The nonlinear Schroedinger equation for the delta-comb potential: quasi-classical chaos and bifurcations of periodic stationary solutions

The nonlinear Schroedinger equation is studied for a periodic sequence of delta-potentials (a delta-comb) or narrow Gaussian potentials. For the delta-comb the time-independent nonlinear Schroedinger equation can be solved analytically in terms of Jacobi elliptic functions and thus provides useful insight into the features of nonlinear stationary states of periodic potentials. Phenomena well-known from classical chaos are found, such as a bifurcation of periodic stationary states and a transition to spatial chaos. The relation of new features of nonlinear Bloch bands, such as looped and period doubled bands, are analyzed in detail. An analytic expression for the critical nonlinearity for the emergence of looped bands is derived. The results for the delta-comb are generalized to a more realistic potential consisting of a periodic sequence of narrow Gaussian peaks and the dynamical stability of periodic solutions in a Gaussian comb is discussed.Comment: Enhanced and revised version, to appear in J. Nonlin. Math. Phy

Comparison of emission ratios from on-road sources using a mobile laboratory under various driving and operational sampling modes

International audienceMobile sources produce a significant fraction of the total anthropogenic emissions burden in large cities and have harmful effects on air quality at multiple spatial scales. Mobile emissions are intrinsically difficult to estimate due to the large number of parameters affecting the emissions variability within and across vehicles types. The MCMA-2003 Campaign in Mexico City has showed the utility of using a mobile laboratory to sample and characterize specific classes of motor vehicles to better quantify their emissions characteristics as a function of their driving cycles. The technique clearly identifies "high emitter" vehicles via individual exhaust plumes, and also provides fleet average emission rates. We have applied this technique to Mexicali during the Border Ozone Reduction and Air Quality Improvement Program for the Mexicali-Imperial Valley in 2005. In this paper we analyze the variability of measured emission ratios for emitted NOx, CO, specific VOCs, NH3, and some primary fine particle components and properties obtained during the Border Ozone Reduction and Air Quality Improvement Program for the Mexicali-Imperial Valley in 2005 by deploying a mobile laboratory in roadside stationary sampling, chase and fleet average operational sampling modes. The measurements reflect various driving modes characteristic of the urban fleets. The observed variability for all measured gases and particle emission ratios is greater for the chase and roadside stationary sampling than for fleet average measurements. The fleet average sampling mode captured the effects of traffic conditions on the measured on-road emission ratios, allowing the use of fuel-based emission ratios to assess the validity of traditional "bottom-up" emissions inventories. Using the measured on-road emission ratios, we estimate CO and NOx mobile emissions of 175±62 and 10.4±1.3 metric tons/day, respectively, for the gasoline vehicle fleet in Mexicali. Comparisons with similar on-road emissions data from Mexico City indicated that fleet average NO emission ratios were around 20% higher in Mexicali than in Mexico City whereas HCHO and NH3 emission ratios were higher by a factor of 2 in Mexico City than in Mexicali. Acetaldehyde emission ratios did not differ significantly whereas selected aromatics VOCs emissions were similar or smaller in Mexicali. On-road heavy-duty diesel truck (HDDT) nitrogen oxides emissions were measured near Austin, Texas, as well as in both Mexican cities, with NOy emission ratios in Austin < Mexico City < Mexicali

Novel method of generation of Ca(HCO3)2 and CaCO3 aerosols and first determination of hygroscopic and cloud condensation nuclei activation properties

Atmospheric mineral aerosols contain CaCO3 as a reactive component. A novel method to produce CaCO3 aerosol was developed by spraying Ca(HCO3)2 solution, which was generated from a CaCO3 suspension and CO2. By aerosol mass spectrometry the freshly sprayed and dried aerosol was characterized to consist of pure Ca(HCO3)2 which under annealing in a tube furnace transformed into CaCO3. Transmission Electron Microscopy demonstrated that the particles produced were spherical. The method was able to generate aerosol of sufficient concentration and proper size for the study of physiochemical properties and investigations of heterogeneous reactions of mineral aerosol. The dried Ca(HCO3)2 particles were somewhat more hygroscopic than CaCO3 particles. However, during humidification a restructuring took place and &sim;2/3 of the Ca(HCO3)2 was transformed to CaCO3. The mixed Ca(HCO3)2/CaCO3(s) particles were insoluble with a growth factor of 1.03 at 95% (hygroscopicity parameter &kappa;=0.011&plusmn;0.007) relative humidity. This compares to a corresponding growth factor of 1.01 for CaCO3(s) (&kappa;=0.0016&plusmn;0.0004). Mass spectrometric composition analysis, restructuring, and insolubility of the mixed particles suggested that solid Ca(HCO3)2(s) was observed. This would be in contrast to the current belief that Ca(HCO3)2(s) is thermodynamically instable. The CCN activity of Ca(HCO3)2(s) aerosol (&kappa;&asymp;0.15) is remarkably higher than that of CaCO3 aerosol (&kappa;=0.0019&plusmn;0.0007) and less than that of Ca(NO3)2. The noticeable but limited solubility of Ca(HCO3)2 of &asymp;0.01 mol/l explains limited hygroscopic growth and good CCN activity. Experiments in the Large Jülich Aerosol Chamber indicated that Ca(HCO3)2(s) could exist for several hours under dry atmospheric conditions. However, it was likely buried in a protective layer of CaCO3(s). We conclude that Ca(HCO3)2 may be formed in the atmosphere in cloud droplets of activated mineral dust by reaction of CaCO3 with CO2 and H2O. The presence of Ca(HCO3)2 and as a consequence an enhanced CCN activity may alter the influence of mineral aerosol on global climate

Gas phase formation of extremely oxidized pinene reaction products in chamber and ambient air

High molecular weight (300–650 Da) naturally charged negative ions have previously been observed at a boreal forest site in Hyytiälä, Finland. The long-term measurements conducted in this work showed that these ions are observed practically every night between spring and autumn in Hyytiälä. The ambient mass spectral patterns could be reproduced in striking detail during additional measurements of α-pinene (C&lt;sub&gt;10&lt;/sub&gt;H&lt;sub&gt;16&lt;/sub&gt;) oxidation at low-OH conditions in the Jülich Plant Atmosphere Chamber (JPAC). The ions were identified as clusters of the nitrate ion (NO&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;&amp;minus;&lt;/sup&gt;) and α-pinene oxidation products reaching oxygen to carbon ratios of 0.7–1.3, while retaining most of the initial ten carbon atoms. Attributing the ions to clusters instead of single molecules was based on additional observations of the same extremely oxidized organics in clusters with HSO&lt;sub&gt;4&lt;/sub&gt;&lt;sup&gt;&amp;minus;&lt;/sup&gt; (Hyytiälä) and C&lt;sub&gt;3&lt;/sub&gt;F&lt;sub&gt;5&lt;/sub&gt;O&lt;sub&gt;2&lt;/sub&gt;&lt;sup&gt;&amp;minus;&lt;/sup&gt; (JPAC). The most abundant products in the ion spectra were identified as C&lt;sub&gt;10&lt;/sub&gt;H&lt;sub&gt;14&lt;/sub&gt;O&lt;sub&gt;7&lt;/sub&gt;, C&lt;sub&gt;10&lt;/sub&gt;H&lt;sub&gt;14&lt;/sub&gt;O&lt;sub&gt;9&lt;/sub&gt;, C&lt;sub&gt;10&lt;/sub&gt;H&lt;sub&gt;16&lt;/sub&gt;O&lt;sub&gt;9&lt;/sub&gt;, and C&lt;sub&gt;10&lt;/sub&gt;H&lt;sub&gt;14&lt;/sub&gt;O&lt;sub&gt;11&lt;/sub&gt;. The mechanism responsible for forming these molecules is still not clear, but the initial reaction is most likely ozone attack at the double bond, as the ions are mainly observed under dark conditions. β-pinene also formed highly oxidized products under the same conditions, but less efficiently, and mainly C&lt;sub&gt;9&lt;/sub&gt; compounds which were not observed in Hyytiälä, where β-pinene on average is 4–5 times less abundant than α-pinene. Further, to explain the high O/C together with the relatively high H/C, we propose that geminal diols and/or hydroperoxide groups may be important. We estimate that the night-time concentration of the sum of the neutral extremely oxidized products is on the order of 0.1–1 ppt (~10&lt;sup&gt;6&lt;/sup&gt;–10&lt;sup&gt;7&lt;/sup&gt; molec cm&lt;sup&gt;−3&lt;/sup&gt;). This is in a similar range as the amount of gaseous H&lt;sub&gt;2&lt;/sub&gt;SO&lt;sub&gt;4&lt;/sub&gt; in Hyytiälä during day-time. As these highly oxidized organics are roughly 3 times heavier, likely with extremely low vapor pressures, their role in the initial steps of new aerosol particle formation and growth may be important and needs to be explored in more detail in the future

Real-Time Measurements of Engine-Out Trace Elements: Application of a Novel Soot Particle Aerosol Mass Spectrometer for Emissions Characterization

Lubricant-derived trace element emissions are the largest contributors to the accumulation of incombustible ash in diesel particulate filters (DPF), eventually leading to filter plugging and an increase in engine fuel consumption. Particulate trace element emissions also pose adverse health effects and are the focus of increasingly stringent air quality regulations. To date, the rates and physical and chemical properties of lubricant-derived additive emissions are not well characterized, largely due to the difficulties associated with conducting the measurements. This work investigated the potential for conducting real-time measurements of lubricant-derived particle emissions. The experiment used the Soot Particle Aerosol Mass Spectrometer (SP-AMS) developed by Aerodyne Research to measure the size, mass and composition of submicron particles in the exhaust. Results confirm the ability of the SP-AMS to measure engine-out emissions of calcium, zinc, magnesium, phosphorous, and sulfur. Further, emissions of previously difficult to detect elements, such as boron, and low-level engine wear metals, such as lead, were also measured. This paper provides an overview of the results obtained with the SP-AMS, and demonstrates the utility of applying real-time techniques to engine-out and tailpipe-out trace element emissions. Application of the SP-AMS for engine exhaust characterization followed a two-part approach: (1) measurement validation, and (2) measurement of engine-out exhaust. Measurement validation utilized a diesel burner with precise control of lubricant consumption. Results showed a good correlation between CJ-4 oil consumption and measured levels of lubricant-derived trace elements in the particle phase. Following measurement validation, the SP-AMS measured engine-out emissions from a medium-duty diesel engine, operated over a standard speed/load matrix. This work demonstrates the utility of state-of-the-art online techniques (such as the SP-AMS) to measure engine-out emissions, including trace species derived from lubricant additives. Results help optimize the combined engine-lubricant-aftertreatment system and provide a real-time characterization of emissions. As regulations become more stringent and emission controls more complex, advanced measurement techniques with high sensitivity and fast time response will become an increasingly important part of engine characterization studies.United States. Environmental Protection Agency (Grant RD834560

Comparison of emissions from on-road sources using a mobile laboratory under various driving and operational sampling modes

Mobile sources produce a significant fraction of the total anthropogenic emissions burden in large cities and have harmful effects on air quality at multiple spatial scales. Mobile emissions are intrinsically difficult to estimate due to the large number of parameters affecting the emissions variability within and across vehicles types. The MCMA-2003 Campaign in Mexico City has showed the utility of using a mobile laboratory to sample and characterize specific classes of motor vehicles to better quantify their emissions characteristics as a function of their driving cycles. The technique clearly identifies "high emitter" vehicles via individual exhaust plumes, and also provides fleet average emission rates. We have applied this technique to Mexicali during the Border Ozone Reduction and Air Quality Improvement Program (BORAQIP) for the Mexicali-Imperial Valley in 2005. We analyze the variability of measured emission ratios for emitted NOx [NO subscript x], CO, specific VOCs, NH3 [NH subscript 3], and some primary fine particle components and properties by deploying a mobile laboratory in roadside stationary sampling, chase and fleet average operational sampling modes. The measurements reflect various driving modes characteristic of the urban fleets. The observed variability for all measured gases and particle emission ratios is greater for the chase and roadside stationary sampling than for fleet average measurements. The fleet average sampling mode captured the effects of traffic conditions on the measured on-road emission ratios, allowing the use of fuel-based emission ratios to assess the validity of traditional "bottom-up" emissions inventories. Using the measured on-road emission ratios, we estimate CO and NOx [NO subscript x] mobile emissions of 175±62 and 10.4±1.3 metric tons/day, respectively, for the gasoline vehicle fleet in Mexicali. Comparisons with similar on-road emissions data from Mexico City indicated that fleet average NO emission ratios were around 20% higher in Mexicali than in Mexico City whereas HCHO and NH3 [NH subscript 3] emission ratios were higher by a factor of 2 in Mexico City than in Mexicali. Acetaldehyde emission ratios did not differ significantly whereas selected aromatics VOCs emissions were similar or smaller in Mexicali. Nitrogen oxides emissions for on-road heavy-duty diesel truck (HDDT) were measured near Austin, Texas, as well as in both Mexican cities, with NOy [NO subscript y] emission ratios in Austin < Mexico City < Mexicali.Mexico. Comisión Ambiental MetropolitanaNational Science Foundation (U.S.) (Grant ATM-0528227)Molina Center for Energy and the EnvironmentUniversity of Texas at AustinLatin American Scholarship Program of American Universitie

Transcriptional regulation of the B-Globin locus: of mice and men

The aim of this thesis was to get more insight into the mechanism of transcriptional activation of the human B-globin locus. Chapter 1 serves as an introduction to chromatin. The different aspects of chromatin are briefly described. Chapter 2 reviews the work on the human B-globin locus over the last decade. This review aims to present some background information for the more. recent experiments that are described in chapters 3 to 6. Chapter 3 shows the results of individual hypersensitive site deletions of the p-globin LCR: the trans genes become subject to position effects and a novel position effect is described. In chapter 4 one of the parameters that is important in the activation of the globin genes is described: the frequency of LCR-gene . interactions. Chapter 5 presents evidence that the locus control region activates only one gene at a time. Finally in chapter 6 detailed analyses of the mouse p-globin locus is shown and the data suggest that the mechanism of gene activation is conserved during evolution. In concluding remarks I discuss some implications of our work and future experiments. For more detailed considerations of specific findings, the reader is referred to the discussion of chapters 3 to 6

Continuous limits of residual neural networks in case of large input data

Residual deep neural networks (ResNets) are mathematically described as interacting particle systems. In the case of infinitely many layers the ResNet leads to a system of coupled system of ordinary differential equations known as neural differential equations. For large scale input data we derive a mean-field limit and show well-posedness of the resulting description. Further, we analyze the existence of solutions to the training process by using both a controllability and an optimal control point of view. Numerical investigations based on the solution of a formal optimality system illustrate the theoretical findings

Cross-Disciplinarity in the Advance of Antarctic Ecosystem Research

The biodiversity, ecosystem services and climate variability of the Antarctic continent, and the Southern Ocean are major components of the whole Earth system. Antarctic ecosystems are driven more strongly by the physical environment than many other marine and terrestrial ecosystems. As a consequence, to understand ecological functioning, cross-disciplinary studies are especially important in Antarctic research. The conceptual study presented here is based on a workshop initiated by the Research Programme Antarctic Thresholds - Ecosystem Resilience and Adaption of the Scientific Committee on Antarctic Research, which focused on challenges in identifying and applying cross-disciplinary approaches in the Antarctic. Novel ideas, and first steps in their implementation, were clustered into eight themes, ranging from scale problems, risk maps, organism and ecosystem responses to multiple environmental changes, to evolutionary processes. Scaling models and data across different spatial and temporal scales were identified as an overarching challenge. Approaches to bridge gaps in the research programmes included multi-disciplinary monitoring, linking biomolecular findings and simulated physical environments, as well as integrative ecological modelling. New strategies in academic education are proposed. The results of advanced cross-disciplinary approaches can contribute significantly to our knowledge of ecosystem functioning, the consequences of climate change, and to global assessments that ultimately benefit humankind