95,173 research outputs found
Mathematical models of avascular cancer
This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions
On the algorithmic complexity of twelve covering and independence parameters of graphs
The definitions of four previously studied parameters related to total coverings and total matchings of graphs can be restricted, thereby obtaining eight parameters related to covering and independence, each of which has been studied previously in some form. Here we survey briefly results concerning total coverings and total matchings of graphs, and consider the aforementioned 12 covering and independence parameters with regard to algorithmic complexity. We survey briefly known results for several graph classes, and obtain new NP-completeness results for the minimum total cover and maximum minimal total cover problems in planar graphs, the minimum maximal total matching problem in bipartite and chordal graphs, and the minimum independent dominating set problem in planar cubic graphs
Convergence to suitable weak solutions for a finite element approximation of the Navier-Stokes equations with numerical subgrid scale modeling
In this work we prove that weak solutions constructed by a variational
multiscale method are suitable in the sense of Scheffer. In order to prove this
result, we consider a subgrid model that enforces orthogonality between subgrid
and finite element components. Further, the subgrid component must be tracked
in time. Since this type of schemes introduce pressure stabilization, we have
proved the result for equal-order velocity and pressure finite element spaces
that do not satisfy a discrete inf-sup condition.Comment: 23 pages, no figure
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