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Home > Faculty > Michael J. Miksis
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Research: Theoretical and Computational Fluid Mechanics, Biofluids and Materials Science: Free Boundary Problems, Multiphase Flows, Porous Media, Stability Theory, Asymptotic and Perturbation Methods. Professor Miksiss research interests are concerned with interface problems in fluid dynamics, materials sciences and biology. For example, he has recently been studying the dynamics of rising gas bubbles. These bubbles play an important role in many physical and biological processes, such as the dynamics of multiphase flows, cavitation processes, and the flow of bubbles in the bloodstream. Along with his graduate student Catherine Norman, a level-set numerical method was developed to study the dynamics of rising bubbles and to investigate their interaction with solid walls. This investigation also required an accurate numerical method to study the dynamics of the liquid/solid/gas three-phase line. Professor Miksis has also been investigating problems in nanotechnology. In these problems, the traditional approach of using continuum models is no longer sufficient. This is because the scales are so small (sometimes just a few nanometers). Hence models need to be developed that bridge information occurring at the atomic (microscopic) scale with the behavior on the macroscopic scale where a modified continuum theory can be used. Our research has involved using information from either ab-initio or molecular-dynamics calculations into new continuum theories valid at the macroscopic scale. We have also been concerned with the effects of anisotropic surface energy on the behavior of crystal interfaces. Two problems of current interest in biology are the dynamics of vesicles (lipid bilayer interfaces) and the formation and stability of intracranial aneurysms. Lipid bilayers are the basic component of cell membranes. Our aim is to develop solution methods and to investigate the behavior of the mathematical models governing the dynamics of these biological interfaces. This investigation can lead to a better understanding of cell membranes, but also has applications to enhanced drug delivery processes. Another project under current investigation is concerned with the mathematical modeling, analysis and characterization of intracranial aneurysms. Here the goal is to understand the physiologic features of the aneurysms that may lead to instability, resulting in subsequent growth or rupture. Efforts to improve our knowledge of aneurysm dynamics may lead to more patient specific guidelines to treat aneurysms before they rupture. The proposed research is interdisciplinary and is in collaboration with investigators from the Department of Neurosurgery at the Medical School. Selected References “"Effective Equations for Multiphase Flows - Waves in a Bubbly Liquid'', (with L. Ting), Advances in Applied Mechanics, 28, eds. J. W. Hutchinson and T. Y. Wu, 141-260, 1991. “"Contact Lines, in A Celebration of Mathematical Modelling: The Joseph B. Keller Anniversary Volume, eds." D. Givoli, M.J. Grote, G.C. Papanicolaou, Kluwer Academic Publishers, The Netherlands, 2004. “"Dynamics of a Gas Bubble in an Inclined Channel at Finite Reynolds Number", (with C. Norman), Phys. Fluids, 17(2), 022102, 2005 “"Gas Bubble with a Moving Contact Line Rising in an Inclined Channel at Finite Reynolds Number", (with C. Norman) Physica D, 209, 191-204, 2005. “"Evolution of material voids for highly anisotropic surface energy, (with M. Siegel and P.Voorhees)", J. Mech. Phys. Solids, 52, 1319-1353, 2004. “"Role of Strain-Dependent Surface Energies in Ge/Si(100) Island Formation", (with O.E. Shklyaev, M.J. Beck, M. Asta, and P.W. Voorhees), PRL 94, 176102, 2005 “"The Effect of Contact Lines on the Rayleigh Instability with Anisotropic Surface Energy", (with K.F. Gurski and G.B. McFadden), SIAM J. Applied Math. 66(4), 1163-1187, 2006. “"Equilibrium Shapes of Strained Islands with Finite Contact Angle", (with O. Shklyaev and P.W. Voorhees), J. Mech. Phys. Solids 54, 2111-2135, 2006. “"Orientation Dependence of Strained-Ge Surface Energies Near (001): Role of Dimer-Vacancy-Lines and Their Interactions with Steps", (with C.J. Moore, C.M. Retford, M.J. Beck, M. Asta and P.W. Voorhees), PRL 96 (12), 126101, 2006. “"Energetics of {105}-faceted Ge nanowires on Si(001): An atomistic calculation of edge contributions," (with C.M. Retford, M. Asta, P.W. Voorhees, and E.B. Webb), Physical Review B 75, 075311, 2007. |
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