One-way multigrid method in electronic structure calculations

We propose a simple and efficient one-way multigrid method for self-consistent electronic structure calculations based on iterative diagonalization. Total energy calculations are performed on several different levels of grids starting from the coarsest grid, with wave functions transferred to each finer level. The only changes compared to a single grid calculation are interpolation and orthonormalization steps outside the original total energy calculation and required only for transferring between grids. This feature results in a minimal amount of code change, and enables us to employ a sophisticated interpolation method and noninteger ratio of grid spacings. Calculations employing a preconditioned conjugate gradient method are presented for two examples, a quantum dot and a charged molecular system. Use of three grid levels with grid spacings 2h, 1.5h, and h decreases the computer time by about a factor of 5 compared to single level calculations.Comment: 10 pages, 2 figures, to appear in Phys. Rev. B, Rapid Communication

Ground-state properties of tubelike flexible polymers

In this work we investigate structural properties of native states of a simple model for short flexible homopolymers, where the steric influence of monomeric side chains is effectively introduced by a thickness constraint. This geometric constraint is implemented through the concept of the global radius of curvature and affects the conformational topology of ground-state structures. A systematic analysis allows for a thickness-dependent classification of the dominant ground-state topologies. It turns out that helical structures, strands, rings, and coils are natural, intrinsic geometries of such tubelike objects

Evaluation of the BCS Approximation for the Attractive Hubbard Model in One Dimension

The ground state energy and energy gap to the first excited state are calculated for the attractive Hubbard model in one dimension using both the Bethe Ansatz equations and the variational BCS wavefunction. Comparisons are provided as a function of coupling strength and electron density. While the ground state energies are always in very good agreement, the BCS energy gap is sometimes incorrect by an order of magnitude, particularly at half-filling. Finite size effects are also briefly discussed for cases where an exact solution in the thermodynamic limit is not possible. In general, the BCS result for the energy gap is poor compared to the exact result.Comment: 25 pages, 5 Postscript figure

The Shapes of Dirichlet Defects

If the vacuum manifold of a field theory has the appropriate topological structure, the theory admits topological structures analogous to the D-branes of string theory, in which defects of one dimension terminate on other defects of higher dimension. The shapes of such defects are analyzed numerically, with special attention paid to the intersection regions. Walls (co-dimension 1 branes) terminating on other walls, global strings (co-dimension 2 branes) and local strings (including gauge fields) terminating on walls are all considered. Connections to supersymmetric field theories, string theory and condensed matter systems are pointed out.Comment: 24 pages, RevTeX, 21 eps figure

Mixed initial conditions to estimate the dynamic critical exponent in short-time Monte Carlo simulation

We explore the initial conditions in short-time critical dynamics to propose a new method to evaluate the dynamic exponent z. Estimates are obtained with high precision for 2D Ising model and 2D Potts model for three and four states by performing heat-bath Monte Carlo simulations.Comment: Latex paper, 2 eps figure

Exact boundary conditions at finite distance for the time-dependent Schrodinger equation

Exact boundary conditions at finite distance for the solutions of the time-dependent Schrodinger equation are derived. A numerical scheme based on Crank-Nicholson method is proposed to illustrate its applicability in several examples.Comment: Latex.tar.gz file, 20 pages, 9 figure

Turbulent diffusion and drift in galactic magnetic fields and the explanation of the knee in the cosmic ray spectrum

We reconsider the scenario in which the knee in the cosmic ray spectrum is explained as due to a change in the escape mechanism of cosmic rays from the Galaxy from one dominated by transverse diffusion to one dominated by drifts. We solve the diffusion equations adopting realistic galactic field models and using diffusion coefficients appropriate for strong turbulence (with a Kolmogorov spectrum of fluctuations) and consistent with the assumed magnetic fields. We show that properly taking into account these effects leads to a natural explanation of the knee in the spectrum, and a transition towards a heavier composition above the knee is predicted.Comment: 17 pp., 6 figures; revised version with minor changes. To appear in JHE

Split-domain calibration of an ecosystem model using satellite ocean colour data

The application of satellite ocean colour data to the calibration of plankton ecosystem models for large geographic domains, over which their ideal parameters cannot be assumed to be invariant, is investigated. A method is presented for seeking the number and geographic scope of parameter sets which allows the best fit to validation data to be achieved. These are independent data not used in the parameter estimation process. The goodness-of-fit of the optimally calibrated model to the validation data is an objective measure of merit for the model, together with its external forcing data. Importantly, this is a statistic which can be used for comparative evaluation of different models. The method makes use of observations from multiple locations, referred to as stations, distributed across the geographic domain. It relies on a technique for finding groups of stations which can be aggregated for parameter estimation purposes with minimal increase in the resulting misfit between model and observations.The results of testing this split-domain calibration method for a simple zero dimensional model, using observations from 30 stations in the North Atlantic, are presented. The stations are divided into separate calibration and validation sets. One year of ocean colour data from each station were used in conjunction with a climatological estimate of the station’s annual nitrate maximum. The results demonstrate the practical utility of the method and imply that an optimal fit of the model to the validation data would be given by two parameter sets. The corresponding division of the North Atlantic domain into two provinces allows a misfit-based cost to be achieved which is 25% lower than that for the single parameter set obtained using all of the calibration stations. In general, parameters are poorly constrained, contributing to a high degree of uncertainty in model output for unobserved variables. This suggests that limited progress towards a definitive model calibration can be made without including other types of observations

Detection Limits for Super-Hubble Suppression of Causal Fluctuations

We investigate to what extent future microwave background experiments might be able to detect a suppression of fluctuation power on large scales in flat and open universe models. Such suppression would arise if fluctuations are generated by causal processes, and a measurement of a small suppression scale would be problematic for inflation models, but consistent with many defect models. More speculatively, a measurement of a suppression scale of the order of the present Hubble radius could provide independent evidence for a fine-tuned inflation model leading to a low-density universe. We find that, depending on the primordial power spectrum, a suppression scale modestly larger than the visible Horizon can be detected, but that the detectability drops very rapidly with increasing scale. For models with two periods of inflation, there is essentially no possibility of detecting a causal suppression scale.Comment: 8 pages, 4 figures, revtex, In Press Physical Review D 200

Physical tests for Random Numbers in Simulations

We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of n successive numbers. We apply the tests to show that recent errors in high precision simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences. We also determine the length of these correlations.Comment: 16 pages, Post Script file, HU-TFT-94-