By Dietrich Stoyan (auth.), Klaus R. Mecke, Dietrich Stoyan (eds.)
Modern physics is faced with a wide number of advanced spatial styles. even though either spatial statisticians and statistical physicists examine random geometrical buildings, there was simply little interplay among the 2 in past times as a result of various traditions and languages.
This quantity goals to alter this example by way of proposing in a transparent manner primary options of spatial records that are of significant capability worth for condensed subject physics and fabrics sciences normally, and for porous media, percolation and Gibbs procedures particularly. Geometric points, particularly principles of stochastic and crucial geometry, play a significant function all through. With nonspecialist researchers and graduate scholars additionally in brain, widespread physicists provide a very good advent the following to trendy rules of statistical physics pertinent to this intriguing box of research.
Read or Download Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and Pattern Formation PDF
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Extra resources for Statistical Physics and Spatial Statistics: The Art of Analyzing and Modeling Spatial Structures and Pattern Formation
Example text
4). Indeed, the volume density m0 (Ar ) equals the spherical contact distribution or equivalently the void probability minus one: m0 (Ar ) = F (r) = Hs (r) = P0 (Br ) − 1 (see also Sect. 2). Expressions relating the Minkowski functionals of such a set Ar , with the n–point correlation functions of the underlying point–process may be found in [73,74] and [101] and the contribution by K. Mecke in this volume. Already for moderate radii r nearly the whole space is filled with up by Ar , leading to m0 (Ar ) ≈ 1 and mµ (Ar ) ≈ 0, with µ > 0.
G. a segment, a circle, a polygon - is attached to each point. These figures are referred to as marks. For such structures the quantitative analysis of the underlying point pattern can also be of interest but, furthermore, the probability distribution of the marks has to be taken into consideration. For the example of segments as marks one can investigate • the mean total length of segments per unit area, • the mean number per unit area of points marked with segments of a direction in a certain sector of angles, • the mean total length per unit area of segments with its direction in a certain sector of angles.
Rev. 62, pp. 99-117 7. V. Mardia (1998): Statistical Shape Analysis (J. Wiley & Sons, Chichester) 8. W. (1993): ‘Random and cooperative adsorption’. Rev. Modern Phys 65, pp. 1281–1329 9. R. (1983): Probability, Statistical Optics, and Data Testing (SpringerVerlag, Berlin, Heidelberg, New York) 10. -O. (1976): ‘Canonical and grand canonical Gibbs states for continuum systems’. Comm. Math. Phys. 48, pp. 31–51 11. Geyer, C. (1999): ‘Likelihood inference for spatial point processes’. In: [2], pp. 79–140.
