Parallel-tempering cluster algorithm for computer simulations of critical phenomena

In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an adaptive routine to find the temperature window of interest, we introduce a flexible and powerful method for systematic investigations of critical phenomena. As a result, we gain one to two orders of magnitude in the performance for 2D and 3D Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic algorithm, which is already a great improvement over the standard multicanonical variant.Comment: pages, 5 figures, and 2 table

Make life simple: unleash the full power of the parallel tempering algorithm

We introduce a new update scheme to systematically improve the efficiency of parallel tempering simulations. We show that by adapting the number of sweeps between replica exchanges to the canonical autocorrelation time, the average round-trip time of a replica in temperature space can be significantly decreased. The temperatures are not dynamically adjusted as in previous attempts but chosen to yield a 50% exchange rate of adjacent replicas. We illustrate the new algorithm with results for the Ising model in two and the Edwards-Anderson Ising spin glass in three dimensionsComment: 4 pages, 5 figure

Formed platelet combustor liner construction feasibility, phase A

Environments generated in high pressure liquid rocket engines impose severe requirements on regeneratively cooled combustor liners. Liners fabricated for use in high chamber pressures using conventional processes suffer from limitations that can impair operational cycle life and can adversely affect wall compatibility. Chamber liners fabricated using formed platelet technology provide an alternative to conventional regeneratively cooled liners (an alternative that has many attractive benefits). A formed platelet liner is made from a stacked assembly of platelets with channel features. The assembly is diffusion bonded into a flat panel and then three-dimensionally formed into a section of a chamber. Platelet technology permits the liner to have very precisely controlled and thin hot gas walls and therefore increased heat transfer efficiency. Further cooling efficiencies can be obtained through enhanced design flexibility. These advantages translate into increased cycle life and enhanced wall compatibility. The increased heat transfer efficiency can alternately be used to increase engine performance or turbopump life as a result of pressure drop reductions within the regeneratively cooled liner. Other benefits can be obtained by varying the materials of construction within the platelet liner to enhance material compatibility with operating environment or with adjoining components. Manufacturing cost savings are an additional benefit of a formed platelet liner. This is because of reduced touch labor and reduced schedule when compared to conventional methods of manufacture. The formed platelet technology is not only compatible with current state-of-the art combustion chamber structural support and manifolding schemes, it is also an enabling technology that allows the use of other high performance and potentially low cost methods of construction for the entire combustion chamber assembly. The contract under which this report is submitted contains three phases: (1) phase A - feasibility study and technology development; (2) phase B - sub-scale fabrication feasibility; and (3) phase C - large scale fabrication validation. This report covers the Phase A activities, which began in December of 1988

An Adaptive Curriculum Students with Special Needs

The purpose of this project was to adapt existing social studies program materials for use with students with special needs in selected Washington State middle/junior high school. To accomplish this purpose, a comprehensive literature review of research related to social studies curricular and students with special needs was conducted. Existing curriculum was adapted, with special attention given to Washington State Essential Academic Learning Requirements (EALR) requirements. The project materials relate to European history from ancient to modern times, and may be a model for adapting other materials by other teachers

Monte Carlo study of the evaporation/condensation transition on different Ising lattices

In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous proof for the behavior of the 2D Ising lattice gas, at a finite volume and a fixed excess \delta M of particles (spins) above the ambient gas density (spontaneous magnetisation). By identifying a dimensionless parameter \Delta (\delta M) and a universal constant \Delta_c, they showed in the limit of large system sizes that for \Delta < \Delta_c the excess is absorbed in the background (``evaporated'' system), while for \Delta > \Delta_c a droplet of the dense phase occurs (``condensed'' system). To check the applicability of the analytical results to much smaller, practically accessible system sizes, we performed several Monte Carlo simulations for the 2D Ising model with nearest-neighbour couplings on a square lattice at fixed magnetisation M. Thereby, we measured the largest minority droplet, corresponding to the condensed phase, at various system sizes (L=40, >..., 640). With analytic values for for the spontaneous magnetisation m_0, the susceptibility \chi and the Wulff interfacial free energy density \tau_W for the infinite system, we were able to determine \lambda numerically in very good agreement with the theoretical prediction. Furthermore, we did simulations for the spin-1/2 Ising model on a triangular lattice and with next-nearest-neighbour couplings on a square lattice. Again, finding a very good agreement with the analytic formula, we demonstrate the universal aspects of the theory with respect to the underlying lattice. For the case of the next-nearest-neighbour model, where \tau_W is unknown analytically, we present different methods to obtain it numerically by fitting to the distribution of the magnetisation density P(m).Comment: 14 pages, 17 figures, 1 tabl

Error estimation and reduction with cross correlations

Besides the well-known effect of autocorrelations in time series of Monte Carlo simulation data resulting from the underlying Markov process, using the same data pool for computing various estimates entails additional cross correlations. This effect, if not properly taken into account, leads to systematically wrong error estimates for combined quantities. Using a straightforward recipe of data analysis employing the jackknife or similar resampling techniques, such problems can be avoided. In addition, a covariance analysis allows for the formulation of optimal estimators with often significantly reduced variance as compared to more conventional averages.Comment: 16 pages, RevTEX4, 4 figures, 6 tables, published versio

Lattice Models of Quantum Gravity

Standard Regge Calculus provides an interesting method to explore quantum gravity in a non-perturbative fashion but turns out to be a CPU-time demanding enterprise. One therefore seeks for suitable approximations which retain most of its universal features. The $Z_2$-Regge model could be such a desired simplification. Here the quadratic edge lengths $q$ of the simplicial complexes are restricted to only two possible values $q=1+\epsilon\sigma$, with $\sigma=\pm 1$, in close analogy to the ancestor of all lattice theories, the Ising model. To test whether this simpler model still contains the essential qualities of the standard Regge Calculus, we study both models in two dimensions and determine several observables on the same lattice size. In order to compare expectation values, e.g. of the average curvature or the Liouville field susceptibility, we employ in both models the same functional integration measure. The phase structure is under current investigation using mean field theory and numerical simulation.Comment: 4 pages, 1 figure