Many metallurgical processes involve the heat treatment of granular material due to large alternating currents. To understand how the current propagates through the material, one must understand the bulk resistivity, that is, the resistivity of the granular material as a whole. The literature suggests that the resistance due to contacts between particles contributes significantly to the bulk resistivity, therefore one must pay particular attention to these contacts.
My work is focused on understanding the precise impact of small contacts on the current propagation. The scale of the contacts is several order of magnitude smaller than that of the furnace itself, therefore we apply matched asymptotics methods to study how the current varies with the size of the contact.
- Junior Applied Mathematics Seminar