Toric Poisson Ideals in Cluster Algebras

This paper investigates the Poisson geometry associated to a cluster algebra over the complex numbers, and its relationship to compatible torus actions. We show, under some assumptions, that each Noetherian cluster algebra has only finitely many torus invariant Poisson prime ideals and we show how to obtain using the exchange matrix of an initial seed. In fact, these ideals are independent of the choice of compatible Poisson structure. In many interesting cases the ideals can be described more explicitly.Comment: Completely revised and shortened, the argumentation is now algebraic, not analyti

Structural and electronic properties of an azamacrocycle, C26H18N6

We compute the structure of an azamacrocycle, C26H18N6. Two approximatively planar elliptical structures with C2 or CI symmetry are found to be nearly degenerate. The roughly circular conformation observed in metal complexes turns out to be ~ 0.6 eV higher in energy. We suggest that this difference is mainly due to electrostatic interactions. We discuss the results on various levels of theory (Hartree-Fock, local density and gradient corrected density functional calculations).Comment: to appear in J Phys Chem

Fermi surface and heavy masses for UPd2_2Al3_3

We calculate the Fermi surface and the anisotropic heavy masses of UPd2Al3 by keeping two of the 5f electrons as localized. Good agreement with experiments is found. The theory contains essentially no adjustable parameter except for a small shift of the position of the Fermi energy of the order of a few meV. A discussion is given why localization of two f electrons is justified.Comment: 4 pages, 2 figure

Higher Sobolev Regularity of Convex Integration Solutions in Elasticity: The Dirichlet Problem with Affine Data in int(Klc)\text{int}(K^{lc})

In this article we continue our study of higher Sobolev regularity of flexible convex integration solutions to differential inclusions arising from applications in materials sciences. We present a general framework yielding higher Sobolev regularity for Dirichlet problems with affine data in $\text{int}(K^{lc})$. This allows us to simultaneously deal with linear and nonlinear differential inclusion problems. We show that the derived higher integrability and differentiability exponent has a lower bound, which is independent of the position of the Dirichlet boundary data in $\text{int}(K^{lc})$. As applications we discuss the regularity of weak isometric immersions in two and three dimensions as well as the differential inclusion problem for the geometrically linear hexagonal-to-rhombic and the cubic-to-orthorhombic phase transformations occurring in shape memory alloys.Comment: 50 pages, 13 figure