Domain Growth and Finite-Size-Scaling in the Kinetic Ising Model

This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed, and tested with extensive Monte-Carlo simulations of domain growth in the 2-D spin-flip kinetic Ising model. The scaling properties of the distribution functions serve to elucidate the configurational self-similarity that underlies the dynamic scaling picture. Moreover, it is demonstrated that the application of finite-size-scaling techniques facilitates the accurate determination of the bulk growth exponent even in the presence of strong finite-size effects, the scale and character of which are graphically exposed by the order parameter distribution function. In addition it is found that one commonly used measure of domain size--the scaled second moment of the magnetisation distribution--belies the full extent of these finite-size effects.Comment: 13 pages, Latex. Figures available on request. Rep #9401

Scaling relation for determining the critical threshold for continuum percolation of overlapping discs of two sizes

We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical percolation threshold as a function of the ratio of sizes of discs, for different values of the relative areal densities of two discs, can be described in terms of a scaling function of only one variable. The recent accurate Monte Carlo estimates of critical threshold by Quintanilla and Ziff [Phys. Rev. E, 76 051115 (2007)] are in very good agreement with the proposed scaling relation.Comment: 4 pages, 3 figure

Fate of Zero-Temperature Ising Ferromagnets

We investigate the relaxation of homogeneous Ising ferromagnets on finite lattices with zero-temperature spin-flip dynamics. On the square lattice, a frozen two-stripe state is apparently reached approximately 1/4 of the time, while the ground state is reached otherwise. The asymptotic relaxation is characterized by two distinct time scales, with the longer stemming from the influence of a long-lived diagonal stripe ``defect''. In greater than two dimensions, the probability to reach the ground state rapidly vanishes as the size increases and the system typically ends up wandering forever within an iso-energy set of stochastically ``blinking'' metastable states.Comment: 4 pages in column format, 6 figure

Damage Spreading During Domain Growth

We study damage spreading in models of two-dimensional systems undergoing first order phase transitions. We consider several models from the same non-conserved order parameter universality class, and find unexpected differences between them. An exact solution of the Ohta-Jasnow-Kawasaki model yields the damage growth law $D \sim t^{\phi}$, where $\phi = t^{d/4}$ in $d$ dimensions. In contrast, time-dependent Ginzburg-Landau simulations and Ising simulations in $d= 2$ using heat-bath dynamics show power-law growth, but with an exponent of approximately $0.36$, independent of the system sizes studied. In marked contrast, Metropolis dynamics shows damage growing via $\phi \sim 1$, although the damage difference grows as $t^{0.4}$. PACS: 64.60.-i, 05.50.+qComment: 4 pags of revtex3 + 3 postscript files appended as a compressed and uuencoded file. UIB940320

Random Geometric Graphs

We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size of the largest cluster. We derive an analytical expression for the cluster coefficient which shows that the graphs are distinctly different from standard random graphs, even for infinite dimensionality. Insights relevant for graph bi-partitioning are included.Comment: 16 pages, 10 figures. Minor changes. Added reference

Percolation approach to Quark Gluon Plasma and J/ψJ/\psi suppression

It is shown that the critical threshold for percolation of the overlapping strings exchanged in heavy ion collisions can naturally explain the sharp strong suppresion of $J/\psi$ shown by the experimental data on central Pb--Pb collisions, which does not occur in central O--U and S--U collisions.Comment: 11 pages in LaTeX plus 1 postscript figur

Numerical Study of a Field Theory for Directed Percolation

A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened sensitivity to fluctuationsattending multiplicative noise in the vicinity of an absorbing state, a useful method requires discretization of the field variable as well as of space and time. When applied to the field theory for directed percolation in 1+1 dimensions, the method yields critical exponents which compare well against accepted values.Comment: 18 pages, LaTeX, 6 figures available upon request LC-CM-94-00

Sicily statement on classification and development of evidence-based practice learning assessment tools

<p>Abstract</p> <p>Background</p> <p>Teaching the steps of evidence-based practice (EBP) has become standard curriculum for health professions at both student and professional levels. Determining the best methods for evaluating EBP learning is hampered by a dearth of valid and practical assessment tools and by the absence of guidelines for classifying the purpose of those that exist. Conceived and developed by delegates of the Fifth International Conference of Evidence-Based Health Care Teachers and Developers, the aim of this statement is to provide guidance for purposeful classification and development of tools to assess EBP learning.</p> <p>Discussion</p> <p>This paper identifies key principles for designing EBP learning assessment tools, recommends a common taxonomy for new and existing tools, and presents the Classification Rubric for EBP Assessment Tools in Education (CREATE) framework for classifying such tools. Recommendations are provided for developers of EBP learning assessments and priorities are suggested for the types of assessments that are needed. Examples place existing EBP assessments into the CREATE framework to demonstrate how a common taxonomy might facilitate purposeful development and use of EBP learning assessment tools.</p> <p>Summary</p> <p><it>The widespread adoption of EBP into professional education requires valid and reliable measures of learning. Limited tools exist with established psychometrics. This international consensus statement strives to provide direction for developers of new EBP learning assessment tools and a framework for classifying the purposes of such tools</it>.</p

LETTER TO THE EDITOR: Efficient measurement of the percolation threshold for fully penetrable discs

We study the percolation threshold for fully penetrable discs by measuring the average location of the frontier for a statistically inhomogeneous distribution of fully penetrable discs. We use two different algorithms to efficiently simulate the frontier, including the continuum analogue of an algorithm previously used for gradient percolation on a square lattice. We find that φc = 0.676 339±0.000 004, thus providing an extra significant digit of accuracy to this constant.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48838/2/a042l4.pd