# Robert F. Sekerka

## University Professor Emeritus

**Address:**

6319 Wean Hall

Department of Mathematical Sciences

Carnegie Mellon University

5000 Forbes Avenue

Pittsburgh, PA 15213

**P:** 412-268-2362**F:** 412-681-0648

# Education

Ph.D., Harvard University

# Research

Most of my research is interdisciplinary and is concerned with theoretical problems in materials science that lead to challenging problems in physics and mathematics. Examples are the thermodynamics of stressed solids, transport phenomena, surfaces and interfaces, phase transformations, the precise definition of chemical potentials in stressed solids, the fundamental basis of the Onsager reciprocal relations in multi-component diffusion and heat flow, and the influence of anisotropic surface tension on crystal shape. Problems dealing with phase transformations lead to difficult free boundary problems that are generalizations of the classical Stefan problem because of boundary conditions that depend on the curvature of the free boundary. One seeks to calculate and understand the factors that determine the shapes of the interfaces that separate the growing phase from the nutrient phase.

Linear stability theory is used to analyze the conditions under which bodies of simple shape evolve spontaneously into more complex patterns. Non-linear analyses, frequently requiring numerical techniques, are used to track freely growing shapes and to ascertain fundamental aspects of the cellular and dendritic patterns that often result. Recent work involves the phase field model (diffuse interface) in which an additional PDE is solved in lieu of boundary tracking. The phase field model has been used to calculate the operating state (tip speed and radius of curvature) of dendrites grown at large supercoolings. Finally, there is interest in modeling the effects of g-jitter on interdiffusion in the microgravity environment of space as a stochastic process as well as the influence of fluid convection on dendritic growth on Earth.

# Select Publications

Robert F. Sekerka and Shun-Lien Wang, "Moving Phase Boundary Problems," in "Lectures on the Theory of Phase Transformations," 2nd Edition, Edited by Hubert I. Aaronson (Warrandale, PA; TMS 2000) pp. 231–284

Stanislav G. Pavlik , Robert F. Sekerka, "Fluctuations in the phase field model of solidification," Physica A 277 415–431 (2000)

G.B. McFadden, S.R. Coriell and Robert F. Sekerka, "Analytic solution for a non-axisymmetric isothermal dendrite," J. Crystal Growth 208 726–745 (2000)

Bayard K. Johnson, Robert F. Sekerka and Robert Almgren, "Thermodynamic basis for a variational model for crystal growth, " Phys. Rev. E 60 705–714 (1999)

Stanislav G. Pavlik, Robert F. Sekerka, "Forces due to fluctuations in the anisotropic phase-field model of solidification," Physica A 268 283–290 (1999)

S. R. Coriell, G. B. McFadden and R. F. Sekerka, "Selection mechanism for multiple similarity solutions for solidification and melting," J. Crystal Growth 200 276–286 (1999)

Zhiqiang Bi and Robert F. Sekerka, "Phase-field model of solidification of a binary alloy," Physica A 261 95–106 (1998)

S. R. Coriell, G. B. McFadden, R. F. Sekerka and W. J. Boettinger, "Multiple similarity solutions for solidification and melting, " J. Crystal Growth 191 573–585 (1998)

K. Tsulomoto, E. Yokoyama, S. Maruyama, K. Maiwa, K. Shimizu, R. F. Sekerka, T. S. Morita and S. Yoda, "Transient Crystyal Growth Rate in Microgravity: Report from TR-IA-4 Rocket Experiment," J. Japan Microgravity Appl. 15 2–9 (1998)

Shun-Lien Wang and Robert F. Sekerka, "Computation of the Dendritic Operating State at Large Supercoolings by the Phase Field Model," Phys. Rev. E 53 3760–3776 (1996)