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Title:  Behavior of intruders in a granular flow 
Other Titles:  Li zi xi tong zhong wu ti de yun dong yan jiu 粒子系統中物體的運動研究 
Authors:  Gao, Ming (高明) 
Department:  Department of Mathematics 
Degree:  Master of Philosophy 
Issue Date:  2008 
Publisher:  City University of Hong Kong 
Subjects:  Granular materials  Fluid dynamics. 
Notes:  CityU Call Number: TA418.78 .G36 2008 v, 81 leaves : ill. 30 cm. Thesis (M.Phil.)City University of Hong Kong, 2008. Includes bibliographical references (leaves [80]81) 
Type:  thesis 
Abstract:  In this thesis, we investigate the behavior of intruders in a 2dimensional granular
system composed of rigid, frictionless, inelastic disks. The system is driven by adding
energy at the boundary which is held at constant temperature in a thermodynamic
sense. We consider an intruder with the shape of a circular segment. In the simulations,
we fix one end point of the intruder in the center of the system. If all the collisions in
the system are elastic, the rotation of the intruder behaves like a Brownian motion with
zero drift. However, in the inelastic case the intruder will rotate towards a preferred
direction. We give an explanation of this phenomenon and also present a theoretical
analysis of the force exerted on the intruder in the dilute case. The result from the
simulation validates our theory. We also consider an intruder with a “_” shape. Similar
phenomena are observed, and a theoretical analysis is also performed in the dilute case.
Then we study the behavior of two intruders in the granular flow and find that in the
elastic case the positions of the two intruders are uniformly distributed in the system.
However, in the inelastic case the two intruders have a clear trend to stay together. We
investigate the “attractive force” between the two intruders and find that the “attractive
force” comes from two sources: a) Each intruder exerts a force towards the center of
the system because of the temperature gradient caused by interparticle collisions. b)
There exists an interaction between the two intruders caused by the inelastic particleintruder
collisions. We present a theoretical analysis of the interaction between the two
intruders in the dilute case. The theoretical prediction is in excellent agreement with
the result from the simulation in the dilute case. In the less dilute case, the theory can
still give qualitative predictions about the interaction between the two intruders.
In the latter part of the thesis, we study the interaction of a rigid, frictionless, in elastic particle with a rigid boundary that has a corner. Typically, two possible final
outcomes can occur in such a system: the particle escapes from the corner after experiencing
a certain number of collisions with the boundary, or the particle experiences
an inelastic collapse in which an infinite number of collisions can occur in a finite time
interval. For the former case, we determine the number of collisions that the particle
will experience with the boundary before escaping the corner. For the latter case, we
determine the conditions for which inelastic collapse can occur. For a corner composed
of two straight walls, we derive simple analytic solutions and show that for a given coefficient
of restitution, there is a critical corner angle above which inelastic collapse
cannot occur. We show that as the corner angle tends to the critical corner angle from
below, the process of inelastic collapse takes infinitely long. We also show that if the
corner has the form of a cusp, then inelastic collapse can occur without the velocity
of the particle becoming zero. Surprisingly, this means that the particle can have an
infinite number of collisions with the boundary in a finite time interval without losing
all of its energy, and eventually escapes from the corner. 
Online Catalog Link:  http://lib.cityu.edu.hk/record=b2340674 
Appears in Collections:  MA  Master of Philosophy

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