Introduction to Mathematical Physics - download pdf or read online

By Charles A. Harper

ISBN-10: 0134875389

ISBN-13: 9780134875385

ISBN-10: 8120302621

ISBN-13: 9788120302624

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Boxes) and porosity is estimated in each subarea, a distribution of the measure “porosity” is obtained for the image. 48 Even though we are focusing on porosity, any geometrical quantity is susceptible to the local concept. Imagine an image formed by pixels arranged in a square lattice of side L. A distribution of local porosity is obtained if this lattice is subdivided in n(δ) boxes of size δ from δ = 1 to δ = L/4 and in every box the number of pixels belonging to the pore class, Nj, is recorded.

B. Multifractal measures. , Jurgens, H. , Springer, New York, 1992, 921. 40. Meneveau, C. R. Measurement of f(α) from scaling of histograms, and applications to dynamical systems and fully developed turbulence. Phys. , A137, 103, 1989. 41. Chhabra, A. V. Direct determination of the f(α) singularity spectrum. Phys. Rev. , 62, 1327, 1989. 42. Q. Multifractal analysis of the spatial distribution of the film surfaces with different roughening mechanisms. Phys. Rev. , 58, 2213, 1998. 43. , and Borondo, F.

47 provided a rigorous connection between the configuration entropy H(δ) and the local porosity concept. 19) where H max ( δ ) = log(δ 2 + 1) H*(δ) is called the normalized configuration entropy of the two-dimensional morphology of the image. 47 calculated H* for two generated images of simple models (Bernoulli site percolation model and Poisson grain model) and two microstructures from experimental images (gold film deposit on a glass substrate and a natural sandstone). 4). The authors concluded that L*, and the curvature of H* around this value, characterize the microstructure.

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Introduction to Mathematical Physics by Charles A. Harper

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