line-profiles, the standard, symmetrical Stark line profiles, shifted as the whole by PS-effect, were applied to all spectrally active layers of the WD atmosphere. At present, in each of the WD layers, the Stark-line-profiles (especially of $H_β$) are immanently asymmetrical and shifted due to the effects of strong inhomogeneity of the perturbing fields in plasma. To calculate the Stark line-profiles in successive layers of the WD atmosphere we used the modified Full Computer Simulation Method (mFCSM), able to take adequately into account the complexity of local elementary quantum processes in plasma. In the case of the $H_α$ line, the present value of Stark-induced shift of the synthetic $H_α$ line-profile is about twice smaller than the previous one (ApJ'87) and it is negligible in comparison with the gravitational red shift. In the case of the $H_β$ line, the present value of Stark-induced shift of the synthetic $H_β$ line-profile is about twice larger than the previous one. The source of this extra shift is the asymmetry of $H_β$ peaks.

astro-ph.SR↗

arXiv2014

Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands

We report a fast, efficient and credible statistical reconstruction of any two-phase patterns of islands of miscellaneous shapes and poly-dispersed in sizes. In the proposed multi-scale approach called a weighted doubly-hybrid, two different pairs of hybrid descriptors are used. As the first pair, we employ entropic quantifiers, while correlation functions are the second pair. Their competition allows considering a wider spectrum of morphological features. Instead of a standard random initial configuration, a synthetic one with the same number of islands as that of the target is created by a cellular automaton. This is the key point for speeding-up of microstructure reconstruction, making use of the simulated annealing technique. The program procedure allows requiring the same values for the reconstructed and target interface. The reconstruction terminates when three conditions related to the accuracy, interface and number of islands are fulfilled. We verify the approach on digitized images of a thin metallic film and a concrete sample cross-section. For a given accuracy, our method significantly reduces the number of accepted Monte Carlo steps when compared to the standard approach. At the same time, it provides credible shapes and similar areas of islands, keeping their number and the total interface of the target. To the best of our knowledge, this is the first attempt to obtain such an outcome. The cost-effective reconstructions suggest that the present technique could also be used for patterns of islands with strongly jagged border lines.

cond-mat.stat-mech↗

arXiv2014

On multi-scale percolation behaviour of the effective conductivity for the lattice model

Macroscopic properties of heterogeneous media are frequently modelled by regular lattice models, which are based on a relatively small basic cluster of lattice sites. Here, we extend one of such models to any cluster's size kxk. We also explore its modified form. The focus is on the percolation behaviour of the effective conductivity of random two- and three-phase systems. We consider only the influence of geometrical features of local configurations at different length scales k. At scales accessible numerically, we find that an increase in the size of the basic cluster leads to characteristic displacements of the percolation threshold. We argue that the behaviour is typical of materials, whose conductivity is dominated by a few linear, percolation-like, conducting paths. Such a system can be effectively treated as one-dimensional medium. We also develop a simplified model that permits of an analysis at any scale. It is worth mentioning that the latter approach keeps the same thresholds predicted by the former one. We also briefly discuss a three-phase system, where the double-thresholds paths appear on model surfaces.

cond-mat.stat-mech↗

arXiv2012

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.

cond-mat.stat-mech↗