Dynamic scaling fractals

Otsuka and Iwasald [16] have employed AFM method to observe the self-affine fractal structure of the electrochemically roughened Ag electrode surfaces [17]. Later, they have described the dynamic scaling in recrystallization of this electrode surface in water. 

The equations derived from the dynamic scaling theory are valid for self-afiBne and self-similar surfaces. Accordingly, the theory provides information about fractal properties and growth mechanisms of rough surfaces. 

Kozlov, G. V Malkanduev Yu.A. Zaikov, G. E. Fractal analysis of polymers molecular mass distribution. Dynamic scaling. J. Balkan Tribological Association, 2003, 9(2), 252-256. 

Miyashita S, Saito Y, Uwaha M (1997) Experimental evidence of dynamical scaling in a two-dimensional fractal growth. J Phys Soc Japan 66(4) 929-932... 

Mosco,U. Invaritmt field metrics and dynamical scalings on fractals. Phys. Rev. Lett. 79(21), 4067-4070 (1997). http //link.aps.org/abstract/PRL/v79/p4067... 

The authors [42 4] continued to study autoacceleration effect at DMDAACh radical polymerization within the frameworks of fractal and scaling approaches. In paper [39], two hmiting asymptotic regimes for the description of dynamical scaling of the aggregates growth in bath with particles initial concentration c. were considered. For these regimes definition the authors [39] introduced the... 

Hence, the dynamical scaling of DMDAACh radical polymerization allows to describe quantitatively the kinetic curve Q, and can be used for its prediction. In this approach base the key physical principles and models (scaling, universahty classes, irreversible aggregation models, fractal analysis) are placed. The three key process properties, characterized reactive centers concentration (c ), diffusive characteristics of reactive medium (q) and accessibility degree of reactive centers (Df), are used for the kinetic cmves description. It is supposed, that the offered approach will be vahd for the description of radical polymerization process of any polymer. 

Ren, S.-Z., Tombacz, E. and Rice, J.A. (1996). Dynamic light scattering from fractals in solution Application of dynamic scaling theory to humic acid. Phys. Rev. E, S3, 2980-2983. 

The variation of the fractal dimension of kaolinite floes with pH was found using the method of dynamic scaling. Weitz et al (9) showed that for a rapidly aggregating system (a condition fulfilled by kaolinite) that... 

To date, the dynamic scaling in heteroaggregation within the PBE approach was mainly tested for the simplified kernels. Practical applications of Eq. 51 for kernel estimation is restricted because of the absence of detailed relations for interactions of real particles with the fractal structure or rough surface. 

Alexander S., Courtens E., Vacher R. Vibrations of fractals dynamic scaling, couelation functions and inelastic light scattering. Physica A 1993 195 286-318... 

Materials consisting of a concentrated set of fractal aggregates embedded in a homogeneous solid or liquid matrix may also exhibit the dynamical scaling property. In this case, the same properties described in section nanophase separation and dynamical scaling are expected to hold, however the quotient of exponents (a ja) is not equal to the space dimension, rf, = 3, but to the fractal dimension D. 

P — where is the dynamical scaling exponent. In order to introduce the idea of polymeric fractals we have to extend the considerations of ordinary fractals, i.e. those created on a lattice. It has been shown that at least three fractal dimensions are necessary to characterize crudely a fractal object. Indeed in random fractals like percolation clusters or diffusion-limited... 

To get a first crude estimate of the frequency dependence of the modulus we put forward a simple dynamic scaling argument. It uses d in the same spirit as the exponent z in the dynamic scaling hypothesis in phase transitions according to the theory of Halperin and Hohenberg. Consider the modulus of an entropy-dominated or Brownian system which can be written from dimensional analysis as G kT/V, where V is the volume and kT the thermal energy unit. Here K is a fractal... 

The current status of computer simulations and laboratory experiments on fractal aerogels is reviewed and compared to predictions based on dynamical scaling assumptions that have been made by Alexander and collaborators. The experimental results are so far in remarkable agreement with the single-length-scale postulate for fractons and with scaling hypotheses. 

A mathematically definable structure which exhibits the property of always appearing to have the same morphology, even when the observer endlessly enlarges portions of it. In general, fractals have three features heterogeneity, setf-similarity, and the absence of a well-defined scale of length. Fractals have become important concepts in modern nonlinear dynamics. See Chaos Theory... 

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