Monika Balázsová

Abstract: TBA

Michal Beneš, Alexandr Žák, Martina Sobotková, Tissa H. Illangasekare, Lea Keller

Abstract: In the contribution, we present the model of freezing and thawing in a fully saturated porous medium. The phase transition occurs in pores of the porous medium with grains intact but participating in the heat transfer, and is accompanied by mechanical effects. The research is motivated by the development of advanced materials as well as by the climate changes inducing thawing of permanently frozen land with further environmental impact. Freezing and thawing inside the porous medium is accompanied by complex processes affected by the material %composition, micro-scale interfaces between phases within the soil, bulk properties of the presented phases, and ambient physical conditions. Volumetric changes of the liquid presented in pores subjected to phase change conditions is one of crucial phenomena. Due to the generic inhomogeneity of volume occupied by the freezing porous medium, we focus on treating the phase transition at microscale. We have developed a micro-scale model describing mechanical, thermal, and phase change processes within a small sample of a porous medium. The phase change is described in the Lagrangian framework by means of the energy, Navier, and phase-field equations. A coupling of multi-physics and multiple phases is introduced. The model provides spatio-temporal dependencies of primary variables, the resulting forces exerted on grain surfaces by the change in specific volume due to phase transition, and possibly, the mean values of the key quantities useful for upscaling. The role of the model is demonstrated on several computational studies which follow recently published results.

Miroslav Kolář

Abstract: TBA

Jaromír Kukal, Michal Beneš

Abstract:

There are many ways how to approximate the fractional Laplacian. Preferring d-dimensional linear difference schemes and regular grids (cubic, hexagonal, dodecahedral), we obtained novel formulas with approximation order 4 - alpha. We start with principal value integral expression of the fractional Laplacian. After splitting it into singular and regular parts, we balance the approximation errors and obtained optimal radius of singularity capturing. This radius is only a function of the exponent alpha and the topology of regular grid and therefore, it can be calculated before the grid calculations.  Final formula is only a linear combination of traditional Laplacian stencil and simple d-dimensional sum.

Dana Majerová

Abstract: Digital image processing involves many techniques. One of them is image enhancement. This presentation is devoted to the processing of biomedical images using simple and advanced fuzzy filters and several kinds of min-max fuzzy networks (MMFNs). The MMFN combines selected fuzzy filters to compute a better image. The results of all fuzzy filters and the output from min-max fuzzy networks are compared on biomedical images obtained by magnetic resonance.

Petr Pauš

Abstract: This contribution deals with the numerical simulation of dislocation-precipitate interaction in copper crystals by means of discrete dislocation dynamics. We consider a dislocation gliding in a slip plane under an external stress field and a precipitate located in the same slip plane also generating a stress field. The precipitate stress field forces the dislocation to perform a cross-slip mechanism (i.e., change the slip plane). We present a comparison of the deterministic approach to the cross-slip mechanism with a probabilistic approach governed by a normal distribution of probability.

Tomáš Princ, Michal Sněhota

Abstract:

The relationship between entrapped air content (ω) and the corresponding hydraulic conductivity (K) was investigated experimentally for two coarse sands. Additionally the pore-network model based on OpenPNM platform was used to attempt simulation of a redistribution of the air bubbles after infiltration. Two packed samples of 5 cm height and 7.2 cm diameter were prepared for each sand. The cycles of infiltration and drainage led to entrapping of the air. The value of K was determined using Darcy’s law by repetitive falling-head infiltration experiments. The entrapped air content was determined from gravimetrically after each infiltration run. The amount and distribution of air bubbles were quantified by X-ray computed tomography (CT) for selected runs. The obtained K( ω) relationship agreed well with Faybishenko’s formula. CT imaging revealed that entrapped air contents and bubbles sizes were increasing with the height of the sample. It was found that the size of the air bubbles and clusters increased with each repetition of the experimental cycle. The relationship between initial and residual gas saturation was successfully fitted with a linear model. The combination of X-ray computed tomography and infiltration experiments has a potential to explore the effects of entrapped air on water flow.

Pavel Strachota, Tereza Vorlová, Ondřej Šrámek

Abstract:

Let's start by a quote from the 1997 movie "The Devil's Advocate":

Kevin Lomax:
Why the law? Cut the sh*t, Dad! Why the lawyers? Why the law?

John Milton:
Because the law, my boy, puts us into everything. It's the ultimate backstage pass. It's the new priesthood, baby. Did you know there are more students in law school than lawyers walking the Earth?

Quang Van Tran

Abstract: The price dynamics of financial assets is traditionally modeled by a Wiener process. However, this process cannot capture the heavy tail property of assets returns. One way to solve this problem is to replace the Wiener process by the variance gamma process. However, the resulting stochastic process is more complicated and direct evaluation of option price under risk neutral measure is computationally time-consuming. As an alternative, option pricing is performed through fourier transform making use of the existence of the characteristic function of the variance gamma process. We analyze the efficency of this procedure and the effect of parameters of  numerical procedure on its precision as well as its time demandingness.