Generalized solutions and distributional shadows for Dirac equations

We discuss the application of recent results on generalized solutions to the Cauchy problem for hyperbolic systems to Dirac equations with external fields. In further analysis we focus on the question of existence of associated distributional limits and derive their explicit form in case of free Dirac fields with regularizations of initial values corresponding to point-like probability densities

Generalized Fourier Integral Operators on spaces of Colombeau type

Generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is based on a theory of generalized oscillatory integrals (OIs) whose phase functions as well as amplitudes may be generalized functions of Colombeau type. The mapping properties of these FIOs are studied as the composition with a generalized pseudodifferential operator. Finally, the microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wave front sets are investigated. This theory of generalized FIOs is motivated by the need of a general framework for partial differential operators with non-smooth coefficients and distributional data

Application of a virtual watershed in academic education

International audienceHydrologic models of watersheds often represent complex systems which are difficult to understand regarding to their structure and dynamics. Virtual watersheds, i.e. watersheds which exist only in the virtual reality of a computer system, are an approach to simplify access to this real-world complexity. In this study we present the virtual watershed KIELSHED-1, a 117 km2 v-shaped valley with grassland on a "Cambisol" soil type. Two weather scenarios are delivered with the watershed: a simplified artificial weather scenario based on long-term data of a German weather station as well as an unmodified data record. The input data and parameters are compiled according to the conventions of the SWAT 2000 hydrological model. KIELSHED-1 is mainly used for education, and illustrative application examples, i.e. calculation of water balance, model calibration, development of land use scenarios, give an insight to the capabilities of the virtual watershed

Topological properties of regular generalized function algebras

We investigate density of various subalgebras of regular generalized functions in the special Colombeau algebra of generalized functions.Comment: 6 page

Dynamic structure factor of the antiferromagnetic Kitaev model in large magnetic fields

We investigate the dynamic structure factor of the antiferromagnetic Kitaev honeycomb model in a magnetic field by applying perturbative continuous unitary transformations about the high-field limit. One- and two-quasi-particle properties of the dressed elementary spin flip excitations of the high-field polarized phase are calculated which account for most of the spectral weight in the dynamic structure factor. We discuss the evolution of spectral features in these quasi-particle sectors in terms of one-quasi-particle dispersions, two-quasi-particle continua, the formation of anti-bound states, and quasi-particle decay. In particular, a comparably strong spectral feature above the upper edge of the upmost two-quasi-particle continuum represents three anti-bound states which form due to nearest-neighbor density-density interactions.Comment: 14 pages, 10 figure

Static and dynamic water structures at interfaces: A case study with focus on Pt(111)

An accurate atomistic treatment of aqueous solid–liquid interfaces necessitates the explicit description of interfacial water ideally via ab initio molecular dynamics simulations. Many applications, however, still rely on static interfacial water models, e.g., for the computation of (electro)chemical reaction barriers and focus on a single, prototypical structure. In this work, we systematically study the relation between density functional theory-derived static and dynamic interfacial water models with specific focus on the water–Pt(111) interface. We first introduce a general construction protocol for static 2D water layers on any substrate, which we apply to the low index surfaces of Pt. Subsequently, we compare these with structures from a broad selection of reference works based on the Smooth Overlap of Atomic Positions descriptor. The analysis reveals some structural overlap between static and dynamic water ensembles; however, static structures tend to overemphasize the in-plane hydrogen bonding network. This feature is especially pronounced for the widely used low-temperature hexagonal ice-like structure. In addition, a complex relation between structure, work function, and adsorption energy is observed, which suggests that the concentration on single, static water models might introduce systematic biases that are likely reduced by averaging over consistently created structural ensembles, as introduced here

Stabilization of the γ-Sn phase in tin nanoparticles and nanowires

Structures of Sn nanoparticles and nanowires are studied using density functional theory in conjunction with thermodynamic considerations. Besides the low-temperature α and room-temperature β phases, the high-temperature γ phase is considered. Results show that at ambient temperatures for sizes smaller than 50 nm, metallic β- and γ-Sn nanoparticles are more stable than semimetallic α-Sn ones because of their lower surface energies. Moreover, very small Sn nanostructures, exemplified by nanowires, are expected to exhibit the γ phase even at 0 K

Identification of valid reference genes during the differentiation of human myoblasts

<p>Abstract</p> <p>Background</p> <p>Analysis of RNA expression using real-time PCR (qRT-PCR) traditionally includes reference genes (RG) as an internal control. This practice is being questioned as it becomes increasingly clear that RG may vary considerably under certain experimental conditions. Thus, the validity of a particular RG must be determined for each experimental setting. We used qRT-PCR to measure the levels of six RG, which have been reported in the literature to be invariant. The RG were analyzed in human myoblast cultures under differentiation conditions. We examined the expression by qRT-PCR of mRNA encoding Beta-actin (ACTB), Beta-2-microglobulin (B2M), glyceraldehyde-3-phosphate dehydrogenase (GAPDH), peptidylprolyl isomerase A (PPIA), TATA box binding protein (TBP) and ribosomal protein, large, P0 (RPLPO). The mRNA expression of the following genes of interest (GOI) were analyzed: skeletal muscle alpha 1 actin (ACTA1), myogenin/myogenic factor 4 (MYOG), embryonic skeletal muscle myosin heavy chain 3 (MYH3) and the activity of creatine phosphokinase (CK). The geNorm, NormFinder and BestKeeper software programs were used to ascertain the most suitable RG to normalize the RNA input.</p> <p>Results</p> <p>Using the geNorm program, RPLPO and TBP were found to be the most stable genes, additionally a suitable normalization factor (NF) was calculated. The NormFinder software showed that RPLPO was the most stable, whereas TBP ranked second. BestKeeper program also revealed that RPLPO and TBP as stable genes, but PPIA was the most stable reference gene, whereas GAPDH and ACTB were the worst ranked.</p> <p>Conclusion</p> <p>RNA expression analyses including three independent softwares revealed that RPLPO, TBP as reference genes or NF calculated by geNorm software, are suitable to normalize the mRNA expression in myoblast after culture under differentiation conditions. Significant correlations can be identified between the differentiations markers ACTA1, MYOG, MYH3 and creatine phosphokinase (CK) activity, when the expression is normalized with the NF calculated with RPLPO and TBP.</p

Fluence Dependence of Charge Collection of irradiated Pixel Sensors

The barrel region of the CMS pixel detector will be equipped with ``n-in-n'' type silicon sensors. They are processed on DOFZ material, use the moderated p-spray technique and feature a bias grid. The latter leads to a small fraction of the pixel area to be less sensitive to particles. In order to quantify this inefficiency prototype pixel sensors irradiated to particle fluences between $4.7\times 10^{13}$ and 2.6\times 10^{15} \Neq have been bump bonded to un-irradiated readout chips and tested using high energy pions at the H2 beam line of the CERN SPS. The readout chip allows a non zero suppressed analogue readout and is therefore well suited to measure the charge collection properties of the sensors. In this paper we discuss the fluence dependence of the collected signal and the particle detection efficiency. Further the position dependence of the efficiency is investigated.Comment: 11 Pages, Presented at the 5th Int. Conf. on Radiation Effects on Semiconductor Materials Detectors and Devices, October 10-13, 2004 in Florence, Italy, v3: more typos corrected, minor changes required by the refere