Mecke K (1997)
Publication Status: Published
Publication Type: Conference contribution
Publication year: 1997
Publisher: ACTA PHYSICA POLONICA B, JAGELLONIAN UNIV, INST PHYSICS
Book Volume: 28
Pages Range: 1747-1782
Journal Issue: 8
The morphological characterization of patterns is becoming more and more important in Statistical Physics as complex spatial structures now emerge in many systems. A suitable family of morphological measures, known in integral geometry as Minkowski functionals, characterize not only the connectivity but also the content and shape of spatial figures. The Minkowski functionals are related to familiar geometric measures: covered volume. surface area? integral mean curvature, and Euler characteristic. Integral geometry provides powerful theorems and formulae which makes the calculus convenient for many models of stochastic geometries, e.g. for the Boolean grain model. The measures are: in particular, applicable to random patterns which consist of non-regular, fluctuating domains of homogeneous phases on a mesoscopic scale. Therefore, we illustrate the integral geometric approach by applying the morphological measures to such diverse topics as porous media, chemical-reaction patterns, and spinodal decomposition kinetics: (A) The percolation threshold of porous media can be estimated accurately in terms of the morphology of the distributed pores. (B) Turing patterns observed in chemical reaction-diffusion systems can be analyzed in tel ms of morphological measures, which turn out to be cubic polynomials in the grey-level. We observe a symmetry-breaking of the polynomials when the type of pattern changes. Therefore, the morphological measures are useful order parameters to describe pattern transitions quantitatively. (C) The time evolution of the morphology of homogeneous phases during spinodal decomposition is described, focusing: on the scaling: behavior of the morphology, Integral geometry provides a means to define the characteristic length scales and to define the cross over from the early stage decomposition to the late stage domain growth.
APA:
Mecke, K. (1997). Morphology of spatial patterns - Porous media, spinodal decomposition and dissipative structures. (pp. 1747-1782). ACTA PHYSICA POLONICA B, JAGELLONIAN UNIV, INST PHYSICS.
MLA:
Mecke, Klaus. "Morphology of spatial patterns - Porous media, spinodal decomposition and dissipative structures." ACTA PHYSICA POLONICA B, JAGELLONIAN UNIV, INST PHYSICS, 1997. 1747-1782.
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