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. |
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) |
