Entropy and Ordering of Hard Rods in One Dimension

Giaquinta, P. V.

doi:10.3390/e10030248

Cited by 21 publications

(17 citation statements)

References 58 publications

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“…These behaviors are very similar to the positional ordering of 1D hard rods (Tonks-gas). 21 At η = 0.7, g(x) becomes very different from the g(x) observed at η = 0.5, it is more structured and smoothly varying function of the longitudinal distance. In addition to this no sign of Tonks-gas behavior survives at high densities.…”

Section: B Three-dimensional Hard Spheres In Cylindrical Porementioning

confidence: 70%

“…20 In the system of 1D hard rods it is shown that structural change may take place upon compression at finite pressure where the fluid structure transforms into a pseudocrystal. 21 In a recent study of Herrera-Velarde et al, 22 fluidlike and solid-like structures were distinguished in several 1D soft model by the help of the linear pair correlation function, which decays exponentially in fluid-like phase, while it has algebraic decay in solid-like phase. It was also shown that the structural change is accompanied by a highly narrow mean peak in the static structure factor with a height of S c = 7 for all studied pair potentials.…”

Section: Introductionmentioning

confidence: 99%

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Pair correlation functions of two- and three-dimensional hard-core fluids confined into narrow pores: Exact results from transfer-matrix method

Gurin

Varga

2013

The Journal of Chemical Physics

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The effect of confinement is studied on the local structure of two- and three-dimensional hard-core fluids. The hard disks are confined between two parallel lines, while the hard spheres are in a cylindrical hard pore. In both cases only nearest neighbour interactions are allowed between the particles. The vertical and longitudinal pair correlation functions are determined by means of the exact transfer-matrix method. The vertical pair correlation function indicates that the wall induced packing constraint gives rise to a zigzag (up-down sequence) shaped close packing structure in both two- and three-dimensional systems. The longitudinal pair correlation function shows that both systems transform continuously from a one-dimensional gas-like behaviour to a zigzag solid-like structure with increasing density.

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Section: B Three-dimensional Hard Spheres In Cylindrical Porementioning

confidence: 70%

Section: Introductionmentioning

confidence: 99%

Pair correlation functions of two- and three-dimensional hard-core fluids confined into narrow pores: Exact results from transfer-matrix method

Gurin

Varga

2013

The Journal of Chemical Physics

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“…When further increasingμ, it then slowly increases towards the asymptotic limit ρ * l = 1. Interestingly, for very largeμ values, finite-size systems experience a transition towards a saturated ρl = 0.85 occupancy state ( Figure 14, blue curve) which has been identified as a pseudo-crystalline state consisting of quasi regularly spaced particles 'self-confined' inside equipartitioned regions of length equal to the average length per particle l m = 1/ρ (Piasecki and Peliti 1993;Giaquinta 2008). In inhomogeneous fluids, this saturation only occurs for the bulk occupancy (ρ b l = l/L L 0 ρ(s) ds) as illustrated in Figure 13 where at the edges near the infinite energy walls, the local occupancy ρ(s)l can reach a value close to one.…”

Section: Nucleosome Densitymentioning

confidence: 99%

Influence of the genomic sequence on the primary structure of chromatin

Chevereau

Arnéodo

Vaillant

2011

Frontiers in Life Science

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International audienceAs an important actor in the regulation of nuclear functions, the nucleosomal organization of the 10 nm chromatin fiber is the subject of increasing interest. Recent high-resolution mapping of nucleosomes along various genomes ranging from yeast to human, have revealed a patchy nucleosome landscape with alternation of depleted, well positioned and fuzzy regions. For many years, the mechanisms that control nucleosome occupancy along eukaryotic chromosomes and their coupling to transcription and replication processes have been under intense experimental and theoretical investigation. A recurrent question is to what extent the genomic sequence dictates and/or constrains nucleosome positioning and dynamics? In that context we have recently developed a simple thermodynamical model that accounts for both sequence specificity of the histone octamer and for nucleosome–nucleosome interactions. As a main issue, our modelling mimics remarkably well in vitro data showing that the sequence signaling that prevails are high energy barriers that locally inhibit nucleosome formation and condition the collective positioning of neighboring nucleosomes according to thermal equilibrium statistical ordering. When comparing to in vivo data, our physical modelling performs as well as models based on statistical learning suggesting that in vivo bulk chromatin is to a large extent controlled by the underlying genomic sequence although it is also subject to finite-range remodelling action of external factors including transcription factors and ATP-dependent chromatin remodellers. On the highly studied S. cerevisiae organism, we discuss the implications of the highlighted ‘positioning via excluding’ mechanism on the structure and function of yeast genes. The generalization of our physical modelling to human is likely to provide new insight on the isochore structure of mammalian genomes in relation with their primary nucleosomal structure

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“…Whether or not the GCM fluid crystallizes in 1D, one can safely expect a far from trivial phase behaviour because of the ever-increasing occurrence, under compression, of soft particle-core overlaps. A natural candidate for the macrostate of minimum Gibbs free energy is a diffusely ordered arrangement formed by more or less equally spaced particles, as is the case of 1D hard rods at high density [14]. However, the thermodynamic competition between energy and entropy may also lead, in a fluid with a soft bounded potential, to even more complex arrangements such as those found in "clustered" or "tower" crystals, where two or more (superimposed) particles are confined within the same cell [11].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic and structural anomalies of the Gaussian-core model in one dimension

2011

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We investigated the equilibrium properties of a one-dimensional system of classical particles which interact in pairs through a bounded repulsive potential with a Gaussian shape. Notwithstanding the absence of a proper fluid-solid phase transition, we found that the system exhibits a complex behaviour, with "anomalies" in the density and in the thermodynamic response functions which closely recall those observed in bulk and confined liquid water. We also discuss the emergence in the cold fluid under compression of an unusual structural regime, characterized by density correlations reminiscent of the ordered arrangements found in clustered crystals.

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Entropy and Ordering of Hard Rods in One Dimension

Cited by 21 publications

References 58 publications

Pair correlation functions of two- and three-dimensional hard-core fluids confined into narrow pores: Exact results from transfer-matrix method

Pair correlation functions of two- and three-dimensional hard-core fluids confined into narrow pores: Exact results from transfer-matrix method

Influence of the genomic sequence on the primary structure of chromatin

Thermodynamic and structural anomalies of the Gaussian-core model in one dimension

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