Self-avoiding walks on irregular networks

Hiley, B. J.; Finney, John; Burke, Tim

doi:10.1088/0305-4470/10/2/009

Cited by 13 publications

(4 citation statements)

References 10 publications

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“…Also Derrida [9,10] has argued that a change in all the statistics of the SAW should occur for any amount of disorder, and in particular, one should observe a difference between the mean value and the most probable value of the number of SAW of a given number of steps. In the first simulations on this subject Hiley et al [11] did not observe such an effect, in agreement with authors quoted above [1][2][3][4]. On the contrary, very recently this effect was observed in 2-d Monte Carlo calculations by Roy and Chakrabarti [12].…”

Section: Introductionsupporting

confidence: 83%

“…The problem of Self-Avoiding Walks (SAW) on a randomly dilute lattice has been studied a lot recently [1][2][3][4][5][6][7][8][9][10][11][12], leading to conflicting conclusions. According to some authors [1,2], the statistical properties are the same as for the pure system, apart from a trivial renormalization of the connective constant; others [4,5] have obtained similar conclusions, except that they give arguments for a change in the correlation length exponent v at, and only at, the percolation threshold Pc.…”

Section: Introductionmentioning

confidence: 99%

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Directed self-avoiding walks on a randomly dilute lattice

Nadal

Vannimenus

1985

J. Phys. France

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We consider a model of Directed Self-Avoiding Walks (DSAW) on a dilute lattice, using various approaches (Cayley Tree, weak-disorder expansion, Monte-Carlo generation of walks up to 2 000 steps). This simple model appears to contain the essential features of the controversial problem of self-avoiding walks in a random medium. It is shown in particular that with any amount of disorder the mean value for the number of DSAW is different from its most probable value

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Section: Introductionsupporting

confidence: 83%

Section: Introductionmentioning

confidence: 99%

Directed self-avoiding walks on a randomly dilute lattice

Nadal

Vannimenus

1985

J. Phys. France

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“…Other work [57,58] has explored the structure of random packings in terms of Dirichlet polyhedra -essentially the dual of the Voronoi polyhedra. Theoretical work has elucidated the statistics of self-avoiding walks and closed loops in random close packings [59]. This interestingly concluded that the irregularity did not significantly affect the results obtained from equivalently coordinated defective crystalline systems, confirming that the critical exponents that arise in the self-avoiding walk problem depends on dimensionality rather than structural regularity.…”

Section: Random Packing and Other Systemsmentioning

confidence: 84%

Bernal’s road to random packing and the structure of liquids

Finney

2013

Philosophical Magazine

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Until the 1960s, liquids were generally regarded as either dense gases or disordered solids, and theoretical attempts at understanding their structures and properties were largely based on those concepts. Bernal, himself a crystallographer, was unhappy with either approach, preferring to regard simple liquids as 'homogeneous, coherent and essentially irregular assemblages of molecules containing no crystalline regions'. He set about realizing this conceptual model through a detailed examination of the structures and properties of random packings of spheres. In order to test the relevance of the model to real liquids, ways had to be found to realize and characterize random packings. This was at a time when computing was slow and in its infancy, so he and his collaborators set about building models in the laboratory, and examining aspects of their structures in order to characterize them in ways which would enable comparison with the properties of real liquids. Some of the imaginative -often time consuming and frustrating -routes followed are described, as well the comparisons made with the properties of simple liquids. With the increase of the power of computers in the 1960s, computational approaches became increasingly exploited in random packing studies. This enabled the use of packing concepts, and the tools developed to characterize them, in understanding systems as diverse as metallic glasses, crystal-liquid interfaces, protein structures, enzyme-substrate interactions and the distribution of galaxies, as well as their exploitation in, for example, oil extraction, understanding chromatographic separation columns, and packed beds in industrial processes.

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“…What I noticed was that some of these properties, essentially combinatorial in nature, depended only on the dimensionality of the embedding space and not on the detailed structure of the tessellation. In other words, simply by counting embeddings, one could determine the dimensionality of the embedding space [13]. It was only later that I became aware of the fact that the partition function could be obtained much more simply using an algebraic approach used in knot theory.…”

Section: The Common Groundmentioning

confidence: 99%

Aspects of Algebraic Quantum Theory: A Tribute to Hans Primas

Hiley

2016

From Chemistry to Consciousness

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Self-avoiding walks on irregular networks

Cited by 13 publications

References 10 publications

Directed self-avoiding walks on a randomly dilute lattice

Directed self-avoiding walks on a randomly dilute lattice

Bernal’s road to random packing and the structure of liquids

Aspects of Algebraic Quantum Theory: A Tribute to Hans Primas

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