Diffusional screening in treelike spaces: an exactly solvable diffusion-reaction model.

A renormalization approach is used to derive an analytic formula for the total current crossing the reactive surface of a Cayley tree of cylindrical tubes under a Helmholtz-type approximation to the full diffusion-reaction problem. We provide analytic conditions for the emergence of a plateau in the current-a region of maximum insensitivity of the current to variations in either the reaction rate (membrane permeability) or the diffusivity. The occurrence of such a plateau is associated with a partial screening regime wherein most of the active surface is screened to incoming diffusing particles.

Reverse engineering of oxygen transport in the lung: adaptation to changing demands and resources through space-filling networks.

The space-filling fractal network in the human lung creates a remarkable distribution system for gas exchange. Landmark studies have illuminated how the fractal network guarantees minimum energy dissipation, slows air down with minimum hardware, maximizes the gas- exchange surface area, and creates respiratory flexibility between rest and exercise. In this paper, we investigate how the fractal architecture affects oxygen transport and exchange under varying physiological conditions, with respect to performance metrics not previously studied.

Heterogeneity explains features of "anomalous" thermodynamics and statistics.

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 of which can be found from Earth sciences to astrophysics, and even in the social sciences.

Power-law distribution of pressure fluctuations in multiphase flow.

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.

Nonstandard roughness of terraced surfaces.

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.