Monte Carlo computation of correlation times of independent relaxation modes at criticality

We investigate aspects of universality of Glauber critical dynamics in two dimensions. We compute the critical exponent $z$ and numerically corroborate its universality for three different models in the static Ising universality class and for five independent relaxation modes. We also present evidence for universality of amplitude ratios, which shows that, as far as dynamic behavior is concerned, each model in a given universality class is characterized by a single non-universal metric factor which determines the overall time scale. This paper also discusses in detail the variational and projection methods that are used to compute relaxation times with high accuracy

Universal Dynamics of Independent Critical Relaxation Modes

Scaling behavior is studied of several dominant eigenvalues of spectra of Markov matrices and the associated correlation times governing critical slowing down in models in the universality class of the two-dimensional Ising model. A scheme is developed to optimize variational approximants of progressively rapid, independent relaxation modes. These approximants are used to reduce the variance of results obtained by means of an adaptation of a quantum Monte Carlo method to compute eigenvalues subject to errors predominantly of statistical nature. The resulting spectra and correlation times are found to be universal up to a single, non-universal time scale for each model

High-growth firms: introduction to the special section

High-growth firms (HGFs) have attracted considerable attention recently, as academics and policymakers have increasingly recognized the highly skewed nature of many metrics of firm performance. A small number of HGFs drives a disproportionately large amount of job creation, while the average firm has a limited impact on the economy. This article explores the reasons for this increased interest, summarizes the existing literature, and highlights the methodological considerations that constrain and bias research. This special section draws attention to the importance of HGFs for future industrial performance, explores their unusual growth trajectories and strategies, and highlights the lack of persistence of high growth. Consequently, while HGFs are important for understanding the economy and developing public policy, they are unlikely to be useful vehicles for public policy given the difficulties involved in predicting which firms will grow, the lack of persistence in high growth levels, and the complex and often indirect relationship between firm capability, high growth, and macro-economic performance

Transfer-matrix approach to the three-dimensional bond percolation: An application of Novotny's formalism

A transfer-matrix simulation scheme for the three-dimensional (d=3) bond percolation is presented. Our scheme is based on Novotny's transfer-matrix formalism, which enables us to consider arbitrary (integral) number of sites N constituting a unit of the transfer-matrix slice even for d=3. Such an arbitrariness allows us to perform systematic finite-size-scaling analysis of the criticality at the percolation threshold. Diagonalizing the transfer matrix for N =4,5,...,10, we obtain an estimate for the correlation-length critical exponent nu = 0.81(5)

Optimization of ground and excited state wavefunctions and van der Waals clusters

A quantum Monte Carlo method is introduced to optimize excited state trial wavefunctions. The method is applied in a correlation function Monte Carlo calculation to compute ground and excited state energies of bosonic van der Waals clusters of upto seven particles. The calculations are performed using trial wavefunctions with general three-body correlations

The Dynamic Exponent of the Two-Dimensional Ising Model and Monte Carlo Computation of the Sub-Dominant Eigenvalue of the Stochastic Matrix

We introduce a novel variance-reducing Monte Carlo algorithm for accurate determination of autocorrelation times. We apply this method to two-dimensional Ising systems with sizes up to $15 \times 15$, using single-spin flip dynamics, random site selection and transition probabilities according to the heat-bath method. From a finite-size scaling analysis of these autocorrelation times, the dynamical critical exponent $z$ is determined as $z=2.1665$ (12)

Anomalous dynamics in two- and three- dimensional Heisenberg-Mattis spin glasses

We investigate the spectral and localization properties of unmagnetized Heisenberg-Mattis spin glasses, in space dimensionalities $d=2$ and 3, at T=0. We use numerical transfer-matrix methods combined with finite-size scaling to calculate Lyapunov exponents, and eigenvalue-counting theorems, coupled with Gaussian elimination algorithms, to evaluate densities of states. In $d=2$ we find that all states are localized, with the localization length diverging as $\omega^{-1}$, as energy $\omega \to 0$. Logarithmic corrections to density of states behave in accordance with theoretical predictions. In $d=3$ the density-of-states dependence on energy is the same as for spin waves in pure antiferromagnets, again in agreement with theoretical predictions, though the corresponding amplitudes differ.Comment: RevTeX4, 9 pages, 9 .eps figure

Potts and percolation models on bowtie lattices

We give the exact critical frontier of the Potts model on bowtie lattices. For the case of $q=1$, the critical frontier yields the thresholds of bond percolation on these lattices, which are exactly consistent with the results given by Ziff et al [J. Phys. A 39, 15083 (2006)]. For the $q=2$ Potts model on the bowtie-A lattice, the critical point is in agreement with that of the Ising model on this lattice, which has been exactly solved. Furthermore, we do extensive Monte Carlo simulations of Potts model on the bowtie-A lattice with noninteger $q$. Our numerical results, which are accurate up to 7 significant digits, are consistent with the theoretical predictions. We also simulate the site percolation on the bowtie-A lattice, and the threshold is $s_c=0.5479148(7)$. In the simulations of bond percolation and site percolation, we find that the shape-dependent properties of the percolation model on the bowtie-A lattice are somewhat different from those of an isotropic lattice, which may be caused by the anisotropy of the lattice.Comment: 18 pages, 9 figures and 3 table

Biological and physical forcing of carbonate chemistry in an upwelling filament off northwest Africa: Results from a Lagrangian study

The Mauritanian upwelling system is one of the most biologically productive regions of the world's oceans. Coastal upwelling transfers nutrients to the sun-lit surface ocean, thereby stimulating phytoplankton growth. Upwelling of deep waters also supplies dissolved inorganic carbon (DIC), high levels of which lead to low calcium carbonate saturation states in surface waters, with potentially adverse effects on marine calcifiers. In this study an upwelled filament off the coast of northwest Africa was followed using drifting buoys and sulphur hexafluoride to determine how the carbonate chemistry changed over time as a result of biological, physical and chemical processes. The initial pHtot in the mixed layer of the upwelled plume was 7.94 and the saturation states of calcite and aragonite were 3.4 and 2.2, respectively. As the plume moved offshore over a period of 9 days, biological uptake of DIC (37 ?mol kg?1) reduced pCO2 concentrations from 540 to 410 ?atm, thereby increasing pHtot to 8.05 and calcite and aragonite saturation states to 4.0 and 2.7 respectively. The increase (25 ?mol kg?1) in total alkalinity over the 9 day study period can be accounted for solely by the combined effects of nitrate uptake and processes that alter salinity (i.e., evaporation and mixing with other water masses). We found no evidence of significant alkalinity accumulation as a result of exudation of organic bases by primary producers. The ongoing expansion of oxygen minimum zones through global warming will likely further reduce the CaCO3 saturation of upwelled waters, amplifying any adverse consequences of ocean acidification on the ecosystem of the Mauritanian upwelling system