Michal Beneš, Miroslav Kolář and Daniel Ševčovič

Abstract:

We discuss the motion of closed non-intersecting space curves by curvature in binormal and normal directions with application in vortex dynamics. We formulate the general motion law in space by binormal and normal curvature and mention its analytical properties. The finite-volume scheme allows to solve the motion numerically. We demonstrate behavior of the solution on several computational studies combining normal and binormal velocity and mutual interactions.

Jooyoung Hahn

Abstract:

This study introduces a novel approach combining two-dimensional gas chromatography (GC x GC), high-resolution time-of-flight mass spectrometry (HR-TOF-MS), and topological data analysis (TDA) to identify unique chemical signatures in botrytized wines from Austria, Hungary, Slovakia, and France. Employing the ball mapper algorithm, we manage the high-dimensional data generated by HR-TOF-MS, simplifying the complex dataset into a representative set of chemical compounds for each wine. This method allows us to visualize and analyze chemical diversity and relationships in a more accessible two-dimensional form, facilitating the identification of distinct chemical profiles unique to wines from different regions. The application of this technique not only enhances our understanding of the compositional variations in European wines but also demonstrates the potential of TDA in analytical chemistry for complex mixture analysis such as food authentication and environmental studies. Our findings provide a new perspective on the standard analytical approaches, offering advancements in the field of computational geometric design applied to chemometrics.

Tomáš Halada

Abstract:

In Smoothed Particle Hydrodynamics (SPH) method, dealing with free surface flows using weakly compressible model of fluid, artificial viscosity is frequently used to stabilize the computations. Artificial viscosity is associated with excessive dissipation. However, using only the physical viscosity, issues with stability arise. In fact, artificial viscosity hides some of the problems of a widely used SPH schemes. In order to resolve stability issues, we employed conservative modification of boundary integrals formulation of boundary conditions together with midpoint scheme to solve free surface flows in three-dimensional complex geometries including open boundaries. Next to the numerical properties of SPH schemes, open source SPH solver TNL-SPH developed as a submodule of Template Numerical Library is presented.

Pavel Hron

Abstract: We explore the mathematical foundations and computational implementations of Fluid-Structure Interaction (FSI) simulations across diverse engineering domains. FSI represents a challenging surface-coupled problem where the state of the fluid domain depends on the structural interface displacement, while the structural domain state depends on fluid traction at the interface. We examine the mathematical formulation of these coupled systems and demonstrate how modern numerical methods—including Finite Volume for fluids and Finite Element for structures—can be effectively implemented to solve complex FSI problems ranging from aeroelasticity in aerospace applications to hemodynamics in biomedical engineering. The presentation will highlight both one-way and two-way coupling methodologies, showcasing how these computational approaches enable engineers to design lightweight, flexible structures through reduced conservatism and improved predictive capabilities.

Vladimír Jarý, Jozef Hrdý, Jan Chrastina, Matěj Michálek, Josef Nový, Jan Oršl, Daria Soboleva, Samuel Zahorec

Abstract:

Modern particle physics experiments strongly depend on the efective implementation of the data acquisition (DAQ) systems. In this paper, we will focus on development of the DAQ of the AMBER experiment at CERN. We will start with brief overview of the scientific program of the experiment. Next we will explain the standard architecture of the traditional DAQ systems that heavily rely on fast trigger subsystems that select potential event candidates in distributed, high rate environment. We will discuss disadvantages of such triggered DAQ system and the we will introduce innovative triggerless DAQ system that has been development for the AMBER experiment. In this system, filtering logic is moved to higher levels which allows to use more advanced algorithms for event candidates selection. We will describe current status of development that involves work of student of Bachelor's and Master's degree courses at our faculty.

Miroslav Kolář

Abstract:

We present an overview of spatially dependent description of spread of an infectious disease. We focus on the class of so called SIR models where an individual in the target population belongs either in the Susceptible, Infected or Recovered class. Such models can be described by a system of reaction-diffusion equations for the population densities and further enhanced by additional effects, like e.g. a demography. We also briefly discuss Hopf bifurcation and Turing bifurcation for classical SIR systems and also for nonlinear SIR systems.

Petr Pauš, Ondřej Sakala, Radek Richtr

Abstract: This talk presents the project called Most: A city that did not disappear, an initiative focused on the 3D reconstruction and immersive presentation of a historical city through web and virtual reality platforms. The project encompasses several key stages, including the creation of detailed 3D models and the development of robust application frameworks. A significant challenge encountered was the generation and application of realistic textures, particularly given the need for an automatic process derived from real-world data. To address this, our methodology incorporated the innovative use of AI image generation, specifically leveraging Stable Diffusion, to create high-quality textures. Furthermore, we developed a novel approach for generating textures from multiple photographic views and accurately mapping them onto 3D objects. This entire process has been encapsulated within a custom Blender module, streamlining the workflow and enabling efficient content creation for this ambitious digital preservation effort.

Daniel Sevcovic, Miroslav Kolar

Abstract:

We investigate the motion of a family of closed curves evolving on an embedded or immersed manifold in three dimensional Euclidean space  according to the geometric evolution law.  We derive a system of nonlinear parabolic equations describing the motion of curves belonging to a given two-dimensional manifold. We consider both embedded and immersed manifolds. Using the abstract theory of analytic semiflows, we prove the local existence, uniqueness of H\"older smooth solutions to the governing system of nonlinear parabolic equations for the position vector parametrization of evolving curves. We apply the method of flowing finite volumes in combination with the methods of lines for numerical approximation of the governing equations. Numerical experiments support the analytical conclusions and demonstrate the efficiency of the method.

Pavel Strachota

Abstract:

This work deals with numerical simulation of water freezing and thawing in a complex three-dimensional geometry of a porous medium. The porous structure is represented by a virtual container filled with glass beads. Phase transition modeling is approached at both macro-scale and micro-scale, combining heat transfer in a heterogeneous medium and a phase-field approximation of the Gibbs-Thomson relation by means of the Allen-Cahn equation. The formulation of the model contains novel components tailored for the given purpose. In addition to this general model, two limit scenarios are considered: At the macro-scale, surface tension effects are negligible and phase transition focusing based on temperature can replace the Allen-Cahn equation. In contrast to that, simulations of equilibrium states at the micro-scale allow to eliminate the heat equation by assuming constant supercooling. For numerical solution, an efficient hybrid parallel algorithm based on the finite volume method and the Runge-Kutta-Merson solver with adaptive time stepping are employed. The results of different model variants at different scales are discussed. In a parametric study, the full phase-field model is demonstrated to deliver consistent results across a wide range of surface tension values, exhibiting curvature-induced premelting if surface tension is artificially exaggerated. As surface tension tends to the realistic values, the results of the phase-field approach those of the simplified temperature-driven phase transition model. In addition, micro-scale simulations of water freezing at different supercooling values aim to predict the unfrozen water content and compare the results with data from literature. Numerical stability, accuracy, and computational costs are also discussed.

Robert Straka

Abstract:

Quang Van Tran

Abstract:

The banking sector is rarely included in a macroeconomic model as it is difficult to capture its behavior. This research studies the behavior of the banking sector, which takes deposits from households and provides loans to other entities. First, the model is derived and calibrated. Then, an impulse response analysis is performed to get the reactions of economic variables to various types of external shocks. The results of this analysis can be used to tailor appropriate economic policies for dealing with actual fluctuations in a real economy.