The Dirichlet problem for the Bellman equation at resonance

We generalize the Donsker-Varadhan minimax formula for the principal eigenvalue of a uniformly elliptic operator in nondivergence form to the first principal half-eigenvalue of a fully nonlinear operator which is concave (or convex) and positively homogeneous. Examples of such operators include the Hamilon-Jacobi-Bellman operator and the Pucci extremal operators. In the case that the two principal half-eigenvalues are not equal, we show that the measures which achieve the minimum in this formula provide a partial characterization of the solvability of the corresponding Dirichlet problem at resonance.Comment: Appendix added. 28 page

Principal eigenvalues and an anti-maximum principle for homogeneous fully nonlinear elliptic equations

We study the fully nonlinear elliptic equation $F(D^2u,Du,u,x) = f$ in a smooth bounded domain $\Omega$, under the assumption the nonlinearity $F$ is uniformly elliptic and positively homogeneous. Recently, it has been shown that such operators have two principal "half" eigenvalues, and that the corresponding Dirichlet problem possesses solutions, if both of the principal eigenvalues are positive. In this paper, we prove the existence of solutions of the Dirichlet problem if both principal eigenvalues are negative, provided the "second" eigenvalue is positive, and generalize the anti-maximum principle of Cl\'{e}ment and Peletier to homogeneous, fully nonlinear operators.Comment: 32 page

Guerrero Accelerograph Array: Status and Selected Results

This paper summarizes the history and rational for installation of the Guerrero accelerograph array. The array is producing unprecedented quantities of high quality digital strong motion data. Recent research using the array data has included studies on attenuation, site effects, scaling of spectra with magnitude, the ratio of vertical to horizontal accelerations, and the source of the September 19, 1985 earthquake

Long-range Kondo signature of a single magnetic impurity

The Kondo effect, one of the oldest correlation phenomena known in condensed matter physics, has regained attention due to scanning tunneling spectroscopy (STS) experiments performed on single magnetic impurities. Despite the sub-nanometer resolution capability of local probe techniques one of the fundamental aspects of Kondo physics, its spatial extension, is still subject to discussion. Up to now all STS studies on single adsorbed atoms have shown that observable Kondo features rapidly vanish with increasing distance from the impurity. Here we report on a hitherto unobserved long range Kondo signature for single magnetic atoms of Fe and Co buried under a Cu(100) surface. We present a theoretical interpretation of the measured signatures using a combined approach of band structure and many-body numerical renormalization group (NRG) calculations. These are in excellent agreement with the rich spatially and spectroscopically resolved experimental data.Comment: 7 pages, 3 figures + 8 pages supplementary material; Nature Physics (Jan 2011 - advanced online publication

Regional and seasonal radiative forcing by perturbations to aerosol and ozone precursor emissions

Predictions of temperature and precipitation responses to changes in the anthropogenic emissions of climate forcers require the quantification of the radiative forcing exerted by those changes. This task is particularly difficult for near-term climate forcers like aerosols, methane, and ozone precursors because their short atmospheric lifetimes cause regionally and temporally inhomogeneous radiative forcings. This study quantifies specific radiative forcing, defined as the radiative forcing per unit change in mass emitted, for eight near-term climate forcers as a function of their source regions and the season of emission by using dedicated simulations by four general circulation and chemistry-transport models. Although differences in the representation of atmospheric chemistry and radiative processes in different models impede the creation of a uniform dataset, four distinct findings can be highlighted. Firstly, specific radiative forcing for sulfur dioxide and organic carbon are stronger when aerosol–cloud interactions are taken into account. Secondly, there is a lack of agreement on the sign of the specific radiative forcing of volatile organic compound perturbations, suggesting they are better avoided in climate mitigation strategies. Thirdly, the strong seasonalities of the specific radiative forcing of most forcers allow strategies to minimise positive radiative forcing based on the timing of emissions. Finally, European and shipping emissions exert stronger aerosol specific radiative forcings compared to East Asia where the baseline is more polluted. This study can therefore form the basis for further refining climate mitigation options based on regional and seasonal controls on emissions. For example, reducing summertime emissions of black carbon and wintertime emissions of sulfur dioxide in the more polluted regions is a possible way to improve air quality without weakening the negative radiative forcing of aerosols

Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure

Incorporation of aerosol into the COSPv2 satellite lidar simulator for climate model evaluation

Atmospheric aerosol has substantial impacts on climate, air quality and biogeochemical cycles, and its concentrations are highly variable in space and time. A key variability to evaluate within models that simulate aerosol is the vertical distribution, which influences atmospheric heating profiles and aerosol–cloud interactions, to help constrain aerosol residence time and to better represent the magnitude of simulated impacts. To ensure a consistent comparison between modeled and observed vertical distribution of aerosol, we implemented an aerosol lidar simulator within the Cloud Feedback Model Intercomparison Project (CFMIP) Observation Simulator Package version 2 (COSPv2). We assessed the attenuated total backscattered (ATB) signal and the backscatter ratios (SRs) at 532 nm in the U.S. Department of Energy's Energy Exascale Earth System Model version 1 (E3SMv1). The simulator performs the computations at the same vertical resolution as the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP), making use of aerosol optics from the E3SMv1 model as inputs and assuming that aerosol is uniformly distributed horizontally within each model grid box. The simulator applies a cloud masking and an aerosol detection threshold to obtain the ATB and SR profiles that would be observed above clouds by CALIOP with its aerosol detection capability. Our analysis shows that the aerosol distribution simulated at a seasonal timescale is generally in good agreement with observations. Over the Southern Ocean, however, the model does not produce the SR maximum as observed in the real world. Comparison between clear-sky and all-sky SRs shows little differences, indicating that the cloud screening by potentially incorrect model clouds does not affect the mean aerosol signal averaged over a season. This indicates that the differences between observed and simulated SR values are due not to sampling errors, but to deficiencies in the representation of aerosol in models. Finally, we highlight the need for future applications of lidar observations at multiple wavelengths to provide insights into aerosol properties and distribution and their representation in Earth system models.</p

Defining the economic scope for ecosystem-based fishery management

Ecosystem-based fisheries management provides a framework for incorporating ecological linkages between fisheries into policymaking. However, relatively little attention has been given to economic linkages between fisheries: If fishers consider multiple fisheries when deciding where, when, and how much to fish, there is potential for management decisions in one fishery to generate spillover impacts in other fisheries. We evaluate changes in participation and economic connectivity of fisheries following the implementation of Alaska�s catch-share programs. Catch shares are increasingly used worldwide and typically implemented and evaluated on a single-fishery basis. We provide evidence that changes beyond the catch-share fishery have occurred, suggesting that spillovers should be considered when designing and evaluating catch-share policies.The emergence of ecosystem-based fisheries management (EBFM) has broadened the policy scope of fisheries management by accounting for the biological and ecological connectivity of fisheries. Less attention, however, has been given to the economic connectivity of fisheries. If fishers consider multiple fisheries when deciding where, when, and how much to fish, then management changes in one fishery can generate spillover impacts in other fisheries. Catch-share programs are a popular fisheries management framework that may be particularly prone to generating spillovers given that they typically change fishers� incentives and their subsequent actions. We use data from Alaska fisheries to examine spillovers from each of the main catch-share programs in Alaska. We evaluate changes in participation�a traditional indicator in fisheries economics�in both the catch-share and non�catch-share fisheries. Using network analysis, we also investigate whether catch-share programs change the economic connectivity of fisheries, which can have implications for the socioeconomic resilience and robustness of the ecosystem, and empirically identify the set of fisheries impacted by each Alaska catch-share program. We find that cross-fishery participation spillovers and changes in economic connectivity coincide with some, but not all, catch-share programs. Our findings suggest that economic connectivity and the potential for cross-fishery spillovers deserve serious consideration, especially when designing and evaluating EBFM policies

On the determination of a cloud condensation nuclei from satellite : Challenges and possibilities

We use aerosol size distributions measured in the size range from 0.01 to 10+ μm during Transport and Chemical Evolution over the Pacific (TRACE-P) and Aerosol Characterization Experiment-Asia (ACE-Asia), results of chemical analysis, measured/modeled humidity growth, and stratification by air mass types to explore correlations between aerosol optical parameters and aerosol number concentration. Size distributions allow us to integrate aerosol number over any size range expected to be effective cloud condensation nuclei (CCN) and to provide definition of a proxy for CCN (CCNproxy). Because of the internally mixed nature of most accumulation mode aerosol and the relationship between their measured volatility and solubility, this CCNproxy can be linked to the optical properties of these size distributions at ambient conditions. This allows examination of the relationship between CCNproxy and the aerosol spectral radiances detected by satellites. Relative increases in coarse aerosol (e.g., dust) generally add only a few particles to effective CCN but significantly increase the scattering detected by satellite and drive the Angstrom exponent (α) toward zero. This has prompted the use of a so-called aerosol index (AI) on the basis of the product of the aerosol optical depth and the nondimensional α, both of which can be inferred from satellite observations. This approach biases the AI to be closer to scattering values generated by particles in the accumulation mode that dominate particle number and is therefore dominated by sizes commonly effective as CCN. Our measurements demonstrate that AI does not generally relate well to a measured proxy for CCN unless the data are suitably stratified. Multiple layers, complex humidity profiles, dust with very low α mixed with pollution, and size distribution differences in pollution and biomass emissions appear to contribute most to method limitations. However, we demonstrate that these characteristic differences result in predictable influences on AI. These results suggest that inference of CCN from satellites will be challenging, but new satellite and model capabilities could possibly be integrated to improve this retrieval

Aerosol effects on clouds are concealed by natural cloud heterogeneity and satellite retrieval errors

One major source of uncertainty in the cloud-mediated aerosol forcing arises from the magnitude of the cloud liquid water path (LWP) adjustment to aerosol-cloud interactions, which is poorly constrained by observations. Many of the recent satellite-based studies have observed a decreasing LWP as a function of cloud droplet number concentration (CDNC) as the dominating behavior. Estimating the LWP response to the CDNC changes is a complex task since various confounding factors need to be isolated. However, an important aspect has not been sufficiently considered: the propagation of natural spatial variability and errors in satellite retrievals of cloud optical depth and cloud effective radius to estimates of CDNC and LWP. Here we use satellite and simulated measurements to demonstrate that, because of this propagation, even a positive LWP adjustment is likely to be misinterpreted as negative. This biasing effect therefore leads to an underestimate of the aerosol-cloud-climate cooling and must be properly considered in future studies