Abrams_Daniel_Michael_dissertation

Abrams_Daniel_Michael_dissertation - TWO COUPLED OSCILLATOR...

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Unformatted text preview: TWO COUPLED OSCILLATOR MODELS: THE MILLENNIUM BRIDGE AND THE CHIMERA STATE A Dissertation Presented to the Faculty of the Graduate School of Cornell University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy by Daniel Michael Abrams August 2006 This document is in the public domain. TWO COUPLED OSCILLATOR MODELS: THE MILLENNIUM BRIDGE AND THE CHIMERA STATE Daniel Michael Abrams, Ph.D. Cornell University 2006 Ensembles of coupled oscillators have been seen to produce remarkable and unex- pected phenomena in a wide variety of applications. Here we present two math- ematical models of such oscillators. The first model is applied to the case of Londons Millennium Bridge, which underwent unexpected lateral vibration due to pedestrian synchronization on opening day in 2000. The second model analyzes a new mode of collective behavior observed for a ring of nonlocally coupled phase oscillators. BIOGRAPHICAL SKETCH Danny Abrams grew up in Houston, Texas. He attended Bellaire High School and the California Institute of Technology, where he graduated with a Bachelor of Science in Applied Physics. He has many hobbiese.g., basketball, squash, foreign languages but his favorite is still science. iii Dedicated to those who had no opportunity for a quality education. iv ACKNOWLEDGEMENTS If you wish your merit to be known, acknowledge that of other people. Oriental Proverb This dissertation would not have been possible without an incredible amount of help and support by many people in my life. My advisor, Steve Strogatz, has been an amazing mentor. Hes made my time at Cornell really enjoyable, giving me great advice and guidance, and always coming up with interesting projects to work on. Sometimes I think I should have delayed graduating to keep our collaboration going for longer! Richard Rand, a member of my special committee, gave useful feedback at both A and B exams, and taught me a lot about perturbation theory in his courses in TAM. My other special committee member, David Hysell, did a great job with feed- back at both A and B exams. I wish I had the opportunity to get to know more about his research. Richard Wiener was a good friend and mentor to me during my first years at Cornell. His enthusiasm is contagious, and our new collaboration should soon bear fruit. My longtime house-mate Marc Favata contributed to both my research and my quality of life through long conversations about science and everything else. Hes been a great friend, and it will be hard getting used to life without him next year. All of my other friends and housemates from Caltechs Ruddock HouseZach Medin, Ryan Gutenkunst, David Fang, and Chris Liuhave been great pals over the past several years, and Id like to thank them for that....
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This note was uploaded on 04/24/2010 for the course MATH 9374 taught by Professor Smith during the Spring '10 term at University of California, Berkeley.

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Abrams_Daniel_Michael_dissertation - TWO COUPLED OSCILLATOR...

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