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    Free Surface Waves And Interacting Bouncing Droplets: A Parametric Resonance Case Study

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    Francisco_Obando_Thesis .pdf
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    Thesis
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    Type
    Thesis
    Authors
    Borja, Francisco J.
    Advisors
    Kasimov, Aslan R. cc
    Committee Members
    Ketcheson, David I. cc
    Thoroddsen, Sigurdur T.
    Program
    Applied Mathematics and Computational Science
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2013-07
    Permanent link to this record
    http://hdl.handle.net/10754/296760
    
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    Abstract
    Parametric resonance is a particular type of resonance in which a parameter in a system changes with time. A particularly interesting case is when the parameter changes in a periodic way, which can lead to very intricate behavior. This di↵ers from periodic forcing in that solutions are not necessarily periodic. A system in which parametric resonance is realized is when a fluid bath is shaken periodically, which leads to an e↵ective time dependent gravitational force. This system will be used to study the onset of surface waves in a bath with non-uniform topography. A linear model for the surface waves is derived from the Euler equations in the limit of shallow waves, which includes the geometry of the bottom and surface tension. Experiments are performed to compare with the proposed model and good qualitative agreement is found. Another experiment which relies on a shaking fluid bath is that of bouncing fluid droplets. In the case of two droplets the shaking allows for a larger bouncing droplet to attract a smaller moving droplet in a way that creates a bound system. This bound system is studied and shows some analogous properties to quantum systems, so a quantum mechanical model for a two dimensional atom is studied, as well as a proposed model for the droplet-wave system in terms of equations of fluid mechanics.
    DOI
    10.25781/KAUST-U7674
    ae974a485f413a2113503eed53cd6c53
    10.25781/KAUST-U7674
    Scopus Count
    Collections
    Applied Mathematics and Computational Science Program; Theses; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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