Avalanche dynamics, surface roughening and self-organized criticality - experiments on a 3 dimensional pile of rice

We present a two-dimensional system which exhibits features of self-organized criticality. The avalanches which occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical exponents are $\tau$ = 1.21(2) for the avalanche size distribution and $D$ = 1.99(2) for the cut-off size. Furthermore the geometry of the avalanches is studied leading to a fractal dimension of the active sites of $d_B$ = 1.58(2). Using a set of scaling relations, we can calculate the roughness exponent $\alpha = D - d_B$ = 0.41(3) and the dynamic exponent $z = D(2 - \tau)$ = 1.56(8). This result is compared with that obtained from a power spectrum analysis of the surface roughness, which yields $\alpha$ = 0.42(3) and $z$ = 1.5(1) in excellent agreement with those obtained from the scaling relations.Comment: 7 pages, 8 figures, accepted for publication in PR

Melting and Dimensionality of the Vortex Lattice in Underdoped YBa2Cu3O6.60

Muon spin rotation measurements of the magnetic field distribution in the vortex state of the oxygen deficient high-Tc superconductor YBa{2}Cu{3}O{6.60} reveal a vortex-lattice melting transition at much lower temperature than that in the fully oxygenated material. The transition is best described by a model in which adjacent layers of ``pancake'' vortices decouple in the liquid phase. Evidence is also found for a pinning-induced crossover from a solid 3D to quasi-2D vortex lattice, similar to that observed in the highly anisotropic superconductor Bi{2+x}Sr{2-x}CaCu{2}O{8+y}.Comment: 8 pages, 4 figures, 5 postscript file

Muon-Spin Rotation Spectra in the Mixed Phase of High-T_c Superconductors : Thermal Fluctuations and Disorder Effects

We study muon-spin rotation (muSR) spectra in the mixed phase of highly anisotropic layered superconductors, specifically Bi_2+xSr_2-xCaCu_2O_8+delta (BSCCO), by modeling the fluid and solid phases of pancake vortices using liquid-state and density functional methods. The role of thermal fluctuations in causing motional narrowing of muSR lineshapes is quantified in terms of a first-principles theory of the flux-lattice melting transition. The effects of random point pinning are investigated using a replica treatment of liquid state correlations and a replicated density functional theory. Our results indicate that motional narrowing in the pure system, although substantial, cannot account for the remarkably small linewidths obtained experimentally at relatively high fields and low temperatures. We find that satisfactory agreement with the muSR data for BSCCO in this regime can be obtained through the ansatz that this ``phase'' is characterized by frozen short-range positional correlations reflecting the structure of the liquid just above the melting transition. This proposal is consistent with recent suggestions of a ``pinned liquid'' or ``glassy'' state of pancake vortices in the presence of pinning disorder. Our results for the high-temperature liquid phase indicate that measurable linewidths may be obtained in this phase as a consequence of density inhomogeneities induced by the pinning disorder. The results presented here comprise a unified, first-principles theoretical treatment of muSR spectra in highly anisotropic layered superconductors in terms of a controlled set of approximations.Comment: 50 pages Latex file, including 10 postscript figure

25 Years of Self-organized Criticality: Concepts and Controversies

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers

A sandpile model for the distribution of rainfall?

Recently, Peters et al. (Phys. Rev. Lett. 88 (2002) 018701)) have found power-law behaviour in the distribution of rain events. Here it is shown that the observed self-similar features in both the reservoir level and the distribution of rain events, can quantitatively be reproduced from an extension to two dimensions of the Oslo-model developed to describe the dynamics of a pile of rice. Furthermore, it is argued that the sandpile model may be able to reproduce more detailed features such as the shape of cumulus clouds. In addition, many other systems, which show self-similarity in their time variations with the same quantitative characterizations, are discussed. © 2002 Elsevier Science B.V. All rights reserved

Model for the robust establishment of precise proportions in the early Drosophila embryo

During embryonic development, a spatial pattern is formed in which proportions are established precisely. As an early pattern formation step in Drosophila embryos, an anterior-posterior gradient of Bicoid (Bcd) induces hunchback (hb) expression (Nature 337 (1989) 138; Nature 332 (1988) 281). In contrast to the Bcd gradient, the Hb profile includes information about the scale of the embryo. Furthermore, the resulting hb expression pattern shows a much lower embryo-to-embryo variability than the Bcd gradient (Nature 415 (2002) 798). An additional graded posterior repressing activity could theoretically account for the observed scaling. However, we show that such a model cannot produce the observed precision in the Hb boundary, such that a fundamentally different mechanism must be at work. We describe and simulate a model that can account for the observed precise generation of the scaled Hb profile in a highly robust manner. The proposed mechanism includes Staufen (Stau), an RNA binding protein that appears essential to precision scaling (Nature 415 (2002) 798). In the model, Stau is released from both ends of the embryo and relocalizes hb RNA by increasing its mobility. This leads to an effective transport of hb away from the respective Stau sources. The balance between these opposing effects then gives rise to scaling and precision. Considering the biological importance of robust precision scaling and the simplicity of the model, the same principle may be employed more often during developmen

Structural similarity between the magnetic-flux profile in superconductors and the surface of a 2d rice pile

We analyze the magnetic-flux profile in the critical state of an YB

Surface roughening and self-organized criticality: The influence of quenched disorder

Self-organized criticality (SOC) has attracted considerable interest due to its possible wide ranging implications on a broad range of subjects. However, the experimental observation of SOC using stringent criteria has been difficult and the question of the critical parameters to observe SOC remains open. This is partly due to the fact that there are different criteria applied in order to claim SOC. Here we endeavour to study two aspects of this. First of all, we study the influence of the presence of quenched disorder on the appearance of SOC in the vortex dynamics in niobium by changing the amount of hydrogen impurities. Furthermore, we study whether the roughness properties of the pile surface can be used as a criterion for the appearance of SOC on a par with the observation of finite-size scaling. For this purpose, we compare the roughness and dynamic exponents of the vortex landscape to the avalanche size distribution for different amounts of disorder. The absence of a transition to SOC in the roughness exponent implies that the presence of a rough surface by itself cannot be used as a sufficient criterion for the observation of SOC. A determination of the dynamics of the surface properties, however, shows a transition similar to that of the avalanche properties. © EDP Sciences