1,255 research outputs found

### 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

### 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

### Simultaneous Implicit Surface Reconstruction and Meshing

We investigate an implicit method to compute a piecewise linear representation of a surface from a set of sample points. As implicit surface functions we use the weighted sum of piecewise linear kernel functions. For such a function we can partition Rd in such a way that these functions are linear on the subsets of the partition. For each subset in the partition we can then compute the zero level set of the function exactly as the intersection of a hyperplane with the subset

### 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

### 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

### Bounds on the k-neighborhood for locally uniform sampled surfaces

Given a locally uniform sample set P of a smooth surface S. We derive upper and lower bounds on the number k of nearest neighbors of a sample point p that have to be chosen from P such that this neighborhood contains all restricted Delaunay neighbors of p. In contrast to the trivial lower bound, the upper bound indicates that a sampling condition that is used in many computational geometry proofs is quite reasonable from a practical point of view

### Bounds on the k-neighborhood for locally uniform sampled surfaces

Given a locally uniform sample set P of a smooth surface S. We derive upper and lower bounds on the number k of nearest neighbors of a sample point p that have to be chosen from P such that this neighborhood contains all restricted Delaunay neighbors of p. In contrast to the trivial lower bound, the upper bound indicates that a sampling condition that is used in many computational geometry proofs is quite reasonable from a practical point of view

### 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

### 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

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