Related papers: Minimal resonances in annular non-Euclidean strips
Elastic strips provide a canonical system for studying the mechanisms governing elastic shape transitions. Buckling, linear snap-through, and nonlinear snap-through have been observed in boundary-actuated strips and linked to the type of…
We examine analytically equilibrium conformations of elastic chains of paramagnetic beads in the presence of a precessing magnetic field. Conformations of these filaments are determined by minimizing their total energy, given in the…
The spin dynamics of bilayer cuprate compounds are studied in a basic model. The magnetic spectral properties are calculated in linear spin-wave theory for several stripe configurations which differ by the relative location of the stripes…
Engineered bacteria in which motility is reduced by local cell density generate periodic stripes of high and low density when spotted on agar plates. We study theoretically the origin and mechanism of this process in a kinetic model that…
Periodic assemblies of nanoparticles are central to surface patterning, with applications in biosensing, energy conversion, and nanofabrication. Evaporation of colloidal droplets on substrates provides a simple yet effective route to…
Competing inhomogeneous orders are a central feature of correlated electron materials including the high-temperature superconductors. The two- dimensional Hubbard model serves as the canonical microscopic physical model for such systems.…
We study the effect of dipolar interactions on a magnetic striped monolayer with a microscopic unit cell of square symmetry, and of size $(N_x\times N_y)$ spins. Even if the aspect ratio $r=N_x/N_y$ is very large, an in-plane shape…
We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models…
We use minimal area metrics to generate all nonorientable string diagrams. The surfaces in unoriented string theory have nontrivial open curves and nontrivial closed curves whose neighborhoods are either annuli or Mobius strips. We define a…
We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…
It is well known that an elastic sheet loaded in tension will wrinkle and that the length scale of the wrinkles tends to zero with vanishing thickness of the sheet [Cerda and Mahadevan, Phys. Rev. Lett. 90, 074302 (2003)]. We give the first…
We investigate the response of two-dimensional pattern forming systems with a broken up-down symmetry, such as chemical reactions, to spatially resonant forcing and propose related experiments. The nonlinear behavior immediately above…
Thin sheets respond to confinement by smoothly wrinkling, or by focusing stress into small, sharp regions. From engineering to biology, geology, textiles, and art, thin sheets are packed and confined in a wide variety of ways, and yet…
A dielectric elastomer whose edges are held fixed will buckle, given sufficient applied voltage, resulting in a nontrivial out-of-plane deformation. We study this situation numerically using a nonlinear elastic model which decouples two of…
A thin circular elastic sheet floating on a drop-like liquid substrate is deformed due to incompatibility between the curved substrate and the planar sheet. We adopt a variational viewpoint by minimizing the non-convex membrane energy…
The shear-induced self-organization of active rotors into stripy aggregates is studied by carrying out computational simulations. The rotors, modeled by monolayers of frictional spheres, develop to stripy microstructures only when they…
For monodomain nematic elastomers, we construct generalised elastic-nematic constitutive models combining purely elastic and neoclassical-type strain-energy densities. Inspired by recent developments in stochastic elasticity, we extend…
A general expression for the strain energy of a homogeneous, isotropic, plane extensible elastica with an arbitrary undeformed configuration is derived. This energy constitutes the correct expression for one-dimensional models of polymers…
Ever since the discovery of graphene and subsequent explosion of interest in single atom thick materials, studying their mechanical properties has been an active area of research. New length scales often necessitate a rethinking of physical…
We investigate the behavior of non-Euclidean plates with constant negative Gaussian curvature using the F\"oppl-von K\'arm\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic…