Geometric explanation of anomalous finite-size scaling in high dimensions

We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on five-dimensional hypercubic lattices with free and periodic boundary conditions, by using geometric representations and recently introduced Markov-chain Monte Carlo algorithms. We show that previously observed anomalous behaviour for correlation functions, measured on the standard Euclidean scale, can be removed by defining correlation functions on a scale which correctly accounts for windings.Comment: 5 pages, 4 figure

Sorbent extraction of some metal ions on a gas chromatographic stationary phase prior to their flame atomic absorption determinations

An enrichment/separation system for atomic absorption spectrometric determinations of Cu(II), Fe(III), Ni(II) and Co(II) has been established. The procedure is based on the adsorption of the analytes as calmagite chelates on Chromosorb-102. The effects of some parameters including pH, amount of ligand, salt matrix, flow rates of sample and eluent solutions were investigated. Under optimized conditions, the relative standard deviation of the combined method of sample treatment, preconcentration and determination with FAAS (N=5) is generally lower than 5%. The limit of detection (3σ) was between 6.0-112. 9 μg/L. The results were used for preconcentration of analytes from some sodium and ammonium salt

Lifted Worm Algorithm for the Ising Model

We design an irreversible worm algorithm for the zero-field ferromagnetic Ising model by using the lifting technique. We study the dynamic critical behavior of an energy estimator on both the complete graph and toroidal grids, and compare our findings with reversible algorithms such as the Prokof'ev-Svistunov worm algorithm. Our results show that the lifted worm algorithm improves the dynamic exponent of the energy estimator on the complete graph, and leads to a significant constant improvement on toroidal grids.Comment: 9 pages, 6 figure

Extractable trace metals content of dust from vehicle air filters as determined by sequential extraction and flame atomic absorption spectrometry

A modified four-step sequential extraction procedure developed within the Standards, Measurement, and Testing Program (formally the Community Bureau of Reference) of the European Commission was applied to determine the distribution of Cd, Cu, Fe, and Mn in air filter dust samples collected from vehicles. The four fractions were acid-soluble, reducible, oxidizable, and residual. These fractions have the advantage of providing better insight into the mechanism of association of metals in the dust. The determination of trace metals in dust samples was performed by flame atomic absorption spectrometry. The results obtained after applying the sequential extraction scheme indicated that Cu was the most abundant metal in the organic and residual fractions of the dust matrix. Fe was found mainly in the residual fraction, and the major amounts of Mn and Cd were present in the acidsoluble and bound-to-carbonate fraction. The mean values of Cd, Cu, Fe, and Mn were found to be 15.58, 33.54,1625, and 180 μg/g, respectively. The results obtained are in agreement with data reported in the literature

Fragmentation of Fractal Random Structures

We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model allows us to discuss a wide range of systems with fractal properties including trees as well as dense clusters. We present exact results for the densities of fragmenting edges and the distribution of fragment sizes for critical clusters in two dimensions. Dynamical fragmentation with a size cutoff leads to broad distributions of fragment sizes. The resulting power laws are shown to encode characteristic fingerprints of the fragmented objects.Comment: Thoroughly revised version. Final version published in Physical Review Letter

Simultaneous preconcentration of trace metals in environmental samples using amberlite XAD-2010/8-hydroxyquinoline system

A simple and sensitive system for simultaneous preconcentration of Mn(II), Fe(III), Co(II), Ni(II), Cu(II), Zn(II), Pb(II) and Cd(II) at trace level by flame atomic absorption spectrometry (FAAS) is proposed. Amberlite XAD-2010 packed in a column was used as sorbent. Analyte ions were sorbed in the column as their 8-hydroxyquinoline chelates; they could then be eluted by 1 mol L -1 HNO3 in acetone. The analytical conditions including pH, amounts of 8-hydroxyquinoline, sample volume etc. on the quantitative recoveries of the analytes were investigated. The effects of the concomitants ions on the recoveries of the analytes column were also studied. The detection limits, corresponding to three times the standard deviation of the blank, were found to be in the range of 0.10-0.40 μg L-1. The accuracy of the procedure was measured by analyte determinations in certified reference materials (CRM NIES No. 7 Tea Leaves and TMDW-500 Drinking Water). The applications of the presented system were performed by the analysis of some environmental samples including water samples

On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model

We consider the coupling from the past implementation of the random-cluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster fugacity at least one. We make a number of conjectures regarding the asymptotic behaviour of the coupling time, motivated by rigorous results in one dimension and Monte Carlo simulations in dimensions two and three. Amongst our findings, we observe that, for generic parameter values, the distribution of the appropriately standardized coupling time converges to a Gumbel distribution, and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time. Perhaps surprisingly, we observe these results to hold both off criticality, where the coupling time closely mimics the coupon collector's problem, and also at the critical point, provided the cluster fugacity is below the value at which the transition becomes discontinuous. Finally, we consider analogous questions for the single-spin Ising heat-bath process

Efficient simulation of the random-cluster model

The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of the Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation. However, it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well-known algorithm due to Swendsen and Wang. Here, we present an efficient implementation of Sweeny's approach for the random-cluster model using recent algorithmic advances in dynamic connectivity algorithms.Comment: RevTeX 4.1, 14 pages, 8 figures, 3 tables, version as publishe