Defect structures in nematic liquid crystal shells of different shapes

Mirantsev, L. V.; Oliveira, E. J. L. de; Oliveira, I. N. de; Lyra, M. L.

doi:10.1080/21680396.2016.1183151

Cited by 15 publications

(9 citation statements)

References 52 publications

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“…Droplets with holes can be formed either in stress-yield mediums [85] or by confining a LC in handlebody shaped polymer cavities [86]. Thin spherical LC shells with planar anchoring have been researched extensively both theoretically and experimentally [87]. The Poincaré-Hopf theorem, which connects the sum of the winding numbers of 2D defects on a closed surface to its genus, has been verified for LC shells numerically [88,89] and experimentally [90,91].…”

Section: Liquid Crystal Dropletsmentioning

confidence: 99%

Topological Formations in Chiral Nematic Droplets

Posnjak¹

2018

Springer Theses

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Section: Liquid Crystal Dropletsmentioning

confidence: 99%

Topological Formations in Chiral Nematic Droplets

Posnjak¹

2018

Springer Theses

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“…Since the seminal paper of Nelson [1], much has been written about possible technological applications of nematic shells, some perhaps more visionary than others. We refer the interested reader to a number of reviews [8][9][10][11][12] which also summarize the most recent advances in this field, from both the theoretical and experimental approaches. Here we shall be content with showing how a mathematical theory for nematic shells based on a single director description can effectively be phrased on a flat plane.…”

Section: Nematic Shellsmentioning

confidence: 99%

Lifting ordered surfaces: Ellipsoidal nematic shells

Mirantsev¹,

Sonnet²,

Virga³

2018

Phys. Rev. E

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When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeler faces an alternative. Either the order is described on the curved, physical surface where it belongs, or it is described on a flat surface that is unrolled as preimage of the physical surface under a suitable height function. This paper applies a general method that pursues the latter avenue by lifting whatever order tensor is deemed appropriate from a flat to a curved surface. We specialize this method to nematic shells, for which it also provides a simple but perhaps convincing interpretation of the outcomes of some molecular dynamics experiments on ellipsoidal shells.

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“…Since the seminal paper of Nelson [1], much has been written about possible technological applications of nematic shells, some perhaps more visionary than others. We refer the interested reader to a number of reviews [8][9][10][11][12] which also summarize the most recent advances in this field, from both the theoretical and experimental approach. Here we shall be content with showing how a mathematical theory for nematic shells based on a single director description can effectively be phrased on a flat plane.…”

Section: Nematic Shellsmentioning

confidence: 99%

Lifting map for ordered surfaces

Mirantsev,

Sonnet,

Virga

2018

Preprint

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When a material surface is functionalized so as to acquire some type of order, functionalization of which soft condensed matter systems have recently provided many interesting examples, the modeller faces an alternative. Either the order is described on the curved, physical surface where it belongs, or it is described on a flat surface that is unrolled as pre-image of the physical surface under a suitable height function. This paper proposes a general method that pursues the latter avenue by lifting whatever order tensor is deemed appropriate from a flat to a curved surface. To produce a specific application, we specialize this method to nematic shells, for which it also provides a simple, but convincing interpretation of the outcomes of some molecular-dynamics experiments on ellipsoidal shells.

show abstract

Defect structures in nematic liquid crystal shells of different shapes

Cited by 15 publications

References 52 publications

Topological Formations in Chiral Nematic Droplets

Topological Formations in Chiral Nematic Droplets

Lifting ordered surfaces: Ellipsoidal nematic shells

Lifting map for ordered surfaces

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