A better understanding of how hemodynamic factors affect the integrity and function of the vascular endothelium is necessary to appreciate more fully how atherosclerosis is initiated and promoted. A novel technique is presented to assess the relation between fluid dynamic variables and the permeability of the endothelium to macromolecules. Fully anesthetized, domestic swine were intravenously injected with the albumin marker Evans blue dye, which was allowed to circulate for 90 min. After the animals were euthanized, silicone casts were made of the abdominal aorta and its iliac branches. Pulsatile flow calculations were subsequently made in computational regions derived from the casts. The distribution of the calculated time-dependent wall shear stress in the external iliac branches was directly compared on a point-by-point basis with the spatially varying in vivo uptake of Evans blue dye in the same arteries. The results indicate that in vivo endothelial permeability to albumin decreases with increasing time-average shear stress over the normal range. Additionally, endothelial permeability increases slightly with oscillatory shear index.

A self-healing system based on conventional epoxy resin was successfully developed in this work. Epoxy and its hardener mercaptan were microencapsulated as two-component healing agent, and then the microcapsules were embedded in epoxy matrix. Attractive healing effect can be acquired at low capsule content (e.g., 43.5% healing efficiency with 1 wt % capsules and 104.5% healing efficiency with 5 wt % capsules at 20 °C for 24 h). Since only a few healant proves to be sufficient for crack repairing, a better balance between strength and toughness restoration can thus be achieved. As a result of high flowability, fast consolidation, and molecular miscibility of the released healing agent consisting of epoxy and mercaptan, self-healing was allowed to proceed rapidly offering satisfactory repair effectiveness.

Proof: Let T > 0. Parabolic regularity ensures that Itô's formula can be applied to (t,for t ∈ [0, T ). Taking the limit as t → T , we have:

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Summary.Here we discuss the regularity of solutions of SDE's and obtain conditions under which a SDE on a complete Riemannian manifold M has a global smooth solution flow, in particular improving the usual global Lipschitz hypothesis when M --R n. There are also results on non-explosion of diffusions.