Approximation properties of the qq-sine bases

For $q>12/11$ the eigenfunctions of the non-linear eigenvalue problem associated to the one-dimensional $q$-Laplacian are known to form a Riesz basis of $L^2(0,1)$. We examine in this paper the approximation properties of this family of functions and its dual, in order to establish non-orthogonal spectral methods for the $p$-Poisson boundary value problem and its corresponding parabolic time evolution initial value problem. The principal objective of our analysis is the determination of optimal values of $q$ for which the best approximation is achieved for a given $p$ problem.Comment: 20 pages, 11 figures and 2 tables. We have fixed a number of typos and added references. Changed the title to better reflect the conten

Estimates for the ergodic measure and polynomial stability of plane stochastic curve shortening flow

We establish moment estimates for the invariant measure of a stochastic partial differential equation describing motion by mean curvature flow in (1+1) dimension, leading to polynomial stability of the associated Markov semigroup. We also prove maximal dissipativity for the related Kolmogorov operator

Source apportionment of submicron organic aerosols at an urban site by linear unmixing of aerosol mass spectra

International audienceSubmicron ambient aerosol was characterized in summer 2005 at an urban background site in Zurich, Switzerland, during a three-week measurement campaign. Highly time-resolved samples of non-refractory aerosol components were analyzed with an Aerodyne aerosol mass spectrometer (AMS). Positive matrix factorization (PMF) was used for the first time for AMS data to identify the main components of the total organic aerosol and their sources. The PMF retrieved factors were compared to measured reference mass spectra and were correlated with tracer species of the aerosol and gas phase measurements from collocated instruments. Six factors were found to explain virtually all variance in the data and could be assigned either to sources or to aerosol components such as oxygenated organic aerosol (OOA). Our analysis suggests that at the measurement site only a small (1 originates from freshly emitted fossil fuel combustion. Other primary sources identified to be of similar or even higher importance are charbroiling (10?15%) and wood burning (~10%), along with a minor source interpreted to be influenced by food cooking (6%). The fraction of all identified primary sources is considered as primary organic aerosol (POA). This interpretation is supported by calculated ratios of the modelled POA and measured primary pollutants such as elemental carbon (EC), NOx, and CO, which are in good agreement to literature values. A high fraction (60?69%) of the measured organic aerosol mass is OOA which is interpreted mostly as secondary organic aerosol (SOA). This oxygenated organic aerosol can be separated into a highly aged fraction, OOA I, (40?50%) with low volatility and a mass spectrum similar to fulvic acid, and a more volatile and probably less processed fraction, OOA II (on average 20%). This is the first publication of a multiple component analysis technique to AMS organic spectral data and also the first report of the OOA II component

Investigation of four-year chemical composition and organic aerosol sources of submicron particles at the ATOLL site in northern France

This study presents the first long-term online measurements of submicron (PM1) particles at the ATOLL (ATmospheric Observations in liLLe) platform, in northern France. The ongoing measurements using an Aerosol Chemical Speciation Monitor (ACSM) started at the end of 2016 and the analysis presented here spans through December 2020. At this site, the mean PM1 concentration is 10.6 μg m-3, dominated by organic aerosols (OA, 42.3%) and followed by nitrate (28.9%), ammonium (12.3%), sulfate (8.6%), and black carbon (BC, 8.0%). Large seasonal variations of PM1 concentrations are observed, with high concentrations during cold seasons, associated with pollution episodes (e.g. over 100 μg m-3 in January 2017). To study OA origins over this multiannual dataset we performed source apportionment analysis using rolling positive matrix factorization (PMF), yielding two primary OA factors, a traffic-related hydrocarbon-like OA (HOA) and biomass-burning OA (BBOA), and two oxygenated OA (OOA) factors. HOA showed a homogeneous contribution to OA throughout the seasons (11.8%), while BBOA varied from 8.1% (summer) to 18.5% (winter), the latter associated with residential wood combustion. The OOA factors were distinguished between their less and more oxidized fractions (LO-OOA and MO-OOA, on average contributing 32% and 42%, respectively). During winter, LO-OOA is identified as aged biomass burning, so at least half of OA is associated with wood combustion during this season. Furthermore, ammonium nitrate is also a predominant aerosol component during cold-weather pollution episodes - associated with fertilizer usage and traffic emissions. This study provides a comprehensive analysis of submicron aerosol sources at the recently established ATOLL site in northern France from multiannual observations, depicting a complex interaction between anthropogenic and natural sources, leading to different mechanisms of air quality degradation in the region across different seasons

Organic Aerosol source apportionment in London 2013 with ME-2:Exploring the solution space with annual and seasonal analysis

The multilinear engine (ME-2) factorization tool is being widely used following the recent development of the Source Finder (SoFi) interface at the Paul Scherrer Institute. However, the success of this tool, when using the <i>a</i> value approach, largely depends on the inputs (i.e. target profiles) applied as well as the experience of the user. A strategy to explore the solution space is proposed, in which the solution that best describes the organic aerosol (OA) sources is determined according to the systematic application of predefined statistical tests. This includes trilinear regression, which proves to be a useful tool for comparing different ME-2 solutions. Aerosol Chemical Speciation Monitor (ACSM) measurements were carried out at the urban background site of North Kensington, London from March to December 2013, where for the first time the behaviour of OA sources and their possible environmental implications were studied using an ACSM. Five OA sources were identified: biomass burning OA (BBOA), hydrocarbon-like OA (HOA), cooking OA (COA), semivolatile oxygenated OA (SVOOA) and low-volatility oxygenated OA (LVOOA). ME-2 analysis of the seasonal data sets (spring, summer and autumn) showed a higher variability in the OA sources that was not detected in the combined March–December data set; this variability was explored with the triangle plots <i>f</i>44 : <i>f</i>43 <i>f</i>44 : <i>f</i>60, in which a high variation of SVOOA relative to LVOOA was observed in the <i>f</i>44 : <i>f</i>43 analysis. Hence, it was possible to conclude that, when performing source apportionment to long-term measurements, important information may be lost and this analysis should be done to short periods of time, such as seasonally. Further analysis on the atmospheric implications of these OA sources was carried out, identifying evidence of the possible contribution of heavy-duty diesel vehicles to air pollution during weekdays compared to those fuelled by petrol

Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise

The Primitive Equations are a basic model in the study of large scale Oceanic and Atmospheric dynamics. These systems form the analytical core of the most advanced General Circulation Models. For this reason and due to their challenging nonlinear and anisotropic structure the Primitive Equations have recently received considerable attention from the mathematical community. In view of the complex multi-scale nature of the earth's climate system, many uncertainties appear that should be accounted for in the basic dynamical models of atmospheric and oceanic processes. In the climate community stochastic methods have come into extensive use in this connection. For this reason there has appeared a need to further develop the foundations of nonlinear stochastic partial differential equations in connection with the Primitive Equations and more generally. In this work we study a stochastic version of the Primitive Equations. We establish the global existence of strong, pathwise solutions for these equations in dimension 3 for the case of a nonlinear multiplicative noise. The proof makes use of anisotropic estimates, $L^{p}_{t}L^{q}_{x}$ estimates on the pressure and stopping time arguments.Comment: To appear in Nonlinearit

Effect of photochemical ageing on the ice nucleation properties of diesel and wood burning particles

A measurement campaign (IMBALANCE) conducted in 2009 was aimed at characterizing the physical and chemical properties of freshly emitted and photochemically aged combustion particles emitted from a log wood burner and diesel vehicles: a EURO3 Opel Astra with a diesel oxidation catalyst (DOC) but no particle filter and a EURO2 Volkswagen Transporter TDI Syncro without emission aftertreatment. Ice nucleation experiments in the deposition and condensation freezing modes were conducted with the Portable Ice Nucleation Chamber (PINC) at three nominal temperatures, −30 °C, −35 °C and −40 °C. Freshly emitted diesel particles showed ice formation only at −40 °C in the deposition mode at 137% relative humidity with respect to ice (RH&lt;sub&gt;i&lt;/sub&gt;) and 92% relative humidity with respect to water (RH&lt;sub&gt;w&lt;/sub&gt;), and photochemical ageing did not play a role in modifying their ice nucleation behaviour. Only one diesel experiment where α-pinene was added for the ageing process, showed an ice nucleation enhancement at −35 °C. Wood burning particles also act as ice nuclei (IN) at −40 °C in the deposition mode at the same conditions as for diesel particles and photochemical ageing also did not alter the ice formation properties of the wood burning particles. Unlike diesel particles, wood burning particles form ice via condensation freezing at −35 °C whereas no ice nucleation was observed at −30 °C. Photochemical ageing did not affect the ice nucleation ability of the diesel and wood burning particles at the three different temperatures investigated but a broader range of temperatures below −40 °C need to be investigated in order to draw an overall conclusion on the effect of photochemical ageing on deposition/condensation ice nucleation across the entire temperature range relevant to cold clouds

Modelling winter organic aerosol at the European scale with CAMx : evaluation and source apportionment with a VBS parameterization based on novel wood burning smog chamber experiments

We evaluated a modified VBS (volatility basis set) scheme to treat biomass-burning-like organic aerosol (BBOA) implemented in CAMx (Comprehensive Air Quality Model with extensions). The updated scheme was parameterized with novel wood combustion smog chamber experiments using a hybrid VBS framework which accounts for a mixture of wood burning organic aerosol precursors and their further functionalization and fragmentation in the atmosphere. The new scheme was evaluated for one of the winter EMEP intensive campaigns (February March 2009) against aerosol mass spectrometer (AMS) measurements performed at 11 sites in Europe. We found a considerable improvement for the modelled organic aerosol (OA) mass compared to our previous model application with the mean fractional bias (MFB) reduced from 61 to 29 %. We performed model-based source apportionment studies and compared results against positive matrix factorization (PMF) analysis performed on OA AMS data. Both model and observations suggest that OA was mainly of secondary origin at almost all sites. Modelled secondary organic aerosol (SOA) contributions to total OA varied from 32 to 88 % (with an average contribution of 62 %) and absolute concentrations were generally under-predicted. Modelled primary hydrocarbon-like organic aerosol (HOA) and primary biomass-burning-like aerosol (BBPOA) fractions contributed to a lesser extent (HOA from 3 to 30 %, and BBPOA from 1 to 39 %) with average contributions of 13 and 25 %, respectively. Modelled BBPOA fractions were found to represent 12 to 64 % of the total residential-heating-related OA, with increasing contributions at stations located in the northern part of the domain. Source apportionment studies were performed to assess the contribution of residential and non-residential combustion precursors to the total SOA. Non-residential combustion and road transportation sector contributed about 30-40 % to SOA formation (with increasing contributions at urban and near industrialized sites), whereas residential combustion (mainly related to wood burning) contributed to a larger extent, around 60-70 %. Contributions to OA from residential combustion precursors in different volatility ranges were also assessed: our results indicate that residential combustion gas-phase precursors in the semivolatile range (SVOC) contributed from 6 to 30 %, with higher contributions predicted at stations located in the southern part of the domain On the other hand, the oxidation products of higher-volatility precursors (the sum of intermediate-volatility compounds (IVOCs) and volatile organic compounds (VOCs)) contribute from 15 to 38 % with no specific gradient among the stations. Although the new parameterization leads to a better agreement between model results and observations, it still under predicts the SOA fraction, suggesting that uncertainties in the new scheme and other sources and/or formation mechanisms remain to be elucidated. Moreover, a more detailed characterization of the semivolatile components of the emissions is needed.Peer reviewe

Organic molecular markers and signature from wood combustion particles in winter ambient aerosols: aerosol mass spectrometer (AMS) and high time-resolved GC-MS measurements in Augsburg, Germany

The impact of wood combustion on ambient aerosols was investigated in Augsburg, Germany during a winter measurement campaign of a six-week period. Special attention was paid to the high time resolution observations of wood combustion with different mass spectrometric methods. Here we present and compare the results from an Aerodyne aerosol mass spectrometer (AMS) and gas chromatographic &ndash; mass spectrometric (GC-MS) analysed PM₁ filters on an hourly basis. This includes source apportionment of the AMS derived organic matter (OM) using positive matrix factorisation (PMF) and analysis of levoglucosan as wood combustion marker, respectively. <br><br> During the measurement period nitrate and OM mass are the main contributors to the defined submicron particle mass of AMS and Aethalometer with 28% and 35%, respectively. Wood combustion organic aerosol (WCOA) contributes to OM with 23% on average and 27% in the evening and night time. Conclusively, wood combustion has a strong influence on the organic matter and overall aerosol composition. Levoglucosan accounts for 14% of WCOA mass with a higher percentage in comparison to other studies. The ratio between the mass of levoglucosan and organic carbon amounts to 0.06. <br><br> This study is unique in that it provides a one-hour time resolution comparison between the wood combustion results of the AMS and the GC-MS analysed filter method at a PM₁ particle size range. The comparison of the concentration variation with time of the PMF WCOA factor, levoglucosan estimated by the AMS data and the levoglucosan measured by GC-MS is highly correlated (<i>R</i>² = 0.84), and a detailed discussion on the contributors to the wood combustion marker ion at mass-to-charge ratio 60 is given. At the end, both estimations, the WCOA factor and the levoglucosan concentration estimated by AMS data, allow to observe the variation with time of wood combustion emissions (gradient correlation with GC-MS levoglucosan of <i>R</i>² = 0.84). In the case of WCOA, it provides the estimated magnitude of wood combustion emission. Quantitative estimation of the levoglucosan concentration from the AMS data is problematic due to its overestimation in comparison to the levoglucosan measured by the GC-MS

Organic aerosol concentration and composition over Europe: insights from comparison of regional model predictions with aerosol mass spectrometer factor analysis

A detailed three-dimensional regional chemical transport model (Particulate Matter Comprehensive Air Quality Model with Extensions, PMCAMx) was applied over Europe, focusing on the formation and chemical transformation of organic matter. Three periods representative of different seasons were simulated, corresponding to intensive field campaigns. An extensive set of AMS measurements was used to evaluate the model and, using factor-analysis results, gain more insight into the sources and transformations of organic aerosol (OA). Overall, the agreement between predictions and measurements for OA concentration is encouraging, with the model reproducing two-thirds of the data (daily average mass concentrations) within a factor of 2. Oxygenated OA (OOA) is predicted to contribute 93% to total OA during May, 87% during winter and 96% during autumn, with the rest consisting of fresh primary OA (POA). Predicted OOA concentrations compare well with the observed OOA values for all periods, with an average fractional error of 0.53 and a bias equal to −0.07 (mean error = 0.9 μg m−3, mean bias = −0.2 μg m−3). The model systematically underpredicts fresh POA at most sites during late spring and autumn (mean bias up to −0.8 μg m−3). Based on results from a source apportionment algorithm running in parallel with PMCAMx, most of the POA originates from biomass burning (fires and residential wood combustion), and therefore biomass burning OA is most likely underestimated in the emission inventory. The sensitivity of POA predictions to the corresponding emissions' volatility distribution is discussed. The model performs well at all sites when the Positive Matrix Factorization (PMF)-estimated low-volatility OOA is compared against the OA with saturation concentrations of the OA surrogate species C* ≤ 0.1 μg m−3 and semivolatile OOA against the OA with C* > 0.1 μg m−3