J. M. Singer

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.

Search-space smoothing for combinatorial optimization problems

Commonly there are two types of local search approaches known to treat combinatorial optimization problems with very complex search-space structure: One is to introduce very complicated types of local move classes, allowing a bypass of high energetic barriers separating different minima. The second is introducing a control-parameter (i.e. temperature in physics terminology) dependent state space walker, which is — depending on this control parameter — more or less easily able to climb over barriers. A third, less well-known, but very obvious approach is to smooth the search space, i.e. to eliminate barriers between low-energy configurations and therefore to allow a fast and easy approach to the global optimum. This procedure will be discussed in depth in the following work.

Magnetic field induced phase transitions in

Abstract:The c-axis resistivity measurements in from Hussey et al. for magnetic field orientations along the c-axis as well as within the ab-plane are analyzed and interpreted using the scaling theory for static and dynamic classical critical phenomena. We identify a superconductor to normal conductor transition for both field orientations as well as a normal conductor to insulator transition at a critical field with dynamical critical exponent z=1, leading to a multicritical point where superconducting, normal conducting and insulating phases coexist.

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.

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.

Fundamental constraints for the mechanism of superconductivity in cuprates

Abstract:Considerable progress has been made over the last decade in understanding the phenomenological properties of the cuprate high-Tc superconductors and in producing well characterized high quality materials. Nevertheless, the pairing mechanism itself remains controversial. We establish a criterion to test theories for layered superconductors relying on a substantial interlayer contribution. The criterion is based on the ratio of the interlayer contribution to the total superfluid density, which is traced back to the inverse squared effective mass anisotropy, . can be measured rather accurately by various experimental techniques. It turns out that models relying on interlayer pairing cannot be considered as serious candidates for the mechanism of superconductivity in cuprate superconductors.

Quantum Monte Carlo Evidence for d-wave Pairing in the 2D Hubbard Model at a van Hove Singularity

We implement a Quantum Monte Carlo calculation for a repulsive Hubbard model with nearest and next-nearest neighbor hopping interactions on clusters up to 12x12. A parameter region where the Fermi level lies close to the van Hove singularity at the Saddle Points in the bulk band structure is investigated. A pairing tendency in the

Quantum Monte Carlo Simulations of the Two-Dimensional Attractive Hubbard Model: Phase Diagram and Spectral Properties

d_{x^2-y^2}

Quantum Monte Carlo evidence for {ital d}-wave pairing in the two-dimensional Hubbard model at a van Hove singularity

symmetry channel, but no other channel, is found. Estimates of the effective pairing interaction show that it is close to the value required for a 40 K superconductor. Finite-size scaling compares with the attractive Hubbard model.