1,881 research outputs found
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 -Regge model could be such a desired
simplification. Here the quadratic edge lengths of the simplicial complexes
are restricted to only two possible values , with
, 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
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