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Quantification accuracy of abrasive process
Řehák, Pavel ; Sedlák, Josef (referee) ; Prokop, Jaroslav (advisor)
In this work, there is described an abrasive process including technological terms with an identification of motions and a speed of grinding. Then there are described abrasive tools, machines, their distribution and description. Further technological factors on accuracy of abrasive process and some reached parameters of the accuracy and their statistic interpretation.
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Periodic solutions to nonautonmous Duffing equation
Zamir, Qazi Hamid ; Řehák, Pavel (referee) ; Šremr, Jiří (advisor)
Ordinary differential equations of various types appear in the mathematical modelling in mechanics. Differential equations obtained are usually rather complicated nonlinear equations. However, using suitable approximations of nonlinearities, one can derive simple equations that are either well known or can be studied analytically. An example of such "approximative" equation is the so-called Duffing equation. Hence, the question on the existence of a periodic solution to the Duffing equation is closely related to the existence of periodic vibrations of the corresponding nonlinear oscillator.
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Nonlinear differential equations in the framework of the Karamata theory
Bukotin, Denys ; Opluštil, Zdeněk (referee) ; Řehák, Pavel (advisor)
Cílem této diplomové práce je sjednotit a zobecnit známé výsledky z literatury, studovat asymptotické chování kladných regulárně se měnících řešení jisté třídy nelineárních diferenciálních rovnic (tzv. skoro pololineárních diferenciálních rovnic) pomocí dostupných nástrojů. Tato práce zahrnuje popis teorie regulární variace, některé informace o nelineárních diferenciálních rovnicích různých typů, detailní odvození výsledků týkajících se asymptotického chování řešení a příklady aplikace získaných výsledků.
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Difference calculus and difference equations
Bukotin, Denys ; Opluštil, Zdeněk (referee) ; Řehák, Pavel (advisor)
This thesis deals with application of difference equations for describing real processes. The aim of this work is to show the applicability of this kind of equations for solving some problems. We define some concepts of difference calculus, theory of difference equations and stability theory, also we show some similarities with theory of differential equations. Then we investigate a particular mathematical model and the behavior of its solutions. We examine Nicholson-Bailey model, as an example of population models and we show that difference equations are a useful tool for describing real processes.
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Pursuit problems: basic models and their analysis
Neugebauer, Tomáš ; Řehák, Pavel (referee) ; Čermák, Jan (advisor)
This thesis is focused on creation of mathematical models and analysis of basic pursuit problems. In particular, the Perrault's problem, the Bouguer's problem, the Hathaway’s problem, the snail–racehorse problem and the Bailey's problem are involved. Each of the problems is solved analytically or numerically, including qualitative analysis.
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Energy saving of large objects
Řehák, Pavel ; Brázdil, Marian (referee) ; Pospíšil, Jiří (advisor)
The aim of this diploma thesis is to evaluate the economical measures using own heat and power production using cogeneration units, use of renewable resources to partially cover the consumption of objects, reduction of thermal losses by evaporation in the outdoor swimming pool and overall increase of waste heat utilization by exchanger heat exchangers from flue gas and heat from waste water.
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The Lorenz system: A route from stability to chaos
Arhinful, Daniel Andoh ; Šremr, Jiří (referee) ; Řehák, Pavel (advisor)
The theory of deterministic chaos has generated a lot of interest and continues to be one of the much-focused research areas in the field of dynamics today. This is due to its prevalence in essential parts of human lives such as electrical circuits, chemical reactions, the flow of blood through the human system, the weather, etc. This thesis presents a study of the Lorenz equations, a famous example of chaotic systems. In particular, it presents the analysis of the Lorenz equations from stability to chaos and various bifurcation scenarios with numerical and graphical interpretations. It studies concepts of non-linear dynamical systems such as equilibrium points, stability, linearization, bifurcation, Lyapunov function, etc. Finally, it discusses how the Lorenz equations serve as a model for the waterwheel (in detail), and the convection roll for fluid.
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Functional analysis and the mathematical pendulum
Čaputa, Daniel ; Šremr, Jiří (referee) ; Řehák, Pavel (advisor)
This thesis is focused on existence of periodic solutions of nonlinear model of mathematical pendulum with continuous, odd and periodic forcing term. In thesis, the differential equation of motion of pendulum is derived and the associated boundary value problem is rewritten as the integral equation. This equation is considered in a wider set of integral equations (Hammerstein equations). Fixed point theorems are applied on these equations what results in existence and uniqueness of solution. These results are applied on model of mathematical pendulum and the condition for uniqueness of solution is deeper discussed.
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Solar energy storage
Řehák, Pavel ; Pospíšil, Jiří (referee) ; Poláčik, Ján (advisor)
This thesis aims to find solution that deals with excess energy produced by solar systems. Main point in this Bachelor's thesis is to solve off-grid solar power system that is completely self-sufficient. Introduction examines how solar panels works and the best weather conditions of operating. Analytics part of this thesis focuses on basic information about types of power accumulation with their advantages and disadvantages. Practical part proposes system used and also mathematical solution of solar system.
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