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Physical Sciences and Mathematics Commons™
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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Asymptotic Dynamics Of Attractive-Repulsive Swarms, Andrew J. Leverentz '08, Chad M. Topaz, Andrew J. Bernoff
Asymptotic Dynamics Of Attractive-Repulsive Swarms, Andrew J. Leverentz '08, Chad M. Topaz, Andrew J. Bernoff
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We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel’s first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly supported population has edges that behave like traveling waves whose speed, density, and slope we calculate. …
Turing Patterns On Growing Spheres: The Exponential Case, Julijana Gjorgjieva, Jon T. Jacobsen
Turing Patterns On Growing Spheres: The Exponential Case, Julijana Gjorgjieva, Jon T. Jacobsen
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We consider Turing patterns for reaction-diffusion systems on the surface of a growing sphere. In particular, we are interested in the effect of dynamic growth on the pattern formation. We consider exponential isotropic growth of the sphere and perform a linear stability analysis and compare the results with numerical simulations.
A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu
A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu
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In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to …