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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, as well as cell shapes and solute segregations during
directional solidification of alloys. Finally, there is interest in modeling the effects of g-jitter on
interdiffusion in the microgravity environment of space as a stochastic process
by using Lattice-Boltzmann models.
Selected Publications
Robert F. Sekerka and John W.
Cahn, "Solid-Liquid Equilibrium for Non-Hydrostatic Stress," Acta Materialia
52 (2004) 1663-1668
Robert F. Sekerka, “Theory of
Crystal Growth Morphology,” in Crystal Growth – From Fundamentals to Technology,
G. Müller, J. J. Metois, P. Rudolph, eds. (Elsevier, Amsterdam 2004) 55-93
Robert F. Sekerka, “Analytical
criteria for missing orientations on three-dimensional equilibrium shapes,”
J. Crystal Growth 275 (2005) 77-82 of crystals: how do they differ
and why should we care?” Crystal Research Technology 40 (2005) 291-306
Victor Sofonea and Robert F.
Sekerka, “Diffuse reflection boundary conditions for a thermal lattice Boltzmann
model in two dimensions: evidence of temperature jump and slip velocity in
micro-channels,” Phys.
Rev. E 71
(2005) 066709-1-10
J.A. Dantzig, W.J. Boettinger,
J.A. Warren, G.B. McFadden, S.R. Coriell, and R.F. Sekerka, “Numerical Modeling
of Diffusion-induced Deformation,”
Met Trans
37A (2006) 2701- 2714
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