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Reversible polymerizations and aggregations
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79953230313
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The length of n-chain equals n as it is measured in unimer sizes
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The length of n-chain equals n as it is measured in unimer sizes.
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15
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Hierarchical self-assembly of columnar aggregates
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Nanda, V.S.1
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30
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79953195713
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-2.
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-2.
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31
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79953180381
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0 1 in the present case
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0 1 in the present case.
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32
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79953218915
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1 ≃ 1, but does not affect much the CLD for n 1 (see Sec.).
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1 ≃ 1, but does not affect much the CLD for n 1 (see Sec.).
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33
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79953198091
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A weaker condition, 1, x , ensures that c(x, ) is just close to c(x); however, this latter condition is not sufficient for the validity of Eq..
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A weaker condition, 1, x, ensures that c(x, ) is just close to c(x); however, this latter condition is not sufficient for the validity of Eq..
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34
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79953166623
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w/2N-1), respectively, in the present paper
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w/2N-1), respectively, in the present paper.
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35
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79953190929
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f in the present paper
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f in the present paper.
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36
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79953204457
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22 in the present notations
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22 in the present notations.
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37
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79953204798
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1=N2/2 is plotted in Fig. according to Eq. (B4) with (t) defined in Eq.
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1=N2/2 is plotted in Fig. according to Eq. (B4) with (t) defined in Eq.
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38
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79953174448
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The analytical expression for the mean chain length derived in Ref. is approximate as it is based on the approximate results for the unimer and dimer concentrations, and because indirect processes were neglected there, which is a rather uncontrolled approximation introduced to simplify evaluation of the integrals in Eq. (36) of that paper.
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The analytical expression for the mean chain length derived in Ref. is approximate as it is based on the approximate results for the unimer and dimer concentrations, and because indirect processes were neglected there, which is a rather uncontrolled approximation introduced to simplify evaluation of the integrals in Eq. (36) of that paper.
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39
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79953229383
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2/2 that must be attributed to the horizontal axis in their Figs. 3 and 5
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2/2 that must be attributed to the horizontal axis in their Figs. 3 and 5.
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40
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79953229047
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It is important to ensure that the exact equilibrium distribution is the exact stationary solution of the discretized numerical equations. This feature is not kept with some sophisticated accelerated-stabilized numerical techniques to solve differential equations. The robust numerical scheme we used conserves exactly the total mass M. By contrast, an accelerated technique may lead to a weak drift of M generating a parallel drift of the mean chain length N that can be mistaken for a long-time (power-law) relaxation tail.
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It is important to ensure that the exact equilibrium distribution is the exact stationary solution of the discretized numerical equations. This feature is not kept with some sophisticated accelerated-stabilized numerical techniques to solve differential equations. The robust numerical scheme we used conserves exactly the total mass M. By contrast, an accelerated technique may lead to a weak drift of M generating a parallel drift of the mean chain length N that can be mistaken for a long-time (power-law) relaxation tail.
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41
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79953225350
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n(t) for t → using Eq..
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n(t) for t → using Eq..
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44
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79953197373
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1 is the rate constant of unimer end-evaporation, t is the real time in our notations.
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1 is the rate constant of unimer end-evaporation, t is the real time in our notations.
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45
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36749051716
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Non-linear scission/recombination kinetics of living polymerization
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DOI 10.1140/epje/i2007-10227-y
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I. A. Nyrkova and A. N. Semenov, Eur. Phys. J. E 24, 167 (2007). 10.1140/epje/i2007-10227-y (Pubitemid 50001313)
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European Physical Journal E
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, Issue.2
, pp. 167-183
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Nyrkova, I.A.1
Semenov, A.N.2
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