2005
DOI: 10.1103/physreve.71.011908
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Nucleation and growth in one dimension. I. The generalized Kolmogorov-Johnson-Mehl-Avrami model

Abstract: Motivated by a recent application of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model to the study of DNA replication, we consider the one-dimensional version of this model. We generalize previous work to the case where the nucleation rate is an arbitrary function I(t) and obtain analytical results for the time-dependent distributions of various quantities (such as the island distribution). We also present improved computer simulation algorithms to study the 1D KJMA model. The analytical results and simulations… Show more

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Cited by 69 publications
(77 citation statements)
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“…They were all implemented using the programming language of Igor Pro [30]. The work presented in this chapter has been published [21] and the discussion here closely follows that work. Bechhoefer contributed the method discussed in Sec.…”
Section: Numerical Simulation Algorithmmentioning
confidence: 99%
See 1 more Smart Citation
“…They were all implemented using the programming language of Igor Pro [30]. The work presented in this chapter has been published [21] and the discussion here closely follows that work. Bechhoefer contributed the method discussed in Sec.…”
Section: Numerical Simulation Algorithmmentioning
confidence: 99%
“…Once initiation is done, the eyes grow by Ax, namely, by one lattice size at each end. For more details see [21].…”
Section: The Lattice-model Algorithmmentioning
confidence: 99%
“…[1][2][3][4] The investigation of such systems is a very active research field that includes the theory of nucleation in 1D, [5][6][7][8][9][10] the investigation of atomistic diffusion [11][12][13][14][15][16][17] and epitaxial growth [1][2][3][18][19][20][21] in the presence of steps, the catalytic activity of step sites, 22 electron confinement in 1D states, [23][24][25][26] and the behavior of 1D magnetic materials. [27][28][29][30][31][32][33][34][35] Owing to the increase of binding energy at step sites, and depending on the substrate temperature, adatoms deposited on vicinal surfaces can self-assemble into chainlike structures by decorating the step edges.…”
Section: Introductionmentioning
confidence: 99%
“…The disadvantage of measuring interorigin distances is that as bubbles fuse, the center of the fused bubbles is incorrectly assumed to be an origin and the location of the actual origins is obscured (Herrick et al, 2002). The advantage of measuring interbubble distances is that it avoids the fusion problem and, if origins are randomly distributed, the fusion of bubbles does not affect the exponential character of the distribution of the remaining gaps (Jun et al, 2005). The exponential and Gaussian fits of interbubble distances in the whole genome experiments and the reanalysis of the published budding yeast data were performed using KaleidaGraph (Synergy Software, Reading, PA).…”
mentioning
confidence: 99%