Thomas Husslein

Searching for backbones — an efficient parallel algorithm for the traveling salesman problem

The Traveling Salesman Problem (TSP) plays an important role in Operations Research, Applied Mathematics and Computational Physics. We investigated it using a stochastic approach. Studying several solutions of a special TSP we found that many parts of a good solution are the same in all other good solutions for this problem. In this paper we discuss an efficient parallel method to reduce the TSP to a smaller one by finding these backbones and eliminating them to get even better solutions in a very short time and a few observables of interest corresponding to this parallel approach.

Molecular dynamics simulation of a hydrated diphytanol phosphatidylcholine lipid bilayer containing an alpha-helical bundle of four transmembrane domains of the Influenza A virus M2 protein

An alpha-helical bundle composed of four transmembrane portions of the M2 protein from the Influenza A virus has been studied in a hydrated diphytanol phosphatidylcholine bilayer using molecular dynamics (MD) calculations. Experimentally, the sequence utilized is known to aggregate as a four-helix bundle and act as a pH-gated proton-selective ion channel, which is blocked by the drug amantadine hydrochloride. In the presented simulation, the ion channel was initially set up as a parallel four-helix bundle. The all-atom simulation consisted of almost 16,000 atoms, described classically, using a forcefield from the CHARMM22 database. Bilayers with and without the bundle were shown to be stable throughout the nanosecond timescale of the MD simulation. Structural and dynamical properties of the bilayer both with and without the transmembrane protein are reported.

Comparison of calculations for the Hubbard model obtained with Quantum-Monte-Carlo, exact, and stochastic diagonalization

In this paper we compare numerical results for the ground state of the Hubbard model obtained by Quantum-Monte-Carlo simulations with results from exact and stochastic diagonalizations. We find good agreement for the ground state energy and superconducting correlations for both, the repulsive and attractive Hubbard model. Special emphasis lies on the superconducting correlations in the repulsive Hubbard model, where the small magnitude of the values obtained by Monte-Carlo simulations gives rise to the question, whether these results might be caused by fluctuations or systematic errors of the method. Although we notice that the Quantum-Monte-Carlo method has convergence problems for large interactions, coinciding with a minus sign problem, we confirm the results of the diagonalization techniques for small and moderate interaction strengths. Additionally we investigate the numerical stability and the convergence of the Quantum-Monte-Carlo method in the attractive case, to study the influence of the minus sign problem on convergence. Also here in the absence of a minus sign problem we encounter convergence problems for strong interactions.

Efficient parallelization of the 2D Swendsen-Wang algorithm

We established a fast Swendsen-Wang algorithm for the two-dimensional Ising model on parallel computers with a high efficiency. On an Intel paragon with 140 processors we reached spin update times of only 14 ns with an efficiency of 89%. This algorithm was used to examine the non-equilibrium relaxation of magnetization and energy in large Ising systems of a size up to 17920 × 17920 spins. Nevertheless we observed still a strong finite-size effect for the magnetization. We assume both magnetization and energy decay to behave like (t + Δ)-λe-bt in an infinitely large system. Thus, for long times magnetization and energy show an exponential, asymtotic time-dependence, implying a critical dynamic exponent z of zero.

Application of the SD Technique for Solving a BCS-Reduced Hubbard like Hamiltonian

We present exact and stochastic diagonalization results for a BCS-reduced Hubbard model. The kinetic Hamiltonian is the same as in the single band Hubbard model with additional next nearest neighbor hopping. The interaction of this model is designed to inhibit superconductivity in the dx2-y2 channel. The ground state of this model is studied by exact and stochastic diagonalization technique. We present a review of the technical details of the application of the stochastic diagonalization algorithm on this problem. To verify our results obtained with the stochastic diagonalization, they are compared with the exact diagonalization results. In order to show the convergence of the stochastic diagonalization we give a detailed analysis of the behavior of physical properties with increasing number of states. Finally we study superconductivity in this BCS-reduced Hubbard model. As an indicator of superconductivity we use the occurrence of Off Diagonal Long Range Order. We study the scaling behavior of this model for various attractive interactions and in addition the dependence of the superconducting correlation functions from the filling of the system.

3D Ising model with Swendsen-Wang dynamics: a parallel approach

We propose an efficient parallel implementation of the Swendsen-Wang algorithm for a 3D Ising system. A modified relaxation method was used for the parallelization. The simulations were performed on the Intel Paragon. We discuss the implementation in detail.

Parallelization of the 2D Swendsen-Wang Algorithm

We implemented a parallel Swendsen–Wang algorithm for a 2D Ising system without magnetization in a host–node programming model. The simulations were performed on the Intel Hypercube IPSC/860. Our maximum number of updates/s on 32 nodes ist three times as high as in the implementation by Stauffer and Kertesz on the same machine. With 32 processors we reach half the speed of the simulations by Tamayo and Flanigan on 256 nodes of a CM5. We discuss the non–equilibrium relaxation for the energy and the magnetization.

Parallelization of the exact diagonalization of the t−t′-Hubbard model

We present a new parallel algorithm for the exact diagonalization of the t−t′-Hubbard model with the Lanczos method. By invoking a new scheme of labeling the states we were able to obtain a speedup of up to four on 16 nodes of an IBM SP2 for the calculation of the ground state energy and an almost linear speedup for the calculation of the correlation functions. Using this algorithm we performed an extensive study of the influence of the next-nearest hopping parameter t′ in the t−t′-Hubbard model on ground state energy and the superconducting correlation functions for both attractive and repulsive interaction.

GLASS MODEL, HUBBARD MODEL AND HIGH-TEMPERATURE SUPERCONDUCTIVITY

In this paper we revisit the glass model describing the macroscopic behavior of the High-Temperature superconductors. We link the glass model at the microscopic level to the striped phase phenomenon, recently discussed widely. The size of the striped phase domains is consistent with earlier predictions of the glass model when it was introduced for High-Temperature Superconductivity in 1987. In an additional step we use the Hubbard model to describe the microscopic mechanism for d-wave pairing within these finite size stripes. We discuss the implications for superconducting correlations of the Hubbard model, which are much higher for stripes than for squares, for finite size scaling, and for the new view of the glass model picture.