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Propagation Failure in Discrete Inhomogeneous Media Using a Caricature of the Cubic

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Date Issued:
2015
Abstract/Description:
Spatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle- rosis. We construct steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison formula we de- rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain conditions outlined in their construction. The range of parameter values that satisfy these conditions constitutes the interval of propagation failure, determining under what circumstances a front becomes pinned in the media. Our exact solutions represent a very specific solution to the spatially discrete Nagumo equation. For example, we only consider inhomogeneous media with one defect present. We created an original script in MATLAB which algorithmically solves more general cases of the equation, including the case for multiple defects. The algorithmic solutions are then compared to known exact solutions to determine their validity.
Title: Propagation Failure in Discrete Inhomogeneous Media Using a Caricature of the Cubic.
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Name(s): Lydon, Elizabeth, Author
Moore, Brian, Committee Chair
Choudhury, Sudipto, Committee Member
Kaup, David, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2015
Publisher: University of Central Florida
Language(s): English
Abstract/Description: Spatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle- rosis. We construct steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison formula we de- rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain conditions outlined in their construction. The range of parameter values that satisfy these conditions constitutes the interval of propagation failure, determining under what circumstances a front becomes pinned in the media. Our exact solutions represent a very specific solution to the spatially discrete Nagumo equation. For example, we only consider inhomogeneous media with one defect present. We created an original script in MATLAB which algorithmically solves more general cases of the equation, including the case for multiple defects. The algorithmic solutions are then compared to known exact solutions to determine their validity.
Identifier: CFE0005831 (IID), ucf:50903 (fedora)
Note(s): 2015-08-01
M.S.
Sciences, Mathematics
Masters
This record was generated from author submitted information.
Subject(s): reaction-diffusion equation -- propagation failure -- discrete Nagumo
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0005831
Restrictions on Access: campus 2018-08-15
Host Institution: UCF

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