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

General practice cooperatives: long waiting times for home visits due to long distances?

BACKGROUND: The introduction of large-scale out-of-hours GP cooperatives has led to questions about increased distances between the GP cooperatives and the homes of patients and the increasing waiting times for home visits in urgent cases. We studied the relationship between the patient's waiting time for a home visit and the distance to the GP cooperative. Further, we investigated if other factors (traffic intensity, home visit intensity, time of day, and degree of urgency) influenced waiting times. METHODS: Cross-sectional study at four GP cooperatives. We used variance analysis to calculate waiting times for various categories of traffic intensity, home visit intensity, time of day, and degree of urgency. We used multiple logistic regression analysis to calculate to what degree these factors affected the ability to meet targets in urgent cases. RESULTS: The average waiting time for 5827 consultations was 30.5 min. Traffic intensity, home visit intensity, time of day and urgency of the complaint all seemed to affect waiting times significantly. A total of 88.7% of all patients were seen within 1 hour. In the case of life-threatening complaints (U1), 68.8% of the patients were seen within 15 min, and 95.6% of those with acute complaints (U2) were seen within 1 hour. For patients with life-threatening complaints (U1) the percentage of visits that met the time target of 15 minuts decreased from 86.5% (less than 2.5 km) to 16.7% (equals or more than 20 km). DISCUSSION AND CONCLUSION: Although home visits waiting times increase with increasing distance from the GP cooperative, it appears that traffic intensity, home visit intensity, and urgency also influence waiting times. For patients with life-threatening complaints waiting times increase sharply with the distance

Morphology of ledge patterns during step flow growth of metal surfaces vicinal to fcc(001)

The morphological development of step edge patterns in the presence of meandering instability during step flow growth is studied by simulations and numerical integration of a continuum model. It is demonstrated that the kink Ehrlich-Schwoebel barrier responsible for the instability leads to an invariant shape of the step profiles. The step morphologies change with increasing coverage from a somewhat triangular shape to a more flat, invariant steady state form. The average pattern shape extracted from the simulations is shown to be in good agreement with that obtained from numerical integration of the continuum theory.Comment: 4 pages, 4 figures, RevTeX 3, submitted to Phys. Rev.

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

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

Detection of a dense clump in a filament interacting with W51e2

In the framework of the Herschel/PRISMAS Guaranteed Time Key Program, the line of sight to the distant ultracompact HII region W51e2 has been observed using several selected molecular species. Most of the detected absorption features are not associated with the background high-mass star-forming region and probe the diffuse matter along the line of sight. We present here the detection of an additional narrow absorption feature at ~70 km/s in the observed spectra of HDO, NH3 and C3. The 70 km/s feature is not uniquely identifiable with the dynamic components (the main cloud and the large-scale foreground filament) so-far identified toward this region. The narrow absorption feature is similar to the one found toward low-mass protostars, which is characteristic of the presence of a cold external envelope. The far-infrared spectroscopic data were combined with existing ground-based observations of 12CO, 13CO, CCH, CN, and C3H2 to characterize the 70 km/s component. Using a non-LTE analysis of multiple transitions of NH3 and CN, we estimated the density (n(H2) (1-5)x10^5 cm^-3) and temperature (10-30 K) for this narrow feature. We used a gas-grain warm-up based chemical model with physical parameters derived from the NH3 data to explain the observed abundances of the different chemical species. We propose that the 70 km/s narrow feature arises in a dense and cold clump that probably is undergoing collapse to form a low-mass protostar, formed on the trailing side of the high-velocity filament, which is thought to be interacting with the W51 main cloud. While the fortuitous coincidence of the dense clump along the line of sight with the continuum-bright W51e2 compact HII region has contributed to its non-detection in the continuum images, this same attribute makes it an appropriate source for absorption studies and in particular for ice studies of star-forming regions.Comment: Accepted for publication in A&

The Effects of Next-Nearest-Neighbor Interactions on the Orientation Dependence of Step Stiffness: Reconciling Theory with Experiment for Cu(001)

Within the solid-on-solid (SOS) approximation, we carry out a calculation of the orientational dependence of the step stiffness on a square lattice with nearest and next-nearest neighbor interactions. At low temperature our result reduces to a simple, transparent expression. The effect of the strongest trio (three-site, non pairwise) interaction can easily be incorporated by modifying the interpretation of the two pairwise energies. The work is motivated by a calculation based on nearest neighbors that underestimates the stiffness by a factor of 4 in directions away from close-packed directions, and a subsequent estimate of the stiffness in the two high-symmetry directions alone that suggested that inclusion of next-nearest-neighbor attractions could fully explain the discrepancy. As in these earlier papers, the discussion focuses on Cu(001).Comment: 8 pages, 3 figures, submitted to Phys. Rev.