Driving sandpiles to criticality and beyond

A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation. This theory predicts that the stationary density of the abelian sandpile model equals the threshold density of the fixed-energy sandpile. We refute this prediction for a wide variety of underlying graphs, including the square grid. Driven dissipative sandpiles continue to evolve even after reaching criticality. This result casts doubt on the validity of using fixed-energy sandpiles to explore the critical behavior of the abelian sandpile model at stationarity.Comment: v4 adds referenc

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

The dimension of loop-erased random walk in 3D

We measure the fractal dimension of loop-erased random walk (LERW) in 3 dimensions, and estimate that it is 1.62400 +- 0.00005. LERW is closely related to the uniform spanning tree and the abelian sandpile model. We simulated LERW on both the cubic and face-centered cubic lattices; the corrections to scaling are slightly smaller for the face-centered cubic lattice.Comment: 4 pages, 4 figures. v2 has more data, minor additional change

Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation

We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessary correlations are always present in practice. We show that introducing hidden variables and introducing rotation in the RNG output, accompanied with the proper initialization, dramatically suppress these correlations. We analyze the mechanisms of the single-cat-map correlations analytically and show how to diminish them. We generalize the Percival-Vivaldi theory in the case of the ensemble of maps, find the period of the proposed RNG analytically, and also analyze its properties. We present efficient practical realizations for the RNGs and check our predictions numerically. We also test our RNGs using the known stringent batteries of statistical tests and find that the statistical properties of our best generators are not worse than those of other best modern generators.Comment: 18 pages, 3 figures, 9 table

Algorithm for normal random numbers

We propose a simple algorithm for generating normally distributed pseudo random numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and that a Maxwell like distribution that may be used as a source of normally distributed random deviates follows when N tends to infinity. The algorithm passes various performance tests, including Monte Carlo simulation of a finite 2D Ising model using Wolff's algorithm. It only requires four simple lines of computer code, and is approximately ten times faster than the Box-Muller algorithm.Comment: 5 pages, 3 encapsulated Postscript Figures. Submitted to Phys.Rev.Letters. For related work, see http://pipe.unizar.es/~jf

Fast Monte Carlo Simulation for Patient-specific CT/CBCT Imaging Dose Calculation

Recently, X-ray imaging dose from computed tomography (CT) or cone beam CT (CBCT) scans has become a serious concern. Patient-specific imaging dose calculation has been proposed for the purpose of dose management. While Monte Carlo (MC) dose calculation can be quite accurate for this purpose, it suffers from low computational efficiency. In response to this problem, we have successfully developed a MC dose calculation package, gCTD, on GPU architecture under the NVIDIA CUDA platform for fast and accurate estimation of the x-ray imaging dose received by a patient during a CT or CBCT scan. Techniques have been developed particularly for the GPU architecture to achieve high computational efficiency. Dose calculations using CBCT scanning geometry in a homogeneous water phantom and a heterogeneous Zubal head phantom have shown good agreement between gCTD and EGSnrc, indicating the accuracy of our code. In terms of improved efficiency, it is found that gCTD attains a speed-up of ~400 times in the homogeneous water phantom and ~76.6 times in the Zubal phantom compared to EGSnrc. As for absolute computation time, imaging dose calculation for the Zubal phantom can be accomplished in ~17 sec with the average relative standard deviation of 0.4%. Though our gCTD code has been developed and tested in the context of CBCT scans, with simple modification of geometry it can be used for assessing imaging dose in CT scans as well.Comment: 18 pages, 7 figures, and 1 tabl

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

The observed state of the water cycle in the early twenty-first century

Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Climate 28 (2015): 8289–8318, doi:10.1175/JCLI-D-14-00555.1.This study quantifies mean annual and monthly fluxes of Earth’s water cycle over continents and ocean basins during the first decade of the millennium. To the extent possible, the flux estimates are based on satellite measurements first and data-integrating models second. A careful accounting of uncertainty in the estimates is included. It is applied within a routine that enforces multiple water and energy budget constraints simultaneously in a variational framework in order to produce objectively determined optimized flux estimates. In the majority of cases, the observed annual surface and atmospheric water budgets over the continents and oceans close with much less than 10% residual. Observed residuals and optimized uncertainty estimates are considerably larger for monthly surface and atmospheric water budget closure, often nearing or exceeding 20% in North America, Eurasia, Australia and neighboring islands, and the Arctic and South Atlantic Oceans. The residuals in South America and Africa tend to be smaller, possibly because cold land processes are negligible. Fluxes were poorly observed over the Arctic Ocean, certain seas, Antarctica, and the Australasian and Indonesian islands, leading to reliance on atmospheric analysis estimates. Many of the satellite systems that contributed data have been or will soon be lost or replaced. Models that integrate ground-based and remote observations will be critical for ameliorating gaps and discontinuities in the data records caused by these transitions. Continued development of such models is essential for maximizing the value of the observations. Next-generation observing systems are the best hope for significantly improving global water budget accounting.This research was funded by multiple grants from NASA’s Energy and Water Cycle Study (NEWS) program.2016-05-0