Stability Properties of Feynman's Operational Calculus for Exponential Functions of Noncommuting Operators

Stability properties of Feynman's operational calculus are addressed in the setting of exponential functions of noncommuting operators. Applications of some of the stability results are presented. In particular, the time-dependent perturbation theory of nonrelativistic quantum mechanics is presented in the setting of the operational calculus and application of the stability results of this paper to the perturbation theory are discussed.     

Fundamental processes in long air gap discharges

The development of atmospheric lightning is initiated and sustained by the formation in virgin air of ‘streamer corona’ and ‘leader’ discharges, very similar to those observed in laboratory long sparks. Therefore, the experimental and theoretical investigations of these laboratory discharges have become of large interest to improve the physical knowledge of the lightning process and to develop self-consistent models that could be applied to new protection concepts.In the present paper the fundamental processes of the subsequent phases of long air gap discharges are analyzed, from the first corona inception and development to the leader channel formation and propagation. For all these processes simulations models are discussed that have been essentially derived and simplified by the authors, in order to develop sequential time-dependent simulation of the laboratory breakdown, with both positive and negative voltages. The possibility of extending these models to the case of natural lightning is discussed in the companion paper, presented in this same volume. To cite this article: I. Gallimberti et al., C. R. Physique 3 (2002) 1335–1359.     

Towards Treating Correlations in Bose Condensates

 We use the adiabatic hyperspheric expansion and the Faddeev decomposition of the wave function with only s-waves. We derive for a fixed hyperradius an integro-differential equation for the angular eigenvalue and wave function. The correlations lower the interaction energy for N = 20 by about a factor of 5. Received October 22, 2001; accepted for publication November 5, 2001     

Amplifiers and Lasers in PCF Configurations

In this paper we will present an overview of the use of photonic crystal fibers as fiber amplifiers. We will describe the basic concepts of optical amplification, and how to do numerical modelling of such components. We will then identify advantages and disadvantages of amplifiers based on PCF technology compared to conventional fibers, and then go into greater detail on some of these specific applications, such as low pump power amplifiers, and high-power double-clad amplifiers and lasers.     

Characterization of sulfate-reducing bacteria in yeast industry waste by microcalorimetry and PCR amplification

Sulfate-reducing bacteria (SRB) were isolated from anaerobic sludge of yeast factory wastewater treatment plant by cultivation on Postgate C medium. Microcalorimetry was used to monitor the anaerobic digestion processes and to measure the growth rates of sulfate-reducing bacteria. The maximum growth rates determined by microcalorimetry and ATP analysis were different—μ_max(dQ/dt) = 0.165 ± 0.008 h⁻¹ and μ_max(N_ATP) = 0.207 ± 0.013 h⁻¹. Experiments on the cultivation of SRB from yeast industry wastewater treatment plant in batch culture showed that during the first 20 h the concentration of sulfate decreased from 78.3 mM down to 62.2 mM while the increase of sulfide production was negligible. Perceptible amount of sulfide (7.82 mM) appeared on the 33.5 h of fermentation together with a peak on the power–time curve and considerable increase in the cell count (1.26 × 10⁹). First steps of sulfate metabolism (activation of sulfate by ATP sulfurylase, production of H₂) are accompanied by endothermic heat effects, therefore the values of thermal power remain moderate until the evolution of sulfide starts. The influence of green microalgae Chlorococcum sp. (preparation Biotreat 100) on the growth characteristics of microorganisms was also studied. Identification of one SRB strain was started by sequencing of PCR-amplified 16S rRNA gene. Two sets of primers were used for PCR amplification, both specific for domain Bacteria but giving different gene fragments. PCR-products were purified with JETQUICK kit according to the manufacturer instructions.     

Hexaphyrin(1.0.1.0.0.0). A new colorimetric actinide sensor

Hexaphyrin(1.0.1.0.0.0) (isoamethyrin) undergoes a significant color change in the presence of UO₂²⁺, PuO₂²⁺, and NpO₂²⁺. The complexation of the first of these dioxo actinide cations was studied in semi-quantitative fashion in 1:1 MeOH-CH₂Cl₂. Under these conditions, the detection limit for UO₂²⁺ was found to be ca. 5.8 ppm by naked eye monitoring and <28 ppb by UV-vis spectroscopy. Isoamethyrin does not undergo a color change in the presence of most transition metals or when exposed to Gd(III). Isoamethyrin thus constitutes an attractive alternative to 2,2′(1,8-dihydroxy-3,6-disulfonaphthylene-2,7-bisazo)-bisbenzenarsonic acid (AzIII) and 2-(5-bromo-2-pyridylazo)-5-(diethylamino)phenol (BrPADAP), systems currently used as actinide cation sensors.     

Experimental design and the optimization of a polymer supported palladium complex for use in the Heck reaction

Optimization of the Heck reaction of 4-bromoacetophenone with styrene by a polymer supported, sulfur-containing palladacycle, varying 6 factors at a total of 28 different levels, corresponding to 5760 different possibilities was undertaken. Conversion improved from 34%, with large observable leaching to 88% with no leaching. This was accomplished using a Design of Experiments approach facilitated by the Statistical Design Package, MODDE 7.0^TM.