Crystalline order on catenoidal capillary bridges

Bowick, Mark J.; Yao, Zhenwei

doi:10.1209/0295-5075/93/36001

Cited by 17 publications

(29 citation statements)

References 43 publications

(63 reference statements)

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“…The frustration associated with the interplay of curvature and order [30,68,69] has many consequences for crystals [70][71][72][73][74], tethered membranes [75,76], liquid crystalline membranes [77][78][79], and jammed and glassy systems [80,81]. The presence of activity adds an entirely new nonequilibrium dimension to the whole story, allowing for completely new physics arising from competing order, curvature, and the active drive.…”

Section: Discussionmentioning

confidence: 99%

Topological Sound and Flocking on Curved Surfaces

2017

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Active systems on curved geometries are ubiquitous in the living world. In the presence of curvature, orientationally ordered polar flocks are forced to be inhomogeneous, often requiring the presence of topological defects even in the steady state because of the constraints imposed by the topology of the underlying surface. In the presence of spontaneous flow, the system additionally supports long-wavelength propagating sound modes that get gapped by the curvature of the underlying substrate. We analytically compute the steady-state profile of an active polar flock on a two-sphere and a catenoid, and show that curvature and active flow together result in symmetry-protected topological modes that get localized to special geodesics on the surface (the equator or the neck, respectively). These modes are the analogue of edge states in electronic quantum Hall systems and provide unidirectional channels for information transport in the flock, robust against disorder and backscattering.

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Section: Discussionmentioning

confidence: 99%

Topological Sound and Flocking on Curved Surfaces

2017

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“…As in crystalline particle arrays on curved geometries where the variation of curvature induces the evolution of defect patterns (12,13,36), increasing the parameter Γ in our planar system can generate rich defect motifs, including those not observed on curved surfaces. Neutral topological defects start to emerge as Γ reaches 2.2 in the hexagonal system (Fig.…”

Section: Resultsmentioning

confidence: 85%

“…Disclinations are building blocks for a variety of defect motifs such as dislocations (5, 7), scars (11), and pleats (12). Recently, crystalline colloidal arrays confined on capillary bridges with variable Gaussian curvatures have been studied experimentally and theoretically (12)(13)(14). The fascinating particle fractionalization event is observed where an interstitial is fissioned into two dislocations (topological dipoles composed of a pair of oppositely charged disclinations) that are later absorbed by other defects; in this event the role of defects switches from order disrupting to order restoring (14).…”

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confidence: 99%

Polydispersity-driven topological defects as order-restoring excitations

Yao

Cruz

2014

Proc. Natl. Acad. Sci. U.S.A.

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The engineering of defects in crystalline matter has been extensively exploited to modify the mechanical and electrical properties of many materials. Recent experiments on manipulating extended defects in graphene, for example, show that defects direct the flow of electric charges. The fascinating possibilities offered by defects in two dimensions, known as topological defects, to control material properties provide great motivation to perform fundamental investigations to uncover their role in various systems. Previous studies mostly focus on topological defects in 2D crystals on curved surfaces. On flat geometries, topological defects can be introduced via density inhomogeneities. We investigate here topological defects due to size polydispersity on flat surfaces. Size polydispersity is usually an inevitable feature of a large variety of systems. In this work, simulations show well-organized induced topological defects around an impurity particle of a wrong size. These patterns are not found in systems of identical particles. Our work demonstrates that in polydispersed systems topological defects play the role of restoring order. The simulations show a perfect hexagonal lattice beyond a small defective region around the impurity particle. Elasticity theory has demonstrated an analogy between the elementary topological defects named disclinations to electric charges by associating a charge to a disclination, whose sign depends on the number of its nearest neighbors. Size polydispersity is shown numerically here to be an essential ingredient to understand short-range attractions between like-charge disclinations. Our study suggests that size polydispersity has a promising potential to engineer defects in various systems including nanoparticles and colloidal crystals.crystallography | geometric frustration | soft particles | dislocation

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“…The spontaneous formation of the perversion line from individual perversions (as shown in Fig. 5C), which are defects themselves in an otherwise uniform helical structure, is strongly analogous to the self-organization of individual disclinations to form ordered compound defects like scars and pleats over curved crystals (27)(28)(29). Note that the coalescence of perversions is not observed when their separation exceeds about two helical periods in the surveys of typical bistrip systems.…”

Section: Resultsmentioning

confidence: 87%

Emergent perversions in the buckling of heterogeneous elastic strips

Liu

Yao

Chiou

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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A perversion in an otherwise uniform helical structure, such as a climbing plant tendril, refers to a kink that connects two helices with opposite chiralities. Such singularity structures are widely seen in natural and artificial mechanical systems, and they provide the fundamental mechanism of helical symmetry breaking. However, it is still not clear how perversions arise in various helical structures and which universal principles govern them. As such, a heterogeneous elastic bistrip system provides an excellent model to address these questions. Here, we investigate intrinsic perversion properties which are independent of strip shapes. This study reveals the rich physics of perversions in the 3D elastic system, including the condensation of strain energy over perversions during their formation, the repulsive nature of the perversion-perversion interaction, and the coalescence of perversions that finally leads to a linear defect structure. This study may have implications for understanding relevant biological motifs and for use of perversions as energy storers in the design of micromuscles and soft robotics.S pontaneous symmetry breaking provides a unifying conceptual understanding of emergent ordered structures arising in various condensed matters (1). In an elastic medium, which is one of the simplest organizations of matter, symmetry-breaking instabilities via buckling can lead to extraordinarily rich patterns and generate a wealth of shapes at multiple length scales that can be exploited in many scientific disciplines (2). A prototype of elastic buckling is the Euler instability of a homogeneous elastic rod under uniaxial compression at the ends that finally breaks the rotational symmetry (3). Introduction of extra structures in an elastic medium like mechanical heterogeneities (4), nonlinearity of materials (2), geometric asymmetry (5), or intrinsic curvature (6) provides new dimensions that can produce even richer buckling modes, including helices and perversions (6, 7), wavy structures (8), regular networks of ridges (9), and even selfsimilar fractal patterns (2, 10). Of these emergent symmetry broken structures, the helical shapes are of particular interest due to their ubiquitousness in nature and the strong connection with biological motifs, as noticed by Darwin in his 1875 book describing the curl of plant tendrils (11). Remarkably, biological helical structures permeate over several length scales from the developed helical valve on opening seed pods (12), to the regular chiral structures in the flagella of bacteria (13), the spiral ramps of rough endoplasmic reticulum (14), and the chromosome of Escherichia coli (15, 16).The proliferation of perversions in an otherwise uniform helical structure can further break the helical symmetry (Fig. 1A shows a typical perversion in the helix) (4, 6, 17). Here, a perversion refers to a kink that connects two helices with opposite chiralities. Therefore, perversions belong to a large class of fundamental defects in systems with discrete symmetry which have the n...

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Crystalline order on catenoidal capillary bridges

Cited by 17 publications

References 43 publications

Topological Sound and Flocking on Curved Surfaces

Topological Sound and Flocking on Curved Surfaces

Polydispersity-driven topological defects as order-restoring excitations

Emergent perversions in the buckling of heterogeneous elastic strips

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