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Doctoral Thesis
DOI
10.11606/T.3.2011.tde-09122011-101051
Document
Author
Full name
Douglas Ricardo Slaughter Nyimi
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Grimoni, José Aquiles Baesso (President)
José Neto, João
Pessoa Junior, Osvaldo Frota
Reis, Lineu Belico dos
Santos Filho, Gildo Magalhães dos
Title in Portuguese
Computabilidade e limites da matemática das teorias físicas: aplicações em sistemas elétricos de potência.
Keywords in Portuguese
Caos
Computabilidade
Determinismo
Física
Laplace
Limitações
Matemática
Modelos matemáticos
Sistemas elétricos de potência
Turing
Abstract in Portuguese
Apesar dos modelos usados em engenharia serem, em sua maioria, reconhecidamente aproximados, acredita-se que a matemática usada na física e nos próprios modelos é infinitamente precisa e que tais teorias físicas poderiam prever completamente qualquer evento relacionado às variáveis equacionadas. No limite, seria possível prever o estado do universo em qualquer instante, crença esta chamada de determinismo. Claro está que essa pretensão é apenas de princípio, sendo impossível na prática. No entanto, pesquisas sobre os fundamentos da matemática e outras teorias matemáticas desenvolvidas no século XX sugerem que a matemática (e, consequentemente, a física) teria certos limites inerentes. A análise feita nesta tese fundamenta seus argumentos na Teoria das Funções Recursivas e Computabilidade Efetiva e na Teoria do Caos Determinístico. O objetivo principal é tratar de apurar a existência de limites inerentes e como tais limites se aplicariam aos sistemas elétricos de potência (mais especificamente nos tópicos fluxo de carga, transitórios eletromecânicos, transitórios eletromagnéticos e eletrônica de potência) e à engenharia de controle.
Title in English
Computability and limits of physical theories mathematics: applications in electric power systems.
Keywords in English
Chaos
Computability
Determinism
Laplace
Limitations
Mathematical models
Mathematics
Physics
Power electric systems
Turing
Abstract in English
Although the models used in engineering are, in most cases, admittedly approximated, it is believed that the Mathematics used in Physics and in these models, is infinitely precise and that such physical theories could fully predict any event related to variables in equations. In the limit, it would be possible to predict the state of the universe at any moment, this belief is called determinism. It is clear that this claim is only in principle, impossible in practice. However, research on the foundations of Mathematics and other mathematical theories developed in the 20th century suggest that the Mathematics (and hence Physics) would have certain inherent limitations. The analysis made in this thesis has the arguments based on the Theory of Recursive Functions and Effective Computability and the Theory of Deterministic Chaos. The main objective is to find out the existence of inherent limits and how these limits could be applied to electric power systems (more specifically to the topics load flow, electromechanical transient and electromagnetic transient and power electronics) and control engineering.
 
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Pre_Texto_Tese.pdf (104.93 Kbytes)
Publishing Date
2011-12-12
 
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