Ein technologisches Konzept zur Erzeugung adaptiver hierarchischer Netze für FEM-Schemata

Adaptive finite element methods for the solution of partial differential equations require effective methods of mesh refinement and coarsening, fast multilevel solvers for the systems of FE equations need a hierarchical structure of the grid. In the paper a technology is presented for the application of irregular hierarchical triangular meshes arising from refinement by only dividing elements into four congruent triangles. The paper describes the necessary data structures and data structure management, the principles and algorithms of refining and coarsening the mesh, and also a specific assembly technique for the FE equations system. Aspects of the parallel implementation on MIMD computers with a message passing communication are included

Lokale Realisierung von Vektoroperationen auf Parallelrechnern

For the basic algebraic vector operations several variants of a local implementation on distributed memory parallel computers are presented and discussed systematically. In particular necessary and sufficient conditions are shown for the local realizability of the multiplication matrix by vector

Crystal structures and freezing of dipolar fluids

We investigate the crystal structure of classical systems of spherical particles with an embedded point dipole at T=0. The ferroelectric ground state energy is calculated using generalizations of the Ewald summation technique. Due to the reduced symmetry compared to the nonpolar case the crystals are never strictly cubic. For the Stockmayer (i.e., Lennard-Jones plus dipolar) interaction three phases are found upon increasing the dipole moment: hexagonal, body-centered orthorhombic, and body-centered tetragonal. An even richer phase diagram arises for dipolar soft spheres with a purely repulsive inverse power law potential $\sim r^{-n}$. A crossover between qualitatively different sequences of phases occurs near the exponent $n=12$. The results are applicable to electro- and magnetorheological fluids. In addition to the exact ground state analysis we study freezing of the Stockmayer fluid by density-functional theory.Comment: submitted to Phys. Rev.

Vesicles in solutions of hard rods

The surface free energy of ideal hard rods near curved hard surfaces is determined to second order in curvature for surfaces of general shape. In accordance with previous results for spherical and cylindrical surfaces it is found that this quantity is non-analytical when one of the principal curvatures changes signs. This prohibits writing it in the common Helfrich form. It is shown that the non-analytical terms are the same for any aspect ratio of the rods. These results are used to find the equilibrium shape of vesicles immersed in solutions of rod-like (colloidal) particles. The presence of the particles induces a change in the equilibrium shape and to a shift of the prolate-oblate transition in the vesicle phase diagram, which are calculated within the framework of the spontaneous curvature model. As a consequence of the special form of the energy contribution due to the rods these changes cannot be accounted for by a simple rescaling of the elastic constants of the vesicle as for solutions of spherical colloids or polymers.Comment: 11 pages, 7 figures, submitted to Phys. Rev.

Decomposition of operator semigroups on W*-algebras

We consider semigroups of operators on a W$^*$-algebra and prove, under appropriate assumptions, the existence of a Jacobs-DeLeeuw-Glicksberg type decomposition. This decomposition splits the algebra into a "stable" and "reversible" part with respect to the semigroup and yields, among others, a structural approach to the Perron-Frobenius spectral theory for completely positive operators on W$^*$-algebras.Comment: referee's comments incorporated. To appear in Semigroup Foru

Homogeneous Open Quantum Random Walks on a lattice

We study Open Quantum Random Walks for which the underlying graph is a lattice, and the generators of the walk are translation-invariant. We consider the quantum trajectory associated with the OQRW, which is described by a position process and a state process. We obtain a central limit theorem and a large deviation principle for the position process, and an ergodic result for the state process. We study in detail the case of homogeneous OQRWs on a lattice, with internal space $h={\mathbb C}^2$

The instability of Alexander-McTague crystals and its implication for nucleation

We show that the argument of Alexander and McTague, that the bcc crystalline structure is favored in those crystallization processes where the first order character is not too pronounced, is not correct. We find that any solution that satisfies the Alexander-McTague condition is not stable. We investigate the implication of this result for nucleation near the pseudo- spinodal in near-meanfield systems.Comment: 20 pages, 0 figures, submitted to Physical Review

Orientational Ordering in Spatially Disordered Dipolar Systems

This letter addresses basic questions concerning ferroelectric order in positionally disordered dipolar materials. Three models distinguished by dipole vectors which have one, two or three components are studied by computer simulation. Randomly frozen and dynamically disordered media are considered. It is shown that ferroelectric order is possible in spatially random systems, but that its existence is very sensitive to the dipole vector dimensionality and the motion of the medium. A physical analysis of our results provides significant insight into the nature of ferroelectric transitions.Comment: 4 pages twocolumn LATEX style. 4 POSTSCRIPT figures available from [email protected]

Two New LBV Candidates in the M33 Galaxy

We present two new luminous blue variable (LBV) candidate stars discovered in the M33 galaxy. We identified these stars (Valeev et al. 2010) as massive star candidates at the final stages of evolution, presumably with a notable interstellar extinction. The candidates were selected from the Massey et al. (2006) catalog based on the following criteria: emission in Halpha, V<18.5 and 0.35<(B-V)<1.2. The spectra of both stars reveal a broad and strong Halpha emission with extended wings (770 and 1000 km/s). Based on the spectra we estimated the main parameters of the stars. Object N45901 has a bolometric luminosity log(L/Lsun)=6.0-6.2 with the value of interstellar extinction Av=2.3+-0.1. The temperature of the star's photosphere is estimated as Tstar~13000-15000K its probable mass on the Zero Age Main Sequence is M~60-80Msun. The infrared excess in N45901 corresponds to the emission of warm dust with the temperature Twarm~1000K, and amounts to 0.1% of the bolometric luminosity. A comparison of stellar magnitude estimates from different catalogs points to the probable variability of the object N45901. Bolometric luminosity of the second object, N125093, is log(L/Lsun)=6.3-6.6, the value of interstellar extinction is Av=2.75+-0.15. We estimate its photosphere's temperature as Tstar~13000-16000K, the initial mass as M~90-120Msun. The infrared excess in N125093 amounts to 5-6% of the bolometric luminosity. Its spectral energy distribution reveals two thermal components with the temperatures Twarm~1000K and Tcold~480K. The [CaII] lines (7291A and 7323A), observed in LBV-like stars VarA and N93351 in M33, are also present in the spectrum of N125093. These lines indicate relatively recent gas eruptions and dust activity linked with them. High bolometric luminosity of these stars and broad Halpha emissions allow classifying the studied objects as LBV candidates.Comment: 14 pages, 4 figure

Quantum Einstein Gravity

We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum approach based upon the effective average action, we summarize the state of the art of the field with a particular focus on the evidence supporting the existence of the non-trivial renormalization group fixed point at the heart of the construction. As an application, the multifractal structure of the emerging space-times is discussed in detail. In particular, we compare the continuum prediction for their spectral dimension with Monte Carlo data from the Causal Dynamical Triangulation approach.Comment: 87 pages, 13 figures, review article prepared for the New Journal of Physics focus issue on Quantum Einstein Gravit