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Motivated by recent studies of Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)], we study self-organized criticality in models of ``running'' sandpiles. Our analysis reveals rich temporal structures in the flow of sand: at very short time scales, the flow is dominated by single avalanches. These avalanches overlap at intermediate time scales; their interactions lead to 1/f noise in the flow. We show that scaling in this region is a consequence of conservation laws and is exhibited in many examples of driven-diffusion equations for transport. At very long time scales, the sandpiles exhibit system-wide discharge events. These events also obey scaling and are found to be anticorrelated. We derive the ${\mathit{f}}^{1/2}$ mean-field power spectrum for these events and show that a threshold instability of the model, coupled with some stochasticity, is the underlying origin of the long-time anticorrelation.

Strong-coupling properties of the Burgers\char21{}Kardar-Parisi-Zhang equation describing nonequilibrium interface growth are studied. A physical coupling constant is defined and related to the height-height correlation function for arbitrary substrate dimension. In 1+1 dimensions, the exact universal coupling constant and scaling function are computed using a mode-coupling theory. It is found that a finite surface tension is generated from zero, suggesting that macroscopic properties are not affected by the absence of microscopic surface tension.

We report an experimental study of polymerized membranes using graphite oxide (GO) suspension. Dry samples of GO are analyzed using electron microscopy and electron diffraction. They are found to be composed of thin solid membranes. The conformation of these membranes in solution is investigated using light scattering and is found to be fractal.

The Burgers equation is the simplest nonlinear generalization of the diffusion equation. We present a detailed dynamical renormalization-group analysis of this equation subject to random noise. The noise itself can be the product of another stochastic process and is hence allowed to have correlations in space and/or time. In dimensions higher than a critical ${d}_{c}$ weak and strong noise lead to different scaling exponents, while for d${d}_{c}$ any amount of noise is relevant resulting in strong-coupling behavior. In the absence of temporal correlations we find two regimes for d${d}_{c}$: either the hydrodynamic behavior is determined by white noise and correlations are unimportant, or correlations dominate and the resulting scaling exponents can be obtained exactly. With temporal correlations present, the hydrodynamic behavior is much more complex, as renormalization predicts a complicated dependence of the effective noise spectrum on frequency in certain regimes. The relevance of these results to two interesting problems is discussed. One is the anomalous transverse fluctuations of a directed polymer in a random medium, and the other is a description of a growing interface. Various recent numerical simulations are reviewed in the light of these results. For example, we show that an exponent identity observed in all simulations so far follows simply from the Galilean invariance of the equation in the absence of temporal correlations.