Load-depth sensing of isotropic, linear viscoelastic materials using rigid axisymmetric indenters

An indentation experiment involves five variables: indenter shape, material behavior of the substrate, contact size, applied load and indentation depth. Only three variable are known afterwards, namely, indenter shape, plus load and depth as function of time. As the contact size is not measured and the determination of the material properties is the very aim of the test; two equations are needed to obtain a mathematically solvable system. For elastic materials, the contact size can always be eliminated once and for all in favor of the depth; a single relation between load, depth and material properties remains with the latter variable as unknown. For viscoelastic materials where hereditary integrals model the constitutive behavior, the relation between depth and contact size usually depends also on the (time-dependent) properties of the material. Solving the inverse problem, i.e., determining the material properties from the experimental data, therefore needs both equations. Extending Sneddon's analysis of the indentation problem for elastic materials to include viscoelastic materials, the two equations mentioned above are derived. To find the time dependence of the material properties the feasibility of Golden and Graham's method of decomposing hereditary integrals (J.M. Golden and G.A.C. Graham. Boundary value problems in linear viscoelasticity, Springer, 1988) is investigated and applied to a single load-unload process and to sinusoidally driven stationary state indentation processes.Comment: 116 pages, 29 figure

Crushing singularities in spacetimes with spherical, plane and hyperbolic symmetry

It is shown that the initial singularities in spatially compact spacetimes with spherical, plane or hyperbolic symmetry admitting a compact constant mean curvature hypersurface are crushing singularities when the matter content of spacetime is described by the Vlasov equation (collisionless matter) or the wave equation (massless scalar field). In the spherically symmetric case it is further shown that if the spacetime admits a maximal slice then there are crushing singularities both in the past and in the future. The essential properties of the matter models chosen are that their energy-momentum tensors satisfy certain inequalities and that they do not develop singularities in a given regular background spacetime.Comment: 19 page

Reactive oxygen molecule-mediated injury in endothelial and renal tubular epithelial cells in vitro

Reactive oxygen molecule-mediated injury in endothelial and renal tubular epithelial cells in vitro. To investigate renal tubular epithelial cell injury mediated by reactive oxygen molecules and to explore the relative susceptibility of epithelial cells and endothelial cells to oxidant injury, we determined cell injury in human umbilical vein endothelial cells and in four renal tubular epithelial cell lines including LLC-PK1, MDCK, OK and normal human kidney Cortical epithelial cells (NHK-C). Cells were exposed to reactive oxygen molecules including superoxide anion, hydrogen peroxide and hydroxy 1 radical generated by xanthine oxidase and hypoxanthine. We determined early sublethal injury with efflux of 3H-adenine metabolites and a decline in ATP levels, while late lytic injury and cell detachment were determined by release of51 chromium. When the cells were exposed to 25, 50, and 100 mU/ml xanthine oxidase with 5.0mM hypoxanthine, ATP levels were significantly lower (P < 0.001) in LLC-PK1, NHK-C and OK cells compared to MDCK cells while ATP levels were significantly lower (P < 0.01) in endothelial cells compared to all tubular cell lines. A similar pattern of injury was seen with efflux of 3H-adenine metabolites. When the cells were exposed to 50 mU/ml xanthine oxidase with 5.0mM hypoxanthine for five hours, total 51chromium release was significantly (P < 0.001) greater in LLC-PK1, NHK-C and OK cells compared to MDCK cells, while total 51chromium release was significantly (P < 0.001) greater in endothelial cells compared to all tubular cells. However, lytic injury was the greatest in LLC-PK1 cells and NHK-C cells while cell detachment was the greatest in endothelial cells. MDCK cells were remarkably resistant to oxidant-mediated cell detachment and cell lysis. In addition, we determined ATP levels, 3H-adenine release and 51chromium release in LLC-PK1, NHK-C and endothelial cells in the presence of superoxide dismutase to dismute superoxide anion, catalase to metabolize hydrogen peroxide, DMPO to trap hydroxyl radical and DMTU to scavenge hydrogen peroxide and hydroxyl radical. We found that catalase and DMTU (scavengers of hydrogen peroxide) provided significant protection from ATP depletion, prevented efflux of 3H-adenine metabolites and cell detachment while DMPO (scavenger of hydroxyl radical) prevented lytic injury. In addition, we found that the membrane-permeable iron chelator, phenanthroline, and preincubation with deferoxamine prevented cell detachment and cell lysis, confirming the role of hydroxyl radical in cell injury. We conclude that among tubular epithelial cells, cells with proximal tubular characteristics including LLC-PK1, NHK-C and OK cells were more susceptible to oxidant injury than MDCK cells which originate from distal tubules. Endothelial cells responded to oxidant injury with a greater fall in ATP levels, efflux of 3H-adenine metabolites and cell detachment, while tubular epithelial cells demonstrated greater cell lysis. Finally, it appears that hydrogen peroxide mediates ATP depletion and efflux of 3H-adenine metabolites while hydrogen peroxide and hydroxyl radical mediate cell detachment and cell lysis