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For spatio-temporal chaos observed in numerical simulations of the complex Ginzburg–Landau equation (CGL) and in experiments on inclined-layer convection (ILC) we report numerical and experimental data on the statistics of defects and of defect loops. These loops consist of defect trajectories in space–time that are connected to each other through the pairwise annihilation or creation of the associated defects. While most such loops are small and contain only a few defects, the loop distribution functions decay only slowly with the quantities associated with the loop size, consistent with power-law behavior. For the CGL, two of the three power-law exponents are found to agree, within our computational precision, with those from previous investigations of a simple lattice model. In certain parameter regimes of the CGL and ILC, our results for the single-defect statistics show significant deviations from the previously reported findings that the defect dynamics are consistent with those of random walkers that are created with fixed probability and annihilated through random collisions. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Fluctuations of the local volume fraction within granular materials have previously been observed to decrease as the system approaches jamming. We experimentally examine the role of boundary conditions and interparticle friction μ on this relationship for a dense granular material of bidisperse particles driven under either constant volume or constant pressure. Using a radical Voronoï tessellation, we find the variance of the local volume fraction ∅ monotonically decreases as the system becomes more dense, independent of boundary condition and μ. We examine the universality and origins of this trend using experiments and the recent granocentric model [M. Clusel, E. I. Corwin, A. O. N. Siemens, and J. Brujić, Nature (London) 460, 611(2009); E. I. Corwin, M. Clusel, A. O. N. Siemens, and J. Brujić, Soft Matter 6, 2949 (2010)], modified to draw particle locations from an arbitrary distribution P(s) of neighbor distances s. The mean and variance of the observed 2(s) are described by a single length scale controlled by∅-. Through the granocentric model, we observe that diverse functional forms of P(s) all produce the trend of decreasing fluctuations, but only the experimentally observed P(s) provides quantitative agreement with the measured ∅ fluctuations. Thus, we find that both P(s) and P(∅) encode similar information about the ensemble of observed packings and are connected to each other by the local granocentric model. [ABSTRACT FROM AUTHOR]