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SUMMARY:A tribute to Marian Smoluchowski's legacy on colloid type matter a
ggregation\, and related issues
DTSTART;VALUE=DATE-TIME:20170904T123000Z
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UID:indico-contribution-162@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Adam Gadomski (UTP University of Science and Technol
ogy Bydgoszcz\, Poland)\, Marcel Ausloos (GRAPES\, Liège\, Belgium & Univ
ersity of Leicester\, UK)\n\nIn 1916 Marian Smoluchowski proposed a case o
f constant-kernel cluster cluster aggregation\, for which it is manageable
to find analitycally by employing scaling arguments\, a solution in terms
of the cluster size (k) distribution function\, n(k) [1\,2].\nBy applying
this scaling function it is then possible to get\, within the long times'
limit\, the results for the mean cluster size {k} and the total number of
the clusters N\, both scalable in terms of time t with a single exponent\
, g [2].\nThe clustering arguments\, first introduced by Smoluchowski [1]\
, are easily applicable to statistical description of physical-metallurgic
al processes and ceramic-polycrystalline evolutions\, termed the normal gr
ain growth\, in which bigger clusters grow at the expense of their smaller
neighboring counterparts due to capillary conditions [3].\nThe normal gra
in growth\, and its dynamics\, can be expressed in d-dimensional space (d
- Euclidean dimension of the space). Upon identifying {k} from the Smoluch
owski description with {R}\, the mean cluster radius' size from the normal
grain growth approach\, and by taking the "extreme" condition of k >> 0\,
one is able to embark on their equivalence by stating rigorously that g=1
/(d+1)\, since the asymptotic scaling rule for N (here: the number of grai
ns) goes via a simple logarithmic depiction as: ln[N]~-ln[g].\nThe crucial
assumption\, however\, that assures the equivalence claimed\, appears to
be fully feasible when rearranging the time domain by substituting t in a
way such that a new rescaled time variable T(t) is given by a definite int
egral in [0\,t] upon dT(t)=dt/f(t)\, with an adjustable function f\, comin
g from the dispersive or long-tail\, or fractal kinetics' arguments [4].\
nThe arguments may at least qualitatively concern biomembranes dynamics\;
they can also contribute to nucleation-growth processes in (psychodynamic-
clustering) living matter conditions [5-7].\n\n$ $\n\n[1] M. von Smoluchow
ski\, Physikalische Zeitschrift **17**\, 585 (1916).\n\n[2] R. Jullien\, C
roatica Chemica Acta **65**(2)\, pp. 215-235 (1992).\n\n[3] P.A. Mulheran\
, J.H. Harding\, Materials Science Forum **94-96**\, pp. 367-372\, 1992.\n
\n[4] A. Plonka\, Dispersive Kinetics\, Kluwer\, Dordrecht\, 2002.\n\n[5]
A. Gadomski\, A. Gadomski\, European Physical Journal B **9**\, 569 - 571
(1999).\n\n[6] A. Gadomski\, M. Ausloos\, T. Casey\, Nonlinear Dynamics in
Psychology & Life Sciences **21**/2\, 129-141 (2017).\n\n[7] A. Gadomski
\, Philosophical Magazine Letters **70**\, 335 (1994).\n\nhttps://zakopane
.if.uj.edu.pl/event/4/contributions/162/
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RELATED-TO:indico-event-4@zakopane.if.uj.edu.pl
URL:https://zakopane.if.uj.edu.pl/event/4/contributions/162/
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