Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems

In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty quantification problems in subsurface flow. We extend the convergence analysis in [Graham et al., Numer. Math. 2014] to multilevel Quasi-Monte Carlo finite element discretizations and give a constructive proof of the dimension-independent convergence of the QMC rules. More precisely, we provide suitable parameters for the construction of such rules that yield the required variance reduction for the multilevel scheme to achieve an $\varepsilon$-error with a cost of $\mathcal{O}(\varepsilon^{-\theta})$ with $\theta < 2$, and in practice even $\theta \approx 1$, for sufficiently fast decaying covariance kernels of the underlying Gaussian random field inputs. This confirms that the computational gains due to the application of multilevel sampling methods and the gains due to the application of QMC methods, both demonstrated in earlier works for the same model problem, are complementary. A series of numerical experiments confirms these gains. The results show that in practice the multilevel QMC method consistently outperforms both the multilevel MC method and the single-level variants even for non-smooth problems.Comment: 32 page

Dinuclear Tb and Dy complexes supported by hybrid Schiff-base/calixarene ligands: synthesis, structures and magnetic properties

The synthesis of the new lanthanide complexes [HNEt$_{3}$][Dy$_{2}$(HL$^{1}$)(L$^{1}$)] (5), and [Ln$_{2}$(L$_{2}$)$_{2}$] (Ln = Tb$^{III}$ (7), Dy$^{III}$ (8)) supported by the hybrid Schiff-base/calix[4]arene ligands H$_{4}$L$^{1}$ (25-[2-((2-methylphenol)imino)ethoxy]-26,27,28-trihydroxy-calix[4]arene) and H$_{3}$L$^{2}$ (25-[2-((2-methylpyridine)imino)ethoxy]-26,27,28-trihydroxy-calix[4]arene) are reported. Spectroscopic data (for 5) and X-ray crystallographic analysis (for 7·4MeCN, 8·4MeCN) reveal the presence of dimeric structures, featuring doubly-bridged NO$_{4}$Ln(μ-O)$_{2}$LnO$_{4}$N (5) or N$_{2}$O$_{3}$Ln(μ-O)$_{2}$LnO$_{3}$N$_{2}$ cores (7, 8) with seven-coordinated Ln$^{3+}$ ions. The magnetic properties of polycrystalline samples of 5, 7 and 8 were studied by variable temperature dc and ac magnetic susceptibility measurements. The χ′′(T) vs. T plots show no maxima in zero field, but the maxima can be detected under a 3 kOe dc field. The relaxation times τ obey the Arrhenius law above 5 K. Anisotropy barriers of ∼18 cm$^{-1}$ (26 K) for 5 and ∼23 cm$^{-1}$ (33 K) for 8 were determined

Integration of airborne and ground observations of nitryl chloride in the Seoul metropolitan area and the implications on regional oxidation capacity during KORUS-AQ 2016

Nitryl chloride (ClNO2) is a radical reservoir species that releases chlorine radicals upon photolysis. An integrated analysis of the impact of ClNO2 on regional photochemistry in the Seoul metropolitan area (SMA) during the Korea-United States Air Quality Study (KORUS-AQ) 2016 field campaign is presented. Comprehensive multiplatform observations were conducted aboard the NASA DC-8 and at two ground sites (Olympic Park, OP; Taehwa Research Forest, TRF), representing an urbanized area and a forested suburban region, respectively. Positive correlations between daytime Cl2 and ClNO2 were observed at both sites, the slope of which was dependent on O3 levels. The possible mechanisms are explored through box model simulations constrained with observations. The overall diurnal variations in ClNO2 at both sites appeared similar but the nighttime variations were systematically different. For about half of the observation days at the OP site the level of ClNO2 increased at sunset but rapidly decreased at around midnight. On the other hand, high levels were observed throughout the night at the TRF site. Significant levels of ClNO2 were observed at both sites for 4-5 h after sunrise. Airborne observations, box model calculations, and back-trajectory analysis consistently show that these high levels of ClNO2 in the morning are likely from vertical or horizontal transport of air masses from the west. Box model results show that chlorine-radical-initiated chemistry can impact the regional photochemistry by elevating net chemical production rates of ozone by 25% in the morning

Measurement of the total neutron cross section on argon in the 20 to 70 keV energy range

The cross section for neutron interactions on argon is an important design and operational parameter for a number of neutrino, dark matter, and neutrinoless double beta decay experiments which use liquid argon as a detection or shielding medium. There is a discrepancy between the evaluated total cross section in the $20$ to $70~\rm$\,keV neutron kinetic energy region given in the ENDF database and a single measurement conducted by an experiment with a thin target (0.2 atoms/barn) optimized for higher cross sections. This gives rise to significant uncertainty in the interaction length of neutrons in liquid argon. This discrepancy is now resolved by new results presented here from the Argon Resonance Transport Interaction Experiment (ARTIE), a thick target experiment (3.3 atoms/barn) optimized for the small cross sections in this energy region.Comment: 6 pages, 4 figures. Submitted to PRC based on reviewer's recommendation

Fission prompt gamma-ray multiplicity distribution measurements and simulations at DANCE

The nearly energy independence of the DANCE efficiency and multiplicity response to {gamma} rays makes it possible to measure the prompt {gamma}-ray multiplicity distribution in fission. We demonstrate this unique capability of DANCE through the comparison of {gamma}-ray energy and multiplicity distribution between the measurement and numerical simulation for three radioactive sources {sup 22}Na, {sup 60}Co, and {sup 88}Y. The prospect for measuring the {gamma}-ray multiplicity distribution for both spontaneous and neutron-induced fission is discussed

First direct measurements of formaldehyde flux via eddy covariance: implications for missing in-canopy formaldehyde sources

We report the first observations of formaldehyde (HCHO) flux measured via eddy covariance, as well as HCHO concentrations and gradients, as observed by the Madison Fiber Laser-Induced Fluorescence Instrument during the BEACHON-ROCS 2010 campaign in a rural, Ponderosa Pine forest northwest of Colorado Springs, CO. A median noon upward flux of ~80 &amp;mu;g m&lt;sup&gt;&amp;minus;2&lt;/sup&gt; h&lt;sup&gt;&amp;minus;1&lt;/sup&gt; (~24 ppt&lt;sub&gt;v&lt;/sub&gt; m s&lt;sup&gt;&amp;minus;1&lt;/sup&gt;) was observed with a noon range of 37 to 131 &amp;mu;g m&lt;sup&gt;&amp;minus;2&lt;/sup&gt; h&lt;sup&gt;&amp;minus;1&lt;/sup&gt;. Enclosure experiments were performed to determine the HCHO branch (3.5 &amp;mu;g m&lt;sup&gt;-2&lt;/sup&gt; h&lt;sup&gt;&amp;minus;1&lt;/sup&gt;) and soil (7.3 &amp;mu;g m&lt;sup&gt;&amp;minus;2&lt;/sup&gt; h&lt;sup&gt;&amp;minus;1&lt;/sup&gt;) direct emission rates in the canopy. A zero-dimensional canopy box model, used to determine the apportionment of HCHO source and sink contributions to the flux, underpredicted the observed HCHO flux by a factor of 6. Simulated increases in concentrations of species similar to monoterpenes resulted in poor agreement with measurements, while simulated increases in direct HCHO emissions and/or concentrations of species similar to 2-methyl-3-buten-2-ol best improved model/measurement agreement. Given the typical diurnal variability of these BVOC emissions and direct HCHO emissions, this suggests that the source of the missing flux is a process with both a strong temperature and radiation dependence

The costs of respiratory illnesses arising from Florida gulf coast Karenia brevis blooms

This is the final version of the article. Available from NIEHS via the DOI in this recordBACKGROUND: Algal blooms of Karenia brevis, a harmful marine algae, occur almost annually off the west coast of Florida. At high concentrations, K. brevis blooms can cause harm through the release of potent toxins, known as brevetoxins, to the atmosphere. Epidemiologic studies suggest that aerosolized brevetoxins are linked to respiratory illnesses in humans. OBJECTIVES: We hypothesized a relationship between K. brevis blooms and respiratory illness visits to hospital emergency departments (EDs) while controlling for environmental factors, disease, and tourism. We sought to use this relationship to estimate the costs of illness associated with aerosolized brevetoxins. METHODS: We developed a statistical exposure-response model to express hypotheses about the relationship between respiratory illnesses and bloom events. We estimated the model with data on ED visits, K. brevis cell densities, and measures of pollen, pollutants, respiratory disease, and intra-annual population changes. RESULTS: We found that lagged K. brevis cell counts, low air temperatures, influenza outbreaks, high pollen counts, and tourist visits helped explain the number of respiratory-specific ED diagnoses. The capitalized estimated marginal costs of illness for ED respiratory illnesses associated with K. brevis blooms in Sarasota County, Florida, alone ranged from $0.5 to$4 million, depending on bloom severity. CONCLUSIONS: Blooms of K. brevis lead to significant economic impacts. The costs of illness of ED visits are a conservative estimate of the total economic impacts. It will become increasingly necessary to understand the scale of the economic losses associated with K. brevis blooms to make rational choices about appropriate mitigation.This research was sponsored by the Florida Fish & Wildlife Conservation Commission (07182) and the Departments of Environmental Protection and Health; the U.S. Centers for Disease Control and Prevention; the Center for Oceans and Human Health at the Woods Hole Oceanographic Institution [National Science Foundation (NSF) OCE-0430724; National Institute of Environmental Health Sciences (NIEHS) P50 ES012742]; the Ocean and Human Health Center at the University of Miami Rosenstiel School (NSF 0CE0432368; NIEHS 1 P50 ES12736); and the NIEHS (PO1 ES 10594)