National Repository of Grey Literature 56 records found  1 - 10nextend  jump to record: Search took 0.01 seconds. 
A traffic flow with a bottelneck
Kovařík, Adam ; Janovský, Vladimír (advisor) ; Vejchodský, Tomáš (referee)
Title: A traffic flow with a bottelneck Author: Adam Kovařík Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Vladimír Janovský, DrSc. Supervisor's e-mail address: janovsky@karlin.mff.cuni.cz Abstract: In this paper we study a microscopic follow-the-leader traffic model on a circu- lar road with a bottleneck. We assume that all drivers are identical and overtaking is not permitted. We sketch a small part of the rich dynamics of the model including Hopf and Neimark-Sacker bifurcations. We introduce so called POM and quasi-POM solutions and an algorithm how to search them. The main goal of this work is to investigate how the optimal velocity model with a bottleneck deals with so called aggressive behavior of dri- vers. The effect of variable reaction time and a combination of both named factors is also tested. Using numerical simulations we'll find out that aggressiveness and faster reactions have positive effect on traffic flow. In the end we discuss models with two bottlenecks and with one extraordinary driver. Keywords: dynamical systems, ODEs, traffic flow, bottleneck, aggressiveness. 1
Numerická optimalizace
Márová, Kateřina ; Janovský, Vladimír (advisor) ; Lukšan, Ladislav (referee)
This thesis addresses the topic of unconstrained optimization. It describes seven derivative-free optimization methods for objective functions of multiple variables. Three groups of methods are distinguished. The Alternating Variable method and the method of Hooke and Jeeves represent the pattern search methods. Then there are two simplex algorithms: one by Spendley, Hext and Himsworth and the amoeba algorithm of Nelder and Mead. The family of methods with adaptive sets of search directions consists of Rosenbrock's method, the method of Davies, Swann and Campey, and Powell's method. All algorithms are implemented in MATLAB and tested on three functions of two variables. Their progression is illustrated by multiple figures and their comparative analysis is given. Powered by TCPDF (www.tcpdf.org)
Numerical solution of ordinary differential equations
Monhartová, Petra ; Feistauer, Miloslav (advisor) ; Janovský, Vladimír (referee)
In the present work we study numerical methods for the nu- merical solution of initial value problems for ordinary differential equations. With the aid of the Taylor formula we derive several one-step methods. We compare numerical solution computed with explicit and implicit Eu- ler methods. Moreove, we are concerned with second-order and fourth-order Runge-Kutta methods. We find how accurately the numerical methods obta- ined with the aid of these methods approximate the exact solution. Further we estimate the error of these method by the half-step method. 1
Transformation of a matrix to bidiagonal form
Kubásek, Petr ; Zítko, Jan (advisor) ; Janovský, Vladimír (referee)
Abstract: In the present work we si udy algorithms lo transform matrix to bidiagonal shape with usage of Householder...
Filippov dynamical systems with applications
Šimonová, Dorota ; Janovský, Vladimír (advisor) ; Ratschan, Stefan (referee)
The thesis is motivated by problems of contact mechanics with friction. At the beginning we describe a class of piecewise smooth systems with discontinuous vector field called Filippov systems. We also show how to solve them. The rest of this thesis is focused on applications, especially dry friction model and finite element model of Coulomb friction with one contact point. We propose a technique for simulation of the second mentioned model which combines sovling methods for Filippov systems and impact oscillators. Powered by TCPDF (www.tcpdf.org)
Overtaking model on a circular road
Krejčiřík, Radek ; Janovský, Vladimír (advisor) ; Kofroň, Josef (referee)
In this work we consider an extended follow-the-leader traffic model which was presented in [9]. The Model simulates movements of N identical cars on a circular road. There are two new aspects in this model included: velocity of each car depends on a variable reaction time and on an aggressiveness of the driver as well. Aggressiveness has a stabilizing effect on the traffic flow and variable reaction time changes the periodic dynamics in the model, but there are still some un-physical solutions. The benefit of this work is in an application of an overtaking-algorithm to the extended model. We also show an equivalent formulation of the problem as a system of ordinary differential equations with a discontinuous right-hand side. We show an existence of periodic solutions with overtaking.
On a model of corruption in a democratic society
Splítek, Martin ; Janovský, Vladimír (advisor) ; Mlčoch, Lubomír (referee)
The aim of this work is to study the behavior of serious social pheno- menon - corruption, and we do this through a mathematical model of corruption in a democratic society, published in [1]. The model is a dynamical system of three differential equations, specified by three variables and ten parameters. The model is studied by means of numerical analysis, namely, the method of nume- rical integration of ordinary differential equations and the method of numerical continuation. We used toolbox Matcont [2], which works in the environment of program MATLAB [3]. The result is commented parametric study of the pheno- menon of corruption. Keywords: ordinary diferential equations, dynamic systems, bifurcation ana- lysis 1
Oscillations in mechanical systems with implicit constitutive relations.
Babováková, Jana ; Pražák, Dalibor (advisor) ; Janovský, Vladimír (referee)
We study a system of differential-algebraic equations, describing motions of a mass-spring-dashpot oscillator by three different forms of implicit constitu- tive relations. For some problems with fully implicit but linear constitutive laws for combined force, we find conditions for solution stability. Assuming monotone relationship between the displacement, velocity and the respective forces, we prove global existence of the solutions. For a linear spring and a dashpot with maximal monotone relationship between the damping force and the velocity, we prove the global existence and uniqueness result. We also solve this problem numerically for Coulomb-like damping term.
Matrix Pseudospectrum
Marková, Hana ; Janovský, Vladimír (advisor) ; Najzar, Karel (referee)
In the present work we study properties, calculation methods and behaviour of pseudospectrum of matrix or linear operator. First we introduce related terms, then we define pseudospectrum in four different ways and show its basic properties. Consequently, we generalize the theory of pseudospectrum for linear operators in Banach spaces. Basic methods of computation including fundamental possibilities of speeding up follow, but especially we go through computations on grid and path following technique. In the end we derive bounds which outline behaviour of dynamical systems. The last chapter contains practical example, which relates to laser theory.

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