Topological modes bound to dislocations in mechanical metamaterials

Mechanical metamaterials are artificial structures with unusual properties, such as negative Poisson ratio, bistability or tunable vibrational properties, that originate in the geometry of their unit cell. At the heart of such unusual behaviour is often a soft mode: a motion that does not significantly stretch or compress the links between constituent elements. When activated by motors or external fields, soft modes become the building blocks of robots and smart materials. Here, we demonstrate the existence of topological soft modes that can be positioned at desired locations in a metamaterial while being robust against a wide range of structural deformations or changes in material parameters. These protected modes, localized at dislocations, are the mechanical analogue of topological states bound to defects in electronic systems. We create physical realizations of the topological modes in prototypes of kagome lattices built out of rigid triangular plates. We show mathematically that they originate from the interplay between two Berry phases: the Burgers vector of the dislocation and the topological polarization of the lattice. Our work paves the way towards engineering topologically protected nano-mechanical structures for molecular robotics or information storage and read-out.Comment: 13 pages, 6 figures; changes to text and figures and added analysis on mode localization; see http://www.lorentz.leidenuniv.nl/~paulose/dislocation-modes/ for accompanying video

Anomalous coupling between topological defects and curvature

We investigate a counterintuitive geometric interaction between defects and curvature in thin layers of superfluids, superconductors and liquid crystals deposited on curved surfaces. Each defect feels a geometric potential whose functional form is determined only by the shape of the surface, but whose sign and strength depend on the transformation properties of the order parameter. For superfluids and superconductors, the strength of this interaction is proportional to the square of the charge and causes all defects to be repelled (attracted) by regions of positive (negative) Gaussian curvature. For liquid crystals in the one elastic constant approximation, charges between 0 and $4\pi$ are attracted by regions of positive curvature while all other charges are repelled.Comment: 5 pages, 4 figures, minor changes, accepted for publication in Phys. Rev. Let

General rules for bosonic bunching in multimode interferometers

We perform a comprehensive set of experiments that characterize bosonic bunching of up to 3 photons in interferometers of up to 16 modes. Our experiments verify two rules that govern bosonic bunching. The first rule, obtained recently in [1,2], predicts the average behavior of the bunching probability and is known as the bosonic birthday paradox. The second rule is new, and establishes a n!-factor quantum enhancement for the probability that all n bosons bunch in a single output mode, with respect to the case of distinguishable bosons. Besides its fundamental importance in phenomena such as Bose-Einstein condensation, bosonic bunching can be exploited in applications such as linear optical quantum computing and quantum-enhanced metrology.Comment: 6 pages, 4 figures, and supplementary material (4 pages, 1 figure

Heat transport in model jammed solids

We calculate numerically the normal modes of vibrations in 3D jammed packings of soft spheres as a function of the packing fraction and obtain the energy diffusivity, a spectral measure of transport that controls sound propagation and thermal conductivity. The crossover frequency between weak and strong phonon scattering is controlled by the coordination and shifts to zero as the system is decompressed towards the critical packing fraction at which rigidity is lost. Below the crossover, the diffusivity displays a power-law divergence with inverse frequency, which suggests that the vibrational modes are primarily transverse waves, weakly scattered by disorder. Above it, a large number of modes appear whose diffusivity plateaus at a nearly constant value independent of the inter-particle potential, before dropping to zero above the Anderson localization frequency. The thermal conductivity of a marginally jammed solid just above the rigidity threshold is calculated and related to the one measured experimentally at room temperature for most glasses.Comment: 15 pages, 7 figure

Analysis of Nematic Liquid Crystals with Disclination Lines

We investigate the structure of nematic liquid crystal thin films described by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the elasticity constant goes to zero a limiting uniaxial texture forms with disclination lines corresponding to a finite number of defects, all of degree 1/2 or all of degree -1/2. We also state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.Comment: 40 pages, 1 figur

Density of states in random lattices with translational invariance

We propose a random matrix approach to describe vibrational excitations in disordered systems. The dynamical matrix M is taken in the form M=AA^T where A is some real (not generally symmetric) random matrix. It guaranties that M is a positive definite matrix which is necessary for mechanical stability of the system. We built matrix A on a simple cubic lattice with translational invariance and interaction between nearest neighbors. We found that for certain type of disorder phonons cannot propagate through the lattice and the density of states g(w) is a constant at small w. The reason is a breakdown of affine assumptions and inapplicability of the elasticity theory. Young modulus goes to zero in the thermodynamic limit. It strongly reminds of the properties of a granular matter at the jamming transition point. Most of the vibrations are delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil. Mag. B v.79, 1715 (1999).Comment: 4 pages, 5 figure

Chemical control of harungana (Harungana madagascariensis) shrubs in Queensland

Harungana (Harungana madagascarien�sis Lam. ex Poir), an aggressive exotic pioneering tree species, is currently invading the Wet Tropics World Heritage areas of north Queensland. A chemical trial involving ten herbicides was undertaken to identify effective chemicals to control harungana. For each herbicide, high volume foliar applications of two concentrations were applied. Of the ten herbicides tested, metsulfuron methyl, dicamba, imazapyr and glyphosate produced 100% mortality, at the rates applied, and the higher rate of fluroxypyr and 2,4-D/picloram killed greater than 95% of the treated plants. Metsulfuron and dicamba were the most target specific, while imazapyr, fluroxypyr, 2,4-D/ picloram and glyphosate had greater impact on non-target, native flora