Application of fractals in condensed-matter physics

Olemskoĭ, A. I.; Flat, A.Ya.

doi:10.3367/ufnr.0163.199312a.0001

Cited by 77 publications

(32 citation statements)

References 20 publications

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“…The crumpled globule is an open macromolecule with hierarchically self-similar packing of the polymer chain. Packing the chain in a crumpled globule is similar to the trajectory of an ultrametric random walk [24,25].…”

Section: Introductionmentioning

confidence: 95%

Additive scaling law for structural organization of chromatin in chicken erythrocyte nuclei

et al. 2017

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Additive scaling law for structural organization of chromatin in chicken erythrocyte nuclei Iashina Important noteTo cite this publication, please use the final published version (if applicable). Please check the document version above. CopyrightOther than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons. Takedown policyPlease contact us and provide details if you believe this document breaches copyrights. We will remove access to the work immediately and investigate your claim. Small-angle neutron scattering (SANS) on nuclei of chicken erythrocytes demonstrates the cubic dependence of the scattering intensity Q −3 in the range of momentum transfer Q ∈ 10 −3 -10 −2 nm −1 . Independent spin-echo SANS measurements give the spin-echo function, which is well described by the exponential law in a range of sizes (3 × 10 2 )-(3 × 10 4 ) nm. Both experimental dependences reflect the nature of the structural organization of chromatin in the nucleus of a living cell, which corresponds to the correlation function γ (r) = ln(ξ/r) for r < ξ, where ξ = (3.69 ± 0.07) × 10 3 nm, the size of the nucleus. It has the specific scaling property of the logarithmic fractal γ (r/a) = γ (r) + ln(a), i.e., the scaling down by a gives an additive constant to the correlation function, which distinguishes it from the mass fractal, which is characterized by multiplicative constant.

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Section: Introductionmentioning

confidence: 95%

Additive scaling law for structural organization of chromatin in chicken erythrocyte nuclei

et al. 2017

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“…As physical example of such situation (characteristic of metals, glasses) one can mention the potential of many complex systems. Such a situation is considered in [30]. Minima of potential correspond to the metastable phases, disproportionate structures, etc.…”

Section: Superstatistics From Distribution Of the Kind (5)mentioning

confidence: 99%

First-passage time: a conception leading to superstatistics

Ryazanov¹,

Shpyrko²

2006

Condens. Matter Phys.

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To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter -the lifetime (the first passage time) of a system. The statistical distributions that can be obtained out of the mesoscopic description characterizing the behaviour of a system by specifying the stochastic processes are written. Superstatistics, introduced in [Beck C., Cohen E.G.D., Physica A, 2003, 322A, 267] as fluctuating quantities of intensive thermodynamical parameters, are obtained from statistical distribution with lifetime (random time to system degeneracy) as thermodynamical parameter (and also generalization of superstatistics).

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“…Since the phase space of complex systems gets intricate fractal structure [28] it is natural to build a distribution on a fractal substrate. As distribution f in (22) it is possible to choose a fractal distributions as in [21] or their generalizations on a case of multifractals, and also other distributions used in [1]. Other various combinations of different distributions in the different purposes are possible as well.…”

Section: Superstatistics From Distribution Of the Kind (5)mentioning

confidence: 99%

“…As physical example of such situation (characteristic for metals, glasses) one can mention the potential of many complex systems of a kind, for example, Figure 1. Such situation is considered in [21]. Minima of potential correspond to the metastable phases, disproportionate structures, etc.…”

Section: Superstatistics From Distribution Of the Kind (5)mentioning

confidence: 99%

Superstatistics and Lifetime

Ryazanov¹

2012

AJMS

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To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter -the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a system by specifying the stochastic processes are written. Superstatistics, introduced as fluctuating quantities of intensive thermodynamical parameters, are obtained from statistical distribution with lifetime (random time to system degeneracy) as thermodynamical parameter (and also generalization of superstatistics). Necessary for this realization condition with expression for average lifetime of equilibrium statistical system obtained from stochastical storage model is consist. The obtained distribution passes in Gibbs or in superstatistics distribution depending on a measure of dissipativity in the system.

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Application of fractals in condensed-matter physics

Cited by 77 publications

References 20 publications

Additive scaling law for structural organization of chromatin in chicken erythrocyte nuclei

Additive scaling law for structural organization of chromatin in chicken erythrocyte nuclei

First-passage time: a conception leading to superstatistics

Superstatistics and Lifetime

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