The linking number in systems with Periodic Boundary Conditions

Panagiotou, Eleni

doi:10.1016/j.jcp.2015.07.058

Cited by 26 publications

(42 citation statements)

References 77 publications

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“…the collections of translation copies of chains, l 0 or J 0 . See [4] for a discussion of the motivation for the following definition. The underlying idea is to calculate the linking between the generating chain in one with all the chains in the other free chain.…”

Section: The Periodic Linking Numbermentioning

confidence: 99%

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Entanglement transitions in one-dimensional confined fluid flows

Millett¹,

Panagioutou²

2018

Fluid Dyn. Res.

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The strength of entanglement present in a tubular structure consisting of short vortex flow filaments is assessed using a periodic boundary condition (PBC) model by employing the magnitude of the eigenvalues of the periodic linking matrix associated to the filamental structure. The effects of tube radius and of the alignment of the filaments on the strength of entanglement are shown to suggest that strongly aligned flow systems exhibit a stronger entanglement than those consisting of randomly aligned filaments of the same density.

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Section: The Periodic Linking Numbermentioning

confidence: 99%

“…The quantification of the linking of a free chain with itself is a bit special and requires a bit more care as there are two contributing cases, the linking of a chain with itself and the linking of a chain with translations of itself. As a consequence, one is lead to the following definitions [4]:…”

Section: The Periodic Self-linking Numbermentioning

confidence: 99%

Entanglement transitions in one-dimensional confined fluid flows

Millett¹,

Panagioutou²

2018

Fluid Dyn. Res.

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“…In this section, we will discuss the basic ideas that form the theoretical foundation for this study of entanglement in PBC systems as described by Panagiotou [15].…”

Section: Linking Entanglement In Olympic Gels Modeled Using Periodic mentioning

confidence: 99%

“…As a consequence, we give the following, limited, definition of linking for chains in the PBC model employed here. For the general case, we refer to Panagiotou [15]:…”

Section: The Linking Number In Pbc Systemsmentioning

confidence: 99%

Resolving critical degrees of entanglement in Olympic ring systems

Igram

Millett

Panagiotou

2016

J. Knot Theory Ramifications

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Olympic systems are collections of small ring polymers whose aggregate properties are largely characterized by the extent (or absence) of topological linking in contrast with the topological entanglement arising from physical movement constraints associated with excluded volume contacts or arising from chemical bonds. First, discussed by de Gennes, they have been of interest ever since due to their particular properties and their occurrence in natural organisms, for example, as intermediates in the replication of circular DNA in the mitochondria of malignant cells or in the kinetoplast DNA networks of trypanosomes. Here, we study systems that have an intrinsic one, two, or threedimensional character and consist of large collections of ring polymers modeled using periodic boundary conditions. We identify and discuss the evolution of the dimensional character of the large scale topological linking as a function of density. We identify the critical densities at which infinite linked subsystems, the onset of percolation, arise in the periodic boundary condition systems. These provide insight into the nature of entanglement occurring in such course grained models. This entanglement is measured using Gauss linking number, a measure well adapted to such models. We show that, with increasing density, the topological entanglement of these systems increases in complexity, dimension, and probability.

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“…The advantage of the Gauss linking integral is that it can be applied to both linear and ring polymers and it is a continuous function of the chain coordinates. Moreover, in [35] it has been shown that it can be extended to systems with 1,2 or 3 PBC to provide a new continuous measure of entanglement. These measures have been applied to study polymer entanglement in both equilibrium and non-equilibrium conditions.…”

Section: Introductionmentioning

confidence: 99%

Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity

2019

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We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear chains. We investigate the rheology of polymeric chains entangled into weaves with varying topologies and levels of chain density. To investigate viscoelastic responses, we perform non-equilibrium molecular simulations over a range of frequencies using sheared Lees–Edwards boundary conditions. We show how our topological characteristics can be used to capture key features of the polymer entanglements related to the viscoelastic responses. We find there is a linear relation over a significant range of frequencies between the mean absolute Writhe W r and the Loss Tangent tan ( δ ) . We also find an approximate inverse linear relationship between the mean absolute Periodic Linking Number L K P and the Loss Tangent tan ( δ ) . Our results show some of the ways topological methods can be used to characterize chain entanglements to better understand the origins of mechanical responses in polymeric materials.

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The linking number in systems with Periodic Boundary Conditions

Cited by 26 publications

References 77 publications

Entanglement transitions in one-dimensional confined fluid flows

Entanglement transitions in one-dimensional confined fluid flows

Resolving critical degrees of entanglement in Olympic ring systems

Topological Methods for Polymeric Materials: Characterizing the Relationship Between Polymer Entanglement and Viscoelasticity

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