Document Type


Date of Award

Summer 8-31-2011

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Lou Kondic

Second Advisor

Denis L. Blackmore

Third Advisor

Robert M. Miura

Fourth Advisor

Richard O. Moore

Fifth Advisor

Pushpendra Singh


The systems built from dense granular materials are very important due to their relevance to a number of technological and other fields. However, they are difficult to study in particular due to a lack of accurate continuum description. In this work, studies on these systems are presented using discrete element simulations that model the granular particles as soft, elastic, and frictional disks which interact when in contact. These simulations are used for the purpose of analyzing a few granular systems with the main emphasis on understanding phenomena of energy and force propagation.

Analysis of energy propagation in a two-dimensional disordered system is carried out by considering the propagation of information away from an oscillating boundary which is characterized by both temporal and spatial structure. This spatial structure, in particular, is important since it makes comparison to any continuum model more challenging and insightful. The results are compared to a simple linear wave equation with damping, and a very good agreement is found. This result suggests, that at least for the dense, compressed, jammed systems considered here, mathematical description of energy propagation based on a simple continuum model is possible.

The simulation is then extended to consider the process of impact of a large- scale intruder on a granular system. In this problem, a detailed investigation is considered on the manner in which energies and forces propagate, and in particular a concentration on the influence of material parameters, such as inter-particle friction, is studied . This analysis has led to better understanding of the scaling relations connecting the intruder’s speed and its depth of penetration.

Finally, the dynamics of dense granular flow in a hopper geometry is modeled and studied, where the flow is sensitive to jamming. Extensive analysis of this problem have been carried out, including large scale statistical analysis of data in order to understand the influence of statistical fluctuations on the results.

Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.