5 research outputs found
A new ghost cell/level set method for moving boundary problems:application to tumor growth
In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth
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Combination Radial-Axial Magnetic Bearing
The design and application of a patented active actuator design that combines the radial and axial actuator into one combination radial-axial actuator is presented. The theory of operation of the actuator is defined and magnetic finite element analysis modeling shown verifying operation. Its mechanical construction is then presented to show how this actuator configuration is successfully integrated into a mechanical system. Applications up to 60,000 rpm are then presented, with a detailed presentation of a 42,000 rpm energy storage flywheel currently under test at the University of Texas Center for Electromechanics.Center for Electromechanic