Scaling Analysis of the Site-Diluted Ising Model in Two Dimensions

A combination of recent numerical and theoretical advances are applied to analyze the scaling behaviour of the site-diluted Ising model in two dimensions, paying special attention to the implications for multiplicative logarithmic corrections. The analysis focuses primarily on the odd sector of the model (i.e., that associated with magnetic exponents), and in particular on its Lee-Yang zeros, which are determined to high accuracy. Scaling relations are used to connect to the even (thermal) sector, and a first analysis of the density of zeros yields information on the specific heat and its corrections. The analysis is fully supportive of the strong scaling hypothesis and of the scaling relations for logarithmic corrections.Comment: 15 pages, 3 figures. Published versio

The Development and Validation of a Universal Enjoyment Measure: The Enjoy Scale

For decades, the concept of enjoyment has been used to measure the psychological benefits of activities and has been shown to determine future behavior toward activities and objects of interest. However, there has been little consensus on the definition and dimensionality of enjoyment. This study introduced a new measure of enjoyment with scale development and validation reported. CFA and EFA findings from 1466 participants across 739 different activities were reported. The instrument developed measured enjoyment across activities, with demonstrated content validity, internal consistency, discriminant and convergent validity. The final 25-item version of the ENJOY scale is composed of 5 factors: pleasure, relatedness, competence, challenge/improvement, and engagement. Discussion of the ENJOY Scale places it within the conceptual framework of Self-Determination Theory

Correlations in nano-scale step fluctuations: comparison of simulation and experiments

We analyze correlations in step-edge fluctuations using the Bortz-Kalos-Lebowitz kinetic Monte Carlo algorithm, with a 2-parameter expression for energy barriers, and compare with our VT-STM line-scan experiments on spiral steps on Pb(111). The scaling of the correlation times gives a dynamic exponent confirming the expected step-edge-diffusion rate-limiting kinetics both in the MC and in the experiments. We both calculate and measure the temperature dependence of (mass) transport properties via the characteristic hopping times and deduce therefrom the notoriously-elusive effective energy barrier for the edge fluctuations. With a careful analysis we point out the necessity of a more complex model to mimic the kinetics of a Pb(111) surface for certain parameter ranges.Comment: 10 pages, 9 figures, submitted to Physical Review

The Development and Validation of a Universal Enjoyment Measure: The Enjoy Scale

For decades, the concept of enjoyment has been used to measure the psychological benefits of activities and has been shown to determine future behavior toward activities and objects of interest. However, there has been little consensus on the definition and dimensionality of enjoyment. This study introduced a new measure of enjoyment with scale development and validation reported. CFA and EFA findings from 1466 participants across 739 different activities were reported. The instrument developed measured enjoyment across activities, with demonstrated content validity, internal consistency, discriminant and convergent validity. The final 25-item version of the ENJOY scale is composed of 5 factors: pleasure, relatedness, competence, challenge/improvement, and engagement. Discussion of the ENJOY Scale places it within the conceptual framework of Self-Determination Theory

Fluctuations, line tensions, and correlation times of nanoscale islands on surfaces

We analyze in detail the fluctuations and correlations of the (spatial) Fourier modes of nano-scale single-layer islands on (111) fcc crystal surfaces. We analytically show that the Fourier modes of the fluctuations couple due to the anisotropy of the crystal, changing the power spectrum of the fluctuations, and that the actual eigenmodes of the fluctuations are the appropriate linear combinations of the Fourier modes. Using kinetic Monte Carlo simulations with bond-counting parameters that best match realistic energy barriers for hopping rates, we deduce absolute line tensions as a function of azimuthal orientation from the analyses of the fluctuation of each individual mode. The autocorrelation functions of these modes give the scaling of the correlation times with wavelength, providing us with the rate-limiting kinetics driving the fluctuations, here step-edge diffusion. The results for the energetic parameters are in reasonable agreement with available experimental data for Pb(111) surfaces, and we compare the correlation times of island-edge fluctuations to relaxation times of quenched Pb crystallites.Comment: 11 pages, 8 figures; to appear in PRB 70, xxx (15 Dec 2004), changes in MC and its implication

Dynamics of surface steps

In the framework of SOS models, the dynamics of isolated and pairs of surface steps of monoatomic height is studied, for step--edge diffusion and for evaporation kinetics, using Monte Carlo techniques. In particular, various interesting crossover phenomena are identified. Simulational results are compared, especially, to those of continuum theories and random walk descriptions.Comment: 13 pages in elsart style, 4 eps figures, submitted to Physica

Surface critical behavior of two-dimensional dilute Ising models

Ising models with nearest-neighbor ferromagnetic random couplings on a square lattice with a (1,1) surface are studied, using Monte Carlo techniques and star-tiangle transformation method. In particular, the critical exponent of the surface magnetization is found to be close to that of the perfect model, beta_s=1/2. The crossover from surface to bulk critical properties is discussed.Comment: 6 pages in RevTex, 3 ps figures, to appear in Journal of Stat. Phy

Boundary critical behaviour of two-dimensional random Ising models

Using Monte Carlo techniques and a star-triangle transformation, Ising models with random, 'strong' and 'weak', nearest-neighbour ferromagnetic couplings on a square lattice with a (1,1) surface are studied near the phase transition. Both surface and bulk critical properties are investigated. In particular, the critical exponents of the surface magnetization, 'beta_1', of the correlation length, 'nu', and of the critical surface correlations, 'eta_{\parallel}', are analysed.Comment: 16 pages in ioplppt style, 7 ps figures, submitted to J. Phys.

Investigation of genetic determinants of cognitive change in later life

Cognitive decline is a major health concern and identification of genes that may serve as drug targets to slow decline is important to adequately support an aging population. Whilst genetic studies of cross-sectional cognition have been carried out, cognitive change is less well-understood. Here, using data from the TOMMORROW trial, we investigate genetic associations with cognitive change in a cognitively normal older cohort. We conducted a genome-wide association study of trajectories of repeated cognitive measures (using generalised estimating equation (GEE) modelling) and tested associations with polygenic risk scores (PRS) of potential risk factors. We identified two genetic variants associated with change in attention domain scores, rs534221751 (p = 1 × 10−8 with slope 1) and rs34743896 (p = 5 × 10−10 with slope 2), implicating NCAM2 and CRIPT/ATP6V1E2 genes, respectively. We also found evidence for the association between an education PRS and baseline cognition (at >65 years of age), particularly in the language domain. We demonstrate the feasibility of conducting GWAS of cognitive change using GEE modelling and our results suggest that there may be novel genetic associations for cognitive change that have not previously been associated with cross-sectional cognition. We also show the importance of the education PRS on cognition much later in life. These findings warrant further investigation and demonstrate the potential value of using trial data and trajectory modelling to identify genetic variants associated with cognitive change