An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary

Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries (which destroy uniform convergence to the solution). In this paper we recast the incompressible (constant density) Navier-Stokes equations (with the velocity prescribed at the boundary) as an equivalent system, for the primary variables velocity and pressure. We do this in the usual way away from the boundaries, by replacing the incompressibility condition on the velocity by a Poisson equation for the pressure. The key difference from the usual approaches occurs at the boundaries, where we use boundary conditions that unequivocally allow the pressure to be recovered from knowledge of the velocity at any fixed time. This avoids the common difficulty of an, apparently, over-determined Poisson problem. Since in this alternative formulation the pressure can be accurately and efficiently recovered from the velocity, the recast equations are ideal for numerical marching methods. The new system can be discretized using a variety of methods, in principle to any desired order of accuracy. In this work we illustrate the approach with a 2-D second order finite difference scheme on a Cartesian grid, and devise an algorithm to solve the equations on domains with curved (non-conforming) boundaries, including a case with a non-trivial topology (a circular obstruction inside the domain). This algorithm achieves second order accuracy (in L-infinity), for both the velocity and the pressure. The scheme has a natural extension to 3-D.Comment: 50 pages, 14 figure

Endogenous Bax Translocation in SH-SY5Y Human Neuroblastoma Cells and Cerebellar Granule Neurons Undergoing Apoptosis

Changes at the mitochondria are an early, required step in apoptosis in various cell types. We used western blot analysis to demonstrate that the proapoptotic protein Bax translocated from the cytosolic to the mitochondrial fraction in SH-SY5Y human neuroblastoma cells undergoing staurosporine- or EGTA-mediated apoptosis. Levels of mitochondrial Bax increased 15 min after staurosporine treatment. In EGTA-treated cells, increased levels of mitochondrial Bax were seen at 4 h, consistent with a slower onset of apoptosis in EGTA versus staurosporine treatments. We also demonstrate the concomitant translocation of cytochrome c from the mitochondrial to the cytosolic fractions. We correlated these translocations with changes in caspase-3-like activity. An increase in caspase-3-like activity was evident 2 h after staurosporine treatment. Inhibition of the mitochondrial permeability transition had no effect on Bax translocation or caspase-3-like activity in staurosporine-treated SH-SY5Y cells. In primary cultures of cerebellar granule neurons undergoing low K + -mediated apoptosis, Bax translocation to the mitochondrial fraction was evident at 3 h. Cytochrome c release into the cytosol was not significant until 8 h after treatment. These data support a model of apoptosis in which Bax acts directly at the mitochondria to allow the release of cytochrome c.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66150/1/j.1471-4159.1999.0721899.x.pd

A high-order immersed boundary method for unsteady incompressible flow calculations

A high-order immersed boundary method (IBM) for the computation of unsteady, incompressible fluid flows on two-dimensional, complex domains is proposed, analyzed, developed and validated. In the IBM, the equations of interest are discretized on a fixed Cartesian grid. As a result, domain boundaries do not always conform to the (rectangular) computational domain boundaries. This gives rise to 'immersed boundaries', i.e., boundaries immersed inside the computational domain. A new IBM is proposed to remedy problems in an older existing IBM that had originally been selected for use in numerical flow control investigations. In particular, the older method suffered from considerably reduced accuracy near the immersed boundary surface where sharp jumps in the solution, i.e., jump discontinuities in the function and/or its derivatives, were smeared out over several grid points. To avoid this behavior, a sharp interface method, originally developed by LeVeque & Li (1994) and Wiegmann & Bube (2000) in the context of elliptic PDEs, is introduced where the numerical scheme takes such discontinuities into consideration in its design. By comparing computed solutions to jump-singular PDEs having known analytical solutions, the new IBM is shown to maintain the formal fourth-order accuracy, in both time and space, of the underlying finite-difference scheme. Further validation of the new IBM code was accomplished through its application to several two-dimensional flows, including flow past a circular cylinder, and T-S waves in a flat plate boundary layer. Comparison of results from the new IBM with results available in the literature found good agreement in all cases

Contribution of the ICE Family to Neurodegeneration

The ICE family of cysteine proteases mediates necrotic or apoptotic events in the nervous system as well as in other tissues. This suggests that inhibitors may be of therapeutic value in acute and, perhaps, chronic neurode-generative disease. In addition, some members of this family may respond to intercellular signals controling proliferation or differentiation. This possibility should be kept in mind as therapeutics are pursued.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75647/1/j.1749-6632.1998.tb09549.x.pd