Bray, David Jonathan (2010) *Statistical properties of a randomly excited granular fluid.* PhD thesis, University of Nottingham.

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## Abstract

In this thesis we describe numerical simulations performed in one- and two-dimensions of a theoretical granular model called the Random Force Model. The properties of non-equilibrium steady state granular media, which this model is a simple example of, are still hotly debated.

We begin by observing that the one-dimensional Random Force Model manifest multi-scaling behaviour brought on by the clustering of particles within the system. For high dissipation we find that the distribution of nearest neighbour distances are approximately renormalisable and devise a geometrical method that accounts for some of the structural features seen in these systems.

We next study two-dimensional systems. The structure factor, S(k), is known to vary, for small k, as a power-law with an exponent D_f, referred to as the fractal dimension. We show that the value of the D_f is unchanged with respect to both dissipation and particle density and that the power-law is different from that given in any previous study. These structural features influence the long distance behaviour of individual particles by affecting the distances travelled by particles between consecutive collision.

The velocity distribution, P(v), is known to strongly deviate away from Maxwell-Boltzmann statistics and we advocate that the velocity distributions have asymptotic shape which is universal over a range of dissipation and particle densities.

This invariance in behaviour of the large-scale structure and velocity properties of the two-dimensional Random Force Model leads us to develop a new self-consistent model based around the motion of single high velocity particles. The background mass of low velocity particles are considered to be arrange as a fractal whereby the high velocity particles move independently in ballistic trajectories between collisions. We use this description to construct the high velocity tail of P(v), which we find to be approximately exponential.

Finally we propose a method of structure formation for these systems that builds self-similarity into the system by consecutively fracturing the system into smaller parts.

Item Type: | Thesis (PhD) |
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Supervisors: | Swift, M.R. |
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Uncontrolled Keywords: | granular, random force, moments of velocity, multi-scaling, structure factor, velocity distribution, multiplicative, nearest neighbour distribution |
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Faculties/Schools: | UK Campuses > Faculty of Science > School of Physics and Astronomy |
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ID Code: | 1041 |
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Deposited By: | Dr D. J. Bray |
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Deposited On: | 13 Sep 2010 10:55 |
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Last Modified: | 13 Sep 2010 10:55 |
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