6,095 research outputs found
Bootstrap Multigrid for the Laplace-Beltrami Eigenvalue Problem
This paper introduces bootstrap two-grid and multigrid finite element
approximations to the Laplace-Beltrami (surface Laplacian) eigen-problem on a
closed surface. The proposed multigrid method is suitable for recovering
eigenvalues having large multiplicity, computing interior eigenvalues, and
approximating the shifted indefinite eigen-problem. Convergence analysis is
carried out for a simplified two-grid algorithm and numerical experiments are
presented to illustrate the basic components and ideas behind the overall
bootstrap multigrid approach
Achieving the Theoretical Depairing Current Limit in Superconducting Nanomesh Films
We show the theoretical depairing current limit can be achieved in a robust fashion in highly ordered superconductor nanomesh films having spatial periodicities smaller than both the superconducting coherence length and the magnetic penetration depth. For a niobium nanomesh film with 34 nm spatial periodicity, the experimental critical current density is enhanced by more than 17 times over the continuous film and is in good agreement with the depairing limit over the entire measured temperature range. The nanomesh superconductors are also less susceptible to thermal fluctuations when compared to nanowire superconductors. T_c values similar to the bulk film are achieved, and the nanomeshes are capable of retaining superconductivity to higher fields relative to the bulk. In addition, periodic oscillations in T_c are observed as a function of field, reflecting the highly ordered nanomesh structure
Scanning Tunneling Microscopy Characterization of the Electrical Properties of Wrinkles in Exfoliated Graphene Monolayers
We report on the scanning tunneling microscopy study of a new class of corrugations in exfoliated monolayer graphene sheets, that is, wrinkles ~10 nm in width and ~3 nm in height. We found such corrugations to be ubiquitous in graphene and have distinctly different properties when compared to other regions of graphene. In particular, a “three-for-six” triangular pattern of atoms is exclusively and consistently observed on wrinkles, suggesting the local curvature of the wrinkle provides a sufficient perturbation to break the 6-fold symmetry of the graphene lattice. Through scanning tunneling spectroscopy, we further demonstrate that the wrinkles have lower electrical conductance and are characterized by the presence of midgap states, which is in agreement with recent theoretical predictions. The observed wrinkles are likely important for understanding the electrical properties of graphene
Computing Perelman's nu-functional
This is a short note in which we show how to calculate the value of
Perelman's nu-functional for a variety of metrics. In particular we complete
the calculation of values for the known 4-dimensional Einstein and shrinking
Ricci soliton metrics.Comment: 9 pages, v2 has new title and slight change of styl
The Microscopic Structure of Adsorbed Water on Hydrophobic Surfaces under Ambient Conditions
The interaction of water vapor with hydrophobic surfaces is poorly understood. We utilize graphene templating to preserve and visualize the microscopic structures of adsorbed water on hydrophobic surfaces. Three well-defined surfaces [H–Si(111), graphite, and functionalized mica] were investigated, and water was found to adsorb as nanodroplets (~10–100 nm in size) on all three surfaces under ambient conditions. The adsorbed nanodroplets were closely associated with atomic-scale surface defects and step-edges and wetted all the hydrophobic substrates with contact angles < ~10°, resulting in total water adsorption that was similar to what is found for hydrophilic surfaces. These results point to the significant differences between surface processes at the atomic/nanometer scales and in the macroscopic world
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