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Stationary fields in black-hole space-times
Čížek, Pavel ; Semerák, Oldřich (advisor) ; Ledvinka, Tomáš (referee) ; Gürlebeck, Norman (referee)
Motivated by modelling of astrophysical black holes surrounded by accretion structures, as well as by theoretical interest, we study two methods how to ob- tain, within stationary and axisymmetric solutions of general relativity, a metric describing the black hole encircled by a thin ring or a disc. The first is a suitable perturbation of a Schwarzschild black hole. Starting from the seminal paper by Will (1974), we showed that it is possible to express the Green functions of the problem in a closed form, which can then be employed to obtain, e.g., a reason- able linear perturbation for a black hole surrounded by a thin finite disc. In the second part we tackle the same problem using the Belinskii-Zakharov generating algorithm, showing/confirming that in a stationary case its outcome is unphysi- cal, yet at least obtaining a modest new result for the (static) "superposition" of a Schwarzschild black hole with the Bach-Weyl ring. 1
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Control Problems in Epidemiology
Čížek, Pavel ; Milota, Jaroslav (advisor) ; Pražák, Dalibor (referee)
Na/.ev prace; Ki/cnf \) eh modeled] Aulor: Pavel Ci/ek Kaledra; Kaledra matemaliekc analy/.y Vcdouef bakala'rskc prace: Doc. KNDr. Jarosla\. CSc. c-inait vedouci'ho: niilota(« karlin.mff.cuni.c/ Ahsirakl: V predlo/cne praci studujeme model maso\. inlekcm mikropara/iiicke epidcinie. Co oduv.eni" modeiu, klcre \ycha/( / hiologickyeh po/nulku o sludovaiicni lypu epideiuii. u\a\liine |eho /a'kladm nialeniaiicke \htslmMi. /.axx'dcni'in ock(i\';ii:i' niotlei iransloriiiujcrnc. I);ile ^o /ah\\anie \laslnosUni feseni piivodm'ho i iransiorinox anelio niodelu a siahililou siaciona'nueli Inidii. PoroMuixanfni vysiedkii pro model puvodm a model iran>Jormovan\, /da je ocko\ain' /.a\edeno spra\-nc. lA.idinie i jiiie mo/noMi jcho /a\'edem. N;is!cdnc se /.ahvvanie cenou Icehy a ockovant'. Illedamc linancne n e j \ i re^cnf ma/k\k \'clikou cast populace oekovat. Tiile; Isi/em \h modeled! Auihor: Pa\el C ' f / e k Departnicnl: Kaledra iimlematickr aiialv/y Sii|)er\: Doe. RNDr. Jaio^lax Miloia. C'Se. Super\s e-mail adress: nii]o{a('1''karliu.n)tT.cuni.c/ Ahsii'acl: In the present work \\ studx a model of a ma^-action mieniparasiue epidoniic. After the deduction of llie motlel. \\lilcli issues from biologic in for uiafioii ahiui! ihe studied l\pe of epidemic. \\ mention basic maihematic.il chaiactcrislies. \\"e transform die...
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Slowly rotating sources around static black holes
Čížek, Pavel ; Semerák, Oldřich (advisor) ; Ledvinka, Tomáš (referee)
In this thesis we study the possibility of perturbative solution of the Einstein equations in the case of stationary and axially symmetric metric. The method is motivated by the pursuit of describing the astrophysically important system of a black hole surrounded by a thin disc or a ring. A Schwarzschild black hole is thus considered as a central source, with a light and/or slowly rotating disc around. We show that the metric can be found in terms of perturbative expansions in relative disc mass or in inverted distance from the hole, and point out where problems occur. The approach can be applied to a disc "given in advance" as well as in the "self-consistent" case when the disc elements orbit on circular geodesics in the desired total eld. It can also be generalised to the discs composed of more dust components.
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Mathematical analysis and numerical simulation of bone remodeling
Čížek, Pavel ; Maršík, František (advisor) ; Hron, Jaroslav (referee)
In the presented work, we study a model of bone deformation caused by action of external forces. After the biological introduction, in which we describe a bone remodelling process and its connection with bone deformation, we deal with conservation laws and material characteristics of a bone. We define weak formulation. Further, we linearize the equations and prove existence and uniqueness of the solution. Consecutively, we describe the finite element method and the programming of this method for the computing of the approximate solution of the problem using the logic of object-oriented programming. We also adduce a description of the used data structures. In the conclusion, we present numerical results reached by the described program that represent deformation of femur and deformation of vertebras and intervertebral foramina.
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Go on Small Boards
Čížek, Pavel ; Hric, Jan (advisor) ; Majerech, Vladan (referee)
In presented work we study applicability of the heuristics used in computer analysis of the chess (to be specific we will consider transposition tables, killer moves, history heuristics and counter-moves) for the valuation of the position in the go. In the first part will try to deal with problems which arises, because rules and behaviour of the chess and go are really different in some ways. Obtained heuristics had been implemented and at the end we will try to evaluate their efficiency and mutual (in)dependence experimentally using this program to solve some simple positions.
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Stationary fields in black-hole space-times
Čížek, Pavel ; Semerák, Oldřich (advisor)
Motivated by modelling of astrophysical black holes surrounded by accretion structures, as well as by theoretical interest, we study two methods how to ob- tain, within stationary and axisymmetric solutions of general relativity, a metric describing the black hole encircled by a thin ring or a disc. The first is a suitable perturbation of a Schwarzschild black hole. Starting from the seminal paper by Will (1974), we showed that it is possible to express the Green functions of the problem in a closed form, which can then be employed to obtain, e.g., a reason- able linear perturbation for a black hole surrounded by a thin finite disc. In the second part we tackle the same problem using the Belinskii-Zakharov generating algorithm, showing/confirming that in a stationary case its outcome is unphysi- cal, yet at least obtaining a modest new result for the (static) "superposition" of a Schwarzschild black hole with the Bach-Weyl ring. 1
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Stationary fields in black-hole space-times
Čížek, Pavel ; Semerák, Oldřich (advisor)
Motivated by modelling of astrophysical black holes surrounded by accretion structures, as well as by theoretical interest, we study two methods how to ob- tain, within stationary and axisymmetric solutions of general relativity, a metric describing the black hole encircled by a thin ring or a disc. The first is a suitable perturbation of a Schwarzschild black hole. Starting from the seminal paper by Will (1974), we showed that it is possible to express the Green functions of the problem in a closed form, which can then be employed to obtain, e.g., a reason- able linear perturbation for a black hole surrounded by a thin finite disc. In the second part we tackle the same problem using the Belinskii-Zakharov generating algorithm, showing/confirming that in a stationary case its outcome is unphysi- cal, yet at least obtaining a modest new result for the (static) "superposition" of a Schwarzschild black hole with the Bach-Weyl ring. 1
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Stationary fields in black-hole space-times
Čížek, Pavel ; Semerák, Oldřich (advisor) ; Ledvinka, Tomáš (referee) ; Gürlebeck, Norman (referee)
Motivated by modelling of astrophysical black holes surrounded by accretion structures, as well as by theoretical interest, we study two methods how to ob- tain, within stationary and axisymmetric solutions of general relativity, a metric describing the black hole encircled by a thin ring or a disc. The first is a suitable perturbation of a Schwarzschild black hole. Starting from the seminal paper by Will (1974), we showed that it is possible to express the Green functions of the problem in a closed form, which can then be employed to obtain, e.g., a reason- able linear perturbation for a black hole surrounded by a thin finite disc. In the second part we tackle the same problem using the Belinskii-Zakharov generating algorithm, showing/confirming that in a stationary case its outcome is unphysi- cal, yet at least obtaining a modest new result for the (static) "superposition" of a Schwarzschild black hole with the Bach-Weyl ring. 1
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