By A. N. Tikhonov

ISBN-10: 0486664228

ISBN-13: 9780486664224

Mathematical physics performs a major position within the research of many actual procedures -- hydrodynamics, elasticity, and electrodynamics, to call quite a few. as a result of huge, immense variety and diversity of difficulties handled by way of mathematical physics, this thorough complicated undergraduate- or graduate-level textual content considers basically these difficulties resulting in partial differential equations.

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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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Categories: Mathematical Physics