Involution and Constrained Dynamics I: The Dirac Approach

We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an involutive system. We discuss the implications of this identification for field theories and argue that the involution analysis is more general and flexible than the Dirac approach. We also derive intrinsic expressions for the number of degrees of freedom.Comment: 28 pages, latex, no figure

Experimental and Numerical Study of the Dispersion and Transport of Automobile Exhaust Gases from Highways

This paper describes examples of modelling and of measurements of the dispersion and transport of exhaust gases from automobiles on a highway. Model runs were performed by a large-eddy-simulation model. The measurements were carried through by the DLR environmental research aircraft lee-side of the highway between München and Augsburg

Stratospheric and tropospheric NO₂ variability on the diurnal and annual scale: a combined retrieval from ENVISAT/SCIAMACHY and solar FTIR at the Permanent Ground-Truthing Facility Zugspitze/Garmisch

International audienceColumnar NO2 retrievals from solar FTIR measurements at the Zugspitze (47.42° N, 10.98° E, 2964 m a.s.l.), Germany were investigated synergistically with columnar NO2 retrieved from SCIAMACHY data by the University of Bremen scientific algorithm UB1.5 for the time span July 2002-October 2004. A new concept to match FTIR data to the time of satellite overpass makes use of the NO2 daytime increasing rate retrieved from the FTIR data set itself [+1.02(6)E+14 cm-2/h]. This measured increasing rate shows no significant seasonal variation. SCIAMACHY data within a 200-km radius around Zugspitze were considered, and a pollution-clearing scheme was developed to select only pixels corresponding to clean background (free) tropospheric conditions, and exclude local pollution hot spots. The resulting difference between SCIAMACHY and FTIR columns (without correcting for the different sensitivities of the instruments) varies between 0.60-1.24E+15 cm-2 with an average of 0.83E+15 cm-2. A day-to-day scatter of daily means of ?7-10% could be retrieved in mutual agreement from FTIR and SCIAMACHY. Both data sets are showing sufficient precisions to make this assessment. Analysis of the averaging kernels gives proof that at high-mountain-site FTIR is a highly accurate measure for the pure stratospheric column, while SCIAMACHY shows significant tropospheric sensitivity. Based on this finding, we set up a combined a posteriori FTIR-SCIAMACHY retrieval for tropospheric NO2, based upon the averaging kernels. It yields an annual cycle of the clean background (free) tropospheric column (-2, an average of 1.09E+15 cm-2, and an intermediate phase between that of the well known boundary layer and stratospheric annual cycles. The outcome is a concept for an integrated global observing system for tropospheric NO2 that comprises DOAS nadir satellite measurements and a set of latitudinally distributed mountain-site or clean-air FTIR stations

How does dynamical downscaling affect model biases and future projections of explosive extratropical cyclones along North America’s Atlantic coast?

Explosive extratropical cyclones (EETCs) are rapidly intensifying low pressure systems that generate severe weather along North America’s Atlantic coast. Global climate models (GCMs) tend to simulate too few EETCs, perhaps partly due to their coarse horizontal resolution and poorly resolved moist diabatic processes. This study explores whether dynamical downscaling can reduce EETC frequency biases, and whether this affects future projections of storms along North America’s Atlantic coast. A regional climate model (CanRCM4) is forced with the CanESM2 GCM for the periods 1981 to 2000 and 2081 to 2100. EETCs are tracked from relative vorticity using an objective feature tracking algorithm. CanESM2 simulates 38% fewer EETC tracks compared to reanalysis data, which is consistent with a negative Eady growth rate bias (−0.1 day−1). Downscaling CanESM2 with CanRCM4 increases EETC frequency by one third, which reduces the frequency bias to −22%, and increases maximum EETC precipitation by 22%. Anthropogenic greenhouse gas forcing is projected to decrease EETC frequency (−15%, −18%) and Eady growth rate (−0.2 day−1, −0.2 day−1), and increase maximum EETC precipitation (46%, 52%) in CanESM2 and CanRCM4, respectively. The limited effect of dynamical downscaling on EETC frequency projections is consistent with the lack of impact on the maximum Eady growth rate. The coarse spatial resolution of GCMs presents an important limitation for simulating extreme ETCs, but Eady growth rate biases are likely just as relevant. Further bias reductions could be achieved by addressing processes that lead to an underestimation of lower tropospheric meridional temperature gradients

A Factorization Algorithm for G-Algebras and Applications

It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous $G$-algebras, are finite factorization domains (FFD for short). Utilizing this result, we contribute an algorithm to find all distinct factorizations of a given element $f \in \mathcal{G}$, where $\mathcal{G}$ is any $G$-algebra, with minor assumptions on the underlying field. Moreover, the property of being an FFD, in combination with the factorization algorithm, enables us to propose an analogous description of the factorized Gr\"obner basis algorithm for $G$-algebras. This algorithm is useful for various applications, e.g. in analysis of solution spaces of systems of linear partial functional equations with polynomial coefficients, coming from $\mathcal{G}$. Additionally, it is possible to include inequality constraints for ideals in the input

Attosecond streaking of photoelectron emission from disordered solids

Attosecond streaking of photoelectrons emitted by extreme ultraviolet light has begun to reveal how electrons behave during their transport within simple crystalline solids. Many sample types within nanoplasmonics, thin-film physics, and semiconductor physics, however, do not have a simple single crystal structure. The electron dynamics which underpin the optical response of plasmonic nanostructures and wide-bandgap semiconductors happen on an attosecond timescale. Measuring these dynamics using attosecond streaking will enable such systems to be specially tailored for applications in areas such as ultrafast opto-electronics. We show that streaking can be extended to this very general type of sample by presenting streaking measurements on an amorphous film of the wide-bandgap semiconductor tungsten trioxide, and on polycrystalline gold, a material that forms the basis of many nanoplasmonic devices. Our measurements reveal the near-field temporal structure at the sample surface, and photoelectron wavepacket temporal broadening consistent with a spread of electron transport times to the surface

A New Look at the Axial Anomaly in Lattice QED with Wilson Fermions

By carrying out a systematic expansion of Feynman integrals in the lattice spacing, we show that the axial anomaly in the U(1) lattice gauge theory with Wilson fermions, as determined in one-loop order from an irrelevant lattice operator in the Ward identity, must necessarily be identical to that computed from the dimensionally regulated continuum Feynman integrals for the triangle diagrams.Comment: 1 figure, LaTeX, 18 page