Synthesis and fluorescent properties of some heterobifunctional and rigidized 7-aminocoumarins

Heterobifunctional fluorescent reagents of coumarin type are synthesized. They possess, in position 7 , a rigidized or un-rigidized amino group and, in position 3 or 4 , a carboxylic function. The fluorescence characteristics of these compounds are described and compared with the 7-amino-4-methylcoumarin. The influence of the relative freedom of rotation of the amino group or the position of the acid function on the fluorescence properties are also studied.     

A Convenient Synthesis of Diversely Substituted N,N-Dimethyl-4-oxo-2-(E)-alkenamides

An efficient synthesis of diversely substituted N,N-dimethyl-4-oxo-2-(E)-alkenamides is reported. These derivatives were obtained in three steps from I,4benzodioxin with fair to good yields     

Characterization of d.c. plasma torch voltage fluctuations

The arc root fluctuations at the anode-nozzle of a d.c. plasma spray torch with a special configuration of the electrodes allowing to work with the same gas flowrate with nozzle diameters ranging from 6 to 10 mm were systematically studied. The plasma gas was Ar/H2 (25 vol % H2), the current was varied between 200 and 600 A and the plasma gas flowrate between 24 and 80 slm. After 30–60 mn working the nozzle wall started to be sufficiently eroded to have a stagnant arc spot which lived until arcing created another one. It was shown that the life time of the upstream arc spots were 30–40 % longer than the downstream ones which could play an important role in the electrode erosion. Dimensional analysis allowed to find a relationship between the nozzle diameter D, the arc current I and gas flow rate G and the mean spot lifetime which is closely connected with the difference between D and the electrical diameter of the arc column. The comparison of voltage signal and light emission at a point of the plasma jet close to the nozzle exit on its axis allowed to determine the mean electrical field within the plasma column and the mean position of the arc root. The comparison with the electrode erosion area for well defined conditions showed a good correlation with the calculated arc root position.     

Rotation-induced breakdown of torsional quantum control

Control of the torsional angles of nonrigid molecules is key for the development of emerging areas like molecular electronics and nanotechnology. Based on a rigorous calculation of the rotation-torsion-Stark energy levels of nonrigid biphenyl-like molecules, we show that, unlike previously believed, instantaneous rotation-torsion-Stark eigenstates of such molecules, interacting with a strong laser field, present a large degree of delocalization in the torsional coordinate even for the lowest energy states. This is due to a strong coupling between overall rotation and torsion leading to a breakdown of the torsional alignment. Thus, adiabatic control of changes on the planarity of this kind of molecule is essentially impossible unless the temperature is on the order of a few Kelvin.     

The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer

To investigate the accuracy of tomographic particle image velocimetry (Tomo-PIV) for turbulent boundary layer measurements, a series of synthetic image-based simulations and practical experiments are performed on a high Reynolds number turbulent boundary layer at Re_θ = 7,800. Two different approaches to Tomo-PIV are examined using a full-volume slab measurement and a thin-volume “fat” light sheet approach. Tomographic reconstruction is performed using both the standard MART technique and the more efficient MLOS-SMART approach, showing a 10-time increase in processing speed. Random and bias errors are quantified under the influence of the near-wall velocity gradient, reconstruction method, ghost particles, seeding density and volume thickness, using synthetic images. Experimental Tomo-PIV results are compared with hot-wire measurements and errors are examined in terms of the measured mean and fluctuating profiles, probability density functions of the fluctuations, distributions of fluctuating divergence through the volume and velocity power spectra. Velocity gradients have a large effect on errors near the wall and also increase the errors associated with ghost particles, which convect at mean velocities through the volume thickness. Tomo-PIV provides accurate experimental measurements at low wave numbers; however, reconstruction introduces high noise levels that reduces the effective spatial resolution. A thinner volume is shown to provide a higher measurement accuracy at the expense of the measurement domain, albeit still at a lower effective spatial resolution than planar and Stereo-PIV.     

Pathwidth of outerplanar graphs

We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a constant c such that the pathwidth of every biconnected outerplanar graph is at most c plus the pathwidth of its dual. They also conjectured that this was actually true with c being one for every biconnected planar graph. Fomin [10] proved that the second conjecture is true for all planar triangulations. First, we construct for each p ≥ 1, a biconnected outerplanar graph of pathwidth 2p + 1 whose (geometric) dual has pathwidth p + 1, thereby disproving both conjectures. Next, we also disprove two other conjectures (one of Bodlaender and Fomin [3], implied by one of Fomin [10]. Finally we prove, in an algorithmic way, that the pathwidth of every biconnected outerplanar graph is at most twice the pathwidth of its (geometric) dual minus one. A tight interval for the studied relation is therefore obtained, and we show that all cases in the interval happen. © 2006 Wiley Periodicals, Inc. J Graph Theory 55: 27–41, 2007