Existence of Ricci flows of incomplete surfaces

We prove a general existence result for instantaneously complete Ricci flows starting at an arbitrary Riemannian surface which may be incomplete and may have unbounded curvature. We give an explicit formula for the maximal existence time, and describe the asymptotic behaviour in most cases.Comment: 20 pages; updated to reflect galley proof correction

Using a spatio-temporal dynamic state-space model with the EM algorithm to patch gaps in daily riverflow series, with examples from the Volta Basin, West Africa

International audienceA spatio-temporal linear dynamic model has been developed for patching short gaps in daily river runoff series. The model was cast in a state-space form in which the state variable was estimated using the Kalman smoother (RTS smoother). The EM algorithm was used to concurrently estimate both parameter and missing runoff values. Application of the model to daily runoff series in the Volta Basin of West Africa showed that the model was capable of providing good estimates of missing runoff values at a gauging station from the remaining series at the station and at spatially correlated stations in the same sub-basin

Ricci flows with unbounded curvature

We show that any noncompact Riemann surface admits a complete Ricci flow g(t), t\in[0,\infty), which has unbounded curvature for all t\in[0,\infty).Comment: 12 pages, 1 figure; updated reference

Correlations in nano-scale step fluctuations: comparison of simulation and experiments

We analyze correlations in step-edge fluctuations using the Bortz-Kalos-Lebowitz kinetic Monte Carlo algorithm, with a 2-parameter expression for energy barriers, and compare with our VT-STM line-scan experiments on spiral steps on Pb(111). The scaling of the correlation times gives a dynamic exponent confirming the expected step-edge-diffusion rate-limiting kinetics both in the MC and in the experiments. We both calculate and measure the temperature dependence of (mass) transport properties via the characteristic hopping times and deduce therefrom the notoriously-elusive effective energy barrier for the edge fluctuations. With a careful analysis we point out the necessity of a more complex model to mimic the kinetics of a Pb(111) surface for certain parameter ranges.Comment: 10 pages, 9 figures, submitted to Physical Review

Tube Width Fluctuations in F-Actin Solutions

We determine the statistics of the local tube width in F-actin solutions, beyond the usually reported mean value. Our experimental observations are explained by a segment fluid theory based on the binary collision approximation (BCA). In this systematic generalization of the standard mean-field approach effective polymer segments interact via a potential representing the topological constraints. The analytically predicted universal tube width distribution with a stretched tail is in good agreement with the data.Comment: Final version, 5 pages, 4 figure

Delaunay Hodge Star

We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay meshes for Discrete Exterior Calculus (DEC) because the discrete Hodge star operator can now be correctly defined for such meshes. This operator is crucial for DEC and is a diagonal matrix with the ratio of primal and dual volumes along the diagonal. A correct definition requires that all entries be positive. DEC is a framework for numerically solving differential equations on meshes and for geometry processing tasks and has had considerable impact in computer graphics and scientific computing. Our result allows the use of DEC with a much larger class of meshes than was previously considered possible.Comment: Corrected error in Figure 1 (columns 3 and 4) and Figure 6 and a formula error in Section 2. All mathematical statements (theorems and lemmas) are unchanged. The previous arXiv version v3 (minus the Appendix) appeared in the journal Computer-Aided Desig

Low-Temperature Orientation Dependence of Step Stiffness on {111} Surfaces

For hexagonal nets, descriptive of {111} fcc surfaces, we derive from combinatoric arguments a simple, low-temperature formula for the orientation dependence of the surface step line tension and stiffness, as well as the leading correction, based on the Ising model with nearest-neighbor (NN) interactions. Our formula agrees well with experimental data for both Ag and Cu{111} surfaces, indicating that NN-interactions alone can account for the data in these cases (in contrast to results for Cu{001}). Experimentally significant corollaries of the low-temperature derivation show that the step line tension cannot be extracted from the stiffness and that with plausible assumptions the low-temperature stiffness should have 6-fold symmetry, in contrast to the 3-fold symmetry of the crystal shape. We examine Zia's exact implicit solution in detail, using numerical methods for general orientations and deriving many analytic results including explicit solutions in the two high-symmetry directions. From these exact results we rederive our simple result and explore subtle behavior near close-packed directions. To account for the 3-fold symmetry in a lattice gas model, we invoke a novel orientation-dependent trio interaction and examine its consequences.Comment: 11 pages, 8 figure

Using the Wigner-Ibach Surmise to Analyze Terrace-Width Distributions: History, User's Guide, and Advances

A history is given of the applications of the simple expression generalized from the surmise by Wigner and also by Ibach to extract the strength of the interaction between steps on a vicinal surface, via the terrace width distribution (TWD). A concise guide for use with experiments and a summary of some recent extensions are provided.Comment: 11 pages, 4 figures, reformatted (with revtex) version of refereed paper for special issue of Applied Physics A entitled "From Surface Science to Device Physics", in honor of the retirements of Prof. H. Ibach and Prof. H. L\"ut

E-Type Delayed Fluorescence of a Phosphine-Supported Cu_2(μ-NAr_2)_2 Diamond Core: Harvesting Singlet and Triplet Excitons in OLEDs

A highly emissive bis(phosphine)diarylamido dinuclear copper(I) complex (quantum yield = 57%) was shown to exhibit E-type delayed fluorescence by variable temperature emission spectroscopy and photoluminescence decay measurement of doped vapor-deposited films. The lowest energy singlet and triplet excited states were assigned as charge transfer states on the basis of theoretical calculations and the small observed S_1−T_1 energy gap. Vapor-deposited OLEDs doped with the complex in the emissive layer gave a maximum external quantum efficiency of 16.1%, demonstrating that triplet excitons can be harvested very efficiently through the delayed fluorescence channel. The function of the emissive dopant in OLEDs was further probed by several physical methods, including electrically detected EPR, cyclic voltammetry, and photoluminescence in the presence of applied current

Tailoring the magnetic properties of Fe asymmetric nanodots

Asymmetric dots as a function of their geometry have been investigated using three-dimensional (3D) object oriented micromagnetic framework (OOMMF) code. The effect of shape asymmetry of the disk on coercivity and remanence is studied. Angular dependence of the remanence and coercivity is also addressed. Asymmetric dots are found to reverse their magnetization by nucleation and propagation of a vortex, when the field is applied parallel to the direction of asymmetry. However, complex reversal modes appear when the angle at which the external field is applied is varied, leading to a non monotonic behavior of the coercivity and remanence.Comment: 5 pages, 7 figure