Levich Institute Seminar Announcement, 03/04/2008
Tuesday, 03/04/2008
2:00 PM
Steinman Hall, Room #312
(Chemical Engineering Conference Room)

Dean David Srolovitz
Yeshiva University
Yeshiva College

"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.


  • 2006 – Present Dean, Yeshiva College, Prof. of Physics, Yeshiva University
  • 2004 – 2006 Chairman, Dept. of Mechanical and Aerospace Engineering, Princeton University
  • 2003 – 2004 Interim Director, Princeton Materials Institute, Princeton University
  • 1999 – 2006 Professor, Princeton University, Dept. of Mechanical ∓ Aerospace Eng., Princeton Inst. for Computational Sci. ∓ Eng., Program in Applied and Comput. Math., Princeton Inst. for Sci. ∓ Tech. of Materials
  • 1997 - 1999 Edward DeMille Campbell Professor of Materials Science ∓ Eng., Univ. of Michigan
  • 1991 - 1999 Professor, Materials Science and Eng. ∓ Applied Physics, Univ. of Michigan
  • 1993 - 1994 Michael Visiting Professor, Weizmann Institute of Science, Israel
  • 1987 - 1991 Associate Professor, Materials Science and Eng. ∓ Applied Physics, Univ. of Michigan
  • 1984 - 1987 Staff Member, Los Alamos National Laboratory


Film growth, grain growth, morphology evolution, crystal defects.