Academic literature on the topic 'Applied theory of oscillations'

This thesis presents work around 3 themes: dark energy, gravitational waves and Bayesian inference. Both dark energy and gravitational wave physics are not yet well constrained. They present interesting challenges for Bayesian inference, which attempts to quantify our knowledge of the universe given our astrophysical data. A dark energy equation of state reconstruction analysis finds that the data favours the vacuum dark energy equation of state $w {=} -1$ model. Deviations from vacuum dark energy are shown to favour the super-negative ‘phantom’ dark energy regime of $w {< } -1$, but at low statistical significance. The constraining power of various datasets is quantified, finding that data constraints peak around redshift $z = 0.2$ due to baryonic acoustic oscillation and supernovae data constraints, whilst cosmic microwave background radiation and Lyman-$\alpha$ forest constraints are less significant. Specific models with a conformal time symmetry in the Friedmann equation and with an additional dark energy component are tested and shown to be competitive to the vacuum dark energy model by Bayesian model selection analysis: that they are not ruled out is believed to be largely due to poor data quality for deciding between existing models. Recent detections of gravitational waves by the LIGO collaboration enable the first gravitational wave tests of general relativity. An existing test in the literature is used and sped up significantly by a novel method developed in this thesis. The test computes posterior odds ratios, and the new method is shown to compute these accurately and efficiently. Compared to computing evidences, the method presented provides an approximate 100 times reduction in the number of likelihood calculations required to compute evidences at a given accuracy. Further testing may identify a significant advance in Bayesian model selection using nested sampling, as the method is completely general and straightforward to implement. We note that efficiency gains are not guaranteed and may be problem specific: further research is needed.

Диссертация на соискание научной степени кандидата технических наук по специальности 05.02.09 – динамика и прочность машин. – Национальный технический университет "Харьковский политехнический институт", Харьков, 2016. Диссертация посвящена разработке подходов, методов и моделей для исследования динамических процессов в виброударных системах с учетом изменяемой во времени массы технологического груза и нелинейной жесткости упругих опор. В данной работе изложен новый подход к учету влияния переменной массы технологического груза на характер динамических процессов в виброударной системе. Разработаны и предложены зависимости, математические модели, которые описывают характер изменения массы технологического груза во времени, как на основе экспериментальных исследований (эмпирический закон), так и в зависимости от количества диссипированной энергии. Установлено, что вследствии нелинейности жесткости упругих опор и в зависимости от их конструктивного исполнения, становится возможной реализация субгармонических режимов, что приводит к росту силы ударного взаимодействия. Для оценки влияния параметров упругих опор (варианты конструктивного исполнения, жесткость пружин) проведены многовариантные исследования, по результатам которых выделены характерные субгармонические режимы и их характеристики (фазовые портреты, временные распределения). Установлена степень влияния изменения различных параметров упругих опор на характер колебательного процесса в ходе их многовариантного варьирования. На базе корпуса усовершенствованной вибромашины, функционирующей в составе автоматизированной линии для выбивки крупного вагонного литья, проведен натурный эксперимент с целью подтверждения точности и адекватности полученных ранее результатов численных исследований.<br>The thesis on competition of a scientific degree of Candidate of technical Science on a specialty 05.02.09 – dynamic and strength of machines. – National Technical University "Kharkiv polytechnical institute", Kharkiv, 2016. This thesis is devoted to the development of approaches, methods and models for investigation of dynamic processes in vibroimpact systems with variable mass of the weight and nonlinear rigidness of elastic supports. In this paper new approach to the accounting of the variable mass influence on the character of dynamical processes in vibroimpact systems was presented. The dependences, that describes the mass change character, based on experimental researches and dependence from dissipated energy were proposed. It was found that the realization of sybharmonical modes became possible because of elastic supports nonlinearity and design features. The realization of subharmonical modes lead to growth of impact interaction force. The approach, based on corresponding values for phase variables at the beginning and the end of period was proposed to periodic solutions search. The criteria for tuning from resonance frequencies that can appear on perturbing force with multiple (partite) frequency were formulated. The machine body designed with taking to the account previously formulated recommen-dations was created. The investigation of stress-strain status was performed and found that improved machine body satisfies strength requirements. The comparison of numerical and experimental data was done. The accuracy and authenticity of numerical investigations was confirmed.

Дисертація на здобуття наукового ступеня кандидата технічних наук за спеціальністю 05.02.09 – динаміка та міцність машин. – Національний технічний університет "Харківський політехнічний інститут", Харків, 2016. Дисертація присвячена розробці підходів, методів і моделей для дослідження динамічних процесів у віброударних системах з урахуванням змінної у часі маси технологічного вантажу та нелінійної жорсткості пружних опор. У роботі викладений новий підхід до урахування впливу змінної маси технологічного вантажу на характер динамічних процесів у віброударній системі. Запропоновані залежності, що описують характер зміни маси як на основі експериментальних досліджень, так і залежно від дисипації енергії при ударі. Встановлено, що внаслідок нелінійної жорсткості пружних опор та залежно від їх конструктивного виконання, можливою є реалізація субгармонійних режимів, що призводить до зростання сили ударної взаємодії. Для пошуку періодичних розв'язків був запропонований новий підхід, що базується на відповідності фазових змінних на початку та в кінці періоду процесу. На основі результатів досліджень сформульовані критерії для відлаштування від резонансу, що може виникнути на кратних (дольних) частотах збудження. З урахування рекомендацій створена удосконалена конструкція корпусу віброударної машини. Проведені дослідження напружено-деформованого стану удосконаленого корпусу вібромашини та встановлено, що він відповідає вимогам міцності. Проведене порівняння отриманих числових результатів досліджень з експериментальними даними. Підтверджена точність і достовірність проведених числових досліджень.<br>The thesis on competition of a scientific degree of Candidate of technical Science on a specialty 05.02.09 – dynamic and strength of machines. – National Technical University "Kharkiv polytechnical institute", Kharkiv, 2016. This thesis is devoted to the development of approaches, methods and models for investigation of dynamic processes in vibroimpact systems with variable mass of the weight and nonlinear rigidness of elastic supports. In this paper new approach to the accounting of the variable mass influence on the character of dynamical processes in vibroimpact systems was presented. The dependences, that describes the mass change character, based on experimental researches and dependence from dissipated energy were proposed. It was found that the realization of sybharmonical modes became possible because of elastic supports nonlinearity and design features. The realization of subharmonical modes lead to growth of impact interaction force. The approach, based on corresponding values for phase variables at the beginning and the end of period was proposed to periodic solutions search. The criteria for tuning from resonance frequencies that can appear on perturbing force with multiple (partite) frequency were formulated. The machine body designed with taking to the account previously formulated recommen-dations was created. The investigation of stress-strain status was performed and found that improved machine body satisfies strength requirements. The comparison of numerical and experimental data was done. The accuracy and authenticity of numerical investigations was confirmed.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Economics, 2019<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references.<br>In "Incomplete Contracting with Endogenous Competition," I consider a variant of the incomplete contracting with renegotiation model introduced by Hart and Moore (1988). I study a trading relation between a buyer and seller, where some ex-ante relationship specific investment on the part of the seller is needed to generate value for the buyer. Uncertainty is revealed ex post, in that prior to the investment stage, the buyer does not know which type of service she may need, and it is impossible to describe under what precise circumstances she needs a particular service. The contract can take only two broad forms: (1) a specification of the nature of a service to be provided under all circumstances, or (2) a general option contract, namely, a menu of services that the seller agrees to provide at predetermined terms.<br>In addition to uncertainty regarding state realizations which was the focus of the literature thus far, I consider a different source of contracting friction, namely, uncertainty about downstream profitability. I show that depending on the specific assumptions, the competitor may invest in, produce and sell an imperfect substitute or free-ride on the incumbent supplier's investment and replicate a perfect substitute with positive probability. However, in a subgame-perfect equilibrium, the incumbent supplier will correctly anticipate potential entrants and change its ex-ante investment to account for downstream competition. It may also distort the level of its ex-ante investment to deter future entry. In this paper, information affects the outcome of economic transactions, but the presence and absence of information is exogenously given by assumptions about the form of competitions.<br>In my paper "Selling Information: Multidimensional Oligopolistic Competition," I model the information structure as a variable endogenously chosen to optimally manage competition. Specifically, I consider a model of an economic transaction between an upstream monopolist and several downstream oligopolists. The downstream parties may be E-commerce retailers who compete over a heterogeneous customer base. Each party may have some prior assessment over the distribution of customer types, but would benefit from incremental knowledge on customer information. The upstream party, in this scenario, is an information vendor, who has access to technology required to develop a targeting device. Since information is valuable, to extract surplus the upstream party would like to improve the quality of information. Such motive is counterbalanced by the incentive to manage competition.<br>The upstream monopolist supplies a menu of multi-dimensional intermediate goods from which the downstream oligopolists select. The oligopolists then use the previously purchased intermediate goods to produce the final products and compete with each other. The model enriches Bonatti (2015)'s multi-dimensional information product model by considering what the information product is used for (competing for heterogeneous customers by per information product. The key feature of the model is that the information good is intermediate, whose value is affected by the extent of ex post competition among the The model captures the indirect externalities conferred in the market for information. Specifically, the value of customer information to a given firm is no longer determined solely by the characteristics of that firm and the those customers. Instead, the value now also depends on the market competition structure among all downstream firms.<br>For example, a model of competition of customer information has features similar to an arms race: having better information over the opponent allows one to better engage in better price discrimination, but it also increases the value of information to the opponent and induces more aggressive demand for information on the part of the opponents. In addition to economic transactions, in my third paper I study the role of information in managing and orienting actions beyond the market. In "Information Theory Foundation of Propaganda," I develop a model of strategic information signaling with an informed sender and a continuum of imperfectly informed receivers. The sender sends a costly signal to disrupt receivers' coordination action and to bias their aggregate action away from the true state towards the sender's desired state. The receivers want to match their actions to the true state and also seek to coordinate with each other.<br>The leading application of the model is an authoritarian regime sending propaganda to its citizens to prevent them from learning the true strength of the regime and taking collective actions. In equilibrium the sender's manipulation does not succeed in changing the mean of the receivers' beliefs, but manipulation makes their interpretation of the signal noisier. This model helps resolve an empirical puzzle: since we observe propaganda, regimes apparently think it works, in some way, but can propaganda work, even if the citizens who see it know it is biased information? In the model, propaganda works not through changing beliefs per se, but through adding noise and confusion into the communication structure, so that citizens, who value coordination, are more likely to redirect their attention across various sources of information.<br>by Lizi Chen.<br>Chapter 1: Incomplete Contracting with Endogenous Competition -- Chapter 2: Selling Information: Multidimensional Oligopolistic Competition -- Chapter 3: Information Theory Foundation of Propaganda.<br>Ph. D.<br>Ph.D. Massachusetts Institute of Technology, Department of Economics

Includes bibliographical references.<br>The Baryon Acoustic Oscillations offer a powerful method of measuring cosmological distances and the expansion history of the Universe. Understanding of the BAO comes from linear physics and allows for accurate predictions of the BAO scale. This will result in accurate measurements of the parameters of the Universe. Currently, most BAO measurements assume a flat cosmology; this work seeks to investigate if the assumption of flatness provides inaccuracies in the measurement process.

This thesis collects three essays in applied microeconomic theory. Chapter 1 studies entry in a market where firms compete in shopping hours and prices. I explore the effect of shopping hours deregulation on social welfare. I show that an incumbent firm can strategically choose its opening hours to deter entry of a new firm, and that shopping hours deregulation can be harmful to consumers and social welfare. Chapter 2 examines the implications of prominence when firms' R&D investment is endogenous and consumers search sequentially. In the benchmark case consumers visit a firm randomly while in the prominence case all consumers visit the prominent firm first. I find that the prominent firm is the most efficient firm. The non-prominent firm is the least efficient firm if R&D cost is high but invests more in R&D than with random search if R&D cost is low. Second, if the efficiency asymmetry is sufficiently low prices with prominence are lower than prices with random search. If the efficiency asymmetry is high prices with prominence are higher than prices with random search. If the efficiency asymmetry is not too low the prominent firm charges a lower price than the non-prominent firm, and the price with random search lies between those prices. Third, when a firm is prominent both consumer surplus and social welfare are higher than with random search. Chapter 3 discusses whether taxes, subsidies and cash incentives are effective in reducing unhealthy food consumption, and which one is the most appropriate policy to tackle the obesity problem in the US and the UK. Cash incentives may be the most effective policy in reducing unhealthy food consumption, yet it can be the most costly one. Taxes are ineffective in reducing unhealthy food consumption. Subsidies have the best balance between effectiveness and monetary benefits to society.