Stable elastic knots with no self-contact

Moulton, Derek E.; Grandgeorge, Paul; Neukirch, Sébastien

doi:10.1016/j.jmps.2018.03.019

Cited by 23 publications

(25 citation statements)

References 40 publications

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“…We therefore considered an alternative model for the elasticity of the rods, namely, the model for ribbon-like structures proposed by Sadowsky [26] and re-examined in Refs. [27][28][29], in order to investigate the impact of the choice of different constitutive models on the force-strain response. When the rods are modeled as narrow elastic ribbons, the energy density of each rod is described as…”

Section: Comparison With Sadowsky's Ribbon Modelmentioning

confidence: 99%

Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

2021

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Nature and technology often adopt structures that can be described as tubular helical assemblies. However, the role and mechanisms of these structures remain elusive. In this paper, we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchhoff rods, arranged in pairs with opposite chirality and connected by pin joints, both analytically and numerically. We first focus on compression and find that, whereas a single helical rod would buckle, the rods of the assembly deform coherently as stable helical shapes wound around a common axis. Moreover, we investigate the response of the assembly under different boundary conditions, highlighting the emergence of a central region where rods remain circular helices. Secondly, we study the effects of different hypotheses on the elastic properties of rods, i.e., stress-free rods when straight versus when circular helices, Kirchhoff’s rod model versus Sadowsky’s ribbon model. Summing up, our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods, as well as some interesting features, and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology. Graphic Abstract We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

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Section: Comparison With Sadowsky's Ribbon Modelmentioning

confidence: 99%

Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

2021

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“…This would for example be relevant in DNA models for topoisomerase action. In 26,36 this fact was used to detect whether solution branches for an elastic tube model were physically valid. A series of evolving elastic equilibria were obtained using a continuation method, when the values of W p jumped by ±2 the could be automatically ruled out as not physically accessible (as elastic tubes cannot self intersect).…”

Section: Self Crossing Detectionmentioning

confidence: 99%

“…This framework has been regularly applied in Solar physics applications since the original paper e.g. [29][30][31][32][33][34][35] and is increasingly being applied in Elastic tube modelling 26,36,37 . However, it has not been widely adopted in the biophysical community, as artificial closures methods are still readily employed for problems such as characterizing DNA supercoiling.…”

Section: Introductionmentioning

confidence: 99%

WASP: A software package for correctly characterizing the topological development of ribbon structures

Sierzega

Wereszczynski

Prior

2020

Preprint

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We introduce the Writhe Application Software Package (WASP) which can be used to characterise the topology of ribbon structures, the underlying mathematical model of DNA, Biopolymers, superfluid vorticies, elastic ropes and magnetic flux ropes. This characterisation is achieved by the general twist-writhe decomposition of both open and closed ribbons, in particular through a quantity termed the polar writhe. We demonstrate how this decomposition is far more natural and straightforward than artificial closure methods commonly utilized in DNA modelling. In particular, we demonstrate how the decomposition of the polar writhe in local and non-local components distinctly characterizes local helical structure and knotting/linking of the ribbon. This decomposition provides additional information not given by alternative approaches. As an example application, the WASP routines are used to characterise the evolving topology (writhe) of DNA minicircle and open ended plectoneme formation magnetic/optical tweezer simulations. Finally it is demonstrated that a number of well known alternative writhe expressions are actually simplifications of the polar writhe measure.

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“…This would, for example, be relevant in DNA models for topoisomerase action. In 26 , 36 , this fact was used to detect whether solution branches for an elastic tube model were physically valid. A series of evolving elastic equilibria were obtained using a continuation method and when the values of jumped by the equilibrium path could be automatically ruled out as not physically accessible (as elastic tubes cannot self intersect).…”

Section: Introduction To the Polar Writhementioning

confidence: 99%

“…This framework has been regularly applied in the field of Solar physics since the original paper e.g. [29][30][31][32][33][34][35] and is increasingly being applied in Elastic tube modelling 26,36,37 as well. However, it has not been widely adopted in the biophysical community and artificial closure methods are still readily employed for problems such as characterizing DNA supercoiling.…”

mentioning

confidence: 99%

WASP: a software package for correctly characterizing the topological development of ribbon structures

Sierzega

Wereszczynski

Prior

2021

Sci Rep

View full text Add to dashboard Cite

We introduce the Writhe Application Software Package (WASP) which can be used to characterisze the topology of ribbon structures, the underlying mathematical model of DNA, Biopolymers, superfluid vorticies, elastic ropes and magnetic flux ropes. This characterization is achieved by the general twist–writhe decomposition of both open and closed ribbons, in particular through a quantity termed the polar writhe. We demonstrate how this decomposition is far more natural and straightforward than artificial closure methods commonly utilized in DNA modelling. In particular, we demonstrate how the decomposition of the polar writhe into local and non-local components distinctly characterizes the local helical structure and knotting/linking of the ribbon. This decomposition provides additional information not given by alternative approaches. As example applications, the WASP routines are used to characterise the evolving topology (writhe) of DNA minicircle and open ended plectoneme formation magnetic/optical tweezer simulations, and it is shown that the decomponsition into local and non-local components is particularly important for the detection of plectonemes. Finally it is demonstrated that a number of well known alternative writhe expressions are actually simplifications of the polar writhe measure.

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Stable elastic knots with no self-contact

Cited by 23 publications

References 40 publications

Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

WASP: A software package for correctly characterizing the topological development of ribbon structures

WASP: a software package for correctly characterizing the topological development of ribbon structures

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