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Continuous mathematical models of population dynamics
Pecka, Luboš ; Opluštil, Zdeněk (referee) ; Franců, Jan (advisor)
The aim of this thesis is to describe the most frequent models describing population dynamics and then to perform some numerical experiments in the MATLAB environment. These simulations should validate our theoretical results. The models are sorted from the basic models to the most complicated and are divided into the models which describe dynamics of one population and models of coexistence of two biological species. The master's thesis icludes also a program for drawing graphs and trajectories of solutions of models described in this thesis including a description of this MATLAB program.
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Dimensional transmutation in quantum theory
Ebr, Jan ; Hořejší, Jiří (advisor) ; Novotný, Jiří (referee)
This work deals with two models - from the quantum eld theory it is the massless scalar electrodynamics (the so-called Coleman-Weinberg model) and from quantum mechanics it is the contact (-function) potential (in two dimensions) - that are apparently invariant under some sort of scale transformations and thus they, in suitably chosen units, contain only dimensionless parameters. It turns out that even in the quantum-mechanical case one has to add an additional procedure to the formal denition of the model and that the use of dierent physical regulators leads to the same results, that furthermore agree with the predictions of the mathematically rigorous method of self-adjoint operator extensions. In this work, we present detailed calculations supporting this result. Contrary to the common literature, we do so in a straightforward manner, which can be followed step by step (with all the necessary elements of functional analysis summarised in the Appendix). In quantum eld theory we apply a similar approach, when we "rediscover" the results of the abstract functional methods in the ordinary perturbation theory. In its framework, we further show how to obtain predictions also for other quantities than particle masses.
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Measurement of transverse relaxation using spin echo methods
Škoch, Antonín ; Tošner, Zdeněk (advisor) ; Hanyková, Lenka (referee)
Title: Measurement of transverse relaxation using spin echo methods Author: MUDr. Antonin Skoch, Ph.D. Department: Department of Low Temperature Physics Supervisor: RNDr. Zdenek ToSner, Ph.D. NMR laboratory, of Faculty of science, Charles University in Prague Supervisor's e-mail address: tosner(o)karlov.mff.cuni.cz Abstract: The study of TI relaxation in systems with homonuclear J-coupling is complicated by modulation in the relaxation curve. This J-modulation can be removed when CPMG sequence is used and the period of repetition of refocusing pulse Tfulfils a condition r « * ( 1 ) Ai' where Av is the frequency difference of coupled nuclei. However, the condition (I) cannot be in practice always fulfilled. The aim of this work was to investigate J-modulation and relaxation behaviour of homonuclear J-coupled system in various parameters of CPMG sequence. Simulations based on numerical solution of Liouville-von Neumann equation and Redfield theory were performed. Relaxation curves of Chh group of citrate were measured on high-resolution NMR spectrometer. It was found that the suppression of J-modulation can be achieved also for T longer than required by the condition (1) providing that the refocusing angle in CPMG for both J-coupling partners 9^180ř. The simulations yielded conditions for T when J-modulation...
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Zpracování a interpretace výnosových map jako podklad pro agronomické rozhodování
Širůček, Petr
Diploma thesis was focused on data yield map processing, their interpretation and analysis of relations with another spatial data. Aims of the work were identification error values, statistical process yield data and with help statistical methods evaluate correlation between yield map and another spatial data. Methods were based on gathering yield data with combine harvester during two years in corn and malting barley in conditions of farm. With using GIS and predefined tolls were removed error values from yield data and created yield maps. Subsequently, yield maps were analyzed with vegetation index NDVI, digital elevation model (DEM), sensor measurements of soil electrical conductivity and historical yield maps. In results was achieved removing from 11,3 to 13,8 % yield points in average, increasing of average yield from 3,6 to 4,7 % and decreasing of variation coefficient between 7,0 and 8,6 % with comparing original yield data and depending on planting crops during data yield processing. In case of evaluation of relations between yield map and NDVI obtained from satellite remote sensing was achieved moderately correlation by corn (r = 0,44) and malting barley (r = 0,65) in average depending on times of imaging and vegetative phase of the crop. In the evaluation relations between yield maps and DEM and slope was achieved weak and very weak direct and indirect correlation. Likewise, by soil electrical conductivity and yield was achieved very weak to negligible correlation. Conversely, the highest correlation was achieved between yield map and historical yield map (r = 0,63) in average. Obtained information serve as starting point for making agronomy decisions in conditions of particular farm in case of replacement of creating yield maps by prediction of yield based on another spatial data.
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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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Control of Inverted Pendulum
Rýc, Jan ; Grepl, Robert (referee) ; Šolc, František (advisor)
In this work the identification of an inverted pendulum system is realised. To gain the mathematical model the second type of Lagrange equation is used. In program Simulink the creation of the nonlinear model from obtained equations and the resulting simulation are realised. Afterwards the system linearization about an equilibrium point is realised. It is described how to transfer the pendulum from its down position to its up position and how to stabilize it here. For this purpose the proposal of the control by the Quadratic Optimal Controller and PD regulator is made. Since the proposed way of stabilisation of the inverted pendulum is then applied on a real system in the laboratory of ÚAMT FEKT, the work also contains the description and the analysis of particular parts of the real model. The verification of the simulated and the real model is realised. Next part of the work deals with the system of an dual-inverted-pendulum which is placed on a cart.
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To the analysis of the bearing stiffness influence on the amplitude frequency characteristic of the gear wheels
Hortel, Milan ; Škuderová, Alena
To the analysis of the bearing stiffness influence on the amplitude frequency characteristic of the gear wheels.This contribution deals with the theory of planar steady damped oscillation of the isolated pair of spur gear, which is in two orthogonal direction elastically suspended. The analysis of the periodical solution was carried out by means of transformation of the differential boundary-value problem to the integral problem with the successive approximation and simulation method. The purpose is the determination of the bearing stiffness influence on the dynamic force in gearing mesh.
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Transport and Deposition of Aerosol in Human Respiratory Tract
Elcner, Jakub ; Kratochvíl, Zdeněk (referee) ; Volavý, Jaroslav (referee) ; Jícha, Miroslav (advisor)
One of approaches in treatment of respiratory system diseases is the use of drug particles suspended in air in the form of aerosol. It is a fast and non-invasive method for the delivery of medicine into tracheobronchial tree or bloodstream. Although the method of the medication dosage by means of inhalers or nebulizers is well known, the effectiveness of that approach is still an actual issue. A significant amount of drugs delivered with the use of the medication dosage never reaches its primary destination and the drugs deposit in antecendent areas of respiratory tract where their presence is not required. This thesis deals with a problem of the passage of monodisperse homogenous aerosol with micron-size particles through the upper parts of the respiratory tract. This work was created with the use of numerical simulations carried out by means of the finite volume method in the commercial code based on computational fluid dynamics. Turbulence was modelled using the Reynolds averaged Navier–Stokes equations with the two-equation eddy viscosity k-omega SST model. The main output of the thesis is the analysis of airflow in two respiratory regimes. Stationary and cyclic cases of the flow behaviour were considered and the validation of simulated results with experiments performed on similar geometries was carried out. Furthermore, the review of simplified lung models and their geometries was made and the acquired results were used for the calculation of air distribution in the respiratory tract. The last part of the thesis deals with the calculation of particle deposition and with the analysis of the results.
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The waste management of the constructed treatment wetlands
Mrvová, Michaela ; Hyánková, Eva (referee) ; Kriška-Dunajský, Michal (advisor)
The thesis is focused on the sludge management at root sewage treatment plants with focus on volum eis highest – sludge manahement. Sludge dewatering using sludge dryiing bed is still condemned designers mainly due to their lack of experience, while at the same time enforcing technologically complex solutions. Therefore, the thesis focuses on the break down balance hydrological equation sludge drying bed, which includes all parameters affecting water balance system. The result is a proposal not only design, but in particular a description of input data and the governing equations in software Reed-Bed, which is calibrated own operational results obtainde for the two sewage treatment plants (village Dražovice and Kotenčice). Reed-Bed software will perform sevetal functions: setting the ground area of sludge bed, investment costs required for the implementation of sludge bed, return on investment, the determination of moisture contene of sludge in the sludge bed and maximum lenght of the dewatering period with regard to wetland vegetation. The second largest item within sludge system creates biomass wetland plants, so work deals with possibilities biomass processing plant at the end of the growing season. Technological processing of biomass was tested on common reed, final product pellets for heating.
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