#### Student workshop on scientific computing 2017

June 8 - 11, 2017

Department of Mathematics, FNSPE CTU in Prague
Děčín, Czech Republic

### List of abstracts

Evaluating the impact of grassland conversions to forest on groundwater recharge in the Nebraska Sand Hills

Abstract:

This presentation is a brief overview of the research I have done thus far in my Undergraduate career. In addition to field experience, my lab experience has been focused on geochemistry. While at Oak Ridge National Laboratory, the objective of our research was to observe and study reactions between minerals and fluids to better understand replacement reactions in carbonate minerals. The use of microscopy, including backscatter imaging on a scanning electron microscope (SEM), X-ray diffraction, and energy dispersive analysis, aided in the analysis of pore structure, chemical composition, and permeability of the initial sample and replacement product(s). The results showed significant changes in some carbonate samples and little change in others.

Effects of replacement reactions on multi-scale porosity
###### Jessica Bozell

Abstract:

This presentation is a brief overview of the research I have done thus far in my Undergraduate career. In addition to field experience, my lab experience has been focused on geochemistry. While at Oak Ridge National Laboratory, the objective of our research was to observe and study reactions between minerals and fluids to better understand replacement reactions in carbonate minerals. The use of microscopy, including backscatter imaging on a scanning electron microscope (SEM), X-ray diffraction, and energy dispersive analysis, aided in the analysis of pore structure, chemical composition, and permeability of the initial sample and replacement product(s). The results showed significant changes in some carbonate samples and little change in others.

Application of Correlation Dimension for Alzheimer Disease Diagnostics
FNSPE CTU in Prague

Abstract:

Fractal dimension is a non-integer characteristic that measures the space-filling of arbitrary set. The conventional methods usually provide biased estimation of the fractal dimension and therefore it is necessary to develop more complex methods for its estimation. For the analysis of correlation dimension, novel approach that employs the spectrum of point set which is averaged via rotation of power pattern will be presented. This approach can be used for the analysis of EEG signal to distinguish between control normal and Alzheimer disease patients. Subsequently, the correlation dimension can provide the indication on which channels there is the most significant difference between the two groups of patients. Apart from rotational spectrum, a new generalized technique based on the entropy calculation will be demonstrated and its efficiency will be shown on the sets with known dimension.

Numerical simulation of the fluid structure interaction based on the Lattice -- Boltzmann method coupled with the Immersed boundary method
FNSPE CTU in Prague

Abstract: We present a numerical study of incompressible, isothermal, newtonian fluid flow based on the Lattice -- Boltzmann method (LBM) coupled with the fluid structure interaction based on the Immersed boundary method (IBM). First, the Cascaded LBM, a modern variant of LBM, is briefly described and in order to determine the experimental order of convergence, the method is analyzed using the Hagen-Poiseuille flow problem. Next, we describe LBM with an implicit model for rigid objects and explicit model for elastic objects. In order to analyze the forces exerted by the solid-fluid interaction, numerical results based on the implicit model for rigid objects are compared to the results obtained by LBM with bounce-back boundaries at fluid-solid interfaces. In the last part, a hyperelastic explicit model for elastic fibers is investigated and applied to the cavity flow benchmark problem in a domain with elastic bottom.

Integration of Hydrogeophysical Datasets for Improved Water Resource Management in Irrigated Systems
###### Catherine Finkerbinen

Abstract:

The major limitation to implementing precision agriculture technologies often lies in the management of spatial datasets and the development of irrigation prescription maps that address variables impacting yield and soil moisture. This study explored the utility of the recently developed cosmic-ray neutron probe (CRNP) which measures soil water content (SWC) in the top ~30cm of the soil profile. The key advantages of CRNP are that the sensor is passive, non-invasive, mobile and soil temperature-invariant, making data collection more compatible with existing farm operations and extending the mapping period. The objectives of this study were to: 1) improve the delineation of management zones within a field and 2) estimate spatial soil hydraulic properties to make effective irrigation prescription maps. To accomplish this, a series of CRNP SWC surveys were collected in a 53-ha field near Sutherland, Nebraska, USA. The SWC surveys were analyzed using Empirical Orthogonal Functions (EOF) to isolate the underlying spatial structure. Results indicated the measured SWC at field capacity and wilting point were better correlated to CRNP EOF as compared to other commonly used datasets. Rising scrutiny for agricultural water-use may increase the adoption of this technology.

The simulation of Bloch equations for quantitative evaluation of relaxation times in MR
###### Kateřina Fricková
FNSPE CTU in Prague

Abstract: This paper deals with the simulation of Bloch equations for quantitative evaluation of relaxation times using especially the MOLLI method during the measurement in magnetic resonance. The Bloch equations are used to calculate the nuclear magnetization M = (Mx, My, Mz) as a function of time where relaxation times T1 and T2, which are characteristic of each tissue, are included. On the basis of these times, some disorders of examined tissue can be detected. Using the MOLLI method during the measurement, eleven points are obtained from the Mz relaxation curve. Each of the eleven points belongs to one magnetic resonance image. The aim is to create a database of these points calculated for a large number of different T1 time values. Using this database and programs written in C ++ and Matlab, it would be possible to create a T1 map based on magnetic resonance images so the examined tissue can be described.

MPI support in TNL
###### Vít Hanousek
FNSPE CTU in Prague

Abstract:

Nowadays, memory and computation requirements of numerical simulations often exceed the capability of a single multicore computer or graphical card. The aim of our work is to implement support of high performance clusters into the Template Numerical Library (TNL). The TNL is a software package for numerical computations on multi-core CPUs and CUDA compatible GPUs which is active developed at the Faculty of Nuclear Sciences and Physical Engineering. This support is implemented using the Message Passing Interface (MPI). The MPI is the most common communication system used on high performance clusters. In this talk, the implementation of basic distributed grid will be presented together with an example of usage. Moreover, the influence of allocation of CPU cores of a cluster on the performance will be discussed shortly.

Forecasting visibility within numerical weather prediction
###### Magdalena E. Haselsteiner
Institute for meteorology and geodynamics Vienna

Abstract: Weather prediction as a field of research is of great public interest for many reasons. First of all, the weather effects most peoples in there everyday life. Another aspect is that weather forecasts help to deal with more severe issues, for example by making it possible to plan appropriate actions concerning up- coming natural disasters. The basis of modern weather forecast is, to describe the atmosphere mathematically as a turbulent fluid and solve the corresponding equations numerically. The atmosphere is an intrinsically chaotic system and therefore it is highly complex to model and predict its behaviour and crucial to take the full range of possible initial conditions into account. This requires enormous computational power and sophisticated parallelization techniques. The improvement of computational facilities in the last recent years enhanced accuracy of the models, which caused Numerical Weather Prediction (NWP) to become the main area of research in meteorology. One of the challenges in NWP is that many different complex physical processes contribute to one atmospheric state. A large number of these processes can not be resolved, due to the mesh size of the grid and computational restrictions. Thus, parameterizations to describe these contributions are needed. Such parameterizations usually contain many uncertainties. Paired with the uncertainties of the initial state and the chaotic nature of the atmosphere, the use of statistical methods becomes inevitable. One wide spread method is ensemble prediction: An ensemble is created by running the model several times with changed initial conditions, parameters or other variables in each run. Then the statistics of the ensemble (e.g. spread) are used to determine, accuracy and range of a forecasted scenario. This talk will be a brief introduction to Numerical Weather Prediction. The visibility will serve as an example, to explain the challenges of finding and using parameterizations of complex physical processes to forecast a single meteorological parameter. Moreover the application of ensemble theory on visibility will be discussed.

Mathematical Model of Signal Propagation in Excitable Media
###### Jakub Kantner
FNSPE CTU in Prague

Abstract:

This paper studies the properties of an excitable media through a numerical study based on the reaction-diffusion FitzHugh-Nagumo (FHN) model. An excitable media is one that possess the property of excitability, that is a small deviation in one direction from stable point can lead to a return through much longer path different from the initial one. The two-variable FHN model is a simplification of four-variable Hodgkin-Huxley (HH) model, but preserves the most important qualities of the original one. Examples of excitable media are nerve tissue, which was the original source of parameters for HH model, or cardiac tissue. In the heart the excitability allows the propagation of signals from pacemaker to the cardiac muscle which afterwards contracts and pumps blood throughout the cardiovascular system. However, if the cardiac tissue is damaged and its properties changed, the signal may not be propagated correctly and dangerous cases of fibrillations and tachycardias can occur. The ultimate aim of the paper is to find parameters describing the cardiac tissue in normal and abnormal state, to study the propagation of signals and the formation and development of fibrillations.

Modeling of double cross-slip by means of geodesic curvature driven flow
###### Miroslav Kolář
FNSPE CTU in Prague

Abstract: In this contribution we analyze the problem of dislocation cross-slip considered as a deterministic, stress-driven elementary dislocation process. Our approach to modeling the dislocation dynamics is based on mathematical theory of smooth curves evolving either in plane or on a two dimensional surface. The motion of dislocation curves is driven by the mean curvature motion law in the form $$B v = T \kappa + F.$$ Here v denotes the normal velocity, F is the normal component of all external forces acting on the dislocation, and parameters B and T denote the drag coefficient and the line tension, respectively. In the case of planar curves, $\kappa$ is the mean curvature, and in the case the dislocation evolving on a surface, $\kappa$ stands for the geodesic curvature. The cross-slip is considered as a deterministic phenomenon controlled by the repulsive exerted by a spherical obstacle. The sharp edges between the primary planes and the cross-slip plane are regularized to ensure the C2 smoothness of the whole glide surface. For numerical experiments, we employ the parametric description of the evolving dislocations and numerical solution is realized by means of the semi-implicit flowing finite volume method. To ensure the numerical stability, the employed semi-implicit scheme is enhanced with the tangential redistribution of the discretization points. Overcoming of a spherical obstacle by double cross-slip is presented as an illustrative example. The results of computational experiments are compared with the results obtained by the established projection method.

Curvature driven flow of space curves in normal and binormal direction
###### Jiří Minarčík
FNSPE CTU in Prague

Abstract: In this contribution, we examine some theoretical aspects of geometric flow of space curves and discuss its applications in vortex dynamics. Vortex filaments are surprisingly stable structures that can be observed during several natural phenomena. Those include tornados, smoke rings formed by volcanos or bubble rings created by whales. The linear induction approximation (LIA) of the Biot–Savart law leads to curvature driven flow in the binormal direction. This geometric flow preserves the length, total torsion and other important global properties of closed curves and exhibits interesting periodical behaviour. Because it depends only on local information, this model can not describe phenomena involving interaction between different vortex filaments. However, the motion law can be modified by a global correction term that accounts for the long range effects and allows us to study the frog leaping effect or vortex collisions involving topological changes.

Heuristic Optimization of Generalized Sub Models
###### Matej Mojzeš
FNSPE CTU in Prague

Abstract: The generalized linear model is based on linear combination of explanatory variables which is used to predict the output value. Traditional linear regression is just one particular case, while logistic, exponential, Poisson, geometric, and binomial regressions are other interesting and useful variants. Generalized linear regressions are based on maximum likelihood technique of point estimation for unknown parameters. It also enables calculation of their confidence intervals and ability to decide whether the coefficients are significantly non-zero. The sub model selection is useful not only for statisticians as a tool for obtaining of the best statistically significant model, e.g. by using stepwise regression, but it is also very helpful for data mining in vector spaces of large dimensions. The optimum sub model can be selected using binary optimization heuristics with reputable Lévy flight mutation over all significant submodels with constrained complexities. The process will be demonstrated on Poisson regression and Rank Mean Field Integer Flight heuristic.

Numerical solution for investment fluctuations in the Kaldor Kalecki model
###### Zuzana Olajcová
FNSPE CTU in Prague

Abstract: This paper studies the investment cycle using a Kaldor-Kalecki model of business cycle. The model is basically a system of differential equations, however due to the existence of a delay between an investment decision and its delivery, it becomes a system of delay differential equations (DDE). Together with features like nonlinearity in the investment function this system can produce rich dynamics such as periodical or non-periodical oscillations. To solve this system of two delay differential equations, several Runge Kutta methods for constant delays are implemented: from generally known Runge Kuttas such as RK4, to advanced RK methods based on arithmetic and harmonic mean. The delay term is approximated by using linear interpolation. First, the effectiveness of these methods is verified on examples with known analytical solutions and the obtained results are accordingly evaluated. Then the best one is used to solve the Kaldor-Kalecki business cycle model. As the precision of numerical methods solving DDE equations heavily depends on the precision of the interpretation, these methods would be enhanced by a more sophisticated interpolation approach as a technical extension of the current work.

The effect of air trapping on quasi-saturated hydraulic conductivity of coarse sand
###### Tomáš Princ, Helena Maria Reis Fideles, Michal Snehota and Milena Cislerova
FCE CTU in Prague

Abstract: The aim of this study was to experimentally determine the relationship between gas residual saturation (Sgr) and actual hydraulic conductivity (K) of coarse sand. Sgr indicates the ratio of entrapped air volume to pore volume of the sample. The value of residual gas saturation value determined in experiments exhibits temporal variability (due to history of wetting and drying, due to redistribution, air dissolution etc.), but many two-phase models assume value of Sgr to be constant. The K(Sgr) relationship was determined in series of constant head infiltration-outflow experiments. The first runs was performed on fully saturated sample. After the first infiltration run and then after each subsequent infiltration run, sample was drained under tension on a sand tank. Sgr was determined gravimetrically before each infiltration run. The value of K was determined using a Darcy’s law from measured steady state flux and each measurement then provided one value of K(Sgr). Several relative hydraulic conductivity models were tested to fit the measured points.

Chemical Analysis of Produced Water
###### Alisha Rodriguez
University of the Pacific

Abstract:

The state of California has been plagued with one of the longest droughts in the state’s history, which has led to the exploration of new sources of water for use in agriculture or industry. This project focused on a chemical analysis of produced water from oil sites in the South Belridge Oil Field, located in California. Data were taken from the California Division of Oil, Gas, and Geothermal Resources (DOGGR) to perform a charge balance, as well as to create evaporation plots, stiff diagrams, and piper diagrams. This analysis can be used in the future to explore viable techniques for purification of these waters.

Non-Rigid Registration of MRI Data
###### Kateřina Solovská
FNSPE CTU in Prague

Abstract: This work deals with non-rigid registration of MRI data. The aim of this work is to propose a method for registration of the images from MOLLI sequences of the heart, which can be afterwards used to create reliable map of T1 relaxation times. The T1 relaxation time characterizes the tissue at a given part of the heart. It is computed using all the images of the MOLLI series and therefore it is convenient to have the images registered prior to the computation. We propose a registration method based on optical flow. The method can not be used for the all images of the sequence directly due to varying intensity of the images. For registration of those images of the sequence, where optical flow based on brightness constancy constraint can not be used we use signed distance function of the segmented left ventricle instead of the original image. Level set method is used to segment the left ventricle of the heart. Methods are implemented and the T1 curves obtained using registered and unregistered data are compared.

Numerical simulation of two-phase compositional flow in porous media in vapor intrusion
FNSPE CTU in Prague, FNSPE CTU in Prague

Abstract: This work deals with two phase compositional flow in porous media with kinetic mass transfer. We propose a numerical method based on the mixed hybrid finite element method with several linear solvers (direct and iterative) and parallel implementation using MPI. First, the method is verified on problems with known solutions. Numerical experiments show that the errors are similar for all variations of the method and the experimentally estimated order of convergence is slightly less than one. However, there are significant differences in the computational performance. Then, we use the numerical scheme to investigate non-equilibrium mass transfer in unsaturated porous media using experimental laboratory data and hypothetical field-scale scenarios of vapor intrusion problems. The experiment was focused on evaporation of dissolved TCE in laboratory scale. In the field scale, we examine effects of water table drop or rainfall events on the dynamics of the vapor intrusion into building basements.

Algorithms for procedural modelling of plants in computer graphics
###### Smrčková Světlana
FNSPE CTU in Prague

Abstract: This work deals with procedural modelling of plants in computer graphics. It consists in designing an algorithm that generates models of plants by using deterministic and context free grammars. To represent the surface of the models, an implicit description is used. Output of the algorithm is the coarse structure of a plant. We present some 3D models obtained by visualization of the data using Paraview.

3D Phase Field Simulation of Multiple Grain Growth with Arbitrary Random Orientations
###### Aleš Wodecki, Pavel Strachota
FNSPE CTU in Prague

Abstract: This contribution will present the basics of the phase field model of single crystal growth in 3D and its extension to multiple grains with random orientations. First, a brief overview of the mathematical formulation and the description of the physical problem will be given. Next, we will describe a novel approach to simulating the growth of multiple crystals carrying the information about their orientation. A hybrid parallel implementation of the proposed algorithm will be explained. The talk will be concluded by the demonstration of some preliminary results.