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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
Development Of Cfl-Free, Explicit Schemes For Multidimensional Advection-Reaction Equations, Hong Wang, Jiangguo Liu
Development Of Cfl-Free, Explicit Schemes For Multidimensional Advection-Reaction Equations, Hong Wang, Jiangguo Liu
Faculty Publications
We combine an Eulerian–Lagrangian approach and multiresolution analysis to develop unconditionally stable, explicit, multilevel methods for multidimensional linear hyperbolic equations. The derived schemes generate accurate numerical solutions even if large time steps are used. Furthermore, these schemes have the capability of carrying out adaptive compression without introducing mass balance error. Computational results are presented to show the strong potential of the numerical methods developed.
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 …
Dirt Road Corrugations, Temple H. Fay, Keith A. Hardie, Stephan V. Joubert
Dirt Road Corrugations, Temple H. Fay, Keith A. Hardie, Stephan V. Joubert
Faculty Publications
WE CONSIDER FACTORS INFLUENCING the build-up of corrugations on dirt roads and the reactions of vehicles to them. We suggest that corrugations are (at least in part) a consequence of a natural tangential oscillation of the tread surface of the car lure that occurs when the vehicle is being driven or braked. Secondly, we suggest that the unpleasant vibration experienced by a vehicle passing over a corrugated road is the result of a beat produced by the difference of the frequency of oscillation of its own tyres and the frequency of the stimulation received by the vehicle due to passage …
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.
An Ellam Scheme For Multidimensional Advection-Reaction Equations And Its Optimal-Order Error Estimate, Hong Wang, Xiquan Shi, Richard E. Ewing
An Ellam Scheme For Multidimensional Advection-Reaction Equations And Its Optimal-Order Error Estimate, Hong Wang, Xiquan Shi, Richard E. Ewing
Faculty Publications
We present an Eulerian-Lagrangian localized adjoint method (ELLAM) scheme for initial-boundary value problems for advection-reaction partial differential equations in multiple space dimensions. The derived numerical scheme is not subject to the Courant-Friedrichs-Lewy condition and generates accurate numerical solutions even if large time steps are used. Moreover, the scheme naturally incorporates boundary conditions into its formulation without any artificial outflow boundary conditions needed, and it conserves mass. An optimal-order error estimate is proved for the scheme. Numerical experiments are performed to verify the theoretical estimate.
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.