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

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

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

Missing peroxy radical sources within a summertime ponderosa pine forest

Organic peroxy (RO₂) and hydroperoxy (HO₂) radicals are key intermediates in the photochemical processes that generate ozone, secondary organic aerosol and reactive nitrogen reservoirs throughout the troposphere. In regions with ample biogenic hydrocarbons, the richness and complexity of peroxy radical chemistry presents a significant challenge to current-generation models, especially given the scarcity of measurements in such environments. We present peroxy radical observations acquired within a ponderosa pine forest during the summer 2010 Bio-hydro-atmosphere interactions of Energy, Aerosols, Carbon, H₂O, Organics and Nitrogen – Rocky Mountain Organic Carbon Study (BEACHON-ROCS). Total peroxy radical mixing ratios reach as high as 180 pptv (parts per trillion by volume) and are among the highest yet recorded. Using the comprehensive measurement suite to constrain a near-explicit 0-D box model, we investigate the sources, sinks and distribution of peroxy radicals below the forest canopy. The base chemical mechanism underestimates total peroxy radicals by as much as a factor of 3. Since primary reaction partners for peroxy radicals are either measured (NO) or underpredicted (HO₂ and RO₂, i.e., self-reaction), missing sources are the most likely explanation for this result. A close comparison of model output with observations reveals at least two distinct source signatures. The first missing source, characterized by a sharp midday maximum and a strong dependence on solar radiation, is consistent with photolytic production of HO₂. The diel profile of the second missing source peaks in the afternoon and suggests a process that generates RO₂ independently of sun-driven photochemistry, such as ozonolysis of reactive hydrocarbons. The maximum magnitudes of these missing sources (~120 and 50 pptv min⁻¹, respectively) are consistent with previous observations alluding to unexpectedly intense oxidation within forests. We conclude that a similar mechanism may underlie many such observations

Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach

Cooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with different preferences or beliefs. Yet, people from different social or cultural backgrounds often meet and interact. This can yield conflict, since behavior that is considered cooperative by one population might be perceived as non-cooperative from the viewpoint of another. To understand the dynamics and outcome of the competitive interactions within and between groups, we study game-dynamical replicator equations for multiple populations with incompatible interests and different power (be this due to different population sizes, material resources, social capital, or other factors). These equations allow us to address various important questions: For example, can cooperation in the prisoner's dilemma be promoted, when two interacting groups have different preferences? Under what conditions can costly punishment, or other mechanisms, foster the evolution of norms? When does cooperation fail, leading to antagonistic behavior, conflict, or even revolutions? And what incentives are needed to reach peaceful agreements between groups with conflicting interests? Our detailed quantitative analysis reveals a large variety of interesting results, which are relevant for society, law and economics, and have implications for the evolution of language and culture as well

Missing Peroxy Radical Sources Within a Rural Forest Canopy

Organic peroxy (RO2) and hydroperoxy (HO2) radicals are key intermediates in the photochemical processes that generate ozone, secondary organic aerosol and reactive nitrogen reservoirs throughout the troposphere. In regions with ample biogenic hydrocarbons, the richness and complexity of peroxy radical chemistry presents a significant challenge to current-generation models, especially given the scarcity of measurements in such environments. We present peroxy radical observations acquired within a Ponderosa pine forest during the summer 2010 Bio-hydro-atmosphere interactions of Energy, Aerosols, Carbon, H2O, Organics and Nitrogen - Rocky Mountain Organic Carbon Study (BEACHON-ROCS). Total peroxy radical mixing ratios reach as high as 180 pptv and are among the highest yet recorded. Using the comprehensive measurement suite to constrain a near-explicit 0-D box model, we investigate the sources, sinks and distribution of peroxy radicals below the forest canopy. The base chemical mechanism underestimates total peroxy radicals by as much as a factor of 3. Since primary reaction partners for peroxy radicals are either measured (NO) or under-predicted (HO2 and RO2, i.e. self-reaction), missing sources are the most likely explanation for this result. A close comparison of model output with observations reveals at least two distinct source signatures. The first missing source, characterized by a sharp midday maximum and a strong dependence on solar radiation, is consistent with photolytic production of HO2. The diel profile of the second missing source peaks in the afternoon and suggests a process that generates RO2 independently of sun-driven photochemistry, such as ozonolysis of reactive hydrocarbons. The maximum magnitudes of these missing sources (approximately 120 and 50 pptv min1, respectively) are consistent with previous observations alluding to unexpectedly intense oxidation within forests. We conclude that a similar mechanism may underlie many such observations

Observation of Scaling Violations in Scaled Momentum Distributions at HERA

Charged particle production has been measured in deep inelastic scattering (DIS) events over a large range of $x$ and $Q^2$ using the ZEUS detector. The evolution of the scaled momentum, $x_p$, with $Q^2,$ in the range 10 to 1280 $GeV^2$, has been investigated in the current fragmentation region of the Breit frame. The results show clear evidence, in a single experiment, for scaling violations in scaled momenta as a function of $Q^2$.Comment: 21 pages including 4 figures, to be published in Physics Letters B. Two references adde

D* Production in Deep Inelastic Scattering at HERA

This paper presents measurements of D^{*\pm} production in deep inelastic scattering from collisions between 27.5 GeV positrons and 820 GeV protons. The data have been taken with the ZEUS detector at HERA. The decay channel $D^{*+}\to (D^0 \to K^- \pi^+) \pi^+$ (+ c.c.) has been used in the study. The $e^+p$ cross section for inclusive D^{*\pm} production with $5<Q^2<100 GeV^2$ and $y<0.7$ is 5.3 \pms 1.0 \pms 0.8 nb in the kinematic region {$1.3<p_T(D^{*\pm})<9.0$ GeV and $| \eta(D^{*\pm}) |<1.5$}. Differential cross sections as functions of p_T(D^{*\pm}), $\eta(D^{*\pm}), W$ and $Q^2$ are compared with next-to-leading order QCD calculations based on the photon-gluon fusion production mechanism. After an extrapolation of the cross section to the full kinematic region in p_T(D^{*\pm}) and $\eta$(D^{*\pm}), the charm contribution $F_2^{c\bar{c}}(x,Q^2)$ to the proton structure function is determined for Bjorken $x$ between 2 $\cdot$ 10$^{-4}$ and 5 $\cdot$ 10$^{-3}$.Comment: 17 pages including 4 figure