Dynamic Monte Carlo Measurement of Critical Exponents

Based on the scaling relation for the dynamics at the early time, a new method is proposed to measure both the static and dynamic critical exponents. The method is applied to the two dimensional Ising model. The results are in good agreement with the existing results. Since the measurement is carried out in the initial stage of the relaxation process starting from independent initial configurations, our method is efficient.Comment: (5 pages, 1 figure) Siegen Si-94-1

Nonequilibrium relaxation of the two-dimensional Ising model: Series-expansion and Monte Carlo studies

We study the critical relaxation of the two-dimensional Ising model from a fully ordered configuration by series expansion in time t and by Monte Carlo simulation. Both the magnetization (m) and energy series are obtained up to 12-th order. An accurate estimate from series analysis for the dynamical critical exponent z is difficult but compatible with 2.2. We also use Monte Carlo simulation to determine an effective exponent, z_eff(t) = - {1/8} d ln t /d ln m, directly from a ratio of three-spin correlation to m. Extrapolation to t = infinity leads to an estimate z = 2.169 +/- 0.003.Comment: 9 pages including 2 figure

The Dynamic Exponent of the Two-Dimensional Ising Model and Monte Carlo Computation of the Sub-Dominant Eigenvalue of the Stochastic Matrix

We introduce a novel variance-reducing Monte Carlo algorithm for accurate determination of autocorrelation times. We apply this method to two-dimensional Ising systems with sizes up to $15 \times 15$, using single-spin flip dynamics, random site selection and transition probabilities according to the heat-bath method. From a finite-size scaling analysis of these autocorrelation times, the dynamical critical exponent $z$ is determined as $z=2.1665$ (12)

Finite Size Scaling and Critical Exponents in Critical Relaxation

We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a new method to measure both the dynamic and static critical exponents are reported, based on the finite size scaling for the dynamics at the early time. From the time-dependent Binder cumulant, the dynamical exponent $z$ is extracted independently, while the static exponents $\beta/\nu$ and $\nu$ are obtained from the time evolution of the magnetization and its higher moments.Comment: 24 pages, LaTeX, 10 figure

Measurement and simulation of the 16/17 April 2010 Eyjafjallajökull volcanic ash layer dispersion in the northern Alpine region

The spatial structure and the progression speed of the first ash layer from the Icelandic Eyjafjallajökull volcano which reached Germany on 16/17 April is investigated from remote sensing data and numerical simulations. The ceilometer network of the German Meteorological Service was able to follow the progression of the ash layer over the whole of Germany. This first ash layer turned out to be a rather shallow layer of only several hundreds of metres thickness which was oriented slantwise in the middle troposphere and which was brought downward by large-scale sinking motion over Southern Germany and the Alps. Special Raman lidar measurements, trajectory analyses and in-situ observations from mountain observatories helped to confirm the volcanic origin of the detected aerosol layer. Ultralight aircraft measurements permitted the detection of the arrival of a second major flush of volcanic material in Southern Germany. Numerical simulations with the Eulerian meso-scale model MCCM were able to reproduce the temporal and spatial structure of the ash layer. Comparisons of the model results with the ceilometer network data on 17 April and with the ultralight aircraft data on 19 April were satisfying. This is the first example of a model validation study from this ceilometer network data