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Klaus R. Mecke Dietrich Stoyan (Eds.)

Statistical Physics

and Spatial Statistics

The Art of Analyzing and Modeling

Spatial Structures and Pattern Formation

Editors

KlausR.Mecke

Fachbereich Physik

Bergische Universitat Wuppertal

42097 Wuppertal, Germany

Dietrich Stoyan

Institut fur Stochastik

TU Bergakademie Freiberg

09596 Freiberg, Germany

Library of Congress Cataloging-in-Publication Data applied for.

Die Deutsche Bibliothek - CIP-Einheitsaufnahme

Statistical physics and spatial statistics : the art of analyzing and

modeling spatial structures and pattern formation / Klaus R. Mecke ;

Dietrich Stoyan (ed.). - Berlin ; Heidelberg ; New York ; Barcelona ;

HongKong;London;Milan;Paris;Singapore;Tokyo:Springer,

2000

(Lecture notes in physics ; Vol. 554)

(Physics and astronomy online library)

ISBN 3-540-67750-X

ISSN 0075-8450

ISBN 3-540-67750-X Springer-Verlag Berlin Heidelberg New York

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Preface

Modern physics is confronted with a large variety of complex spatial structures;

almost every research group in physics is working with spatial data. Pattern for-

mation in chemical reactions, mesoscopic phases of complex ﬂuids such as liquid

crystals or microemulsions, ﬂuid structures on planar substrates (well-known

as water droplets on a window glass), or the large-scale distribution of galax-

ies in the universe are only a few prominent examples where spatial structures

are relevant for the understanding of physical phenomena. Numerous research

areas in physics are concerned with spatial data. For example, in high energy

physics tracks in cloud chambers are analyzed, while in gamma ray astronomy

observational information is extracted from point patterns of Cherenkov photons

hitting a large scale detector ﬁeld. A development of importance to physics in

general is the use of imaging techniques in real space. Methods such as scanning

microscopy and computer tomography produce images which enable detailed

studies of spatial structures.

Many research groups study non-linear dynamics in order to understand

the time evolution of complex patterns. Moreover, computer simulations yield

detailed spatial information, for instance, in condensed matter physics on conﬁg-

urations of millions of particles. Spatial structures also derive from fracture and

crack distributions in solids studied in solid state physics. Furthermore, many

physicists and engineers study transport properties of disordered materials such

as porous media.

Because of the enormous amount of information in patterns, it is di * cult

to describe spatial structures through a ﬁnite number of parameters. However,

statistical physicists need the compact description of spatial structures to ﬁnd

dynamical equations, to compare experiments with theory, or to classify patterns,

for instance. Thus they should be interested in spatial statistics, which provides

the tools to develop and estimate statistically such characteristics. Nevertheless,

until now, the use of the powerful methods provided by spatial statistics such

as mathematical morphology and stereology have been restricted to medicine

and biology. But since the volume of spatial information is growing fast also in

physics and material science, physicists can only gain by using the techniques

developed in spatial statistics.

The traditional approach to obtain structure information in physics is Fourier

transformation and calculation of wave-vector dependent structure functions.

Surely, as long as scattering techniques were the major experimental set-up in

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