Controlling a bunch of multiple filaments by means of a beam diameter

We demonstrate a three orders of magnitude increase and stability in the backscattered fluorescence signal from nitrogen molecules by terawatt femtosecond laser pulse induced air filaments using a new method. The method is based on squeezing the initial beam diameter using a telescope. The effect of laser shot-to-shot fluctuations was included in numerical simulations by a random distribution of the initial intensity in both squeezed and non-squeezed beams. Statistical processing of the simulation results shows that the average diameter of plasma channels as well as the total amount of free electrons generated in a bunch of multiple filaments in air is larger in the squeezed beam. Shot-to-shot stability of the simulated plasma density increases in the squeezed beam. The change of this plasma density with propagation distance is in good qualitative agreement with the change of the range-corrected nitrogen fluorescence signal with distance. PACS 42.65.Jx; 42.60.Jf; 42.68.Ay; 42.68.Wt     

π1-classification of real arrangements with up to eight lines

One of the open questions in the geometry of line arrangements is to what extent does the incidence lattice of an arrangement determine its fundamental group. Line arrangements of up to 6 lines were recently classified by K.M. Fan (Michigan Math. J. 44(2) (1997) 283), and it turns out that the incidence lattice of such arrangements determines the projective fundamental group. We use actions on the set of wiring diagrams, introduced in (Garber et al. (J. Knot Theory Ramf.), to classify real arrangements of up to 8 lines. In particular, we show that the incidence lattice of such arrangements determines both the affine and the projective fundamental groups.     

Flow in a waterfall with large Froude number

An approximate method is developed to solve the full nonlinear equations governing two-dimensional irrotational flow in a free waterfall, falling under the influence of gravity, at high Froude number based on conditions far upstream. Schwarz—Christoffel transformation is used to map the region, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique, for large Froude number, are used as a basis for the approximate solution of the problem. A complete solution, up to second-order approximation, for the downstream free-surfaces profiles, for different Froude number, is discussed and illustrated. The obtained approximate solutions are compared with those of other authors. Favourable agreement with other results suggests that this method is effective in dealing with flow problems strongly influenced by gravity and high Froude number. The results obtained by this method are sufficiently accurate for practical purposes.     

Fabrication and Determination of Refractive Index Profile of the Planar Waveguides by Wedge Technique

Several planar waveguides have been fabricated. The waveguides have been polished for determination of their refractiveindex profiles (RIP) by wedge method. The RIP determined by inserting the sample in a Mach-Zehnder interferometer andapplying fringe analysis methods.     

Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability

The non-linear equations of motion describing the laminar, isothermal and incompressible flow in a rectangular domain bounded by two weakly permeable, moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, are considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which given partial differential equations are invariant, then, the determining equations are derived. The determining equations are a set of linear differential equations, the solution of which gives the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equation may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables in the system. Effect of the permeation Reynolds number R_e and the dimensionless wall dilation rate α on self-axial velocity have been studied both analytically and numerically and the results are plotted.     

Study of interactions of various ionic species with solvents toward the design of receptors

In earlier studies, the interactions of isolated ionic species with various solvents were investigated using ab initio calculations. The ionic species investigated included cations (proton, hydronium, ammonium, and metal cations) and anions (single electron, hydroxide, and halide anions). However in the present study, we investigate the interactions of these ionic species with the solvent in the presence of other competing ionic species. We also elaborate on how the information obtained from these extensive studies have been employed in designing and synthesizing various kinds of novel ionophores and receptors.     

Headspace solvent microextraction of trihalomethane compounds into a single drop

Headspace solvent microextraction (HSME) into a single drop is developed for the determination of six trihalomethanes, CH2Cl2, CHCl3, C4H9Cl, CCl4, C2HCl3, and C2Cl4, in aqueous solution. A drop of benzyl alcohol containing bromoform, as an internal standard, is used for extraction. The analytes are extracted by suspending a 3-microL drop directly from the needle of a microsyringe. The needle passes through the septum of a vessel, and the needle tip appears above the surface of the solution. After the prescribed extraction time, the drop is drawn back into the syringe. The syringe is then removed, and its content is injected directly into a gas chromatography column for analysis. The main parameters affecting the HSME process, such as stirring speed, microdrop volume, sample solution temperature, microsyringe needle temperature, sample volume, solution pH, extracting solvent, and ionic strength of the solution, are studied. Also, the linear range and precision of the method are examined.     

Potentiometric determination of ultratrace amounts of fluoride enriched by zirconia in a flow system

A satisfactory method was described for separation and preconcentration of ultratrace amounts of fluoride ions enriched by zirconia (ZrO₂) as an inorganic ion exchanger. Fluoride ions can be adsorbed rapidly and selectively on zirconia from an acidic solution (pH 4.8) then reversibly desorbed by increasing pH up to 13. A flow system consisting of a column packed with zirconia impregnated on cellulose fibers and an ion-selective electrode was used for the determination of fluoride. The RSD was found to be 1.6% and the detection limit defined by S/N = 3 was 3 × 10⁻⁹ mol L⁻¹. The interference effects of various ions, such as nitrate, sulfate, halides, alkaline, and alkaline earth ions, which may be found in the environmental water, were studied, and it was found that they were tolerated even at high concentrations. The method was applied to determine fluoride in drinking water, which contains ultratrace amounts of fluoride. The concentration of fluoride was found to be 42 μg L⁻¹, which is confirmed by spiking 2 μmol fluoride to the drinking water with a recovery of 99%. Published in Russian in Zhurnal Analiticheskoi Khimii, 2006, Vol. 61, No. 2, pp. 179–183. The text was submitted by the authors in English.     

Synthesis and Spectroscopic Study of Some New Phosphoramidates,Crystal Structures of N‐Benzoyl‐N′,N″‐bis(azetidinyl)phosphoric Triamide and N‐Benzoyl‐N′,N″‐bis(hexamethylenyl)phosphoric Triamide

Some new N‐carbonyl, phosphoramidates with formula C₆H₅C(O)N(H)P(O)R₂ (R = NC₃H₆ ( 1 ), NC₆H₁₂ ( 2 ), NHCH₂CH=CH₂ ( 3 ), N(C₃H₇)₂ ( 4 )) and CCl₃C(O)N(H)P(O)R′₂ (R′ = NC₃H₆ ( 5 ), NHCH₂CH=CH₂ ( 6 )) were synthesized and characterized by ¹H, ¹³C, ³¹P NMR and IR spectroscopy and elemental analysis. The structures were determined for compounds 1 and 2 . Compound 1 exists as two crystallographically independent molecules in crystal lattice. Both compounds 1 and 2 produced dimeric aggregates via intermolecular ‐P=O…H‐N‐ hydrogen bonds, which in compound 2 is a centrosymmetric dimer. In compounds with four‐membered ring amine groups, ³J(P,C)>²J(P,C), in agreement with our previous studies about five‐membered ring amine groups. Also, ³J(P,C) values in compounds 1 and 5 are greater than in compounds with five‐, six‐ and seven‐membered ring amine groups.