Pathways to faceting of vesicles

The interplay between geometry, topology and order can lead to geometric frustration that profoundly affects the shape and structure of a curved surface. In this commentary we show how frustration in this context can result in the faceting of elastic vesicles. We show that, under the right conditions, an assortment of regular and irregular polyhedral structures may be the low energy states of elastic membranes with spherical topology. In particular, we show how topological defects, necessarily present in any crystalline lattice confined to spherical topology, naturally lead to the formation of icosahedra in a homogeneous elastic vesicle. Furthermore, we show that introducing heterogeneities in the elastic properties, or allowing for non-linear bending response of a homogeneous system, opens non-trivial pathways to the formation of faceted, yet non-icosahedral, structures

Spectral analysis for the iron-based superconductors: Anisotropic spin fluctuations and fully gapped s^{\pm}-wave superconductivity

Spin fluctuations are considered to be one of the candidates that drive a sign-reversed s^{\pm} superconducting state in the iron pnictides. In the magnetic scenario, whether the spin fluctuation spectrum exhibits certain unique fine structures is an interesting aspect for theoretical study in order to understand experimental observations. We investigate the detailed momentum dependence of the short-range spin fluctuations using a 2-orbital model in the self-consistent fluctuation exchange approximation and find that a common feature of those fluctuations that are capable of inducing a fully gapped s^{\pm} state is the momentum anisotropy with lengthened span along the direction transverse to the antiferromagnetic momentum transfer. Performing a qualitative analysis based on the orbital character and the deviation from perfect nesting of the electronic structure for the 2-orbital and a more complete 5-orbital model, we gain the insight that this type of anisotropic spin fluctuations favor superconductivity due to their enhancement of intra-orbital, but inter-band, pair scattering processes. The momentum anisotropy leads to elliptically shaped magnetic responses which have been observed in inelastic neutron scattering measurements. Meanwhile, our detailed study on the magnetic and the electronic spectrum shows that the dispersion of the magnetic resonance mode in the nearly isotropic s^{\pm} superconducting state exhibits anisotropic propagating behavior in an upward pattern and the coupling of the resonance mode to fermions leads to a dip feature in the spectral function.Comment: 9 pages, 8 figure

Effects of scars on crystalline shell stability under external pressure

We study how the stability of spherical crystalline shells under external pressure is influenced by the defect structure. In particular, we compare stability for shells with a minimal set of topologically-required defects to shells with extended defect arrays (grain boundary "scars" with non-vanishing net disclination charge). We perform Monte Carlo simulations to compare how shells with and without scars deform quasi-statically under external hydrostatic pressure. We find that the critical pressure at which shells collapse is lowered for scarred configurations that break icosahedral symmetry and raised for scars that preserve icosahedral symmetry. The particular shapes which arise from breaking of an initial icosahedrally-symmetric shell depend on the F\"oppl-von K\'arm\'an number.Comment: 8 pages, 6 figure

Shape-tension coupling produces nematic order in an epithelium vertex model

We study the vertex model for epithelial tissue mechanics extended to include coupling between the cell shapes and tensions in cell-cell junctions. This coupling represents an active force which drives the system out of equilibrium and leads to the formation of nematic order interspersed with prominent, long-lived +1 defects. The defects in the nematic ordering are coupled to the shape of the cell tiling, affecting cell areas and coordinations. This intricate interplay between cell shape, size, and coordination provides a possible mechanism by which tissues could spontaneously develop long-range polarity through local mechanical forces without resorting to long-range chemical patterning

Linear viscoelastic response of the vertex model with internal and external dissipation:Normal modes analysis

We use the normal mode formalism to study the shear rheology of the vertex model for epithelial tissue mechanics in the overdamped linear response regime. We consider systems with external (e.g., cell-substrate) and internal (e.g., cell-cell) dissipation mechanisms, and derive expressions for stresses on cells due to mechanical and dissipative forces. The semi-analytical method developed here is, however, general and can be directly applied to study the linear response of a broad class of soft matter systems with internal and external dissipation. It involves normal mode decomposition to calculate linear loss and storage moduli of the system. Specifically, displacements along each normal mode produce stresses due to elastic deformation and internal dissipation, which are in force balance with loads due to external dissipation. Each normal mode responds with a characteristic relaxation timescale, and its rheological behavior can be described as a combination of a standard linear solid element due to elastic stresses and a Jeffreys model element due to the internal dissipative stresses. The total response of the system is then fully determined by connecting in parallel all the viscoelastic elements corresponding to individual normal modes. This allows full characterization of the potentially complex linear rheological response of the system at all driving frequencies and identification of collective excitations. We show that internal and external dissipation mechanisms lead to qualitatively different rheological behaviors due to the presence or absence of Jeffreys elements, which is particularly pronounced at high driving frequencies. Our findings, therefore, underscore the importance of microscopic dissipation mechanisms in understanding the rheological behavior of soft materials and tissues, in particular

Dynamically generated patterns in dense suspensions of active filaments

We use Langevin dynamics simulations to study dynamical behaviour of a dense planar layer of active semi-flexible filaments. Using the strength of active force and the thermal persistence length as parameters, we map a detailed phase diagram and identify several non-equilibrium phases in this system. In addition to a slowly flowing melt phase, we observe that for sufficiently high activity, collective flow accompanied by signatures of local polar and nematic order appears in the system. This state is also characterised by strong density fluctuations. Furthermore, we identify an activity-driven cross-over from this state of coherently flowing bundles of filaments to a phase with no global flow, formed by individual filaments coiled into rotating spirals. This suggests a mechanism where the system responds to activity by changing the shape of active agents, an effect with no analogue in systems of active particles without internal degrees of freedom.Comment: extended and updated versio

Quantum phase transitions of the diluted O(3) rotor model

We study the phase diagram and the quantum phase transitions of a site-diluted two-dimensional O(3) quantum rotor model by means of large-scale Monte-Carlo simulations. This system has two quantum phase transitions, a generic one for small dilutions, and a percolation transition across the lattice percolation threshold. We determine the critical behavior for both transitions and for the multicritical point that separates them. In contrast to the exotic scaling scenarios found in other random quantum systems, all these transitions are characterized by finite-disorder fixed points with power-law scaling. We relate our findings to a recent classification of phase transitions with quenched disorder according to the rare region dimensionality, and we discuss experiments in disordered quantum magnets.Comment: 11 pages, 14 eps figures, final version as publishe

Nonlinear elastic model for faceting of vesicles with soft grain boundaries

We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in crystalline defects. The elastic heterogeneities are modeled as a second component with reduced elastic parameters. Using simulated annealing Monte Carlo simulations we obtain the vesicle shape by optimizing the distributions of facets and boundaries. Our model allows us to reduce the effects of the residual stress generated by crystalline defects, and reveals a robust faceting mechanism into polyhedra other than the icosahedron.Comment: 4.5 pages, 4 figure

Shape-Tension Coupling Produces Nematic Order in an Epithelium Vertex Model

We study the vertex model for epithelial tissue mechanics extended to include coupling between the cell shapes and tensions in cell-cell junctions. This coupling represents an active force which drives the system out of equilibrium and leads to the formation of nematic order interspersed with prominent, long-lived +1 defects. The defects in the nematic ordering are coupled to the shape of the cell tiling, affecting cell areas and coordinations. This intricate interplay between cell shape, size, and coordination provides a possible mechanism by which tissues could spontaneously develop long-range polarity through local mechanical forces without resorting to long-range chemical patterning