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Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described within the framework of dense active matter, and argue that persistent uncoordinated cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce swirl-like correlations. We obtain this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based cell models, soft elastic particles and the self-propelled Voronoi model together with in-vitro experiments of confluent corneal epithelial cell sheets. Simulations and normal mode analysis perfectly match when tissue-level reorganisation occurs on times longer than the persistence time of cell motility. Our analytical model quantitatively matches measured velocity correlation functions over more than a decade with a single fitting parameter., updated version accepted for publication in Nat. Comm

Stratified assembly of active components drives a tight huddle of proteins on the membrane., Recent in vivo studies reveal that several membrane proteins are driven to form nanoclusters by active contractile flows arising from localized dynamic patterning of F-actin and myosin at the cortex. Since myosin-II assemble as minifilaments with tens of myosin heads, one might worry that steric considerations would obstruct the emergence of nanoclustering. Using coarse-grained, agent-based simulations that account for steric constraints, we find that the patterns exhibited by actomyosin in two dimensions, do not resemble the steady-state patterns in our in vitro reconstitution of actomyosin on a supported bilayer. We perform simulations in a thin rectangular slab, separating the layer of actin filaments from myosin-II minifilaments. This recapitulates the observed features of in vitro patterning. Using super resolution microscopy, we find evidence for such stratification in our in vitro system. Our study suggests that molecular stratification may be an important organizing feature of the cortical cytoskeleton in vivo.

Cells in an epithelial monolayer coordinate motion with their neighbors giving rise to collectively moving packs of sizes spanning multiple cell diameters. The physical mechanism controlling the pack size, however, remains unclear. A potential mechanism comes from assuming that cell–substrate traction forces persist over some time scale: with large enough persistence time, collective cell packs emerge. To test this hypothesis, we measured the velocity and net traction of each cell. The data showed that in addition to having some temporal persistence, tractions were spatially correlated, suggesting that cells coordinate with their neighbors to apply tractions in the same direction. Chemical inhibitors and activators of actomyosin contraction were used to determine effects of altering the traction persistence and alignment. Numerical simulations based on the self-propelled Voronoi model, augmented to include both traction persistence and alignment and calibrated against the experimental data, matched the experimentally measured pack size. The model identified that if there were no alignment of traction between neighboring cells, the size of the collective pack would be substantially smaller than observed in the experiments. Hence, combining experiments and a simple mechanical model, this study confirms the long-standing assumption of traction persistence and adds the notion of traction alignment between neighbors. Together, persistence and alignment are two factors controlling the size of a collectively moving cell pack.

We show that a viscoelastic thin sheet driven out of equilibrium by active structural remodelling develops a rich variety of shapes as a result of a competition between viscous relaxation and activity. In the regime where active processes are faster than viscoelastic relaxation, wrinkles that are formed due to remodelling are unable to relax to a configuration that minimises the elastic energy and the sheet is inherently out of equilibrium. We argue that this non-equilibrium regime is of particular interest in biology as it allows the system to access morphologies that are unavailable if restricted to the adiabatic evolution between configurations that minimise the elastic energy alone. Here, we introduce activity using the formalism of evolving target metric and showcase the diversity of wrinkling morphologies arising from out of equilibrium dynamics.

Recent in-vivo studies have revealed that several membrane proteins are driven to form nanoclusters by active contractile flows arising from F-actin and myosin at the cortex. The mechanism of clustering was shown to be arising from the dynamic patterning of transient contractile platforms (asters) generated by actin and myosin. Myosin-II, which assemble as minifilaments consisting of tens of myosin heads, are rather bulky structures and hence a concern could be that steric considerations might obstruct the emergence of nanoclustering. Here, using coarse-grained, agent-based simulations that respect the size of constituents, we find that in the presence of steric hindrance, the patterns exhibited by actomyosin in two dimensions, do not resemble the steady state patterns observed in our in-vitro reconstitution of actomyosin on a supported bilayer. We then perform simulations in a thin rectangular slab, allowing the separation of a layer of actin filaments from those of myosin-II minifilaments. This recapitulates the observed features of in-vitro patterning. Using super resolution microscopy, we find direct evidence for stratification in our in-vitro system. Our study suggests the possibility that molecular stratification may be an important organising feature of the cortical cytoskeleton in-vivo.

International audience; The structural and functional organization of biological tissues relies on the intricate interplay between chemical and mechanical signaling. Whereas the role of constant and transient mechanical perturbations is generally accepted, several studies recently highlighted the existence of long-range mechanical excitations (i.e., waves) at the supracellular level. Here, we confine epithelial cell monolayers to quasi-onedimensional geometries, to force the establishment of tissue-level waves of well-defined wavelength and period. Numerical simulations based on a self-propelled Voronoi model reproduce the observed waves and exhibit a phase transition between a global and a multinodal wave, controlled by the confinement size. We confirm experimentally the existence of such a phase transition, and show that wavelength and period are independent of the confinement length. Together, these results demonstrate the intrinsic origin of tissue oscillations, which could provide cells with a mechanism to accurately measure distances at the supracellular level.

The cell membrane deforms during endocytosis to surround extracellular material and draw it into the cell. Experiments on endocytosis in yeast all agree that (i) actin polymerizes into a network of filaments exerting active forces on the membrane to deform it and (ii) the large scale membrane deformation is tubular in shape. There are three competing proposals, in contrast, for precisely how the actin filament network organizes itself to drive the deformation. We use variational approaches and numerical simulations to address this competition by analyzing a meso-scale model of actin-mediated endocytosis in yeast. The meso-scale model breaks up the invagination process into three stages: (i) initiation, where clathrin interacts with the membrane via adaptor proteins, (ii) elongation, where the membrane is then further deformed by polymerizing actin filaments, followed by (iii) pinch-off. Our results suggest that the pinch-off mechanism may be assisted by a pearling-like instability. We rule out two of the three competing proposals for the organization of the actin filament network during the elongation stage. These two proposals could possibly be important in the pinch-off stage, however, where additional actin polymerization helps break off the vesicle. Implications and comparisons with earlier modeling of endocytosis in yeast are discussed., 15 pages, 7 figures, accepted to Biophysical Journal

We investigate the effects of cell division and apopotosis on collective dynamics in two-dimensional epithelial tissues. Our model includes three key ingredients observed across many epithelia, namely cell-cell adhesion, cell death and a cell division process that depends on the surrounding environment. We show a rich non-equilibrium phase diagram depending on the ratio of cell death to cell division and on the adhesion strength. For large apopotosis rates, cells die out and the tissue disintegrates. As the death rate decreases, however, we show, consecutively, the existence of a gas-like phase, a gel-like phase, and a dense confluent (tissue) phase. Most striking is the observation that the tissue is self-melting through its own internal activity, ruling out the existence of any glassy phase., Comment: 9 pages, 10 figures

Much of the structural stability of the nucleus comes from meshworks of intermediate filament proteins known as lamins forming the inner layer of the nuclear envelope called the nuclear lamina. These lamin meshworks additionally play a role in gene expression. Abnormalities in nuclear shape are associated with a variety of pathologies, including some forms of cancer and Hutchinson–Gilford Progeria Syndrome, and often include protruding structures termed nuclear blebs. These nuclear blebs are thought to be related to pathological gene expression; however, little is known about how and why blebs form. We have developed a minimal continuum elastic model of a lamin meshwork that we use to investigate which aspects of the meshwork could be responsible for bleb formation. Mammalian lamin meshworks consist of two types of lamin proteins, A type and B type, and it has been reported that nuclear blebs are enriched in A-type lamins. Our model treats each lamin type separately and thus, can assign them different properties. Nuclear blebs have been reported to be located in regions where the fibers in the lamin meshwork have a greater separation, and we find that this greater separation of fibers is an essential characteristic for generating nuclear blebs. The model produces structures with comparable morphologies and distributions of lamin types as real pathological nuclei. Thus, preventing this opening of the meshwork could be a route to prevent bleb formation, which could be used as a potential therapy for the pathologies associated with nuclear blebs.

We investigate the effects of topological defects on the low-energy shapes of single-component two-dimensional elastic membranes with spherical topology. The membrane is described as a closed, triangulated two-dimensional manifold embedded in three-dimensional space using a dynamic triangulation model, thus allowing the creation of topological defects. Low-energy structures and connectivities are explored using a Monte Carlo simulated annealing method while also constraining the internal volume of the membrane to simulate incompressible contents within the membrane, such as in colloidosomes and viruses. We find that since the volume constraint partially suppresses the buckling transition such that the buckled icosahedral shape has a reduced asphericity, defect scars are favorable over a larger range of elastic parameters of the membrane compared with systems having no constraint on volume.

We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural description of the T1 transition events responsible for local tissue rearrangements. The AVM also includes cell alignment, cell-specific mechanical properties, cell growth, division and apoptosis. In addition, the AVM introduces a flexible, dynamically changing boundary of the epithelial sheet allowing for studies of phenomena such as the fingering instability or wound healing. We illustrate these capabilities with a number of case studies., Comment: 33 pages, 14 figure

Coassembled molecular structures are known to exhibit a large variety of geometries and morphologies. A grand challenge of self-assembly design is to find techniques to control the crystal symmetries and overall morphologies of multicomponent systems. By mixing +3 and -1 ionic amphiphiles, we assemble crystalline ionic bilayers in a large variety of geometries that resemble polyhedral cellular crystalline shells and archaea wall envelopes. We combine TEM with SAXS and WAXS to characterize the coassembled structures from the mesoscopic to nanometer scale. The degree of ionization of the amphiphiles and their intermolecular electrostatic interactions are controlled by varying pH. At low and high pH values, we observe closed, faceted vesicles with two-dimensional hexagonal molecular arrangements, and at intermediate pH, we observe ribbons with rectangular-C packing. Furthermore, as pH increases, we observe interdigitation of the bilayer leaflets. Accurate atomistic molecular dynamics simulations explain the pH-dependent bilayer thickness changes and also reveal bilayers of hexagonally packed tails at low pH, where only a small fraction of anionic headgroups is charged. Coarse-grained simulations show that the mesoscale geometries at low pH are faceted vesicles where liquid-like edges separate flat crystalline domains. Our simulations indicate that the curved-to-polyhedral shape transition can be controlled by tuning the tail density in regions where sharp bends can form the polyhedral edges. In particular, the pH acts to control the overall morphology of the ionic bilayers by changing the local crystalline order of the amphiphile tails.

We use molecular dynamics simulations to study the crystallization of spherical nucleic-acid (SNA) gold nanoparticle conjugates, guided by sequence-specific DNA hybridization events. Binary mixtures of SNA gold nanoparticle conjugates (inorganic core diameter in the 8-15 nm range) are shown to assemble into BCC, CsCl, AlB(2), and Cr(3)Si crystalline structures, depending upon particle stoichiometry, number of immobilized strands of DNA per particle, DNA sequence length, and hydrodynamic size ratio of the conjugates involved in crystallization. These data have been used to construct phase diagrams that are in excellent agreement with experimental data from wet-laboratory studies.

We explore the effects of line tension on the shape of two component elastic shells. Segregation between components with different elastic properties combined with the subtleties related to the spherical topology leads to a rich variety of shapes. They range from irregular polyhedra at weak segregation to Janus-like morphologies with spherical and buckled regions coexisting on the same shell for large values of the line tension. We use Monte Carlo simulations to map a detailed phase diagram as a function of the relative fraction of the two components, the ratio of their bending rigidities, and the strength of the line tension.

Using coarse-grained molecular dynamics simulations, we investigate the surface patterns of charged end-group ligands attached to faceted nanoparticles. A competition between electrostatic repulsio...

This paper describes the use of 1H NMR spectroscopy to measure the equilibrium constants for the solution-phase binding of two para-substituted aniline molecules (R-An), p-methoxyaniline (MeO-An) and p-bromoaniline (Br-An), to colloidal 4.1 nm CdSe quantum dots (QDs). Changes in the chemical shifts of the aromatic protons located ortho to the amine group on R-An were used to construct a binding isotherm for each R-An/QD system. These isotherms fit to a Langmuir function to yield Ka, the equilibrium constant for binding of the R-An ligands to the QDs; Ka ≈ 150 M−1 and ΔGads ≈ −19 kJ/mol for both R = MeO and R = Br. 31P NMR indicates that the native octylphosphonate ligands, which, by inductively coupled plasma atomic emission spectroscopy, cover 90% of the QD surface, are not displaced upon binding of R-An. The MeO-An ligand quenches the photoluminescence of the QDs at much lower concentrations than does Br-An; the observation, therefore, that Ka,MeO-An ≈ Ka,Br-An shows that this difference in quenching ef...

We report a GPU implementation in HOOMD Blue of long-range electrostatic interactions based on the orientation-averaged Ewald sum scheme, introduced by Yakub and Ronchi (J. Chem. Phys. 2003, 119, 11556). The performance of the method is compared to an optimized CPU version of the traditional Ewald sum available in LAMMPS, in the molecular dynamics of electrolytes. Our GPU implementation is significantly faster than the CPU implementation of the Ewald method for small to a sizable number of particles (∼10(5)). Thermodynamic and structural properties of monovalent and divalent hydrated salts in the bulk are calculated for a wide range of ionic concentrations. An excellent agreement between the two methods was found at the level of electrostatic energy, heat capacity, radial distribution functions, and integrated charge of the electrolytes.

Thermally fluctuating sheets and ribbons provide an intriguing forum in which to investigate strong violations of Hooke's Law: Large distance elastic parameters are in fact not constant but instead depend on the macroscopic dimensions. Inspired by recent experiments on free-standing graphene cantilevers, we combine the statistical mechanics of thin elastic plates and large-scale numerical simulations to investigate the thermal renormalization of the bending rigidity of graphene ribbons clamped at one end. For ribbons of dimensions $W\ifmmode\times\else\texttimes\fi{}L$ (with $L\ensuremath{\ge}W$), the macroscopic bending rigidity ${\ensuremath{\kappa}}_{R}$ determined from cantilever deformations is independent of the width when $Wl{\ensuremath{\ell}}_{\mathrm{th}}$, where ${\ensuremath{\ell}}_{\mathrm{th}}$ is a thermal length scale, as expected. When $Wg{\ensuremath{\ell}}_{\mathrm{th}}$, however, this thermally renormalized bending rigidity begins to systematically increase, in agreement with the scaling theory, although in our simulations we were not quite able to reach the system sizes necessary to determine the fully developed power law dependence on $W$. When the ribbon length $Lg{\ensuremath{\ell}}_{p}$, where ${\ensuremath{\ell}}_{p}$ is the $W$-dependent thermally renormalized ribbon persistence length, we observe a scaling collapse and the beginnings of large scale random walk behavior.

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 version

Two-dimensional crystalline membranes have recently been realized experimentally in such systems as graphene and molybdenum disulfide, sparking a resurgence in interest in their statistical properties. Thermal fluctuations can significantly affect the effective mechanical properties of properly thermalized membranes, renormalizing both bending rigidity and elastic moduli so that in particular they become stiffer to bending than their bare bending rigidity would suggest. We use molecular dynamics simulations to examine how the mechanical behavior of thermalized two-dimensional clamped ribbons (cantilevers) depends on their precise topology and geometry. We find that a simple slit smooths roughness as measured by the variance of height fluctuations. This counterintuitive effect may be due to the counter-posed coupling of the lips of the slit to twist in the intact regions of the ribbon., 7 pages

We investigate the effects of rare regions on the dynamics of Ising magnets with planar defects, i.e., disorder perfectly correlated in two dimensions. In these systems, the magnetic phase transition is smeared because static long-range order can develop on isolated rare regions. We first study an infinite-range model by numerically solving local dynamic mean-field equations. Then we use extremal statistics and scaling arguments to discuss the dynamics beyond mean-field theory. In the tail region of the smeared transition the dynamics is even slower than in a conventional Griffiths phase: the spin autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small equilibrium value following a power law at late times., 10 pages, 8eps figures included, final version as published

We consider the influence of quenched spatial disorder on phase transitions in classical and quantum systems. We show that rare strong disorder fluctuations can have dramatic effects on critical points. In classical systems with sufficiently correlated disorder or in quantum systems with overdamped dynamics they can completely destroy the sharp phase transition by smearing. This is caused by effects similar to but stronger than Griffiths phenomena: True static order can develop on a rare region while the bulk system is still in the disordered phase. We discuss the thermodynamic behavior in the vicinity of such a smeared transition using optimal fluctuation theory, and we present numerical results for a two-dimensional model system., Comment: 10 pages, 5 eps figures, contribution to the Festschrift for Michael Schreiber's 50th birthday, final version as published

Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behavior of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable with any set of local deformations. In active nematic liquid crystals topological defects not only dictate the global structure of the director, but also act as local sources of motion, behaving as self-propelled particles. In this article we present a detailed analytical and numerical study of the mechanics of topological defects in active nematic liquid crystals., 16 pages, 10 figures

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 nonvanishing net disclination charge). We perform both Monte Carlo and conjugate gradient simulations to compare how shells with and without scars deform quasistatically 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.

Here we show that coupling to curvature has profound effects on collective motion in active systems, leading to patterns not observed in flat space. Biological examples of such active motion in curved environments are numerous: curvature and tissue folding are crucial during gastrulation, epithelial and endothelial cells move on constantly growing, curved crypts and vili in the gut, and the mammalian corneal epithelium grows in a steady-state vortex pattern. On the physics side, droplets coated with actively driven microtubule bundles show active nematic patterns. We study a model of self-propelled particles with polar alignment on a sphere. Hallmarks of these motion patterns are a polar vortex and a circulating band arising due to the incompatibility between spherical topology and uniform motion - a consequence of the hairy ball theorem. We present analytical results showing that frustration due to curvature leads to stable elastic distortions storing energy in the band., 5 pages, 4 figures plus Supporting Information

We have studied the effect of various kinds of damaging that may occur in a neural network whose synaptic bonds have been trained (before damaging) so as to preserve a definite number of patterns. We have used the Hopfield model of the neural network, and applied the Hebbian rule of training (learning). We have studied networks with 600 elements (neurons) and investigated several types of damaging, by performing very extensive numerical investigation. Thus, we have demonstrated that there is no difference between symmetric and asymmetric damaging of bonds. Besides, it turns out that the worst damaging of synaptic bonds is the one that starts with ruining the strongest bonds, whereas in the opposite case, that is, in the case of damaging that starts with ruining the weakest bonds, the learnt patterns remain preserved even for a large percentage of extinguished bonds.

The selectivity of DNA recognition inspires an elegant protocol for designing versatile nanoparticle (NP) assemblies. We use molecular dynamics simulations to analyze dynamic aspects of the assembly process and identify ingredients that are key to a successful assembly of NP superlattices through DNA hybridization. A scale-accurate coarse-grained model faithfully captures the relevant contributions to the kinetics of the DNA hybridization process and is able to recover all experimentally reported to date binary superlattices (BCC, CsCl, AlB2, Cr3Si, and Cs6C60). We study the assembly mechanism in systems with up to 10(6) degrees of freedom and find that the crystallization process is accompanied with a slight decrease of enthalpy. Furthermore, we find that the optimal range of the DNA linker interaction strengths for a successful assembly is 12-16kBT, and the optimal mean lifetime of a DNA hybridization event is 10(-4)-10(-3) of the total time it takes to form a crystal. We also obtain the optimal percentage of hybridized DNA pairs for different binary systems. On the basis of these results, we propose suitable linker sequences for future nanomaterials design.

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.

We study the shapes of pored membranes within the framework of the Helfrich theory under the constraints of fixed area and pore size. We show that the mean curvature term leads to a budding- like structure, while the Gaussian curvature term tends to flatten the membrane near the pore; this is corroborated by simulation. We propose a scheme to deduce the ratio of the Gaussian rigidity to the bending rigidity simply by observing the shape of the pored membrane. This ratio is usually difficult to measure experimentally. In addition, we briefly discuss the stability of a pore by relaxing the constraint of a fixed pore size and adding the line tension. Finally, the flattening effect due to the Gaussian curvature as found in studying pored membranes is extended to two-component membranes. We find that sufficiently high contrast between the components' Gaussian rigidities leads to budding which is distinct from that due to the line tension., Comment: 8 pages, 9 figures

We study closed liquid membranes that segregate into three phases due to differences in the chemical and physical properties of its components. The shape and in-plane membrane arrangement of the phases are coupled through phase-specific bending energies and line tensions. We use simulated annealing Monte Carlo simulations to find low-energy structures, allowing both phase arrangement and membrane shape to relax. The three-phase system is the simplest one in which there are multiple interface pairs, allowing us to analyze interfacial preferences and pairwise distinct line tensions. We observe the system's preference for interface pairs that maximize differences in spontaneous curvature. From a pattern selection perspective, this acts as an effective attraction between phases of most disparate spontaneous curvature. We show that this effective attraction is robust enough to persist even when the interface between these phases is the most penalized by line tension. This effect is driven by geometry and not by any explicit component-component interaction., 6 pages, 6 figures, submitted to Phys. Rev. E, revised version includes improvements of the simulation method and additional references

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 figures

We demonstrate that small charged nanocages can undergo reversible changes of shapes by modifying the ionic conditions including salt concentration, $p\mathrm{H}$, and dielectric permittivity of the medium. Using numerical simulations, we analyze structures with various charge stoichiometric ratios. At zero or low charge densities, the shape of the cage is determined by its elastic properties, and the surface charge pattern is dictated by the globally fixed geometry. As the charge density per molecule increases, the shape is strongly affected by the electrostatic forces. In this regime, the shape of the nanocage is controlled by the charge distribution.

Large crystalline molecular shells, such as some viruses and fullerenes, buckle spontaneously into icosahedra. Meanwhile multicomponent microscopic shells buckle into various polyhedra, as observed in many organelles. Although elastic theory explains one-component icosahedral faceting, the possibility of buckling into other polyhedra has not been explored. We show here that irregular and regular polyhedra, including some Archimedean and Platonic polyhedra, arise spontaneously in elastic shells formed by more than one component. By formulating a generalized elastic model for inhomogeneous shells, we demonstrate that coassembled shells with two elastic components buckle into polyhedra such as dodecahedra, octahedra, tetrahedra, and hosohedra shells via a mechanism that explains many observations, predicts a new family of polyhedral shells, and provides the principles for designing microcontainers with specific shapes and symmetries for numerous applications in materials and life sciences.

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.

Polymer nanocomposites, materials combining polymers and inorganic components such as nanosized crystallites or nanoparticles have attracted significant attention in recent years. A successful strategy for designing polymer nanocomposites is polymer functionalization via attaching functional groups with specific affinity for the inorganic component. In this paper, a systematic investigation by molecular dynamics of polymer functionalization for design of composites combining nanosize crystallites with multiblock polymers in solution is presented. It is shown that functionalization is an example of active self-assembly, where the resulting polymer nanocomposite exhibits a different type of order than the original pure polymer system (without inorganic components). Optimal polymer architectures and concentrations are identified appropriate for different applications, alongside an in-depth analysis on the origin and stability of the resulting phases as well as its experimental implications.

We demonstrate that strong inter-orbital interaction is very efficient to achieve superconductivity due to magnetic fluctuations in the iron pnictides. Fermi surface states that are coupled by the antiferromagnetic wave vector are often of different orbital nature, causing pair-hopping interactions between distinct Fe-3d orbitals to become important. Performing a self-consistent FLEX calculation below $T_{c}$ we determine the superconducting order parameter as function of intra- and inter-orbital couplings. We find an $s^{\pm}$-pairing state with $T_{c}\simeq80\mathrm{K}$ for realistic parameters., 4 pages, 4 figures, revised version accepted for publication as a Rapid Communication in Physical Review B

We consider nanoparticles and functionalized copolymers, block copolymers with attached end groups possessing a specific affinity for nanoparticles, in solution. Using molecular dynamics, we show that nanoparticles are able to direct the self-assembly of the polymer/nanoparticle composite. We perform a detailed study for a wide range of nanoparticle sizes and concentrations. We show that the nanoparticles order in a number of distinct phases: simple cubic, layered hexagonal, hexagonal columnar, gyroid, and a novel square columnar. Our results show that nanoparticles ordered with functionalized block copolymers can provide a simple and efficient tool for assembling novel materials with nanometer scale resolution.

We determine the anisotropy of the spin-fluctuation-induced pairing gap on the Fermi surface of the FeAs-based superconductors as function of the exchange and Hund's coupling ${J}_{H}$. We find that for sufficiently large ${J}_{H}$, nearly commensurate magnetic fluctuations yield a fully gapped ${s}^{\ifmmode\pm\else\textpm\fi{}}$-pairing state with small anisotropy of the gap amplitude on each Fermi-surface sheet, but significant variations of the gap amplitude for different sheets of the Fermi surface. In particular, we obtain the large variation of the gap amplitude on different Fermi-surface sheets, as seen in angular resolved photoemission spectroscopy experiments. For smaller values of Hund's coupling incommensurate magnetic fluctuations yield an ${s}^{\ifmmode\pm\else\textpm\fi{}}$-pairing state with line nodes. Such a state is also possible once the anisotropy of the material is reduced and three-dimensional effects come into play.

We explain in a consistent manner the set of seemingly conflicting experiments on the finite temperature Mott critical point, and demonstrate that the Mott transition is in the Ising universality class. We show that, even though the thermodynamic behavior of the system near such critical point is described by an Ising order parameter, the global conductivity can depend on other singular observables and, in particular, on the energy density. Finally, we show that in the presence of weak disorder the dimensionality of the system has crucial effects on the size of the critical region that is probed experimentally., Comment: 4 pages, 3 figures

The ground state properties and neutron structure factor for the two-dimensional antiferromagnet on the triangular lattice, with uni-directional anisotropy in the nearest-neighbor exchange couplings and a weak Dzyaloshinskii-Moriya (DM) interaction, are studied. This Hamiltonian has been used to interpret neutron scattering measurements on the spin 1/2 spiral spin-density-wave system, Cs_2CuCl_4, [R. Coldea, et al., Phys. Rev. B 68, 134424 (2003)]. Calculations are performed using a 1/S expansion, taking into account interactions between spin-waves. The ground state energy, the shift of the ordering wave-vector, Q, and the local magnetization are all calculated to order 1/S^2. The neutron structure factor, obtained using anharmonic spin-wave Green's functions to order 1/S, is shown to be in reasonable agreement with published neutron data, provided that slightly different parameters are used for the exchange and DM interactions than those inferred from measurements in high magnetic field., Comment: 14 pages, 6 eps figures, submitted to Phys. Rev. B

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 published