Biophysical Chemistry of Fractal Structures and Processes in by P. Baveye

By P. Baveye

Show description

Read Online or Download Biophysical Chemistry of Fractal Structures and Processes in Environmental Systems PDF

Similar biophysics books

Vibrational Spectroscopy in Life Science

The authors describe easy theoretical innovations of vibrational spectroscopy, tackle instrumental features and experimental approaches, and speak about experimental and theoretical tools for analyzing vibrational spectra. it really is proven how vibrational spectroscopy presents details on normal points of proteins, reminiscent of constitution, dynamics, and protein folding.

The Biosocial Nature of Man (Evergreen books)

Has proprietor identify crossed out on first clean web page, has underlining within publication, fresh, little or no put on

Additional resources for Biophysical Chemistry of Fractal Structures and Processes in Environmental Systems

Example text

For a translationally invariant set, it is straightforward to show that ZQ(2) (l) = [ZQ(1) (l)]2 . Under these conditions, (l) becomes identically equal to unity and is independent of l. The algorithm developed by Chappard et al. [46] is based on the sand-box method elaborated earlier by Tél et al. [50]. In this algorithm, a number s of points or ‘seeds’are selected randomly within the geometrical domain occupied by the object under study, with s taken either arbitrarily or equal to the number of seeds at which convergence is reached for a number of targeted summary statistics.

Letting δ → 0, we see that if H s (F ) < ∞, then H t (F ) = 0 for t > s. 13) shows that there is a critical value of s at which H s (F ) ‘jumps’ from infinity to zero. This critical value of s (at which H s (F ) may in general be undefined) is DH , the Hausdorff dimension of F . 262. This latter number is entirely consistent with the von Koch curve being somehow ‘larger than one-dimensional’ (having infinite length within a bounded domain) and ‘smaller than two-dimensional’ (having zero area). 5. Not all Hausdorff dimensions of mathematical ‘monsters’ are fractional.

4 Construction of the triadic von Koch curve. At each step, the number of line segments increases by a factor of 4. curve (the von Koch curve) has an infinite number of vanishingly small segments and has a total length tending to infinity. 4, one takes the part of I4 that corresponds to the interval [0, 1/3] of the initiator, and scales this part up horizontally and vertically by three, one obtains I3 . In the limit n → ∞, however, this same scaling up of any segment of In would reproduce the von Koch curve itself.

Download PDF sample

Rated 4.15 of 5 – based on 5 votes