Pseudorandom Number Generators and the Square Site Percolation Threshold

A select collection of pseudorandom number generators is applied to a Monte Carlo study of the two dimensional square site percolation model. A generator suitable for high precision calculations is identified from an application specific test of randomness. After extended computation and analysis, an ostensibly reliable value of pc = 0.59274598(4) is obtained for the percolation threshold.Comment: 11 pages, 6 figure

Tracing the Arguello Submarine Canyon System from Shelf Origins to an Abyssal Sink

The Arguello submarine canyon/channel system extends over 300 km from the continental shelf off Point Arguello and Point Conception in southern California westward onto the oceanic crust of the Pacific plate. In the northernmost reaches where the canyon system originates, all stages in the evolution of seafloor morphologic fluid flow features—from pockmarks to gullies to converging rills—are observed, similar to what has been described for the Ascension slope, north of Monterey Bay. These features appear to be active today and are linked to fluid leakage from the underlying hydrocarbon basin. The channel dissects a continental slope that exhibits features consistent with large-scale mass wasting. Upslope scarps may be the source of the morphological feature at the base of the slope previously referred to as the "Arguello submarine fan," with topographic expressions (e.g., large channel meanders, ridges) that are more consistent with mass transport deposits than with deep-sea fan depositional lobes. The modern canyon crosscuts these deposits and parallels an older, meandering channel/canyon to the west. Modern seismicity along the shelf and slope may have, and potentially still can, trigger landslides on the slope. Seismicity associated with seamount volcanism, past subduction, and Borderland transrotational and extensional processes most likely played a role in stimulating mass wasting. The presence of abundant nearby petroleum suggests that gas venting and hydrate dissociation cannot be ruled out as a triggering mechanism for the slope destabilization occurring today. The canyon/channel continues due south on a path possibly determined by the structural grain of north–south-aligned abyssal hills underlying oceanic basement. At latitude 33deg 18min N, the channel makes a 90deg turn (bend) to the west at the E–W-striking Arguello transform fault wall and develops into a meandering channel system that crosses over abyssal hill crustal fabric. The system ultimately straightens as it continues west before veering north, curving around a thickened crustal bulge at a corner offset in the Arguello fracture zone in complex basement structure, and then finally empties into an 800-m-deep basin depocenter

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-

Tracing the Arguello Submarine Canyon System from Shelf Origins to an Abyssal Sink

The Arguello submarine canyon/channel system extends over 300 km from the continental shelf off Point Arguello and Point Conception in southern California westward onto the oceanic crust of the Pacific plate. In the northernmost reaches where the canyon system originates, all stages in the evolution of seafloor morphologic fluid flow features—from pockmarks to gullies to converging rills—are observed, similar to what has been described for the Ascension slope, north of Monterey Bay. These features appear to be active today and are linked to fluid leakage from the underlying hydrocarbon basin. The channel dissects a continental slope that exhibits features consistent with large-scale mass wasting. Upslope scarps may be the source of the morphological feature at the base of the slope previously referred to as the "Arguello submarine fan," with topographic expressions (e.g., large channel meanders, ridges) that are more consistent with mass transport deposits than with deep-sea fan depositional lobes. The modern canyon crosscuts these deposits and parallels an older, meandering channel/canyon to the west. Modern seismicity along the shelf and slope may have, and potentially still can, trigger landslides on the slope. Seismicity associated with seamount volcanism, past subduction, and Borderland transrotational and extensional processes most likely played a role in stimulating mass wasting. The presence of abundant nearby petroleum suggests that gas venting and hydrate dissociation cannot be ruled out as a triggering mechanism for the slope destabilization occurring today. The canyon/channel continues due south on a path possibly determined by the structural grain of north–south-aligned abyssal hills underlying oceanic basement. At latitude 33deg 18min N, the channel makes a 90deg turn (bend) to the west at the E–W-striking Arguello transform fault wall and develops into a meandering channel system that crosses over abyssal hill crustal fabric. The system ultimately straightens as it continues west before veering north, curving around a thickened crustal bulge at a corner offset in the Arguello fracture zone in complex basement structure, and then finally empties into an 800-m-deep basin depocenter

The arc arises: The links between volcanic output, arc evolution and melt composition

Subduction initiation is a key process for global plate tectonics. Individual lithologies developed during subduction initiation and arc inception have been identified in the trench wall of the Izu–Bonin–Mariana (IBM) island arc but a continuous record of this process has not previously been described. Here, we present results from International Ocean Discovery Program Expedition 351 that drilled a single site west of the Kyushu–Palau Ridge (KPR), a chain of extinct stratovolcanoes that represents the proto-IBM island arc, active for ∼25 Ma following subduction initiation. Site U1438 recovered 150 m of oceanic igneous basement and ∼1450 m of overlying sediments. The lower 1300 m of these sediments comprise volcaniclastic gravity-flow deposits shed from the evolving KPR arc front. We separated fresh magmatic minerals from Site U1438 sediments, and analyzed 304 glass (formerly melt) inclusions, hosted by clinopyroxene and plagioclase. Compositions of glass inclusions preserve a temporal magmatic record of the juvenile island arc, complementary to the predominant mid-Miocene to recent activity determined from tephra layers recovered by drilling in the IBM forearc. The glass inclusions record the progressive transition of melt compositions dominated by an early ‘calc-alkalic’, high-Mg andesitic stage to a younger tholeiitic stage over a time period of 11 Ma. High-precision trace element analytical data record a simultaneously increasing influence of a deep subduction component (e.g., increase in Th vs. Nb, light rare earth element enrichment) and a more fertile mantle source (reflected in increased high field strength element abundances). This compositional change is accompanied by increased deposition rates of volcaniclastic sediments reflecting magmatic output and maturity of the arc. We conclude the ‘calc-alkalic’ stage of arc evolution may endure as long as mantle wedge sources are not mostly advected away from the zones of arc magma generation, or the rate of wedge replenishment by corner flow does not overwhelm the rate of magma extraction

Hurst's Rescaled Range Statistical Analysis for Pseudorandom Number Generators used in Physical Simulations

The rescaled range statistical analysis (R/S) is proposed as a new method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the RS analysis provides a very sensitive method to reveal hidden long run and short run correlations. Several widely used and also some recently proposed pseudorandom number generators are subjected to this test. In many generators correlations are detected and quantified.Comment: 12 pages, 12 figures, 6 tables. Replaces previous version to correct citation [19

Simulation of truncated normal variables

We provide in this paper simulation algorithms for one-sided and two-sided truncated normal distributions. These algorithms are then used to simulate multivariate normal variables with restricted parameter space for any covariance structure.Comment: This 1992 paper appeared in 1995 in Statistics and Computing and the gist of it is contained in Monte Carlo Statistical Methods (2004), but I receive weekly requests for reprints so here it is

A fast Metropolis-Hastings method for generating random correlation matrices

We propose a novel Metropolis-Hastings algorithm to sample uniformly from the space of correlation matrices. Existing methods in the literature are based on elaborated representations of a correlation matrix, or on complex parametrizations of it. By contrast, our method is intuitive and simple, based the classical Cholesky factorization of a positive definite matrix and Markov chain Monte Carlo theory. We perform a detailed convergence analysis of the resulting Markov chain, and show how it benefits from fast convergence, both theoretically and empirically. Furthermore, in numerical experiments our algorithm is shown to be significantly faster than the current alternative approaches, thanks to its simple yet principled approach.Comment: 8 pages, 3 figures, 2018 conferenc

Numerical Study of a Mixed Ising Ferrimagnetic System

We present a study of a classical ferrimagnetic model on a square lattice in which the two interpenetrating square sublattices have spins one-half and one. This model is relevant for understanding bimetallic molecular ferrimagnets that are currently being synthesized by several experimental groups. We perform exact ground-state calculations for the model and employ Monte Carlo and numerical transfer-matrix techniques to obtain the finite-temperature phase diagram for both the transition and compensation temperatures. When only nearest-neighbor interactions are included, our nonperturbative results indicate no compensation point or tricritical point at finite temperature, which contradicts earlier results obtained with mean-field analysis.Comment: Figures can be obtained by request to [email protected] or [email protected]

Cluster Hybrid Monte Carlo Simulation Algorithms

We show that addition of Metropolis single spin-flips to the Wolff cluster flipping Monte Carlo procedure leads to a dramatic {\bf increase} in performance for the spin-1/2 Ising model. We also show that adding Wolff cluster flipping to the Metropolis or heat bath algorithms in systems where just cluster flipping is not immediately obvious (such as the spin-3/2 Ising model) can substantially {\bf reduce} the statistical errors of the simulations. A further advantage of these methods is that systematic errors introduced by the use of imperfect random number generation may be largely healed by hybridizing single spin-flips with cluster flipping.Comment: 16 pages, 10 figure