Radomir Chabiniok

Abstract:

Translational cardiovascular modeling combines clinical data with physiologically and biophysically based models of heart, large vessels or circulation, while aiming to contribute to diagnosis (e.g. new or more reliable bioindicators for patient stratification) or optimal clinical management (thanks to predictive capabilities of biophysical models). In this talk, an example application of selected cardiovascular models (such as models of ventricular mechanics; flow in large vessels; or image segmentation models with mechanical constrains) will be presented aiming to assess the ventricular function at regular follow up exams or planning of intervention (while coupling the models with detailed clinical data), or at perioperative period or acute exacerbation of heart failure (when coupled with signals monitoring cardiovascular physiology at operation theatre or intensive care unit). Additionally, some aspects of effective interactions between various disciplines will be discussed as a crucial prerequisite to succeed in advancing the novel multi-disciplinary methods into the clinical practice. 

Miroslav Kolář

Abstract: In this talk we present an overview of a parametric model for planar dislocation dynamics developed @ MMG. We introduce the mesoscale model for dynamics of prismatic dislocation loops and show how the model is derived and upscaled by means of molecular dynamics toollbox. Then we present the future perspective how to incorporate such phenomena into our parametric model.

Jaromir Kukal, Michal Benes

Abstract:

The differnce schemes are traditional tools for numeric solution of partial differenitial equations. There are traditional difference schemes for 1D approximation of Riesz derivative which is also called the fractional Laplacian. Symmetric Grunwald-Letnikov, spectral, and signal processing approaches are summarized as referential. The novel approach is based on short support smooth functions and their fractional differentiation.

Dana Majerová

Abstract:

There are many ways to perform image enhancement especially image de-noising.The presentation introduces filters that can be implemented in a simple mathematical model ({\L}ukasiewicz algebra with square root) and then describes min-max fuzzy network (MMFN) that combines selected individual filters. The structure of MMFN and a selection of fuzzy filters are subjects of population-based optimization heuristics. All results were obtained by processing artificial images with different levels of Gaussian noise. The results from MMFN are better than results of individual fuzzy filters. 

Pavel Strachota, Aleš Wodecki, Michal Beneš

Abstract:

We investigate a family of phase field models for simulating dendritic growth of a pure supercooled substance. Our aim is to remove limitations inherent to some existing models both in terms of the applicability to physically realistic situations and the feasibility of mathematical and numerical analysis. The central object of interest is the reaction term in the Allen-Cahn equation, which is responsible for spatial distribution of latent heat release during solidification. Several existing forms of the reaction term are analyzed and new variants are proposed, with consistent asymptotic behavior as the interface thickness tends to zero. The resulting models are tested in a number of numerical simulations focusing on mesh-dependence, model parameter settings, and the applicability to solidification under very large supercooling.

Robert Straka

Abstract:

Lattice Boltzmann Method (LBM) is able to - more or less- efficiently solve Navier-Stokes equations (NSE) together with Advection-Diffusion-Reaction equations (ADRE) for scalars. Simplified models of combustion could be easily solved by LBM, especially when one neglects radiation, temperature dependency of material properties and other stuff related to non-ideal gases. The basic application of LBM in 2D combustion will be presented, a cumulant based kernel is used to solve NSE, while a central moment based kernel is used for ADRE. The amount and quality of examples presented will depend on the time which I have to prepare them before the conference

Akiyasu Tomoeda, Kazuya Okamoto

Abstract:

The researches on traffic flow have been dramatically developed by various sophisticated mathematical models. The first half of this talk, let me briefly explain the background of the phenomenon of traffic flow as a collective motion and some mathematical models. The second half, our new nonlinear difference equation that can be a traffic flow model is presented and the results of some mathematical analyzes are reported.

Quang Van Tran, Jaromír Kukal

Abstract:

We propose a new family of distributions by symmetrization and regularization of one-sided distributions. These new distributions can retain important preperties of their predecessors, but they also gain the properties of two-sided symmetric and smooth distributions. The proposed distributions are used to model returns of financial assets.