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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Modeling The Effects Of Transforming Growth Factor-Beta On Extracellular Matrix Alignment In Dermal Wound Repair, J. C. Dallon, J. A. Sherratt, P. K. Maini
Modeling The Effects Of Transforming Growth Factor-Beta On Extracellular Matrix Alignment In Dermal Wound Repair, J. C. Dallon, J. A. Sherratt, P. K. Maini
Faculty Publications
We present a novel mathematical model for collagen deposition and alignment during dermal wound healing, focusing on the regulatory effects of TGF. Our work extends a previously developed model which considers the interactions between fibroblasts and extracellular matrix, composed of collagen and a fibrin based blood clot, by allowing fibroblasts to orient the collagen matrix, and produce and degrade the extracellular matrix, while the matrix can direct the fibroblasts and control their speed. Here we extend the model by allowing a time varying concentration of TGF to alter the properties of the fibroblasts. Thus we are able to simulate experiments …
Blowup In A Mass-Conserving Convection-Diffusion Equation With Superquadratic Nonlinearity, Todd L. Fisher, Christopher P. Grant
Blowup In A Mass-Conserving Convection-Diffusion Equation With Superquadratic Nonlinearity, Todd L. Fisher, Christopher P. Grant
Faculty Publications
A nonlinear convection-diffusion equation with boundary conditions that conserve the spatial integral of the solution is considered. Previous results on nite-time blowup of solutions and on decay of solutions to the corresponding Cauchy problem were based on the assumption that the nonlinearity obeyed a power law. In this paper, it is shown that assumptions on the growth rate of the nonlinearity, which take the form of weak superquadraticity and strong superlinearity criteria, are suffcient to imply that a large class of nonnegative solutions blow up in nite time.
Gravitational Descendants And The Moduli Space Of Higher Spin Curves, Tyler J. Jarvis, Takashi Kimura, Arkady Vaintrob
Gravitational Descendants And The Moduli Space Of Higher Spin Curves, Tyler J. Jarvis, Takashi Kimura, Arkady Vaintrob
Faculty Publications
The purpose of this note is introduce a new axiom (called the Descent Axiom) in the theory of r-spin cohomological field theories. This axiom explains the origin of gravitational descendants in this theory. Furthermore, the Descent Axiom immediately implies the Vanishing Axiom, explicating the latter (which has no a priori analog in the theory of Gromov-Witten invariants), in terms of the multiplicativity of the virtual class. We prove that the Descent Axiom holds in the convex case, and consequently in genus zero.