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Static and dynamic analysis of plain and fiber-reinforced concrete using discrete meso-scale model
Květoň, Josef ; Vorel,, Jan (referee) ; Šejnoha,, Michal (referee) ; Eliáš, Jan (advisor)
Předkládaná práce se zabývá matematickým modelováním chování betonu. K numerické analýze je použit diskrétní částicový model. Tento model zjednodušuje meso-strukturu materiálu na systém propojených diskrétních částic -- konvexních mnohostěnů. Tyto částice jsou uvažovány ideálně tuhé a jejich vzájemná interakce je předepsána na kontaktech sousedních částic. Při hledání nespojitého pole posunů a rotací jsou zjednodušeně předpokládány malé deformace. Práce popisuje dvě rozšíření implementovaná do stávající verze modelu, konkrétně (i) přidání reprezentace krátké rozptýlené výztuže a (ii) implicitní dynamický řešič. První z hlavních částí práce se zabývá modelováním kompozitů s krátkou rozptýlenou výztuží. Krátká vlákna rozptýlená v materiálu přispívají k zlepšení jinak nepříznivé tahové pevnosti betonu. Vlákna jsou v částicovém modelu reprezentována nepřímo, zohledněním tření mezi vláknem a cementovou matricí silami, které působí proti otevírání trhlin. S pomocí tohoto rozšíření model dokáže předpovídat chování vláknobetonu zahrnující tahové zpevnění i navýšení počtu trhlin. Druhá z hlavních částí se zabývá odezvou materiálu na dynamické zatížení. Beton vykazuje rozdílné chování pro různé rychlosti zatěžování. V případě pomalého, kvazi-statického, zatěžování se počáteční mikro-trhliny lokalizují v makro-trhlinu. Dochází-li k rychlému zatěžování, energie nahromaděná v tělese není spotřebována pouze jednou trhlinou, ale dochází k jejímu větvení. V případě rychlých procesů je hlavním faktorem setrvačnost hmoty, která je zatížením urychlována. Struktura materiálu a setrvačnost částic je v mezo-úrovňovém diskrétním modelu zahrnuta. Přesto ale další jevy probíhající pod rozlišovací úrovní modelu ovlivňují výsledné chování materiálu. Proto je do modelu přidána fenomenologická závislost konstitutivního zákona na rychlosti přetváření. Numerické simulace těles rozličných tvarů zatěžovaných různou rychlostí deformace jsou porovnány s experimenty z literatury.
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Biogenesis, structure and physiological functions of mitochondrial ATP synthase
Eliáš, Jan ; Mráček, Tomáš (advisor) ; Doležal, Pavel (referee)
Mammalian mitochondrial ATP synthase is an enzyme composed of 18 protein subunits, which is localised in the inner mitochondrial membrane. Its main function is to utilise proton gradient, produced by respiratory chain complexes (RCC), for the synthesis of ATP. Aside from the creation of ATP it is known that its dimers contribute to the correct mitochondrial morphology through the formation of cristae apexes. Furthermore, ATP synthase was proposed to have a role in the mitochondrial permeability transition phenomenon, which is important for regulation of programmed cell death. Over the recent years, our understanding of mammalian ATP synthase biogenesis has been tremendously improved. Its assembly process is now clarified, however the knowledge about assembly intermediates of its peripheral stalk and of subunit c are still not sufficient. We focused precisely on those unsolved questions in the fields of ATP synthase biogenesis and its secondary functions, by the production of a KO model of catalytic β subunit of mammalian ATP synthase F1 domain (βKO). This model was successfully prepared on the background of HEK293 cell line. Its characterisation revealed that disruption of the F1 structure resulted in the inability to assemble functional monomer and resulted in a decay of individual subunits. The only...
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Lagrange multipliers in linear elastostatics
Ondášová, Annamária ; Květoň, Josef (referee) ; Eliáš, Jan (advisor)
The thesis deals with the use of Lagrange multipliers, explaining the principle of their use and the calculating process. Lagrange multipliers are introduced into joints of a given truss structure. The calculation is conducted using minimalization of the potential energy and the principle of virtual work. Results are verified by direct elimination of the variables.
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Approximate Polynomial Greatest Common Divisor
Eliaš, Ján ; Zítko, Jan (advisor) ; Hnětynková, Iveta (referee)
Title: Approximate Polynomial Greatest Common Divisor Author: Ján Eliaš Department: Department of Numerical Mathematics, MFF UK Supervisor: Doc. RNDr. Jan Zítko, CSc., Department of Numerical Mathematics, MFF UK Abstract: The computation of polynomial greatest common divisor (GCD) ranks among basic algebraic problems with many applications. The Euclidean algorithm is the oldest and usual technique for computing GCD. However, the GCD computation problem is ill-posed, particularly when some unknown noise is applied to the polyno- mial coefficients. Since the Euclidean algorithm is unstable, new methods have been extensively studied in recent years. Methods based on the numerical rank estimation represent one group of current meth- ods. Their disadvantage is that the numerical rank cannot be computed reliably due to the sensitivity of singular values on noise. The aim of the work is to overcome the ill-posed sensitivity of GCD computation in the presence of noise. Keywords: AGCD, Sylvester matrix, numerical rank, TLS
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CRISPR/Cas9-based genome editing in mice: state of the art and future perspectives
Eliáš, Jan ; Kašpárek, Petr (advisor) ; Čáp, Michal (referee)
Mutant mice are crucial tools for understanding gene functions in vivo. Recently, generation of mouse mutants was revolutionized by rapid developement of programmable nucleases, predominantly by the CRISPR/Cas9 system. Genome editing based on introduction of CRISPR/Cas9 components into early stage mouse embyros allows fast and inexpensive generation of gene-deficient animal models, especially when compared to the traditional techniques based on modification of embryonic stem cells (ESCs). The ability of CRISPR/Cas9 to induce double-strand break (DSB) at a given location of genomic DNA enables effective gene-ablation by random modification of the coding sequences or by complete ablation of the gene. However, precise modification of the gene sequences, such as incorporation of a DNA fragment into specific loci, are still difficult to make. In this work, I present a review of CRISPR/Cas9 system, its use in production of mutant mice and possible modifications of the system to increase the efficiency of precise gene-targeting. Keywords: CRISPR/Cas9, mouse, transgenesis, homologous recombination
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Micropolar continuum and its applications in structural mechanics
Fleischerová, Beáta ; Vořechovský, Miroslav (referee) ; Eliáš, Jan (advisor)
Práca sa zaoberá mechanikou kontinua. Konkrétne je zameraná na lineárnu elasticitu homogénnych izotropných pevných telies. Pre dve rôzne kontinuá – klasické kontinuum a mikropolárne je odvodená silná aj slabá formulácia. Cosseratovo (mikropolárne) kontinuum predstavuje rozšírenie ku klasickému, kde je uvažovaný ďalší stupeň voľnosti - nezávislá rotácia. Mikropolárne kontinuum definuje ďalšie dve materiálové konštanty, ktoré súvisia s rotáciou. V súčasnosti je metóda konečných prvkov veľmi populárny spôsob približného riešenia rovníc lineárnej elasticity. Pre účely diplomovej práce bol vyvinutý program pre MKP riešenie 2D rovinných úloh. Pre lepšiu predstavu o vplyvu rôznych parametrov na správanie sa oboch kontinuí analyzujeme jednoduchý príklad konzolového nosníka. Riešenia analyzujeme s využitím 4-uzlového štvorhranného elementu, ktorý je jedným z najpoužívanejších pre MKP. V Cosseratovom kontinue by mali byť rotácie previazené skrz parameter vnútornej dĺžky, čo by sa malo odzrkadliť zvýšenou tuhosťou telesa. Úlohou práce je porovnať výsledky z oboch kontinuí a potvrdiť tento predpoklad.
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Hellinger-Reissner Variational Principle Based Quadrilateral Finite Element
Středulová, Monika ; Eliáš, Jan
The Finite Element Method is without a doubt one of the most prominent tools in solving the equations governing mechanics of solids. It is an approximative method and, as such, its performance largely depends on the definition of the finite element used in a computation. The simplest elements, based on one primary field, tend to suffer from “locking”, that is excessive stiffness when an element is subjected to bending or the material is nearing the limit of incompressibility. One of the alternatives is the use of an element based on multiple primary fields. The present article aims to describe one such element (based on mixed-field Hellinger-Reissner variational principle) and analyze its robustness in comparison to other methods which were used in the past to mitigate locking. The analysis will be done in the framework of linear elastostatics.
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Generation and analysis of mutant mouse model to study roles of KLKs in cutaneous inflammation
Eliáš, Jan ; Kašpárek, Petr (advisor) ; Drbal, Karel (referee)
Kallikrein-related peptidases (KLKs) are a subgroup of serine proteases of undisputable importance for a variety of functions, whose dysregulation has been linked to several pathological phenotypes. Among those pathologies, the Netherton syndrome stands out, since it is one of the very few that has its mechanism directly linked to KLK proteases as the main culprit of the disease, namely KLK5, KLK7 and to a lesser degree, KLK14. In this case, a mutation in the SPINK5 gene leads to uncontrolled hyperactivity of those proteases, which results in epidermal barrier breach due to excessive epidermal desquamation and severe inflammation of the skin. Inflammation mechanisms of NS are still relatively poorly understood, with important roles being attributed to the activities of KLKs in the processing of immune system molecules and also to the dysregulation of the cutaneous microbiome. TNFα signalling plays a key role in the homeostasis and immune response in the skin. Chronic skin infections may lead to deleterious effects with strong participation of TNFα signalling. To address the degree of its effects on the pathogenesis of NS, we have created a mouse model where the TNFR1 is disrupted by knockout of the Tnfr1 gene on the background of a previously established mouse model of the Netherton syndrome. We...
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Structure and physiological role of the mitochondrial permeability transition pore
Eliáš, Jan ; Mráček, Tomáš (advisor) ; Kalous, Martin (referee)
Mitochondrial permeability transition pore (mPTP) is Ca2+ dependent channel localised in the inner mitochondrial membrane. One of its defining characteristics is inhibition by nanomolar concentrations of immunosuppressant cyclosporine A (CsA). Together with additional interacting proteins, which regulate its opening, mPTP forms a permeability transition protein complex. Persistent opening of mPTP is accompanied by mitochondrial swelling and a subsequent collapse of organelle, which precedes release of proapoptotic proteins and programmed cell death. Channel forming unit of mPTP remains unknown, despite intense and long-lasting study. Numerous proteins were proposed to play a role of channel forming subunit of mPTP, including complex of ANT and VDAC, ANT alone, PiC or even ATP synthase. Despite the fact, that molecular structure remains elusive, mPTP seems to play a role in a range of pathophysiological processes or diseases associated with them. Among others this includes ischemia/reperfusion injury, neurological and muscle dystrophies, or tumorigenesis. Keywords: mitochondria, mitochondrial permeability transition pore, cyclosporine A, programmed cell death, ATP synthase, oxidative phosphorylation apparatus.
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