Packing loops into annular cavities

Sobral, T. A.; Gomes, M. A. F.

doi:10.1103/physreve.95.022312

Cited by 2 publications

(2 citation statements)

References 18 publications

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“…The key concept here is curvature, which links our work to the physics of pattern formation in protein chains and membranes [16] and, not less astonishingly, quantum gravity [17]. Besides, the number of loops gives the jamming length and the dynamic state of the system [18,19]. Note that the type of loops studied here, in which curvature reverses sign along its length, can be unstable or less frequent in the case of 3D confinements, where torsion may have a major influence and the curvature maintains a constant sign [20].…”

Section: Introductionmentioning

confidence: 95%

Deformation of loops in 2D packing of flexible rods

Sobral¹,

Holanda²,

Leal³

et al. 2021

J. Phys. D: Appl. Phys.

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The injection of a long flexible rod into a two-dimensional domain yields a complex pattern commonly studied through the elasticity theory, packing analysis, and fractal geometries. ‘Loop’ is a one-vertex entity that naturally formed in this system. The role of the elastic features of each loop in 2D packing has not yet been discussed. In this work, we point out how the shape of a given loop in the complex structure allows estimating local deformations and forces. First, we build sets of symmetric free loops and perform compression experiments. Then, tight packing configurations are analyzed using image processing. We find that the dimensions of the loops, confined or not, obey the same dependence on the deformation. The results are consistent with a simple model based on 2D elastic theory for filaments, where the rod adopts the shape of Euler’s elasticas between its contact points. The force and the stored energy are obtained from numerical integration of the analytic expressions. In an additional experiment, we obtain that the compression force for deformed loops corroborates the theoretical findings. The importance of the shape of the loop is discussed and we hope that the theoretical curves may allow statistical considerations in future investigations.

show abstract

Section: Introductionmentioning

confidence: 95%

Deformation of loops in 2D packing of flexible rods

Sobral¹,

Holanda²,

Leal³

et al. 2021

J. Phys. D: Appl. Phys.

View full text Add to dashboard Cite

show abstract

“…The key concept here is curvature, which links our work to the physics of pattern formation in protein chains and membranes [16] and, not less astonishingly, quantum gravity [17]. In addition, the number of loops gives the jamming length and the dynamic state of the system [18,19]. Note that the type of loops studied here, in which curvature reverses sign along its length, can be unstable or less frequent in the case of 3D confinements, where torsion may have a major influence and the curvature maintains constant sign [20].…”

Section: Introductionmentioning

confidence: 99%

Deformation of loops in 2D packing of flexible rods

Sobral,

de Holanda,

Leal

et al. 2020

Preprint

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View full text Add to dashboard Cite

The injection of a long piece of flexible rod into a two-dimensional domain yields a complex pattern commonly studied through elasticity theory, packing analysis, and fractal geometries. "Loop" is an one-vertex entity which which is naturally formed in this system. The role of the elastic features of each individual loop in 2D packing has not yet been discussed. In this work we point out how the shape of a given loop in the complex structure allows to estimate local deformations and forces. First, we build sets of symmetric free loops and performed compression experiments. Then, tight packing configurations are analyzed by using image processing. We found that the dimensions of the loops, confined or not, obey the same dependence on the deformation. The result is consistent with a simple model based on 2D elastic theory for filaments, where the rod adopts the shape of Euler's elasticas between its contact points. The force and the stored energy are obtained from numerical integration of the analytic expressions. In an additional experiment, we obtain that the compression force for deformed loops corroborates the theoretical findings. The importance of the shape of the loop is discussed and we hope that the theoretical curves may allow statistical considerations in future investigations.

show abstract

Packing loops into annular cavities

Cited by 2 publications

References 18 publications

Deformation of loops in 2D packing of flexible rods

Deformation of loops in 2D packing of flexible rods

Deformation of loops in 2D packing of flexible rods

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