Avalanche Merging and Continuous Flow in a Sandpile Model

A dynamical transition separating intermittent and continuous flow is observed in a sandpile model, with scaling functions relating the transport behaviors between both regimes. The width of the active zone diverges with system size in the avalanche regime but becomes very narrow for continuous flow. The change of the mean slope, Delta z, on increasing the driving rate, r, obeys Delta z ~ r^{1/theta}. It has nontrivial scaling behavior in the continuous flow phase with an exponent theta given, paradoxically, only in terms of exponents characterizing the avalanches theta = (1+z-D)/(3-D).Comment: Explanations added; relation to other model

Constitutive and life modeling of single crystal blade alloys for root attachment analysis

Work to develop fatigue life prediction and constitutive models for uncoated attachment regions of single crystal gas turbine blades is described. At temperatures relevant to attachment regions, deformation is dominated by slip on crystallographic planes. However, fatigue crack initiation and early crack growth are not always observed to be crystallographic. The influence of natural occurring microporosity will be investigated by testing both hot isostatically pressed and conventionally cast PWA 1480 single crystal specimens. Several differnt specimen configurations and orientations relative to the natural crystal axes are being tested to investigate the influence of notch acuity and the material's anisotropy. Global and slip system stresses in the notched regions were determined from three dimensional stress analyses and will be used to develop fatigue life prediction models consistent with the observed lives and crack characteristics

A Cellular Automaton Model for Diffusive and Dissipative Systems

We study a cellular automaton model, which allows diffusion of energy (or equivalently any other physical quantities such as mass of a particular compound) at every lattice site after each timestep. Unit amount of energy is randomly added onto a site. Whenever the local energy content of a site reaches a fixed threshold $E_{c1}$, energy will be dissipated. Dissipation of energy propagates to the neighboring sites provided that the energy contents of those sites are greater than or equal to another fixed threshold $E_{c2} (\leq E_{c1})$. Under such dynamics, the system evolves into three different types of states depending on the values of $E_{c1}$ and $E_{c2}$ as reflected in their dissipation size distributions, namely: localized peaks, power laws, or exponential laws. This model is able to describe the behaviors of various physical systems including the statistics of burst sizes and burst rates in type-I X-ray bursters. Comparisons between our model and the famous forest-fire model (FFM) are made.Comment: in REVTEX 3.0. Figures available on request. Extensively revised. Accepted by Phys.Rev.

The Boltzmann Equation in Scalar Field Theory

We derive the classical transport equation, in scalar field theory with a V(phi) interaction, from the equation of motion for the quantum field. We obtain a very simple, but iterative, expression for the effective action which generates all the n-point Green functions in the high-temperature limit. An explicit closed form is given in the static case.Comment: 10 pages, using RevTeX (corrected TeX misprints

Supertubes in Matrix model and DBI action

We show the equivalence between the supertube solutions with an arbitrary cross section in two different actions, the DBI action for the D2-brane and the matrix model action for the D0-branes. More precisely, the equivalence between the supertubes in the D2-brane picture and the D0-brane picture is shown in the boundary state formalism which is valid for all order in \alpha'. This is an application of the method using the infinitely many D0-branes and anti-D0-branes which was used to show other equivalence relations between two seemingly different D-brane systems, including the D-brane realization of the ADHM construction of instanton. We also apply this method to the superfunnel type solutions successfully.Comment: 24 pages, references added, version to appear in JHE

Layer Features of the Lattice Gas Model for Self-Organized Criticality

A layer-by-layer description of the asymmetric lattice gas model for 1/f-noise suggested by Jensen [Phys. Rev. Lett. 64, 3103 (1990)] is presented. The power spectra of the lattice layers in the direction perpendicular to the particle flux is studied in order to understand how the white noise at the input boundary evolves, on the average, into 1/f-noise for the system. The effects of high boundary drive and uniform driving force on the power spectrum of the total number of diffusing particles are considered. In the case of nearest-neighbor particle interactions, high statistics simulation results show that the power spectra of single lattice layers are characterized by different $\beta_x$ exponents such that $\beta_x \to 1.9$ as one approaches the outer boundary.Comment: LaTeX, figures upon reques

Effect of discontinuity in threshold distribution on the critical behaviour of a random fiber bundle

The critical behaviour of a Random Fiber Bundle Model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different parameters of the distribution. The discontinuity in the threshold strength distribution of fibers non-trivially modifies the critical stress as well as puts a restriction on the allowed values of parameters for which the recursive dynamics approach holds good. The discontinuity leads to a non-universal behaviour in the avalanche size distribution for smaller values of avalanche size. We observe that apart from the mean field behaviour for larger avalanches, a new behaviour for smaller avalanche size is observed as a critical threshold distribution is approached. The phenomenological understanding of the above result is provided using the exact analytical result for the avalanche size distribution. Most interestingly,the prominence of non-universal behaviour in avalanche size distribution depends on the system parameters.Comment: 6 pages, 4 figures, text and figures modifie

On the random neighbor Olami-Feder-Christensen slip-stick model

We reconsider the treatment of Lise and Jensen (Phys. Rev. Lett. 76, 2326 (1996)) on the random neighbor Olami-Feder-Christensen stik-slip model, and examine the strong dependence of the results on the approximations used for the distribution of states p(E).Comment: 6pages, 3 figures. To be published in PRE as a brief repor

Adaptation to the Edge of Chaos in the Self-Adjusting Logistic Map

Self-adjusting, or adaptive systems have gathered much recent interest. We present a model for self-adjusting systems which treats the control parameters of the system as slowly varying, rather than constant. The dynamics of these parameters is governed by a low-pass filtered feedback from the dynamical variables of the system. We apply this model to the logistic map and examine the behavior of the control parameter. We find that the parameter leaves the chaotic regime. We observe a high probability of finding the parameter at the boundary between periodicity and chaos. We therefore find that this system exhibits adaptation to the edge of chaos.Comment: 3 figure

Boundary effects in a random neighbor model of earthquakes

We introduce spatial inhomogeneities (boundaries) in a random neighbor version of the Olami, Feder and Christensen model [Phys. Rev. Lett. 68, 1244 (1992)] and study the distributions of avalanches starting both from the bulk and from the boundaries of the system. Because of their clear geophysical interpretation, two different boundary conditions have been considered (named free and open, respectively). In both cases the bulk distribution is described by the exponent $\tau \simeq {3/2}$. Boundary distributions are instead characterized by two different exponents $\tau ' \simeq {3/2}$ and $\tau ' \simeq {7/4}$, for free and open boundary conditions, respectively. These exponents indicate that the mean-field behavior of this model is correctly described by a recently proposed inhomogeneous form of critical branching process.Comment: 6 pages, 2 figures ; to appear on PR