Multifractal behavior of linear polymers in disordered media

Ordemann, Anke; Porto, Markus; Roman, H. E.; Havlin, Shlomo; Bunde, Armin

doi:10.1103/physreve.61.6858

Cited by 38 publications

(64 citation statements)

References 35 publications

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“…The exponentially decreased-phase with the uni-fractal dimensions (Barthelemy et al, 2000;Ordemann et al, 2000;Yu et al, 2004) of base(s) at short distances, expressed in y = ae -bx , was observed in not only any genomes or chromosomes, but also even in their artificial genomes or chromosomes with the same genome-size (nt) and molar-contents of four bases as mentioned above. Thus, the uni-fractality expressed as y = ae -bx was the general phenomena in the arrangement of four bases not only in the genomic-DNA, but also in the artificial-DNA generated with the same molar-contents of the four bases and the base numbers as each single-strand of the genomic DNA.…”

Section: Introductionmentioning

confidence: 71%

The Power-Law-Tail in the Distribution of the Nucleotides of Genomes Was Related to the Complexity of Organism: New Classification of Organisms

Takeda¹

2014

IJB

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We proposed a new index of the classification of organisms (cells) based on the appearance frequency of four nucleotides (bases) of various genomes. In double logarithmic plot of L (distance of a base to the next base, x-axis) vs F (frequencies of a base at L, y-axis), each value of four bases was expressed in y = ae -bx at L = 1 ~ 15, and y = Ux + W (power-law-tail) at L = more than 16 bases, respectively, in a single-strand of DNA. The a-, band U-values (slope) of four bases were resulted from the GC-content (%) and the size (nt) of the genome. Moreover, each value was identical as A to T, and as G to C, respectively, in one organism. The power-law-tail should be unique to the genomes of the same species, the eukaryotes, the prokaryotes. The eukaryotic genomes were essentially composed of great number of bases with plural long power-law-tail regions when compared with those of the prokaryotes. In the prokaryotes, the base-distribution was partitioned at L = 20, and the U-values (base-distribution in power-law-tail region) of the archaea were similar to the eukaryotes compared with those of the eubacteria. Thus, the power-law-tail of the genomic DNA should be come from the structural features of the cells, i.e., the size, the GC-content and other characteristics of the genomic DNA. These results indicated that the power-law-tail would be specific for the complexity of organisms in individual genome, and might be a new index for cells.

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Section: Introductionmentioning

confidence: 71%

The Power-Law-Tail in the Distribution of the Nucleotides of Genomes Was Related to the Complexity of Organism: New Classification of Organisms

Takeda¹

2014

IJB

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“…and is normalized according to [15,16]). The interest in studying the PDF P B (ℓ, N) is because fluctuations are definitely smaller in ℓ-space than in r-space, and more accurate results for g r 1 can be derived by determining g ℓ 1 and afterwards using the relation g…”

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confidence: 99%

“…(8) Financial support from the German-Israeli Foundation (GIF), the Minerva Center for Mesoscopics, Fractals, and Neural Networks and the Deutsche Forschungsgemeinschaft is gratefully acknowledged. [16]. In (a) and (c), the whole PDF is shown, plotted as ℓ d B ℓ P B (ℓ, N ) versus ℓ/N ν ℓ , for N = 39 (full circles) and 40 (full squares), averaged over 5 · 10 3 backbone configurations.…”

mentioning

confidence: 99%

“…In (b) and (d), the region with ℓ ≪ N ν ℓ is shown in more detail, plotted as ℓ [26]. Case d = 2: In (a) the continuous line corresponds to the case ℓ ≫ N ν ℓ and is not further discussed here (see [16] for details). For ℓ ≪ N ν ℓ the dashed line in (b) has the slope 0.49 ± 0.05 and is a fit with the ansatz (N ν ℓ ) …”

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confidence: 99%

“…Results for SAW on the backbone of critical percolation clusters (from Ref. [16]). Note that the value of g ℓ 1 slightly differs from the value given in Ref.…”

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confidence: 99%

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“Generalized des Cloizeaux” exponent for self-avoiding walks on the incipient percolation cluster

et al. 2001

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We study the asymptotic shape of self-avoiding random walks (SAW) on the backbone of the incipient percolation cluster in d-dimensional lattices analytically. It is generally accepted that the configurational averaged probability distribution function P B (r, N ) for the end-to-end distance r of an N step SAW behaves as a power law for r → 0. In this work, we determine the corresponding exponent using scaling arguments, and show that our suggested 'generalized des Cloizeaux' expression for the exponent is in excellent agreement with exact enumeration results in two and three dimensions.

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Effect of Lattice Inhomogeneity on Collapsed Phases of Semi-stiff ISAW Polymers

Bradly

Owczarek

2021

J Stat Phys

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We investigate semi-stiff interacting self-avoiding walks on the square lattice with random impurities. The walks are simulated using the flatPERM algorithm and the inhomogeneity is realised as a random fraction of the lattice that is unavailable to the walks. We calculate several thermodynamic and metric quantities to map out the phase diagram and look at how the amount of disorder affects the properties of each phase. On a homogeneous lattice this model has an extended phase and two distinct collapsed phases, globular and crystalline, which differ in the anisotropy of the walks. By adding impurities to the lattice we notice a degree of swelling of the walks for all phases that is commensurate with the fraction of the lattice that is removed. Importantly, the crystal phase disappears with the addition of impurities for sufficiently long walks. For finite length walks we demonstrate that competition on between the size of the average spaces free of impurities and the size of the collapsed polymer describes the crossover between the homogeneous lattice and the impurity dominated situation.

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Multifractal behavior of linear polymers in disordered media

Cited by 38 publications

References 35 publications

The Power-Law-Tail in the Distribution of the Nucleotides of Genomes Was Related to the Complexity of Organism: New Classification of Organisms

The Power-Law-Tail in the Distribution of the Nucleotides of Genomes Was Related to the Complexity of Organism: New Classification of Organisms

“Generalized des Cloizeaux” exponent for self-avoiding walks on the incipient percolation cluster

Effect of Lattice Inhomogeneity on Collapsed Phases of Semi-stiff ISAW Polymers

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