On the efficient numerical solution of lattice systems with low-order couplings

We apply the Quasi Monte Carlo (QMC) and recursive numerical integration methods to evaluate the Euclidean, discretized time path-integral for the quantum mechanical anharmonic oscillator and a topological quantum mechanical rotor model. For the anharmonic oscillator both methods outperform standard Markov Chain Monte Carlo methods and show a significantly improved error scaling. For the quantum mechanical rotor we could, however, not find a successful way employing QMC. On the other hand, the recursive numerical integration method works extremely well for this model and shows an at least exponentially fast error scaling

Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing

We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$. We give a positive answer to the long-standing open question whether this problem is strongly $NP$-complete for $m=4$. As a second result, we improve the lower bound of $\frac{12}{11}$ for approximating pseudo-polynomial Strip Packing to $\frac{5}{4}$. Since the best known approximation algorithm for this problem has a ratio of $\frac{4}{3} + \varepsilon$, this result narrows the gap between approximation ratio and inapproximability result by a significant step. Both results are proven by a reduction from the strongly $NP$-complete problem 3-Partition

Flavour Breaking Effects of Wilson twisted mass fermions

We study the flavour breaking effects appearing in the Wilson twisted mass formulation of lattice QCD. In this quenched study, we focus on the mass splitting between the neutral and the charged pion, determining the neutral pion mass with a stochastic noise method to evaluate the disconnected contributions. We find that these disconnected contributions are significant. Using the Osterwalder-Seiler interpretation of the connected piece of the neutral pion correlator, we compute the corresponding neutral pion mass to study with more precision the scaling behaviour of the mass splitting.Comment: 15 pages, 2 figure

Simulating the Electroweak Phase Transition in the SU(2) Higgs Model

Numerical simulations are performed to study the finite temperature phase transition in the SU(2) Higgs model on the lattice. In the presently investigated range of the Higgs boson mass, below 50 GeV, the phase transition turns out to be of first order and its strength is rapidly decreasing with increasing Higgs boson mass. In order to control the systematic errors, we also perform studies of scaling violations and of finite volume effects.Comment: 46 pages with 16 figures, DESY-94-15

Progress report on the ultra heavy cosmic ray experiment (AO178)

The Ultra Heavy Cosmic Ray Experiment (UHCRE) is based on a modular array of 192 side-viewing solid state nuclear track detector stacks. These stacks were mounted in sets of four in 48 pressure vessels employing sixteen peripheral Long Duration Exposure Facility (LDEF) trays. The extended duration of the LDEF mission has resulted in a greatly enhanced scientific yield from the UHCRE. The geometry factor for high energy cosmic ray nuclei, allowing for Earth shadowing, was 30 sq m-sr, giving a total exposure factor of 170 sq m-sr-y at an orbital inclination of 28.4 degrees. Scanning results indicate that about 3000 cosmic ray nuclei in the charge region with Z greater than 65 were collected. This sample is more than ten times the current world data in the field (taken to be the data set from the HEAO-3 mission plus that from the Ariel-6 mission) and is sufficient to provide the world's first statistically significant sample of actinide (Z greater than 88) cosmic rays. Results to date are presented including details of ultra-heavy cosmic ray nuclei, analysis of pre-flight and post-flight calibration events and details of track response in the context of detector temperature history. The integrated effect of all temperature and age related latent track variations cause a maximum charge shift of +/- 0.8 e for uranium and +/- 0.6 e for the platinum-lead group. The precision of charge assignment as a function of energy is derived and evidence for remarkably good charge resolution achieved in the UHCRE is considered. Astrophysical implications of the UHCRE charge spectrum are discussed