Math Technical Report Series
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Browsing Math Technical Report Series by Author "Edwards, David A."
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Item A Mathematical Model for Blood Clotting(Department of Mathematical Sciences, University of Delaware, 2004-09-01) Swaminathan, Sumanth; Edwards, David A.Many biological phenomena are characterized by extensive fluid mechanical and chemical reactionary systems. As such, it is necessary to understand the manner in which these processes develop and the role that they play in a given system. Vascular blood flow is characterized by convective, diffusive, and reactive processes. Specifically, blood clot formation involves platelet convection within the blood stream, diffusion through the Lévêque boundary layer of the blood vessel, and binding to vascular breaches. Accordingly, in order to understand blood clotting, the fluid mechanics of blood flow as well as the reaction mechanism of platelet adhesion are relevant. In this study, we formulate a mathematical model for blood clotting and associated processes.Item Testing the Validity of the Averaged Approximation for the IAsys(Department of Mathematical Sciences, 2002) Edwards, David A.; Jackson, S.A.One device used to measure rate constants is the IAsys, and the flow in such a device can be modeled as stagnation point flow. Due to the special nature of the flow, the effects of transport on a surface reaction near a stagnation point may be incorporated exactly as long as the initial concentration of bound state is uniform. However, if the bound state is nonuniform initially, a complicated integrodifferential equation arises for the evolution of the bound state. Such a form is inconvenient for data analysis. The averaged approximation replaces the nonuniform initial state with its average, thus simplifying the analysis. This approximation is correct to O(Da) as the Damköhler number Da —> 0. A numerical simulation of the integrodifferential equation is performed which shows that the averaged approximation is useful even outside this regime.