Tree decomposition by eigenvectors

AbstractIn this work a composition–decomposition technique is presented that correlates tree eigenvectors with certain eigenvectors of an associated so-called skeleton forest. In particular, the matching properties of a skeleton determine the multiplicity of the corresponding tree eigenvalue. As an application a characterization of trees that admit eigenspace bases with entries only from the set {0,1,−1} is presented. Moreover, a result due to Nylen concerned with partitioning eigenvectors of tree pattern matrices is generalized

Surface stress of Ni adlayers on W(110): the critical role of the surface atomic structure

Puzzling trends in surface stress were reported experimentally for Ni/W(110) as a function of Ni coverage. In order to explain this behavior, we have performed a density-functional-theory study of the surface stress and atomic structure of the pseudomorphic and of several different possible 1x7 configurations for this system. For the 1x7 phase, we predict a different, more regular atomic structure than previously proposed based on surface x-ray diffraction. At the same time, we reproduce the unexpected experimental change of surface stress between the pseudomorphic and 1x7 configuration along the crystallographic surface direction which does not undergo density changes. We show that the observed behavior in the surface stress is dominated by the effect of a change in Ni adsorption/coordination sites on the W(110) surface.Comment: 14 pages, 3 figures Published in J. Phys.: Condens. Matter 24 (2012) 13500

Fast kinetic Monte Carlo simulation of strained heteroepitaxy in three dimensions

Accelerated algorithms for simulating the morphological evolution of strained heteroeptiaxy based on a ball and spring lattice model in three dimensions are explained. We derive exact Green's function formalisms for boundary values in the associated lattice elasticity problems. The computational efficiency is further enhanced by using a superparticle surface coarsening approximation. Atomic hoppings simulating surface diffusion are sampled using a multi-step acceptance-rejection algorithm. It utilizes quick estimates of the atomic elastic energies from extensively tabulated values modulated by the local strain. A parameter controls the compromise between accuracy and efficiency of the acceptance-rejection algorithm.Comment: 10 pages, 4 figures, submitted to Proceedings of Barrett Lectures 2007, Journal of Scientific Computin

The maximal energy of classes of integral circulant graphs

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs, which can be characterized by their vertex count $n$ and a set $\cal D$ of divisors of $n$ in such a way that they have vertex set $\mathbb{Z}_n$ and edge set ${{a,b}: a,b\in\mathbb{Z}_n, \gcd(a-b,n)\in {\cal D}}$. For a fixed prime power $n=p^s$ and a fixed divisor set size $|{\cal D}| =r$, we analyze the maximal energy among all matching integral circulant graphs. Let $p^{a_1} < p^{a_2} < ... < p^{a_r}$ be the elements of ${\cal D}$. It turns out that the differences $d_i=a_{i+1}-a_{i}$ between the exponents of an energy maximal divisor set must satisfy certain balance conditions: (i) either all $d_i$ equal $q:=\frac{s-1}{r-1}$, or at most the two differences $[q]$ and $[q+1]$ may occur; %(for a certain $d$ depending on $r$ and $s$) (ii) there are rules governing the sequence $d_1,...,d_{r-1}$ of consecutive differences. For particular choices of $s$ and $r$ these conditions already guarantee maximal energy and its value can be computed explicitly.Comment: Discrete Applied Mathematics (2012

The metallicity dependence of WR winds

Wolf-Rayet (WR) stars are the most advanced stage in the evolution of the most massive stars. The strong feedback provided by these objects and their subsequent supernova (SN) explosions are decisive for a variety of astrophysical topics such as the cosmic matter cycle. Consequently, understanding the properties of WR stars and their evolution is indispensable. A crucial but still not well known quantity determining the evolution of WR stars is their mass-loss rate. Since the mass loss is predicted to increase with metallicity, the feedback provided by these objects and their spectral appearance are expected to be a function of the metal content of their host galaxy. This has severe implications for the role of massive stars in general and the exploration of low metallicity environments in particular. Hitherto, the metallicity dependence of WR star winds was not well studied. In this contribution, we review the results from our comprehensive spectral analyses of WR stars in environments of different metallicities, ranging from slightly super-solar to SMC-like metallicities. Based on these studies, we derived empirical relations for the dependence of the WN mass-loss rates on the metallicity and iron abundance, respectively.Comment: 5 pages, 4 figures, to be published in the Proceedings of the IAU Symposium No. 329 "The lives and death-throes of massive stars