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|Title: ||Anomalous behavior of granular particles falling through a funnel|
|Other Titles: ||Li zi zai lou dou zhong xia luo de fan chang xing wei yan jiu|
|Authors: ||Fang, Yuan (方媛)|
|Department: ||Department of Mathematics|
|Degree: ||Master of Philosophy|
|Issue Date: ||2008|
|Publisher: ||City University of Hong Kong|
|Subjects: ||Granular materials -- Mathematical models.|
Particles -- Mathematical models.
|Notes: ||CityU Call Number: TA418.78 .F36 2008|
44 leaves : ill. 30 cm.
Thesis (M.Phil.)--City University of Hong Kong, 2008.
Includes bibliographical references (leaves -44)
|Abstract: ||In this thesis, we show several surprising phenomena that occur in an extremely simple
system of a single frictionless, inelastic, spherical particle falling under gravity through
a symmetric funnel. One might naively expect that particles would fall through funnels
with steeper sides more quickly, exert a smaller total impulse on the funnel walls and
lose less energy. However, we show that there are special ranges of angles of the funnel
walls for which exactly the opposite occurs. Typically, the particle will experience a
sequence of collisions that is highly sensitive to the location that it enters the funnel and
nearby particle trajectories become widely dispersed. However, in the special angular
ranges this is not the case, and the particle can experience sequences of collisions that
have a highly coherent structure. We provide a theoretical analysis that can predict and
explain this surprising behavior.
We further consider the system in which the side walls have friction, and find that
when the coefficient of kinetic friction is relatively large, the particle will stay longer
inside the system when the declined angle of funnel is larger than 45±. We also give a
theoretical explanation to this phenomenon.|
|Online Catalog Link: ||http://lib.cityu.edu.hk/record=b2340672|
|Appears in Collections:||MA - Master of Philosophy |
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