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Dispersion of scale-invariant size-distribution functions

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Abstract

It is shown that the size-distribution function of nanostructures, which obeys scale invariance (scaling), always displays a dispersion proportional to the square of the average size. Theoretical analysis is carried out for the shape and dispersion of a biparametric scale-invariant distribution describing the growth of homogeneous or heterogeneous nanoobjects with monomer capture rates proportional to their size. It is found that the Gaussian distribution is replaced by a broader and asymmetric distribution upon a decrease in the nucleation probability.

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Authors and Affiliations

  1. St. Petersburg Academic University, St. Petersburg, 194021, Russia

    V. G. Dubrovskii

  2. Ioffe Physical Technical Institute, Russian Academy of Sciences, St. Petersburg, 194021, Russia

    V. G. Dubrovskii

  3. St. Petersburg National Research University of Information Technologies, Mechanics, and Optics, St. Petersburg, 197101, Russia

    V. G. Dubrovskii

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  1. V. G. Dubrovskii
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Correspondence to V. G. Dubrovskii.

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Original Russian Text © V.G. Dubrovskii, 2017, published in Pis’ma v Zhurnal Tekhnicheskoi Fiziki, 2017, Vol. 43, No. 9, pp. 3–9.

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Dubrovskii, V.G. Dispersion of scale-invariant size-distribution functions. Tech. Phys. Lett. 43, 413–415 (2017). https://doi.org/10.1134/S1063785017050029

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  • DOI: https://doi.org/10.1134/S1063785017050029

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