Optimal Point Placement for Mesh Smoothing

We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using generalized linear programming. We also give efficient algorithms for some mesh smoothing problems that do not fit into the generalized linear programming paradigm.Comment: 12 pages, 3 figures. A preliminary version of this paper was presented at the 8th ACM/SIAM Symp. on Discrete Algorithms (SODA '97). This is the final version, and will appear in a special issue of J. Algorithms for papers from SODA '9

Urban Regeneration – Strategies of Shrinking Cities in Eastern Germany

This contribution is meant to contrast the often negative images and scenarios of demographic change in eastern German cities by a more differentiated picture, by discussing regeneration processes running parallel – and sometimes even opposite – to shrinking. In this context, the regeneration of cities is understood as a complex process including demographic, socio-economic and physical dimensions. In the first part of the article the term will be discussed and some conceptional aspects will be presented. The second part will present evidence for a differentiated development of mediumsized towns. In the third part, we will present the hypothesis that strategies of urban development influence regeneration processes. This hypothesis will be evaluated by the examples of three cities with different regeneration approaches: Brandenburg an der Havel, Görlitz and Greifswald. Finally we will draw some general conclusions on urban development policy in eastern Germany

Collision induced spatial organization of microtubules

The dynamic behavior of microtubules in solution can be strongly modified by interactions with walls or other structures. We examine here a microtubule growth model where the increase in size of the plus-end is perturbed by collisions with other microtubules. We show that such a simple mechanism of constrained growth can induce ordered structures and patterns from an initially isotropic and homogeneous suspension. First, microtubules self-organize locally in randomly oriented domains that grow and compete with each other. By imposing even a weak orientation bias, external forces like gravity or cellular boundaries may bias the domain distribution eventually leading to a macroscopic sample orientation.Comment: Submitted to Biophysical Journa

Monte Carlo study of the growth of striped domains

We analyze the dynamical scaling behavior in a two-dimensional spin model with competing interactions after a quench to a striped phase. We measure the growth exponents studying the scaling of the interfaces and the scaling of the shrinking time of a ball of one phase plunged into the sea of another phase. Our results confirm the predictions found in previous papers. The correlation functions measured in the direction parallel and transversal to the stripes are different as suggested by the existence of different interface energies between the ground states of the model. Our simulations show anisotropic features for the correlations both in the case of single-spin-flip and spin-exchange dynamics.Comment: 15 pages, ReVTe

Wrapped Branes and Supersymmetry

Configurations of two or more branes wrapping different homology cycles of space-time are considered and the amount of supersymmetry preserved is analysed, generalising the analysis of multiple branes in flat space. For K3 compactifications, these give the Type II or M theory origin of certain supersymmetric four-dimensional heterotic string solutions that fit into spin-3/2 multiplets and which become massless at certain points in moduli space. The interpretation of these BPS states and the possibility of supersymmetry enhancement are discussed.Comment: 18 pages, Latex with Revtex, minor corrections and references added, version to appear in Nuclear Physics

A Tutorial on Advanced Dynamic Monte Carlo Methods for Systems with Discrete State Spaces

Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that preserve the dynamics of the model are described. These include the $n$-fold way algorithm, the Monte Carlo with Absorbing Markov Chains (MCAMC) algorithm, and the Projective Dynamics (PD) algorithm. To demonstrate the use of these algorithms, they are applied to some simplified models of dynamic physical systems. The models studied include a model for ion motion through a pore such as a biological ion channel and the metastable decay of the ferromagnetic Ising model. Non-trivial parallelization issues for these dynamic algorithms, which are in the class of parallel discrete event simulations, are discussed. Efforts are made to keep the article at an elementary level by concentrating on a simple model in each case that illustrates the use of the advanced dynamic Monte Carlo algorithm.Comment: 53 pages, 17 figure