3,929 research outputs found
Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature
We prove convergence results for expanding curvature flows in the Euclidean
and hyperbolic space. The flow speeds have the form , where and
is a positive, strictly monotone and 1-homogeneous curvature function. In
particular this class includes the mean curvature . We prove that a
certain initial pinching condition is preserved and the properly rescaled
hypersurfaces converge smoothly to the unit sphere. We show that an example due
to Andrews-McCoy-Zheng can be used to construct strictly convex initial
hypersurfaces, for which the inverse mean curvature flow to the power
loses convexity, justifying the necessity to impose a certain pinching
condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and
pinching. In the third version we dropped the concavity assumption on F.
Comments are welcom
A Pilot Study of the Performance Characteristics of the D-dimer in Presumed Sepsis
Objectives: To determine if a sensitive D-dimer assay can exclude progression to organ dysfunction, death, and intensive care unit (ICU) admission in patients presenting to the emergency department (ED) with suspected infection, and if increasing levels of D-dimer are predictive of those end points.Methods: The study took place at two academic EDs, both located in tertiary care hospitals. This was a prospective convenience sample of adult patients presenting with an infective process and at least two of four criteria for the Systemic Inflammatory Response Syndrome. We measured D-dimer levels in the participants and abstracted their records for the end points. Sensitivity and specificity were calculated and receiver operating characteristic analysis was performed to determine if a higher cutoff would have a greater specificity for our end points.Results: We enrolled 134 patients. Twelve were excluded from analysis (10 for lack of a D-dimer, one for recent surgery, and one for complete loss to follow up). Using the cutoff of 0.4 established by our laboratories as positive, the D-dimer had a sensitivity of 94% (CI95; 76-99) for organ dysfunction in the ED, 93% (72-99) for organ dysfunction at 48 hours, 93% (81-98) for ICU admission, and 100% (63-100) for 30-day mortality. However, at this cutoff, specificity was not statistically significant. Significantly raising the cutoff for a positive resulted in a decrease in sensitivity but improved specificity.Conclusion: This study was limited by its nonconsecutive patient recruitment and sample size. A normal D-dimer may exclude progression to organ dysfunction, ICU admission, and death and, at higher cutoff levels, could help risk stratify patients presenting to the ED with signs of sepsis.[West J Emerg Med. 2010;11(2):173-179.
Validation and Calibration of Models for Reaction-Diffusion Systems
Space and time scales are not independent in diffusion. In fact, numerical
simulations show that different patterns are obtained when space and time steps
( and ) are varied independently. On the other hand,
anisotropy effects due to the symmetries of the discretization lattice prevent
the quantitative calibration of models. We introduce a new class of explicit
difference methods for numerical integration of diffusion and
reaction-diffusion equations, where the dependence on space and time scales
occurs naturally. Numerical solutions approach the exact solution of the
continuous diffusion equation for finite and , if the
parameter assumes a fixed constant value,
where is an odd positive integer parametrizing the alghorithm. The error
between the solutions of the discrete and the continuous equations goes to zero
as and the values of are dimension
independent. With these new integration methods, anisotropy effects resulting
from the finite differences are minimized, defining a standard for validation
and calibration of numerical solutions of diffusion and reaction-diffusion
equations. Comparison between numerical and analytical solutions of
reaction-diffusion equations give global discretization errors of the order of
in the sup norm. Circular patterns of travelling waves have a maximum
relative random deviation from the spherical symmetry of the order of 0.2%, and
the standard deviation of the fluctuations around the mean circular wave front
is of the order of .Comment: 33 pages, 8 figures, to appear in Int. J. Bifurcation and Chao
Fabrication, Characterisation and Tribological Investigation of Artificial Skin Surface Lipid Films
This article deals with the tribology of lipid coatings that resemble those found on human skin. In order to simulate the lipidic surface chemistry of human skin, an artificial sebum formulation that closely resembles human sebum was spray-coated onto mechanical skin models in physiologically relevant concentrations (5-100μg/cm2). Water contact angles and surface free energies (SFEs) showed that model surfaces with ≤25μg/cm2 lipids appropriately mimic the physico-chemical properties of dry, sebum-poor skin regions. In friction experiments with a steel ball, lipid-coated model surfaces demonstrated lubrication effects over a wide range of sliding velocities and normal loads. In friction measurements on model surfaces as a function of lipid-film thickness, a clear minimum in the friction coefficient (COF) was observed in the case of hydrophilic, high-SFE materials (steel, glass), with the lowest COF (≈0.5) against skin model surfaces being found at 25μg/cm2 lipids. For hydrophobic, low-SFE polymers, the COF was considerably lower (0.4 for PP, 0.16 for PTFE) and relatively independent of the lipid amount, indicating that both the mechanical and surface-chemical properties of the sliders strongly influence the friction behaviour of the skin-model surfaces. Lipid-coated skin models might be a valuable tool not only for tribologists but also for cosmetic chemists, in that they allow the objective study of friction, adhesion and wetting behaviour of liquids and emulsions on simulated skin-surface condition
Self Organization and a Dynamical Transition in Traffic Flow Models
A simple model that describes traffic flow in two dimensions is studied. A
sharp {\it jamming transition } is found that separates between the low density
dynamical phase in which all cars move at maximal speed and the high density
jammed phase in which they are all stuck. Self organization effects in both
phases are studied and discussed.Comment: 6 pages, 4 figure
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