Mathematical models for understanding phenomena: Physical view and mind view

通过数学模型理解现象：物理视角与思维视角

This lecture gives rather biased discussions emphasizing the importance of "understanding" of phenomena. This lecture's purpose is to inspire young researchers to taste the real charms of research by observing the process of development of mathematical models of vortex-induced vibration phenomena of cylinders for understanding their essential mechanism. Generally, research and studies in wind engineering are aimed at solving given problems caused by physical phenomena induced by winds. As such, they have direct and concrete aims such as observation of phenomena, prediction of phenomena, understanding of phenomena, and solution of problems, The last of these can be replaced by design practice. One of the important aims of research and studies is to "understand" phenomena. Simulation and prediction of phenomena can be done without understanding the phenomena. However, the discussions of this lecture focus on "understanding" of phenomena. It first discusses imperfect abilities of human beings in observation of phenomena and important aspects of research. Then, it emphasizes the close relation between understanding and mathematical models, and five conditions for a desirable mathematical model: simplicity; inclusion of all essential properties; possession of physical meanings; wide scope of application; and possibility of development. A mathematical model based on the wake-oscillator, i.e. the Tamura model, applied for vortex-induced oscillation of circular cylinders is discussed as a sample. It refers to Birkhoff's wake-oscillator (1953), Funakawa's early-wake model (1969), Nakamura's 2DOF flutter model (1970), the Hartlen-Currie model(1970), the Iwan-Blevins model (1974), and Tamura's non-linear wake-oscillator model with a variable length (1979). Its development into a mathematical model for combined effects of vortex-induced oscillation and galloping phenomena of square prisms is also introduced, i.e. the Tamura-Shimada model (1987). Some recent developments of the Tamura-Shimada model are also introduced. Then, it discusses the necessity of accurate experimental capture of early-wake behavior and the aerodynamic properties of a target cylinder in each flow condition for further development of Tamura's model and the Tamura-Shimada model. It also emphasizes how the mathematical model can deepen understanding and elucidation of the mechanism of highly nonlinear complicated phenomena. Then, the necessity for efforts to understand phenomena are emphasized. Finally, especially for students, it discusses how to read textbooks and emphasizes the importance of finding out indirect messages hidden between lines.

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Yukio Tamura is a Professor and the Advisory Director of Research Center of Wind Engineering, Environment and Energy, School of Civil Engineering, Chongqing University, China. He is also a Professor Emeritus of Tokyo Polytechnic University (TPU), Japan, and the Honorary Director of the TPU Wind Engineering Research Center. He served as the President of the International Association for Wind Engineering (IAWE) for eight years from 2007 to 2015. He is now serving as the Honorary Chairman of the International Thematic Group for Wind-Related Disaster Risk Reduction under the auspices of the United Nations Office for Disaster Risk Reduction. He is also serving as an Honorary/Guest/Adjunct Professor of around 20 universities/institutes in China, Korea, Malaysia, Poland and USA.

He has received many awards including the ASCE Jack E. Cermak Medal in 2004, the ASCE Robert H. Scanlan Medal in 2016, as well as the lAWE Alan Davenport Medal in 2016. In addition, due to his various professional contributions, he has received other important awards, including the Japan Association for Wind Engineering (JAWE) 2015 Design Award for his contribution to the wind resistant design of the 634m-high Tokyo Sky Tree, the Chinese Government Friendship Award in 2017, Chinese National Science and Technology Development Award in 2024, and Chongqing International Scientific Collaboration Award in 2024.

Professor Yukio Tamura has been a member of the Engineering Academy of Japan since 2011, a Foreign Fellow of the Indian National Academy of Engineering since 2013, and an International Member of the Chinese Academy of Engineering since 2017.