Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model

The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations turn out to be second order differential equations where the second order terms scale as 1/N with the particle number. For large N the evolution reduces to a (classical) Liouvillian dynamics. The phase space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover. In addition, the thermodynamic Bloch equation is analyzed using similar techniques.Comment: 11 pages, Revtex

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

Aerosol chemical composition at Cabouw, The Netherlands as observed in two intensive periods in May 2008 and March 2009

Observations of aerosol chemical composition in Cabauw, the Netherlands, are presented for two intensive measurement periods in May 2008 and March 2009. Sub-micron aerosol chemical composition was measured by an Aerodyne Aerosol Mass Spectrometer (AMS) and is compared to observations from aerosol size distribution measurements as well as composition measurements with a Monitor for AeRosol and GAses (MARGA) based instrument and a Thermal-Desorption Proton-Transfer-Reaction Mass-Spectrometer (TD-PTR-MS). An overview of the data is presented and the data quality is discussed. In May 2008 enhanced pollution was observed with organics contributing 40% to the PM1 mass. In contrast the observed average mass loading was lower in March 2009 and a dominance of ammonium nitrate (42%) was observed. The semi-volatile nature of ammonium nitrate is evident in the diurnal cycles with maximum concentrations observed in the morning hours in May 2008 and little diurnal variation observed in March 2009. Size dependent composition data from AMS measurements are presented and show a dominance of organics in the size range below 200 nm. A higher O:C ratio of the organics is observed for May 2008 than for March 2009. Together with the time series of individual tracer ions this shows the dominance of OOA over HOA in May 2008

COMPETITION AMONG HOSPITALS AND ITS MEASUREMENT: THEORY AND A CASE STUDY

Our paper provides several insights on the characteristics of the concept of “Poles d’Excellence Rurale” (PER) through bilateral comparisons with that of Competitive Pole (CP) and cluster. The concept of PER is a French government’ initiative designed for the development of rural areas similar to that of the Competitive Pole. We emphasize important particularities of these concepts by analyzing some of their similarities and major differences.Pole d’Excellence Rurale, Competitive Pole, cluster, rural development

Kicked Bose-Hubbard systems and kicked tops -- destruction and stimulation of tunneling

In a two-mode approximation, Bose-Einstein condensates (BEC) in a double-well potential can be described by a many particle Hamiltonian of Bose-Hubbard type. We focus on such a BEC whose interatomic interaction strength is modulated periodically by $\delta$-kicks which represents a realization of a kicked top. In the (classical) mean-field approximation it provides a rich mixed phase space dynamics with regular and chaotic regions. By increasing the kick-strength a bifurcation leads to the appearance of self-trapping states localized on regular islands. This self-trapping is also found for the many particle system, however in general suppressed by coherent many particle tunneling oscillations. The tunneling time can be calculated from the quasi-energy splitting of the corresponding Floquet states. By varying the kick-strength these quasi-energy levels undergo both avoided and even actual crossings. Therefore stimulation or complete destruction of tunneling can be observed for this many particle system

Development of Soft Ionization for Particulate Organic Detection with the Aerodyne Aerosol Mass Spectrometer

During this DOE SBIR Phase II project, we have successfully developed several soft ionization techniques, i.e., ionization schemes which involve less fragmentation of the ions, for use with the Aerodyne time-of-flight aerosol mass spectrometer (ToF-AMS). Vacuum ultraviolet single photon ionization was demonstrated in the laboratory and deployed in field campaigns. Vacuum ultraviolet single photon ionization allows better identification of organic species in aerosol particles as shown in laboratory experiments on single component particles, and in field measurements on complex multi-component particles. Dissociative electron attachment with lower energy electrons (less than 30 eV) was demonstrated in the measurement of particulate organics in chamber experiments in Switzerland, and is now a routine approach with AMS systems configured for bipolar, negative ion detection. This technique is particularly powerful for detection of acidic and other highly oxygenated secondary organic aerosol (SOA) chemical functionality. Low energy electron ionization (10 to 12 eV) is also a softer ionization approach routinely available to AMS users. Finally, Lithium ion attachment has been shown to be sensitive to more alkyl-like chemical functionality in SOA. Results from Mexico City are particularly exciting in observing changes in SOA molecular composition under different photochemical/meteorological conditions. More recent results detecting biomass burns at the Montana fire lab have demonstrated quantitative and selective detection of levoglucosan. These soft ionization techniques provide the ToF-AMS with better capability for identifying organic species in ambient atmospheric aerosol particles. This, in turn, will allow more detailed study of the sources, transformations and fate of organic-containing aerosol

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

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<sub>10</sub>H<sub>16</sub>) oxidation at low-OH conditions in the Jülich Plant Atmosphere Chamber (JPAC). The ions were identified as clusters of the nitrate ion (NO<sub>3</sub><sup>−</sup>) 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<sub>4</sub><sup>−</sup> (Hyytiälä) and C<sub>3</sub>F<sub>5</sub>O<sub>2</sub><sup>−</sup> (JPAC). The most abundant products in the ion spectra were identified as C<sub>10</sub>H<sub>14</sub>O<sub>7</sub>, C<sub>10</sub>H<sub>14</sub>O<sub>9</sub>, C<sub>10</sub>H<sub>16</sub>O<sub>9</sub>, and C<sub>10</sub>H<sub>14</sub>O<sub>11</sub>. 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<sub>9</sub> 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<sup>6</sup>–10<sup>7</sup> molec cm<sup>−3</sup>). This is in a similar range as the amount of gaseous H<sub>2</sub>SO<sub>4</sub> 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

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