The illustration of the law of large numbers by simulations

Stochastická konvergence, zákon velkých čísel a centrální limitní věta představují důležitou část teorie pravděpodobnosti, která se často užívá v matematické statistice. Cílem této práce je popsat tuto teorii a demonstrovat ji na příkladech a grafických simulacích. Kromě simulací stochastické konvergence, zákona velkých čísel a centrální limitní věty pro některá diskrétní a spojitá rozdělení pravděpodobnosti práce obsahuje i několik zajímavých simulací a to simulaci Galtonovy desky, Buffonovy úlohy a Bertrandova paradoxu. K vytvoření grafických simulací byl použit programovací jazyk matlab.Stochastic convergence, law of large numbers and central limit theorem is an important part of probability theory, which is often used in mathematical statistics. The aim of this work is to describe this theory and demonstrate it with examples and graphical simulation. In addition simulation of stochastic convergence, law of large numbers and central limit theorem for some discrete and continuous probability distribution the work contains several interesting simulations for example simulation of Galton's box, Buffon's needle problem and Bertrand's paradox. To create a graphic simulation were used programming language matlab.

Spray Cooling at High Temperatures

Sprchové chlazení horkých povrchů se v metalurgickém průmyslu využívá při kontinuálním odlévání, válcování za tepla či při tepelném zpracování. Při sprchovém chlazení v metalurgickém průmyslu je voda rozprašována na chlazený povrch tryskami, přičemž dochází k rozpadu proudu vody na kapky. Sprchové chlazení horkých povrchů lze charakterizovat jako nucenou konvekci za přítomnosti varu. Tento fyzikálně komplikovaný děj je ovlivňován mnoha faktory, jako jsou příměsi a nečistoty ve vodě, teplota vody, průtok vody, velikost kapek, dopadová rychlost kapek, teplota povrchu, drsnost povrchu či přítomnost oxidů (okují) na chlazeném povrchu. Dominantní faktor, který ovlivňuje přenos tepla při sprchovém chlazení je průtok vody na jednotku plochy chlazeného povrchu. Ostatní faktory mají menší avšak též významný vliv. Tato práce se zabývá vlivem teploty vody, drsnosti povrchu a přítomnosti oxidů na intenzitu sprchového chlazení. Tyto faktory jsou studovány za pomocí laboratorních experimentů, při nichž je horký ocelový povrch chlazen vodním sprejem. Vliv vrstvy oxidů na chlazeném povrchu je též studován za pomocí numerické simulace. Získané experimentální výsledky jsou vysvětleny na základě teorie a zobecněny za pomocí matematických metod.Spray cooling of hot surfaces is used in the metallurgical industry during continuous casting, hot rolling or heat treatment. The water is sprayed on the cooled surface by the nozzle which transforms the water stream to droplets. The spray cooling of hot surfaces can be characterized as forced convection with the presence of the boiling. This physically complicated process is influenced by many factors, such as impurities and contaminants in the water, water temperature, water flow rate, droplet size, droplet impact velocity, surface temperature, surface roughness or the presence of oxides (scales) on the cooled surface. The dominant factor that affects the heat transfer during the spray cooling is the water impingement density. Other factors have a smaller but also significant effect. This doctoral thesis deals with the influence of the water temperature, surface roughness and the presence of oxides on the intensity of the spray cooling. These factors are investigated by laboratory experiments in which the hot steel surface is spray cooled. Effect of the oxide layer is also investigated by the numerical simulation. The experimental results are theoretically explained and generalized using mathematical methods.

Statistical Analysis of Extreme Value Distributions for Censored Data

Diplomová práce se zabývá rozdělením extrémních hodnot a cenzorovanými výběry. V teoretické části je popsána metoda maximální věrohodnosti, typy cenzorovaných výběrů a je definováno rozdělení extrémních hodnot. V práci jsou odvozeny věrohodnostní rovnice pro cenzorované výběry z exponenciálního, Weibullova, logaritmicko-normálního, Gumbelova a zobecněného extrémního rozdělení. Pro tato rozdělení jsou též odvozeny asymptotické intervalové odhady a je provedena simulační studie sledující závislost odhadu parametru na procentu cenzorování.The thesis deals with extreme value distributions and censored samples. Theoretical part describes a maximum likelihood method, types of censored samples and introduce a extreme value distributions. In the thesis are derived likelihood equations for censored samples from exponential, Weibull, lognormal, Gumbel and generalized extreme value distribution. For these distributions are also derived asymptotic interval estimates and is made simulation studies on the dependence of the parameter estimate on the percentage of censoring.

Performance Assessments of Technology Transfer Offices of Thirty Major US Research Universities in 2012/2013

The activities and performance of thirty major universities technology transfer offices (TTOs) selected from major US universities are quantitatively assessed and compared. Six leading metrics, including TTOs’ revenue, as well as quantity of invention disclosures, patent applications, patents granted, licenses signed, and startup companies launched, are used to develop a single overall performance metric (OPM) for representing the performance of the TTOs. The OPM are then evaluated for each of the thirty universities and their OPM scores are compared to each other to establish the reliability and effectiveness of a comprehensive OPM. A patenting control ratio (PCR) is also calculated to guide a TTO in setting its patenting strategy and procedures. These two metrics should be able to provide a comprehensive overview of how good is the TTO of a university as compare to those of its peers and, even more importantly, how the program fares globally

Prediction of Leidenfrost Temperature in Spray Cooling for Continuous Casting and Heat Treatment Processes

Spray cooling of hot steel surfaces is an inherent part of continuous casting and heat treatment. When we consider the temperature interval between room temperature and for instance 1000 degrees C, different boiling regimes can be observed. Spray cooling intensity rapidly changes with the surface temperature. Secondary cooling in continuous casting starts when the surface temperature is well above a thousand degrees Celsius and a film boiling regime can be observed. The cooled surface is protected from the direct impact of droplets by the vapour layer. As the surface temperature decreases, the vapour layer is less stable and for certain temperatures the vapour layer collapses, droplets reach the hot surface and heat flux suddenly jumps enormously. It is obvious that the described effect has a great effect on control of cooling. The surface temperature which indicates the sudden change in the cooling intensity is the Leidenfrost temperature. The Leidenfrost temperature in spray cooling can occur anywhere between 150 degrees C and over 1000 degrees C and depends on the character of the spray. This paper presents an experimental study and shows function for prediction of the Leidenfrost temperature based on spray parameters. Water impingement density was found to be the most important parameter. This parameter must be combined with information about droplet size and velocity to produce a good prediction of the Leidenfrost temperature

Heat Transfer during Spray Cooling of Flat Surfaces with Water at Large Reynolds Numbers

We present a new Nusselt number correlation for spray cooling at large Reynolds numbers and high surface temperatures for water sprays impinging perpendicularly onto a flat plate. A large set of experimental data on spray cooling of hot surfaces with water has been analyzed, including the water temperature effects. For large-scale cooling, such as in industrial processes, large number of injection parameters such as number, type, pressure, and angle of the spray injection has led to a multitude of correlations that are difficult for general and practical applications. However, by synthesizing a set of experimental data where all of the above parameters have been varied, we find that the Nusselt number and therefore the heat transfer coefficient can be cast accurately as a function of the Reynolds number. Water is widely used as the coolant during spray cooling, and has a specific phase change characteristic. At large Reynolds number (Re > 100,000) and surface temperature (Ts > 600°C) ranges, which are of interest in large-scale spray cooling, the effect of water temperature is quite significant as it affects the film boiling close to the surface. This effect also has been parameterized using experimental data

Spray cooling heat transfer above leidenfrost temperature

This study considers spray cooling starting at surface temperatures of about 1200 °C and finishing at the Leidenfrost temperature. Cooling is in the film boiling regime. The paper uses experimental techniques for the study of which spray parameters are necessary for good prediction of spray cooling intensity. The research is based on experiments with water and air-mist nozzles. The following spray parameters were measured together with a heat transfer coefficient: water flowrate, water impingement density, impact pressure, droplet size and velocity. Derived parameters as droplet kinetic energy, droplet momentum and droplet Reynolds number are used in the tested correlations as well. Ten combinations of spray parameters used for correlation functions for the heat transfer coefficient (HTC) are studied and discussed. Correlation functions for prediction of HTC are presented and it is shown which spray parameters are necessary for reliable computation of HTC. The best results were obtained when the parameters impact pressure and water impingement density were used together. It was proven that the correlations based only on water impingement density, which are the most frequent in literature, can not provide reliable results