We present a class of surfaces which are simultaneously flat and rough over the same range of lengths. They are self-affine, have well-defined roughness exponents, and consist of terraces of all sizes. The coexistence of flat and rough makes them respond to different external interactions with variable roughness. We demonstrate this for optical scattering (including x rays), two wetting situations, diffusion currents, and catalysis. A terraced Cu

A practical problem in the rational design of a heterogeneous catalyst is to optimize its structure at all scales. By optimizing the large-pore network of a bimodal porous catalyst with a given nanoporosity (for example, zeolite or mesoporous catalyst) for the yield of diffusion-limited first-order reactions, it is found that catalysts typically benefit from a hierarchical pore network with a broad pore-size distribution. When comparing the performance

Bubbling fluidized beds are granular systems, in which a deep layer of particles is set in motion by a vertical gas stream, with the excess gas rising as bubbles through the bed. We show that pressure fluctuations in such a system have non-Gaussian statistics. The probability density function has a power-law drop-off and is very well represented by a Tsallis distribution. Its shape is explained through the folding of the Gaussian distribution of

Phenomena characterized by power-law probability distributions abound in nature and the applied sciences. We show that many of these power laws are well described by the Student, or t, distribution,and we discuss the origin of this universality based on three examples (Brownian motion, Knudsen diffusion in rough pores, and bubbly multiphase flow). These case studies are representative for a large class of systems with heterogeneous features, examples