Fractal geometry, concept

Jung, K.-N., and Pyun, S.-I. 2006a. Effect of pore structure on anomalous behaviour of the lithium intercalation into porous V2O5 film electrode using fractal geometry concept. Electrochimica Acta 51, 2646-2655. 

Many of the adsorbents used have rough surfaces they may consist of clusters of very small particles, for example. It appears that the concept of self-similarity or fractal geometry (see Section VII-4C) may be applicable [210,211]. In the case of quenching of emission by a coadsorbed species, Q, some fraction of Q may be hidden from the emitter if Q is a small molecule that can fit into surface regions not accessible to the emitter [211]. 

See Chaps. 2 and 3 in J. Feder, op. cit.22 An introduction to fractal concepts with more mathematical detail is given by K. Falconer, Fractal Geometry, Wiley, Chichester, UK, 1990. 

Farm and Avnir [113] were the first to use fractal geometry to determine effects of surface morphology on drug dissolution. This was accomplished by the use of the concept of fractal reaction dimension dr [114], which is basically the effective fractal dimension of the solid particle toward a reaction (dissolution in this case). Thus, (5.7) and (5.8) were modified [113] to include surface roughness effects on the dissolution rate of drugs for the entire time course of dissolution... 

It was shown recently that disordered porous media can been adequately described by the fractal concept, where the self-similar fractal geometry of the porous matrix and the corresponding paths of electric excitation govern the scaling properties of the DCF P(t) (see relationship (22)) [154,209]. In this regard we will use the model of electronic energy transfer dynamics developed by Klafter, Blumen, and Shlesinger [210,211], where a transfer of the excitation... 

The emerging concept of fractal geometry has opened a wide area of research. The review will begin with a brief description on the methods for obtaining fractal dimension, followed by the use of fractal concept on pharmaceutical and biological applications with specific examples. 

A different procedure for describing the structure of rugged profiles has been developed from the theorems of fractal geometry. " " The basic concept used in fractal geometry is to add a fractional number to the... 

Kaye, B.H. Characterizing the flowability of powder using the concepts of fractal geometry and chaos theory. Part. Part. Syst. Charact. 1997, 14, 53-66. 

The concept of fractal geometry was first introduced by Mandelbrot and it refers to a rough or fragmented geometric shape that is composed of many smaller copies that have the same shape but different sizes of the whole figure and fractal dimension is a statistical tool to measure how the fractal object rills the space (44). 

In some specific cases other parameters can be considered as important in the characterisation of membrane morphology like the surface roughness, pore anisotropy and porous network connectivity [16,17]. Concepts of percolation and fractal geometry are also of interest to better describe the statistical and random structures of many porous solids [14,18,19]. 

Wheatcraft, S., and S. Tyler. 1988. An explanation of scale dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry. Water Resour. Res. 24 566- 578. 

One of the most exciting developments of the past decade in the study of colloidal silica is the application of the fractal approach to the study of sols and gels. Fractals are disordered systems for which disorder can be described in terms of nonintegral dimension. The concept of fractal geometry, developed by Mandelbrot (II) in the early 1980s, provides a means of quantitatively describing the average structure of certain random objects. The fractal dimension of an object of mass M and radius r is defined by the relation... 

As for electrodes with irregular shape (e.g. rough, porous, scratched, partially blocked, etc.), fractal geometry has been used to analyze the CTs. Following the fractal concept, the generalized Cottrell... 

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