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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
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
W.J. Boettinger, G.B. McFadden, S.R. Coriell, R.F. Sekerka and J.A. Warren,
“Lateral deformation of diffusion couples,”
Acta Materialia 53 (2005) 1995-2008
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
Victor Sofonea and Robert F.
Sekerka,
“Diffusivity of Two Component Isothermal Finite Difference Lattice Boltzmann
Models,” International Journal of Modern Physics C 16 (2005) 1075-1090
Victor Sofonea and Robert F. Sekerka,
“Boundary Conditions for the Upwind Finite Difference Lattice Boltzmann Model:
Evidence of Slip Velocity in Micro-channel Flow,”
J. Computational Physics 207 (2005) 639-659
Robert F. Sekerka,
“Equilibrium and Growth Shapes of Crystals: How Do They Differ and Why Should We Care?,”
Crystal Research Technology 40 (2005) 291-306
Robert F. Sekerka, “Analytical
criteria for missing orientations on three-dimensional equilibrium shapes,”
J. Crystal Growth 275 (2005) 77-82
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