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A Comparison of Preconditioning Methods for Saddle Point Problems with an Application to Porous Media Flow Problems
Axelsson, Owe ; Blaheta, Radim ; Hasal, Martin
The paper overviews and compares some block preconditioners for the solution of saddle point systems, especially systems arising from the Brinkman model of porous media flow. The considered preconditioners involve different Schur complements as inverse free Schur complement in HSS (Hermitian - Skew Hermitian Splitting preconditioner), Schur complement to the velocity matrix and finally Schur complement to a regularization block in the augmented matrix preconditioner. The inverses appearing in most of the considered Schur complements are approximated by simple sparse approximation techniques as element-by-element and Frobenius norm minimization approaches. A special interest is devoted to problems involving various Darcy, Stokes and Brinkman flow regions, the efficiency of preconditioners in this case is demonstrated by some numerical experiments.
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Two phase flow of water and air, flat jet above the plate, jet sloping 75° and 90°
Říha, Zdeněk
The report contains CFD results and description of the two phase flow water and air. Water comes into the computational domain through\nsimplified nozzle which creates water flat jet with spraying angle c. 40o. The flat jet falls on the wall surface where flows along the surface plate in all directions (x,y mainly). The aim of the work is to show how the falling water flows on the wall surface with help of advanced CFD model. Two cases had been solved there with various jets sloping to the surface plate. The first case contains results with configuration of the geometry for the jet sloping 75o and second case contains results with configuration of the geometry for the jet sloping 90o, see enclosures 1 and 2. Given calculation had been done as steady state calculations.
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Modelling, parameter estimation, optimisation and control of transport and reaction processes in bioreactors.
ŠTUMBAUER, Václav
With the significant potential of microalgae as a major biofuel source of the future, a considerable scientific attention is attracted towards the field of biotechnology and bioprocess engineering. Nevertheless the current photobioreactor (PBR) design methods are still too empirical. With this work I would like to promote the idea of designing a production system, such as a PBR, completely \emph{in silico}, thus allowing for the in silico optimization and optimal control determination. The thesis deals with the PBR modeling and simulation. It addresses two crucial issues in the current state-of-the-art PBR modeling. The first issue relevant to the deficiency of the currently available models - the incorrect or insufficient treatment of either the transport process modeling, the reaction modeling or the coupling between these two models. A correct treatment of both the transport and the reaction phenomena is proposed in the thesis - in the form of a unified modeling framework consisting of three interconnected parts - (i) the state system, (ii) the fluid-dynamic model and (iii) optimal control determination. The proposed model structure allows prediction of the PBR performance with respect to the modelled PBR size, geometry, operating conditions or a particular microalgae strain. The proposed unified modeling approach is applied to the case of the Couette-Taylor photobioreactor (CTBR) where it is used for the optimal control solution. The PBR represents a complex multiscale problem and especially in the case of the production scale systems, the associated computational costs are paramount. This is the second crucial issue addressed in the thesis. With respect to the computational complexity, the fluid dynamics simulation is the most costly part of the PBR simulation. To model the fluid flow with the classical CFD (Computational Fluid Dynamics) methods inside a production scale PBR leads to an enormous grid size. This usually requires a parallel implementation of the solver but in the parallelization of the classical methods lies another relevant issue - that of the amount of data the individual nodes must interchange with each other. The thesis addresses the performance relevant issues by proposing and evaluation alternative approaches to the fluid flow simulation. These approaches are more suitable to the parallel implementation than the classical methods because of their rather local character in comparison to the classical methods - namely the Lattice Boltzmann Method (LBM) for fluid flow, which is the primary focus of the thesis in this regard and alternatively also the discrete random walk based method (DRW). As the outcome of the thesis I have developed and validated a new Lagrangian general modeling approach to the transport and reaction processes in PBR - a framework based on the Lattice Boltzmann method (LBM) and the model of the Photosynthetic Factory (PSF) that models correctly the transport and reaction processes and their coupling. Further I have implemented a software prototype based on the proposed modeling approach and validated this prototype on the case of the Coutte-Taylor PBR. I have also demonstrated that the modeling approach has a significant potential from the computational costs point of view by implementing and validating the software prototype on the parallel architecture of CUDA (Compute Unified Device Architecture). The current parallel implementation is approximately 20 times faster than the unparallized one and decreases thus significantly the iteration cycle of the PBR design process.
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Modelling runoff processes in experimental Bystřice River catchmet in the Krušné Mountains
Hasa, Martin ; Jeníček, Michal (advisor) ; Šípek, Václav (referee)
This work deals with the modelling of runoff processes in the experimental Bystřice river catchment in the Krušné Mountains. Rainfall-runoff model WaSiM (Topmodel version) was used for this purpose.Objective of this study was modelling snow accumulation and snowmelt in winter periods 2009/2010 and 2010/2011. Sensitivity analysis of TOPMODEL parameters was performed using Monte Carlo and GLUE methodology. Wasim was calibrated manually for 25 and 250 m grid scales and daily timestep. Results of simulations in both spatial scales different spatial scales differed significantly. Better performance of modelling in finer scale wasn't proved in validation of the model. Results of the simulations pointed out uncertainty in model calibration. Rasters of modeled snow water equivalent were also analyzed in selected days representing periods of snow accumulation and snowmelt. The goal was to examine the functioning of used snow model (combination of temperature index method and energy balance method) within the WaSiM frame. Finer scale raster proved to be practical for this purpose It was found that the spatial heterogeneity in the distribution of snow is determined by evapotranspiration and also by effect of radiation correction (in the case of rainfall).Influence of interception and vegetation effects on...
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Neural Networks Between Integer and Rational Weights
Šíma, Jiří
The analysis of the computational power of neural networks with the weight parameters between integer and rational numbers is refined. We study an intermediate model of binary-state neural networks with integer weights, corresponding to finite automata, which is extended with an extra analog unit with rational weights, as already two additional analog units allow for Turing universality. We characterize the languages that are accepted by this model in terms of so-called cut languages which are combined in a certain way by usual string operations. We employ this characterization for proving that the languages accepted by neural networks with an analog unit are context-sensitive and we present an explicit example of such non-context-free languages. In addition, we formulate a sufficient condition when these networks accept only regular languages in terms of quasi-periodicity of parameters derived from their weights.
Fulltext: content.csg -  PDF
Plný tet: v1237-16 - PDF
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Modelling commodity chain of beef
Nováková, Lucie ; Malý, Michal (advisor) ; Kateřina, Kateřina (referee)
The submitted diploma thesis deals with modeling the commodity chain of beef, namely the
impact of the relevant variables in the production and consumption of beef in the Czech
Republic. The thesis is divided into three parts. The first part deals with econometric modeling
and general characteristics of the commodity chain. The second section summarizes the process
and the economic aspects of beef production in our country. In the practical part there are
formulated, specified, quantified and verified two econometric models. The first model deals
with addiction beef production in selected variables. The second model solves the question of
influences on consumption of beef. The prognosis of future development for the period 2016-
2018 was determined on the basis of these models. The latest model captures the price transfers
within the commodity chain of beef.
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Effect of snowpack on runoff generation during rain on snow event.
Juras, Roman ; Máca, Petr (advisor) ; Ladislav , Ladislav (referee)
During a winter season, when snow covers the watershed, the frequency of rain-on-snow (ROS) events is still raising. ROS can cause severe natural hazards like floods or wet avalanches. Prediction of ROS effects is linked to better understanding of snowpack runoff dynamics and its composition. Deploying rainfall simulation together with hydrological tracers was tested as a convenient tool for this purpose. Overall 18 sprinkling experiments were conducted on snow featuring different initial conditions in mountainous regions over middle and western Europe.
Dye tracer brilliant blue (FCF) was used for flow regime determination, because it enables to visualise preferential paths and layers interface. Snowpack runoff composition was assessed by hydrograph separation method, which provided appropriate results with acceptable uncertainty. It was not possible to use concurrently these two techniques because of technical reasons, however it would extend our gained knowledge. Snowmelt water amount in the snowpack runoff was estimated by energy balance (EB) equation, which is very efficient but quality inputs demanding. This was also the reason, why EB was deployed within only single experiment.
Timing of snowpack runoff onset decrease mainly with the rain intensity. Initial snowpack properties like bulk density or wetness are less important for time of runoff generation compared to the rain intensity. On the other het when same rain intensity was applied, non-ripe snowpack featuring less bulk density created runoff faster than the ripe snowpack featuring higher bulk density. Snowpack runoff magnitude mainly depends on the snowpack initial saturation. Ripe snowpack with higher saturation enabled to generate higher cumulative runoff where contributed by max 50 %. In contrary, rainwater travelled through the non-ripe snowpack relatively fast and contributed runoff by approx. 80 %.
Runoff prediction was tested by deploying Richards equation included in SNOWPACK model. The model was modified using a dual-domain approach to better simulate snowpack runoff under preferential flow conditions. Presented approach demonstrated an improvement in all simulated aspects compared to the more traditional method when only matrix flow is considered.
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The Wine Market in the Czech Republic and the Politics of Wine
Vlašicová, Eliška ; Tomšík, Karel (advisor) ; Malý, Michal (referee)
The dissertation thesis is focusing on the wine market in the Czech Republic. The aim is to identify weaknesses in the wine sector in order to formulate recommendations for improving a current situation in the sector. The Common Agricultural Policy of the European Union and the Common Market Organisation for Wine was presented in the theoretical part of the thesis, where also theoretical aspects of a market including supply and demand were described, as well as an agri-food market and its specifics, wine commodity chain, determinants of demand, supply and prices of wine. In the following chapters an analysis of the wine market, especially with emphasis on the production potential of vineyards in the Czech Republic was created, and demand, supply and price of wine including a price transmission in the commodity chain of wine were modelled based on a regression analysis. The significant influence on demand of wine have had previous values of wine consumption and wine prices, substitutes consumptions (prices of substitutes were not a significant factors), household income and salary, a quality of the wine and awards in international competitions. Significant factors of the side of supply including the price of wine grapes, the price of wine, vineyard area, production of wine grapes, some aspects of weather and certain subsidies. A climate change, which is in progress, may result to the expansion of viticulture and winemaking in the Czech Republic and also to a change of varieties in vineyards. Demand has in the commodity chain of wine greater impact than the supply. It can have a negative effect on growers or winemakers. Planting of vines is not sufficient to maintain current levels of a production potential of vineyards in the Czech Republic. The ideal amount of annual planting vines should be about 655 ha. A related issue is financing a vineyards renewal, which is costly. Based on a financial analysis of small and medium-sized wine companies, it was found that these businesses cannot afford the renewal of vineyards from its own resources and will require grant assistance of the state, eventually EU.
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Feasibility Study of an Interactive Medical Diagnostic Wikipedia
Grim, Jiří
Considering different application possibilities of product distribution mixtures we have proposed three formal tools in the last years, which can be used to accumulate decision-making know-how from particular diagnostic cases. First, we have developed a structural mixture model to estimate multidimensional probability distributions from incomplete and possibly weighted data vectors. Second, we have shown that the estimated product mixture can be used as a knowledge base for the Probabilistic Expert System (PES) to infer conclusions from definite or even uncertain input information. Finally we have shown that, by using product mixtures, we can exactly optimize sequential decision-making by means of the Shannon formula of conditional informativity. We combine the above statistical tools in the framework of an interactive open-access medical diagnostic system with automatic accumulation of decision-making knowledge.
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Service-oriented simulation architecture
Polášek, Petr ; Sklenář, Jaroslav (referee) ; Kavička,, Antonín (referee) ; Češka, Milan (advisor)
This thesis focuses on design, modeling and simulation of heterogeneous systems with emphasis on discrete-event systems. It proposes service-oriented simulation architecture where modeling and simulation is treated as a service and establishes a DEVS Meta Language that is intended for implementation of simulation models based on the DEVS formalism. Special M\&S techniques are described and integration of existing simulation tools is discussed as well.
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