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Simulation of electrophysiological experiments
Kubáček, Svatopluk ; Provazník, Ivo (referee) ; Rychtárik, Milan (advisor)
Simulation of electrophysiological experiments enables to gain valuable data about bioelectrical processes occurring on isolated cells. This thesis deals with basic principals allowing the creation of bioelectrical phenomenons and measuring techniques that need to be used in order to collect information about these phenomenons. The outcome of the thesis is a programme that serves as an instrument for simulation of measuring techniques applied on Luo-Rudy model. The programme contains basic measuring techniques – current clamp and voltage clamp – providing the possibility to change basic parameters of the model. The results of this work are later compared with the accessible literature.
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Electric Circuits Simulations in a Specialized Parallel System
Janko, Roman ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work provides an overview of methods for the numerical solution of differential equations. Options of their parallelization, a division of computational operations on multiple microprocessors, are provided with emphasis placed on the Taylor series. The next part of the work is devoted to the description of a specialized parallel system, which was design to fast solving of these equations. Differential equations are appropriate to describe electrical circuits. An important characteristic of each circuit is its behavior in the frequency domain. The aim of this thesis was to design and implement a program which investigate frequency characteristics of AC circuits. A method for analyzing a circuit and automatically assembling corresponding equations is presented. These differential equations are then solved in TKSL. At the end of this work a time consumption is evaluated and compared with Matlab.
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Differential equations for systems involving bottlenecks
Šimečková, Kateřina ; Horníček, Jan (referee) ; Kisela, Tomáš (advisor)
The thesis deals with an analysis of differential equations for systems involving bottlenecks. The employed mathematical model originates from a hydrodynamical analogy. Further, the notion of sustainability, i.e. a situation when queues in bottlenecks do not exceed allowed limits, is discussed. In particular, conditions and algorithms enabling to describe sustainability properties of a given system are provided. The results are illustrated on several examples.
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CMOS VLSI Circuits Simulation
Šťastná, Hilda ; Kocina, Filip (referee) ; Šátek, Václav (advisor)
This diploma thesis deals with processes of electrical circuits calculations in the last years' worldwide standards like Dymola, MATLAB, Maple or SPICE applications. Circuits calculations are linked with methods for solving linear differential equations, used in this work also by verification of functionality of designed models for CMOS inverter, CMOS NAND, CMOS NOR. Numerical integration method in combination with Taylor series is a suitable method also for parallel calculations of CMOS VLSI circuits. CMOS circuits simulation was implemented with this method in applications in MATLAB language, solving circuits, represented by differential equations. Functionality of the applications was verified by some real examples. Significant acceleration of calculations using Taylor series compared to other methods is an important factor in choosing methods used in circuit simulations.
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Frequency and Transient Responses Based on Differential Equations
Turoňová, Lenka ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This bachelor thesis deals with the investigation of amplitude and phase frequency responses of linear electrical circuits. It compares classical methods of investigation using a symbolic-complex method with investigation using differential equations. For graphical representation of the responses in the case of the symbolic-complex method there was used for demonstration of examples programs MATLAB and Maple. The aim of this work was also to create graphical user interface over TKSL/C, which allows input of differential equations and plotting amplitude and phase frequency responses.
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Electronic circuits with fractal dynamics
Vojtová, Klára ; Guzan,, Milan (referee) ; Petržela, Jiří (advisor)
In the first section of this work is further analyzed the theories of differential equations and their computation and applications. The second part I addict to more detailed description of the Laplace transform, a sentence that is relevant to this area and also using the Laplace transform to solve electronic circuits. The third part of this project involves the theory of electronic circuits, especially the analysis and synthesis. The final and most important part is attended to circuits with fractal dynamics, design fractal approximation of the dynamics of capacitors in the frequency domain, has finally created its own electronic circuit measurement and evaluation results.
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SSI Dividing Numerical Integrator
Suntcov, Roman ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
The thesis deals with numerical integration and hardware division operations. The reader is familiar with the numerical solution of differential equations through several different methods, for example Taylor's series. Furthermore, it is discussed the operation of division in the hardware and the method of its implementation in the FPGA. Subsequently, a parallel-parallel and serial-parallel integrator is designed. The practical aim of the thesis is to design and implement a serial-serial dividing integrator and create a simulator for it.
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Adjoint Differential Equations
Kmenta, Karel ; Pindryč, Milan (referee) ; Kunovský, Jiří (advisor)
This project deals with solving differential equations. The aim is find the correct algorithm transforming differential equations of higher order with time variable coefficients to equivalent systems of differential equations of first order. Subsequently verify its functionality for equations containing the involutioin goniometrical functions and finally implement this algorithm. The reason for this transformation is requirement to solve these differential equations by programme TKSL (Taylor Kunovský simulation language).
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