Volume Comparison for Hypersurfaces in Lorentzian Manifolds and Singularity Theorems

We develop area and volume comparison theorems for the evolution of spacelike, acausal, causally complete hypersurfaces in Lorentzian manifolds, where one has a lower bound on the Ricci tensor along timelike curves, and an upper bound on the mean curvature of the hypersurface. Using these results, we give a new proof of Hawking's singularity theorem.Comment: 15 pages, LaTe

Two-photon absorption and broadband optical limiting with bis-donor stilbenes

Large two-photon absorptivities are reported for symmetrical bis-donor stilbene derivatives with dialkylamino or diphenylamino groups. These molecules exhibit strong optical limiting of nanosecond pulses over a broad spectral range in the visible. Relative to bis(di-n-butylamino)stilbene, bis(diphenylamino)stilbene exhibits a 90-nm red shift of its optical limiting band but only a minimal shift of ~13 nm of its lowest one-photon electronic absorption band. Mixtures of these compounds offer an unprecedented combination of broad optical limiting bandwidth and high linear transparency

Growth of Patterned Surfaces

During epitaxial crystal growth a pattern that has initially been imprinted on a surface approximately reproduces itself after the deposition of an integer number of monolayers. Computer simulations of the one-dimensional case show that the quality of reproduction decays exponentially with a characteristic time which is linear in the activation energy of surface diffusion. We argue that this life time of a pattern is optimized, if the characteristic feature size of the pattern is larger than $(D/F)^{1/(d+2)}$, where $D$ is the surface diffusion constant, $F$ the deposition rate and $d$ the surface dimension.Comment: 4 pages, 4 figures, uses psfig; to appear in Phys. Rev. Let

Numerical test of the damping time of layer-by-layer growth on stochastic models

We perform Monte Carlo simulations on stochastic models such as the Wolf-Villain (WV) model and the Family model in a modified version to measure mean separation $\ell$ between islands in submonolayer regime and damping time $\tilde t$ of layer-by-layer growth oscillations on one dimension. The stochastic models are modified, allowing diffusion within interval $r$ upon deposited. It is found numerically that the mean separation and the damping time depend on the diffusion interval $r$, leading to that the damping time is related to the mean separation as ${\tilde t} \sim \ell^{4/3}$ for the WV model and ${\tilde t} \sim \ell^2$ for the Family model. The numerical results are in excellent agreement with recent theoretical predictions.Comment: 4 pages, source LaTeX file and 5 PS figure

Underrecognition and undertreatment of asthma in Cape Town primary school children

Background. In view of the high local prevalence of asthma, the extent of recognition and appropriate managementof childhood asthma was studied in a large suburban area of Cape Town.Design. Cross-sectional study based on random community sample of schools.Method. 1955 parents of sub B pupils from 16 schools completed a questionnaire, followed by: (f) an interview of parents of 348 symptomatic children; and (if) bronchial responsiveness testing on 254 children. the final case group consisted of 242 children with reported asthma or multiple asthma symptoms on both questionnaires. Children in whom asthma was acknowledged were compared with those in whom it was not.Results. Overall, any past or current ('ever') asthma was acknowledged by respondents in only 53% of the children, and current asthma in only 37.1%. While most children had received treatment in the previous 12 months, 66.1% of therecognised group were on current treatment (23.2% on daily treatment), compared with 37% of the unrecognised group (3% daily). Salbutamol and theophylline syrups were the most common types of medication, while inhalers and antiinflammatory medications were underused. Only a minority of parents reported the child ever having used a peak flow meter, or volunteered knowledge of preventive measures. Current treatment, and to a lesser degree recognition of asthma by parents, were more common among children on medical aid and of higher socio-eonomic status.Conclusions. These findings suggest that ways need to be found: (i) to increase the use of current asthma treatment guidelines by practitioners; (ii) to provide access to comprehensive care by children not on medical aid; and (iii) to improve education of parents in home management measures such as severity assessment and avoidance of smoking, allergen and dietary triggers

Cloud phase identification of Arctic boundary-layer clouds from airborne spectral reflection measurements: Test of three approaches

Arctic boundary-layer clouds were investigated with remote sensing and in situ instruments during the Arctic Study of Tropospheric Aerosol, Clouds and Radiation (ASTAR) campaign in March and April 2007. The clouds formed in a cold air outbreak over the open Greenland Sea. Beside the predominant mixed-phase clouds pure liquid water and ice clouds were observed. Utilizing measurements of solar radiation reflected by the clouds three methods to retrieve the thermodynamic phase of the cloud are introduced and compared. Two ice indices IS and IP were obtained by analyzing the spectral pattern of the cloud top reflectance in the near infrared (1500–1800 nm wavelength) spectral range which is characterized by ice and water absorption. While IS analyzes the spectral slope of the reflectance in this wavelength range, IS utilizes a principle component analysis (PCA) of the spectral reflectance. A third ice index IA is based on the different side scattering of spherical liquid water particles and nonspherical ice crystals which was recorded in simultaneous measurements of spectral cloud albedo and reflectance. Radiative transfer simulations show that IS, IP and IA range between 5 to 80, 0 to 8 and 1 to 1.25 respectively with lowest values indicating pure liquid water clouds and highest values pure ice clouds. The spectral slope ice index IS and the PCA ice index IP are found to be strongly sensitive to the effective diameter of the ice crystals present in the cloud. Therefore, the identification of mixed-phase clouds requires a priori knowledge of the ice crystal dimension. The reflectance-albedo ice index IA is mainly dominated by the uppermost cloud layer (τ<1.5). Therefore, typical boundary-layer mixed-phase clouds with a liquid cloud top layer will be identified as pure liquid water clouds. All three methods were applied to measurements above a cloud field observed during ASTAR 2007. The comparison with independent in situ microphysical measurements shows the ability of the three approaches to identify the ice phase in Arctic boundary-layer clouds

Forest albedo in the context of different cloud situations derived from irradiance measurements at the Leipzig floodplain crane: A pilot study

The surface albedo significantly modulates the atmospheric energy budget and, thus, vertical radiation, energy, and mass fluxes. Therefore, it regulates the local and regional effects of climate warming. Over a forest canopy, the surface albedo mainly depends on the seasonal leaf state. Furthermore, for certain surface types, such as snow, it has been shown that the surface albedo changes as a function of cloudiness. A similar effect is expected over forest surfaces, leading to complex feedback loops between forest surfaces and climate. To investigate these processes, a pilot study was performed at the Leipzig floodplain crane to observe the forest canopy albedo under different atmospheric conditions in 2021. First analyses revealed a dependency of the forest albedo from the cloud state, which is slightly stronger in the near-infrared wavelength range compared to the visible wavelength range.Der atmosphärische Strahlungshaushalt und damit auch die vertikale Strahlungsverteilung, Energie- und Massenflüsse werden signifikant durch die Bodenalbedo gesteuert. Diese regulieren somit lokale und regionale Effekte der Klimaerwärmung. Über einem Wald hängt die Bodenalbedo hauptsächlich vom saisonalen Blattstatus ab. Zudem wurde für bestimmte Bodentypen wie Schneeoberflächen gezeigt, dass die Bodenalbedo eine Funktion der Bewölkung ist. Ähnlicher Effekte werden für Waldoberflächen erwartet, welche zu komplexen Rückkopplungseffekten zwischenWaldoberflächen und dem Klima führen. Um diese Prozesse zu untersuchen wurde im Jahr 2021 eine Vorstudie am Leipziger Auwaldkran durchgeführt, um die Waldalbedo unter verschiedenen atmosphärischen Bedingungen zu beobachten. Erste Analysen zeigen, dass auch die Albedo des Waldes von den Bewölkungsbedingungen abhängt. Der Effekt ist dabei etwas stärker im nah-infrarotem als im sichtbaren Wellenlängenbereich zu beobachten

Rigid Singularity Theorem in Globally Hyperbolic Spacetimes

We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$ time. This result is related to Yau's Lorentzian splitting conjecture.Comment: 3 pages, uses revtex.sty, to appear in Physical Review