On the coadjoint orbits of maximal unipotent subgroups of reductive groups

Let G be a simple algebraic group defined over an algebraically closed field of characteristic 0 or a good prime for G. Let U be a maximal unipotent subgroup of G and \u its Lie algebra. We prove the separability of orbit maps and the connectedness of centralizers for the coadjoint action of U on (certain quotients of) the dual \u* of \u. This leads to a method to give a parametrization of the coadjoint orbits in terms of so-called minimal representatives which form a disjoint union of quasi-affine varieties. Moreover, we obtain an algorithm to explicitly calculate this parametrization which has been used for G of rank at most 8, except E8. When G is defined and split over the field of q elements, for q the power of a good prime for G, this algorithmic parametrization is used to calculate the number k(U(q), \u*(q)) of coadjoint orbits of U(q) on \u*(q). Since k(U(q), \u*(q)) coincides with the number k(U(q)) of conjugacy classes in U(q), these calculations can be viewed as an extension of the results obtained in our earlier paper. In each case considered here there is a polynomial h(t) with integer coefficients such that for every such q we have k(U(q)) = h(q).Comment: 14 pages; v2 23 pages; to appear in Transformation Group

Orbits of parabolic subgroups on metabelian ideals

We consider the action of a parabolic subgroup of the General Linear Group on a metabelian ideal. For those actions, we classify actions with finitely many orbits using methods from representation theory.Comment: 10 pages, 6 eps figure

Classical and all-floating FETI methods for the simulation of arterial tissues

High-resolution and anatomically realistic computer models of biological soft tissues play a significant role in the understanding of the function of cardiovascular components in health and disease. However, the computational effort to handle fine grids to resolve the geometries as well as sophisticated tissue models is very challenging. One possibility to derive a strongly scalable parallel solution algorithm is to consider finite element tearing and interconnecting (FETI) methods. In this study we propose and investigate the application of FETI methods to simulate the elastic behavior of biological soft tissues. As one particular example we choose the artery which is - as most other biological tissues - characterized by anisotropic and nonlinear material properties. We compare two specific approaches of FETI methods, classical and all-floating, and investigate the numerical behavior of different preconditioning techniques. In comparison to classical FETI, the all-floating approach has not only advantages concerning the implementation but in many cases also concerning the convergence of the global iterative solution method. This behavior is illustrated with numerical examples. We present results of linear elastic simulations to show convergence rates, as expected from the theory, and results from the more sophisticated nonlinear case where we apply a well-known anisotropic model to the realistic geometry of an artery. Although the FETI methods have a great applicability on artery simulations we will also discuss some limitations concerning the dependence on material parameters.Comment: 29 page

Non-monotonic density dependence of the diffusion of DNA fragments in low-salt suspensions

The high linear charge density of 20-base-pair oligomers of DNA is shown to lead to a striking non-monotonic dependence of the long-time self-diffusion on the concentration of the DNA in low-salt conditions. This generic non-monotonic behavior results from both the strong coupling between the electrostatic and solvent-mediated hydrodynamic interactions, and from the renormalization of these electrostatic interactions at large separations, and specifically from the dominance of the far-field hydrodynamic interactions caused by the strong repulsion between the DNA fragments.Comment: 4 pages, 2 figures. Physical Review E, accepted on November 24, 200

L² -estimates for the evolving surface finite element method

In this paper we consider the evolving surface finite element method for the advection and diffusion of a conserved scalar quantity on a moving surface. In an earlier paper using a suitable variational formulation in time dependent Sobolev space we proposed and analysed a finite element method using surface finite elements on evolving triangulated surfaces. An optimal order H¹ -error bound was proved for linear finite elements. In this work we prove the optimal error bound in L² (Γ(t)) uniformly in time

The dynamically hot stellar halo around NGC 3311: a small cluster-dominated central galaxy

An important open question is the relation between intracluster light and the halos of central galaxies in galaxy clusters. Here we report results from an on going project with the aim to characterize the dynamical state in the core of the Hydra I (Abell 1060) cluster around NGC 3311. Methods: We analyze deep long-slit absorption line spectra reaching out to ~25 kpc in the halo of NGC 3311. Results: We find a very steep increase in the velocity dispersion profile from a central sigma_0=150 km/s to sigma_out ~450 km/s at R ~ 12 kpc. Farther out, to ~25 kpc, sigma appears to be constant at this value, which is ~60% of the velocity dispersion of the Hydra I galaxies. With its dynamically hot halo kinematics, NGC 3311 is unlike other normal early-type galaxies. Conclusions: These results and the large amount of dark matter inferred from X-rays around NGC 3311 suggest that the stellar halo of this galaxy is dominated by the central intracluster stars of the cluster, and that the transition from predominantly galaxy-bound stars to cluster stars occurs in the radial range 4 to 12 kpc from the center of NGC 3311. We comment on the wide range of halo kinematics observed in cluster central galaxies, depending on the evolutionary state of their host clusters.Comment: 5 pages, 4 figures, 1 table, accepted for publication in A&