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Description & Requirement
The Center for Modeling, Simulation and Imaging in Medicine (CeMSIM) at Rensselaer Polytechnic Institute, Troy, NY, USA invites applications for multiple postdoctoral associate positions to work on projects funded by the NIH on developing virtual surgery technology.  The ideal candidate will develop the next generation surgical simulation technology  based on advanced physics-based computational methods and robotic systems in collaboration with surgeons at Harvard Medical School.

ABSTRACT

Chiqun Zhang          Xiaohan Zhang         Amit Acharya          Dmitry Golovaty          Noel Walkington

Nonsingular disclination dynamics in a uniaxial nematic liquid crystal is modeled within a mathematical framework where the kinematics is a direct extension of the classical way of identifying these line defects with singularities of a unit vector field representing the nematic director. It is well known that the universally accepted Oseen-Frank energy is infinite for configurations that contain disclination line defects. We devise a natural augmentation of the Oseen-Frank energy to account for physical situations where, under certain conditions, infinite director gradients have zero associated energy cost, as would be necessary for modeling half-integer strength disclinations within the framework of the director theory. Equilibria and dynamics (in the absence of flow) of line defects are studied within the proposed model. Using appropriate initial/boundary data, the gradient-flow dynamics of this energy leads to non-singular, line defect equilibrium solutions, including those of half-integer strength. However, we demonstrate that the gradient flow dynamics for this energy is not able to adequately describe defect evolution. Motivated by similarity with dislocation dynamics in solids, a novel 2D-model of disclination dynamics in nematics is proposed. The model is based on the extended Oseen-Frank energy and takes into account thermodynamics and the kinematics of conservation of defect topological charge. We validate this model through computations of disclination equilibria, annihilation, repulsion, and splitting. We show that the energy function we devise, suitably interpreted, can serve as well for the modeling of equilibria and dynamics of dislocation line defects in solids making the conclusions of this paper relevant to mechanics of both solids and liquid crystals.

Abstract:

Amit Acharya                       Michael Widom

To appear in Journal of the Mechanics and Physics of Solids

Motivated by results of the topological theory of glasses accounting for geometric frustration,
we develop the simplest possible continuum mechanical model of defect dynamics in metallic
glasses that accounts for topological, energetic, and kinetic ideas. A geometrical description
of ingredients of the structure of metallic glasses using the concept of local order based on
Frank-Kasper phases and the notion of disclinations as topological defects in these structures is
proposed. This novel kinematics is incorporated in a continuum mechanical framework capable
of describing the interactions of disclinations and also of dislocations (interpreted as pairs of
opposite disclinations). The model is aimed towards the development of a microscopic understanding
of the plasticity of such materials. We discuss the expected predictive capabilities of
the model vis-a-vis some observed physical behaviors of metallic glasses.