The Doctrine of Chances

Moivre, Abraham de

doi:10.1007/978-1-4757-3500-0_6

Cited by 23 publications

(3 citation statements)

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“…Probability is a very old concept but, as will be summarized below, a concept which has multiple meanings. To give an example, classical probability calculus introduced by, e.g., Bernoulli [13] and de Moivre [41], gives the probability of an event as a ratio of equally likely cases that favor it to the total number of equally likely cases possible under the circumstances. The ''equally likely case'' was important.…”

Section: Kolmogorov and The Theoretical Foundation Of Probabilitymentioning

confidence: 99%

Lectures for chemists on statistics. I. Belief, probability, frequency, and statistics: decision making in a floating world

Meinrath

2007

Accred Qual Assur

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A brief account on the development of probability theory and statistics is given. These subjects may help the chemist to interpret the information content of his experimental data. Their source and validity, however, is often unclear. A series of papers, of which this is the first, intends to present a clearer view by illustrating the origin of the data-analysis tools. The major figures in this field are mentioned, their achievements presented and the mutual links outlined. The intention is the provision of a common basis for the discussion of statistical aspects relevant to metrology in chemistry. The chemist should see probability theory and statistics as tools to assist in the daily practice of data interpretation to arrive at an objective conclusion.

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Section: Kolmogorov and The Theoretical Foundation Of Probabilitymentioning

confidence: 99%

Lectures for chemists on statistics. I. Belief, probability, frequency, and statistics: decision making in a floating world

Meinrath

2007

Accred Qual Assur

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“…Apparently, the task was first formulated by de Moivre [10], Problem LXXIV. Renewed interest to the topic arose in connection with the Erdös-Rényi strong law of large numbers [5].…”

Section: Introductionmentioning

confidence: 99%

On the length of the longest head run

Novak¹

2017

Statistics & Probability Letters

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“…where the factorial components of this equation can be simplified using an approximation based on large sets of numbers [174] to yield…”

Section: Formation Of Point Defects In Oxidesmentioning

confidence: 99%

Understanding Phonon Interactions with Defects in Functional Oxide Materials

Donovan¹

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Understanding of nano-scale thermal transport has enabled significant advances in a wide variety of fields including microelectronics, alternative energy, optics, and many more [1][2][3][4]. Utilized in many of these applications are a class of materials known as functional oxides. These materials are oxygen compounds with specific functional properties of interest (e.g., dielectrics [5][6][7][8], piezoelectrics [9][10][11], photovoltaics [12][13][14], thermoelectrics [15][16][17][18][19]). Often it is the defects in these materials that enable functionality and, depending on the processing and operating conditions, the concentration and types of defects that are present in these materials can vary widely [20]. In this dissertation, I aim to identify the role that defects play in functional oxide materials with respect to thermal transport.The major thermal carriers in most functional oxide crystals are collective lattice vibrations, or phonons [21]. Phonon-dominated thermal conductivity is dictated by the scattering of these thermal carriers with a variety of other components or the material system, including defects in the crystal [22,23]. I concentrate on three types of defects that are common in functional oxides: boundaries, extrinsic point defects, and intrinsic point defects.Boundaries such as film boundaries and grain boundaries with nano-scale dimensions can be detrimental to the thermal conductivity of a material. As the length of the uninterrupted crystal reduces to the phonon mean free paths in the crystal, phonons will scatter readily off of nano-scale boundaries and will not be able to propagate as they would in a bulk environment. This becomes particularly relevant in technologies such as the microelectronics industry, where device size scales are well below common phonon mean free paths in the constituent materials. To study this, I turn to one of the more common functional oxides used in the microelectronics industry, BaTiO 3 .I study the effects of nano-scale grains on thin films of BaTiO 3 grown via chemical solution deposition. The films studied are 150 nm and range in grain size from 36 nm -63 nm. I show that the thermal conductivity of these nano-grained films scales with the grain size and film thickness and demonstrate agreement of this trend with analytical models. This result demonstrates that despite a complex crystal structure, there is a mean free path spectrum of phonons in BaTiO 3 that significantly exceeds the dimensions of the grains and film (contrary to the common "gray" mean 2 free path assumption seen in literature).To address the role of extrinsic point defects, or dopants, on the thermal conductivity of functional oxides, I study the effects of dysprosium doping in thin films of cadmium oxide deposited by molecular beam epitaxy. In this experiment, the addition of Dy dopants in CdO actually increases the thermal conductivity initially, owing to a reduction in the equilibrium concentration of oxygen vacancies (a type of defect that is intrinsic to all oxides). The de...

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The Doctrine of Chances

Cited by 23 publications

References 0 publications

Lectures for chemists on statistics. I. Belief, probability, frequency, and statistics: decision making in a floating world

Lectures for chemists on statistics. I. Belief, probability, frequency, and statistics: decision making in a floating world

On the length of the longest head run

Understanding Phonon Interactions with Defects in Functional Oxide Materials

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