Thermalized buckling of isotropically compressed thin sheets

Shankar, Suraj; Nelson, David R.

doi:10.48550/arxiv.2103.07455

Cited by 2 publications

(4 citation statements)

References 49 publications

(127 reference statements)

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“…Notably, our findings are not compatible with a perfect hexagonal network thus refusing the classical model by Cozzarelli [19]. Finally, we discuss our findings in light of the work done on sub-isostatic floppy networks [25] and 2D elastic thermal sheets [26] and predict that the kDNA should display a Young modulus much lower than that of common 2D materials such as lipid membranes.…”

Section: Introductionsupporting

confidence: 47%

“…The competition of compression and bending moduli gives rise to a natural lengthscale called “thermal length-scale” which dictates the behaviour of 2D elastic thermal sheets [26, 44]. This lengthscale is found as When compression deformations are larger than l th , it is more energetically favourable for a 2D elastic sheet to buckle.…”

Section: Resultsmentioning

confidence: 99%

“…The competition of compression and bending moduli gives rise to a natural lengthscale called "thermal lengthscale" which dictates the behaviour of 2D elastic thermal sheets [26,44]. This lengthscale is found as…”

Section: Elasticity Of Kdna As a Sub-isostatic Networkmentioning

confidence: 99%

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Single-Molecule Structure and Topology of Kinetoplast DNA Networks

Katan

Tubiana

et al. 2022

Preprint

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The Kinetoplast DNA (kDNA) is a two-dimensional Olympic-ring-like network of mutually linked 2.5 kb-long DNA minicircles found in certain parasites called Trypanosomes. Understanding the self-assembly and replication of this structure are not only major open questions in biology but can also inform the design of synthetic topological materials. Here we report the first high-resolution, single-molecule study of kDNA network topology using AFM and steered molecular dynamics simulations. We map out the DNA density within the network and the distribution of linking number and valence of the minicircles. We also characterise the DNA hubs that surround the network and show that they cause a buckling transition akin to that of a 2D elastic thermal sheet in the bulk. Intriguingly, we observe a broad distribution of density and valence of the minicircles, indicating heterogeneous network structure and individualism of different kDNA structures. Our findings explain outstanding questions in the field and offer single-molecule insights into the properties of a unique topological material.

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Section: Introductionsupporting

confidence: 47%

Section: Resultsmentioning

confidence: 99%

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Single-Molecule Structure and Topology of Kinetoplast DNA Networks

Katan

Tubiana

et al. 2022

Preprint

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“…A generalization of this result, including the quartic term, to a circular plate can be found in [43]. Using a mean field variational function (up to an arbitrary constant) h(x) = H cos πx 2L , where H serves as the buckling order parame-ter, yields a critical compression…”

mentioning

confidence: 91%

Spontaneous tilt of single-clamped thermal elastic sheets

Chen,

Wan,

Bowick

2021

Preprint

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Very thin elastic sheets, even at zero temperature, exhibit nonlinear elastic response by virtue of their dominant bending modes. Their behavior is even richer at finite temperature. Here we use molecular dynamics (MD) to study the vibrations of a thermally fluctuating two-dimensional elastic sheet with one end clamped at its zero-temperature length. We uncover a tilt phase in which the sheet fluctuates about a mean plane inclined with respect to the horizontal, thus breaking reflection symmetry. We determine the phase behavior as a function of the aspect ratio of the sheet and the temperature. We show that tilt may be viewed as a type of transverse buckling instability induced by clamping coupled to thermal fluctuations and develop an analytic model that predicts the tilted and untilted regions of the phase diagram. Qualitative agreement is found with the MD simulations. Unusual response driven by control of purely geometric quantities like the aspect ratio, as opposed to external fields, offers a very rich playground for two-dimensional mechanical metamaterials.

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Thermalized buckling of isotropically compressed thin sheets

Cited by 2 publications

References 49 publications

Single-Molecule Structure and Topology of Kinetoplast DNA Networks

Single-Molecule Structure and Topology of Kinetoplast DNA Networks

Spontaneous tilt of single-clamped thermal elastic sheets

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