### List of abstracts

###### Martin Dlask, Jaromir Kukal

*FNSPE, CTU in Prague*

Abstract:

The talk presents a methodology of analyzing multidimensional fractional Brownian motion (fBm) and is applied for the identification of cancerous breast lumps from mammography screening images. At first, the exact method for multidimensional fBm images is presented and the accuracy of estimation is verified on simulated data with known Hurst exponent. Unlike approximate methods for generating multidimensional fBm and its Hurst exponent estimation, this approach shows unbiased results for all processes with short memory and most of cases with long memory. We apply the technique on the mamography images while being able to prove that patients with cancerous findings have significantly higher Hurst exponent than those with a benign lump.

###### Pavel Eichler

*FNSPE, CTU in Prague*

Abstract:

In this contribution, recent LBM simulations and progress in LBM will be presented. The application of LBM in the turbulent fluid flow in the fluidized bed reactor will be discussed. The LBM results are compared both with the experimental data and with the result produced with ANSYS Fluent software. Next, since all our previous turbulent fluid flow simulations have significant demands on the computational mesh, the octree structure of the computational mesh can reduce these demands. Although many numerical methods widely use this mesh refinement technique, the interpolation of discrete density functions is not straightforward in LBM. Thus, we will discuss different interpolations of density functions and their influence on the solution.

###### Radek Galabov, Jaroslav Tintera

*FNSPE, CTU in Prague, IKEM in Prague, IKEM*

Abstract:

Atherosclerosis is a leading cause in artery stenosis and occlusion. In recent decades, open surgery has been replaced by endovascular treatment at least for the less complicated lesions. There exist various stenting and angioplastic procedures to remodel the vessel and recover blood flow. However, implanted stents further influence blood dynamics and restenoses do occur. Long-term patency depends on stent design and procedural details, but the particular mechanisms are not yet fully understood. Computational fluid dynamics offers means to investigate some of the underlying causes in occlusion disease.

###### František Gašpar, Jaromír Kukal

*FNSPE, CTU in Prague, FNSPE, CTU in Prague*

Abstract:

Stochastic models of diffusion in spatial domains of noninteger dimension are widely applicable as a basis of simulations. Obtaining data having fractal properties requires the construction of fine enough discrete latices that is computationally expensive. This contribution presents a novel way of representing self-similar fractal models using a generalized coordinate system together with statistical testing of obtained dimension estimates.

###### Jiří Chludil, Pauš Petr

*FF, UHK, FIT, CTU in Prague*

Abstract:

Modern visualization technologies are becoming popular in historical sciences, e.g., digital reconstruction of historical buildings. The whole process, such as tedious work in the archive, digitizing all required materials, 3D modeling, preparation of textures, and importing a model into some visualization framework might be quite a complicated procedure for historians, especially if high standards need to be achieved. Technically demanding processes are often outsourced to external companies, which is usually expensive and time-consuming. The education process of historians nowadays contains an introduction to visualization technologies and digitization, but their knowledge is still rather limited. The process of data preparation and digitization usually goes without problems. However, 3D modeling itself followed by export to the visualization framework is far more complicated. There are usually fundamental problems in 3D models (bad topology and triangulation, etc.) and also issues with supported formats among applications. The goal of this project is to design and develop a system that helps historians to simplify and ease the process of historical buildings reconstruction by means of tools and techniques of software engineering and computer graphics. This study would like to create a full feedback system where all 3D models will be checked for quality (from a historical and computer graphics point of view) by automated and semi-automated tests. Access to all historical data as well as a backup and versioning system will be integrated into the system. Finally, the system will support exporting models to selected visualization frameworks in proper formats by means of client applications. According to the authors’ experience, historians arguably are a very conservative group of scientists. Therefore, designing and testing a proper user interface in a full-fledged UX laboratory is mandatory.

###### Martin Jex, Jiří Mikyška

*FNSPE, CTU in Prague*

Abstract:

This work examines the question of VTN phase stability testing. This problem is solved by global minimization of the TPD (tangent plane distance) function. The global optimization is performed using applying the branch and bound algorithm, which is improved, in comparison to its basic variant, by using a more effective pruning of the tree arising from the algorithm. This improvement is derived from the necessary conditions of an extremum, which leads to suplementary conditions for pressure and chemical potentials. Functions describing theese conditions are not convex, therefore, in this work, we derive and apply its convex-concave decompositions.

###### Léa Keller

*KTH*

Abstract: This contribution studies different experiments and mathematical models of water and soil freezing. Soil freezing has important effects in order to understand deformation of grounds, such as for instance the roads in winter. The model is based on Stefan problem which is a particular type of free boundary problem. Several experiments and models with water, sand and gas are performed and then modelled with the use of Comsol 3.3 in order to visualize the freezing evolution.

###### Jakub Klinkovský

*FNSPE, CTU in Prague*

Abstract:

Multiphase particle-in-cell is an interesting method for modeling particle-fluid interactions in computational fluid dynamics, which combines the advantages of both Eulerian and Lagrangian frameworks. While the motion of particles is tracked using the Lagrangian framework, inter-particle interactions (i.e. collisions) are approximated using averaged quantities on the Eulerian grid where the fluid is simulated. According to the literature, the method is stable in dense particle flows, computationally efficient, and physically accurate, which makes it suitable for the simulation of industrial-scale chemical processes involving particle-fluid flows.

In this talk, we present the governing equations and mathematical background of the MP-PIC method, then we describe its implementation in the OpenFOAM framework and highlight our own improvements that are included in our customized "kotelFoam" solver. Finally, we present our simulations of fluidized particles in a plastic model of a bubbling fluidized bed combustor.

###### Jan Kovář

*FNSPE, CTU in Prague*

Abstract:

This contribution deals with mathematical modeling of contrast agent transport and its transfer through the vessel wall in vascular flow in a two-dimensional computational domain. The problem is solved in the context of myocardial perfusion examination using a contrast agent.

The audience will be briefly introduced to a mathematical model of Newtonian incompressible fluid flow in an isothermal free flow system and a mathematical model of a contrast agent transport, in which the boundary condition modeling the transfer of the contrast agent is included. The numerical scheme of the lattice Boltzmann method used to solve the aforementioned problem will be discussed together with the results obtained by this scheme.

###### Michal Malík

*FNSPE, CTU in Prague*

Abstract:

In this contribution, we will present the possibilities of using the lattice Boltzmann method, LBM for short, to simulate two phase flow. Two numerical models will be described: Shan-Chen LBM and phase-field LBM. Shan-Chen LBM can be used to simulate both miscible and immiscible flow, while phase-field LBM is only capable of the latter. We will discuss the phase separation in Shan-Chen LBM and the initial condition for phase-field LBM. Afterwards, the application of both numerical models in simulating the contact angle between fluid and solid surface will be shown.

###### Niels van der Meer, Michal Beneš

*FNSPE, CTU in Prague*

Abstract:

Cardiovascular diseases account for more than thirty per cent of all deaths which makes them the most common cause of decease worldwide. It is therefore understandable that considerable effort has been exerted to treat and prevent these conditions. This talk(based on a thesis of the same name) probes for the potential contributions of mathematics and its tools developed from the theory of reaction-diffusion equations. The main area of interest is electrocardiology which studies heart rhythm disorders as well as their causes. Some of the mathematical models describing the propagation of a signal in an excitable medium are introduced. One such example is the FitzHugh–Nagumo model whose several variations were numerically analyzed and the results are presented in this talk.

###### Ivan Merta, Jaromir Kukal

*FNSPE, CTU in Prague*

Abstract:

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a widely accepted metaheuristic optimization method. It belongs to a class of stochastic, derivative-free optimization algorithms performing well on a wide range of nonlinear, non-convex black-box functions in a continuous domain. As such, it has attracted researchers to make various modifications to the method.

In classical CMA-ES, new candidate solutions are sampled from a multivariate normal distribution. In our research, we propose a novel heavy-tailed distribution for generating the samples. The steps for generating such values are derived from a spherically symmetric distribution maximizing Renyi entropy. This approach results in a generalization CMAE-ES and classical method with a multivariate normal distribution sampling here becomes an edge case.

The performance is compared with classical CMA-ES on multiple appropriately difficult test functions.

###### Tomáš Smejkal, Jiří Mikyška

*FNSPE, CTU in Prague*

Abstract:

In this contribution, we present a new numerical solution of a multi-phase miscible compressible Darcy's flow of a multi-component mixture in a porous medium. The mathematical model consists of the mass conservation equation of each component, extended Darcy's law for each phase, and an appropriate set of the initial and boundary conditions. The phase split is computed using the constant temperature-volume flash (known as VTN-specification). The transport equations are solved numerically using the mixed-hybrid finite element method and a novel iterative IMPEC scheme. We provide examples showing the performance of the numerical scheme.

###### Jakub Solovský

*FNSPE, CTU in Prague*

Abstract:

In this work, we present the simplified mathematical model of two-phase compositional flow in porous media coupled with heat conduction and phase transitions.

We implement the numerical scheme based on the mixed-hybrid finite element method for solving such problems and demonstrate the capabilities of the model on an artificial scenario inspired by the planned experiments.

Initially, the pore space of a sand-filled container is occupied by ice with entrapped gas bubbles. One wall of the container is heated, the remaining ones are insulated. The ice within a container melts and releases the trapped gas that is then transported in the already melted region and dissolves into the water.

###### Monika Suchomelová

*FNSPE, CTU in Prague*

Abstract:

The mean curvature flow (MCF) in plane is well studied curve dynamics with interesting properties. The hyperbolic version of this flow (HMCF) is defined by the rule that normal acceleration of the curve is equal to curvature. In addition to an initial curve, the initial velocity must be defined.

The studied equation for parametric plane curve is presented. The properties of the flow are demonstrated on computed examples of evolving closed plane curves and compared with the properties of MCF. The interesting situation happens if the initial velocity is set to be equal to initial tangent vector field.

###### Kateřina Škardová

*FNSPE, CTU in Prague*

Abstract:

In this contribution, we discuss how numerical simulations and machine learning can be combined in order to create a framework for tissue parameter estimation. The proposed approach is applied on the problem of T1 relaxation time estimation based on image series acquired by the Modified Look-Locker Inversion Recovery (MOLLI) magnetic resonance imaging sequence.

The main contribution is in combining neural network with numerical minimization. The neural network is trained using synthetic data generated by MOLLI sequence simulations based on Bloch equation. The prediction of neural network is used to initialize the numerical optimisation step. The proposed method is validated using phantoms with wide range of T1 values.

###### Cyril Izuchukwu Udeani, Daniel Sevcovic

*Comenius University, Bratislava*

Abstract:

In this paper, we investigate a fully nonlinear evolutionary Hamilton-Jacobi-Bellman (HJB) parabolic equation utilizing the monotone operator technique. We consider the HJB equation arising from portfolio optimization selection, where the goal is to maximize the conditional expected value of the terminal utility of the portfolio. The fully nonlinear HJB equation is transformed into a quasilinear parabolic equation using the so-called Riccati transformation method. The transformed parabolic equation can be viewed as the porous media type of equation with source term. Under some assumptions, we obtain that the diffusion function to the quasilinear parabolic equation is globally Lipschitz continuous, which is a crucial requirement for solving the Cauchy problem. We employ Banach's fixed point theorem to obtain the existence and uniqueness of a solution to the general form of the transformed parabolic equation in a suitable Sobolev space in an abstract setting. Some financial applications of the proposed result are presented in one-dimensional space.

###### Shimoji Yusaku, Yoshinori Okino

*Meiji University, Meiji University*

Abstract:

There are several known mathematical models that describe snow crystal growth. Yokoyama-Kuroda model is well known as a representative model. In addition, Barrett et al. have proposed a model that takes into account the Gibbs-Thomson law, which was not considered in the derivation of Yokoyama-Kuroda model. Some numerical calculations have already been done for these problems. However, to the best of our knowledge, there are no numerical calculations using the MFS. In this talk, we will report the results of numerical calculations using MFS for these models.