Different hierarchy of avalanches observed in the Bak-Sneppen evolution model

We introduce a new quantity, average fitness, into the Bak-Sneppen evolution model. Through the new quantity, a different hierarchy of avalanches is observed. The gap equation, in terms of the average fitness, is presented to describe the self-organization of the model. It is found that the critical value of the average fitness can be exactly obtained. Based on the simulations, two critical exponents, avalanche distribution and avalanche dimension, of the new avalanches are given.Comment: 5 pages, 3 figure

Exact equqations and scaling relations for f-avalanche in the Bak-Sneppen evolution model

Infinite hierarchy of exact equations are derived for the newly-observed f-avalanche in the Bak-Sneppen evolution model. By solving the first order exact equation, we found that the critical exponent which governs the divergence of the average avalanche size, is exactly 1 (for all dimensions), confirmed by the simulations. Solution of the gap equation yields another universal exponent, denoting the the relaxation to the attractor, is exactly 1. We also establish some scaling relations among the critical exponents of the new avalanche.Comment: 5 pages, 1 figur

A perturbative approach to the Bak-Sneppen Model

We study the Bak-Sneppen model in the probabilistic framework of the Run Time Statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing Self-Organized Criticality. The dynamics is characterized by a self-organization of almost all the species fitnesses above a non-trivial threshold value, and by a lack of spatial and temporal characteristic scales. This results in {\em avalanches} of activity power law distributed. In this letter we use the RTS approach to compute the value of $x_c$, the value of the avalanche exponent $\tau$ and the asymptotic distribution of minimal fitnesses.Comment: 4 pages, 3 figures, to be published on Physical Review Letter

Covariant Coordinate Transformations on Noncommutative Space

We show how to define gauge-covariant coordinate transformations on a noncommuting space. The construction uses the Seiberg-Witten equation and generalizes similar results for commuting coordinates.Comment: 11 pages, LaTeX; email correspondence to [email protected]

3-D inelastic analysis methods for hot section components (base program)

A 3-D inelastic analysis methods program consists of a series of computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of combustor liners, turbine blades, and turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain) and global (dynamics, buckling) structural behavior of the three selected components. These models are used to solve 3-D inelastic problems using linear approximations in the sense that stresses/strains and temperatures in generic modeling regions are linear functions of the spatial coordinates, and solution increments for load, temperature and/or time are extrapolated linearly from previous information. Three linear formulation computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (MARC-Hot Section Technology), and BEST (Boundary Element Stress Technology), were developed and are described

On 3-D inelastic analysis methods for hot section components (base program)

A 3-D Inelastic Analysis Method program is described. This program consists of a series of new computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain)and global (dynamics, buckling) structural behavior of the three selected components. Three computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (Marc-Hot Section Technology), and BEST (Boundary Element Stress Technology), have been developed and are briefly described in this report

Particle-hole symmetry in a sandpile model

In a sandpile model addition of a hole is defined as the removal of a grain from the sandpile. We show that hole avalanches can be defined very similar to particle avalanches. A combined particle-hole sandpile model is then defined where particle avalanches are created with probability $p$ and hole avalanches are created with the probability $1-p$. It is observed that the system is critical with respect to either particle or hole avalanches for all values of $p$ except at the symmetric point of $p_c=1/2$. However at $p_c$ the fluctuating mass density is having non-trivial correlations characterized by $1/f$ type of power spectrum.Comment: Four pages, our figure

Critical Dynamics of Self-Organizing Eulerian Walkers

The model of self-organizing Eulerian walkers is numerically investigated on the square lattice. The critical exponents for the distribution of a number of steps ($\tau_l$) and visited sites ($\tau_s$) characterizing the process of transformation from one recurrent configuration to another are calculated using the finite-size scaling analysis. Two different kinds of dynamical rules are considered. The results of simulations show that both the versions of the model belong to the same class of universality with the critical exponents $\tau_l=\tau_s=1.75\pm 0.1$.Comment: 3 pages, 4 Postscript figures, RevTeX, additional information available at http://thsun1.jinr.dubna.su/~shche

Large Scale Structures, Symmetry, and Universality in Sandpiles

We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the avalanches in the self-organized critical state. It does, however, introduce long-range spatial correlations within the metastable states. We find large scale networks of occupied sites whose density vanishes in the thermodynamic limit, for d>1.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Melting of hexagonal skyrmion states in chiral magnets

Skyrmions are spiral structures observed in thin films of certain magnetic materials (Uchida et al 2006 Science 311 359–61). Of the phases allowed by the crystalline symmetries of these materials (Yi et al 2009 Phys. Rev. B 80 054416), only the hexagonally packed phases (SCh) have been observed. Here the melting of the SCh phase is investigated using Monte Carlo simulations. In addition to the usual measure of skyrmion density, chiral charge, a morphological measure is considered. In doing so it is shown that the low-temperature reduction in chiral charge is associated with a change in skyrmion profiles rather than skyrmion destruction. At higher temperatures, the loss of six-fold symmetry is associated with the appearance of elongated skyrmions that disrupt the hexagonal packing