1,217 research outputs found
Computational Methods and Results for Structured Multiscale Models of Tumor Invasion
We present multiscale models of cancer tumor invasion with components at the
molecular, cellular, and tissue levels. We provide biological justifications
for the model components, present computational results from the model, and
discuss the scientific-computing methodology used to solve the model equations.
The models and methodology presented in this paper form the basis for
developing and treating increasingly complex, mechanistic models of tumor
invasion that will be more predictive and less phenomenological. Because many
of the features of the cancer models, such as taxis, aging and growth, are seen
in other biological systems, the models and methods discussed here also provide
a template for handling a broader range of biological problems
Dynamic p-enrichment schemes for multicomponent reactive flows
We present a family of p-enrichment schemes. These schemes may be separated
into two basic classes: the first, called \emph{fixed tolerance schemes}, rely
on setting global scalar tolerances on the local regularity of the solution,
and the second, called \emph{dioristic schemes}, rely on time-evolving bounds
on the local variation in the solution. Each class of -enrichment scheme is
further divided into two basic types. The first type (the Type I schemes)
enrich along lines of maximal variation, striving to enhance stable solutions
in "areas of highest interest." The second type (the Type II schemes) enrich
along lines of maximal regularity in order to maximize the stability of the
enrichment process. Each of these schemes are tested over a pair of model
problems arising in coastal hydrology. The first is a contaminant transport
model, which addresses a declinature problem for a contaminant plume with
respect to a bay inlet setting. The second is a multicomponent chemically
reactive flow model of estuary eutrophication arising in the Gulf of Mexico.Comment: 29 pages, 7 figures, 3 table
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