It is known that the maximum diameter for the rupture-risk assessment of the abdominal aortic aneurysm is a generally good method, but not sufficient. Alternative features obtained with computational modeling may provide additional useful criteria. Though computational approaches are noninvasive, they are often time-consuming because of the high computational complexity. In this paper, we present a highly parallel algorithm for the numerical simulation of unsteady blood flows in the patient-specific abdominal aorta. We model the blood flow with the unsteady incompressible Navier-Stokes equations, and solve the discretized system with a highly scalable domain decomposition method. With this approach, the complete flow field can be obtained in less than an hour, instead of days with older methods. We show experimentally that the proposed method offers accurate solutions of the pressure, the velocity and the wall shear stress, and the parallel efficiency is higher than 70% on a parallel computer with more than 1,000 processor cores.

Symmetric polynomials are polynomials that are invariant under the action of the symmetric group, and they play an integral role in mathematics. The space of quasiin- variant polynomials, polynomials that are invariant under the action of the symmetric group to a certain order, were introduced by Feigin and Veselov. These spaces are modules over the ring of symmetric polynomials, and their Hilbert series in elds of characteristic 0 were also computed by Feigin and Veselov. In this paper, we study the Hilbert series of these spaces in elds of positive char- acteristic. Braverman, Etingof, and Finkelberg recently introduced spaces of twisted quasiinvariant polynomials, a generalization of quasiinvariant polynomials in which the space is twisted by a monomial. We extend some of their results to spaces twisted by a product of smooth functions and compute the Hilbert series of the space in certain cases.

In the general, this article addresses the nature of, and relation between, canonical and log-canonical singularities of foliations by curves. The case of equivariance under a finite group action has several peculiarities, amongst which are examples from dimension 3 onward where no birational modification can be both Gorenstein and log-canonical. The article in the specific, i.e. a functorial resolution algorithm for foliated 3-folds in the 2-category of Deligne-Mumford champs, is thus not only optimal but natural.

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