Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics

Fractals arise from a variety of sources and have been observed in nature and on computer screens. One of the exceptional characteristics of fractals is that they can be described by a noninteger dimension. The geometry of fractals and the mathematics of fractal dimension have provided useful tools for a variety of scientific disciplines, among which is chaos. Chaotic dynamical systems exhibit trajectories in their phase space that converge to a strange attractor. The fractal dimension of this attractor counts the effective number of degrees of freedom in the dynamical system and thus quantifies its complexity. In recent years, numerical methods have been developed for estimating the dimension directly from the observed behavior of the physical system. The purpose of this paper is to survey briefly the kinds of fractals that appear in scientific research, to discuss the application of fractals to nonlinear dynamical systems, and finally to review more comprehensively the state of the art in numerical methods for estimating the fractal dimension of a strange attractor.

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Estimating fractal dimension

Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity.

Percolation of phases in a three-dimensional cement paste microstructural model

The theory of percolation, originally proposed over 30 years ago to describe flow phenomena in porous media, has undergone enormous development in recent years, primarily in the field of physics. The principal advantage of percolation theory is that it provides universal laws which determine the geometrical and physical properties of the system. This survey discusses developments and results in percolation theory to date, and identifies aspects relevant to problems in groundwater hydrology. The methods of percolation theory are discussed, previous applications of the theory to hydrological problems are reviewed, and future directions for study are suggested.

Percolation theory and its application to groundwater hydrology

Sedimentary rock makes up much of the Earth's surface and contains two of the most vital fluids for our lives—water and hydrocarbons. Yet physicists have paid little attention to rock, mainly because we are discouraged by its apparent complexity. We are well trained in working with idealized models, but when faced with a piece of rock, not only do we not know where to begin, but we also may question whether it is even possible to find interesting physics in such a “dirty” and uncontrolled system. With further thought, however, we should realize that these are but the usual mental barriers that we have to overcome every time we study something new.

Po‐Zen Wong

Papers

The Statistical Physics of Sedimentary Rock