Date of Degree


Document Type


Degree Name





Mark D. Shattuck

Committee Members

Joel Gersten

Joel Koplik

Corey S. O’Hern

Mark Hillery

Subject Categories



Bulk metallic glass; Granular; Soft matter; Statistical physics


Granular matter is composed of particles that are big enough that thermal effects may be neglected. We studied both granular flow and granular statics using numerical simulation. In granular flow, we simulated 2D granular flow in a hopper. A hopper is a container with an opening at the bottom. Simulated disks are placed in the hopper with the bottom closed and then released. We developed a new tangential force model to simulate hopper flow, that matches experiments and shows that the output flux is proportional to the bottom opening size to the 3/2 power. We also see clogging or jamming and estimate the jamming probability. We applied our force model to a 2D rotating drum simulation and studied the statistics of avalanches. In many systems, from earthquakes to plastic deformations the avalanche size probability F(I) is a power-law in avalanche size I. We find F(I) ∞ I-1.29 for our system. We also find that the scaled average avalanche shape is parabolic as predicted by mean-field theoretical models.

In many systems, we would like to measure the degree of crystallization. Q6 is common order metric used to detect hexagonal symmetry, and it works very well in mono-disperse systems. However, when we consider bi-disperse and poly-disperse systems, and other non-hexagonal lattices, Q6 is not as useful. We developed a new order metric, Voronoi entropy, based on Voronoi tessellation and information theory. The main idea of the Voronoi entropy is to detect and quantify unique Voronoi polyhedrons. Voronoi entropy can successfully find lattice order in bi-disperse crystal and other structures like simple cubic, body-centered-cubic, for which Q6 is not sensitive. We performed molecular dynamics (MD) simulations of binary Lennard-Jones systems to model the crystallization process during heating and cooling protocols in metallic glasses. We measured the minimum cooling rate Rc* to crystallize a liquid and the minimum heating rate Rh* to crystallize a glass formed prepared using a fast quench at rate Rp*. We find: (1) Rh* > Rc* in all systems. (2) The asymmetry ratio Rh*/ Rc* increases as Rc* increases. (3) The critical heating rate Rh* (Rp) has an intrinsic contribution Rh* (∞) and protocol-dependent contribution Rh* -- Rh* (∞) that increases with decreasing preparation cooling rates Rp. We show all of these findings are in agreement with classical nucleation theory.

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