Levich Institute Seminar Announcement, 03/04/2008
Steinman Hall, Room #312
(Chemical Engineering Conference Room)
Dean David Srolovitz
"Soap Bubble Evolution and Grain Growth in All Dimensions: Beyond von Neumann-Mullins"
Cellular structures or tessellations are ubiquitous in nature. Metals and ceramics commonly consist of space-filling arrays of single crystal grains separated by a network of grain boundaries. Foams (froths) are networks of gas-filled bubbles separated by liquid walls. Cellular structures also occur in biological tissue, magnetic, ferroelectric, and complex fluid contexts. In many situations, the cell/grain/bubble walls move under the influence of their surface tension (capillarity), with a velocity proportional to the wall's mean curvature. As a result, the cells evolve and the structure coarsens. Using this relation between velocity and mean curvature, the fact that three domain walls meet at $\pi$/3 and basic topology, von Neumann gave an exact formula for the growth rate of a cell in a 2-d cellular structure. This is the basis of modern grain growth theory. Borrowing ideas from geometric probability theory, we present an exact solution for the same problem in 3-d using a mean width measure. Next, we present an exact extension of the fifty year old result into all integer dimensions greater than one in terms of Hadwiger measures. Finally, we discuss some of the numerical issues involved in applying this theory to 3-d bubbles and grains.
BRIEF ACADEMIC/EMPLOYMENT BACKGROUND:
CURRENT RESEARCH INTERESTS:
Film growth, grain growth, morphology evolution, crystal defects.