Two-atom two-photon resonance fluorescence

The excitation spectrum arising from the interaction between two identical two-level atoms, one of which is excited in the presence of a strong electromagnetic field (pump field), is investigated when the atomic transition frequency is nearly twice the frequency of the pump field. The excitation spectrum consists of those describing the symmetric and antisymmetric modes, respectively. The spectral functions for the symmetric and antisymmetric modes are derived and discussed in detail. The possibility to measure directly the magnitude of the dipole-dipole interaction energy is discussed.     

Resonance fluorescence spectrum of a three-level atom

We consider the excitation spectrum arising from the interaction between a three-level atom and a strong electromagnetic field in the frequency region where the two atomic transition frequencies are nearly equal to once and twice the frequency of the pump field respectively. Detailed expressions for the spectral functions are derived describing the two-, one- and zero-photon excitations as well as those arising from the coupling between them, in the limit of high photon densities. The zero-photon excitations describe low frequency modes induced by the pump field under resonance conditions.     

Stimulated Raman spectra of a strong bichromatic field interacting with a three-level atom

We have studied the stimulated Raman spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes ω _a and ω _b are in resonance with the two atomic transition frequencies. The Green's function formalism has been used in the limit of high photon densities to calculate the excitation spectra near the frequencies ω = ± ω _ab = ± (ω _a - ω _b ). Expressions are derived for the relative intensities, which describe, apart from the usual Raman peak at the frequency ω = ω _ab , four pairs of lorentzian lines peaked at the frequencies ω - ω _ab = ± Ω _a /√2, ± Ω _b /√2, ± Ω and ± 2Ω, respectively, and having spectra widths of the order of 3γ₀/4. The parameter Ω is defined as Ω² = (Ω _a ² + Ω _b ²)/2, where Ω _a and Ω _b are the Rabi frequencies of the two laser fields and γ₀ is the spontaneous emission probability. Numerical calculations for selected values of the Rabi frequencies are graphically presented and discussed. Conditions have been established for which Raman gain processes are anticipated to take place.     

Graphs, networks, and linear unbiased estimates

It is shown how a best linear unbiased estimate (blue) in the additive variety-block setting can be interpreted as a network flow, that is, a function on edges that obeys the Kirkhhoff laws, of minimum square norm. An explicit expression is then obtained for the coefficients of the blue in terms of invariants of the underlying network; specifically, the invariants are: the total number of spanning trees and the number of certain selective yet specific spanning forests with just two trees. The blue is also expressed as a linear combination of bases of paths in a constructive manner. It remains a conjecture as to whether there always exists a basis of paths in which the blue is a convex combination. Consequences to design optimality are explored.     

Elongational and shear rheology of carbon nanotube suspensions

Rheological behavior of concentrated suspensions of chemical vapor deposition carbon nanotubes in uniaxial elongation and simple shear is studied experimentally and theoretically. Nanotubes are suspended in viscous host liquids—castor oil or its blends with n-decane. The elongational measurements are performed by analyzing self-thinning (due to surface tension effect) liquid threads of nanotube suspensions. A quasi-one-dimensional model is used to describe the self-thinning process, whereas corrections accounting for thread nonuniformity and necking are introduced a posteriori. The effects of nanotube concentration and aspect ratio, viscosity of the suspending liquid, and initial diameter of the self-thinning thread in uniaxial elongation are elucidated. The results for uniaxial elongation are compared with those for simple shear. The correspondence in the results of the shear and elongational measurements is addressed and interpreted. The results conform to the Herschel–Bulkley rheological constitutive equation (i.e., power law fluids with yield stress). However, the yield stress in elongation is about 40% higher than in simple shear flow, which suggests that the original Herschel–Bulkley model need modification with the yield stress being a function of the second invariant of the deviatoric stress tensor. The present effort is the first to study capillary self-thinning of Herschel–Bulkley liquids, which are exemplified here by suspensions of carbon nanotubes.     

A revisit to the retention mechanism of hydrophilic interaction liquid chromatography using model organic compounds

In this work, a revisit to the retention mechanism of HILIC was attempted to point out critical factors that contribute to the chromatographic regime as well as to bring out subtle details of the relative contribution of partitioning and surface adsorption. In this vein, the retention behaviour of a set of water-soluble vitamins (WSVs) and toluene on three silica based columns was evaluated under varying chromatographic conditions. The data obtained were associated with the hydration degree of the stationary phases and the ability of the organic solvents to disrupt the formation of the water-enriched layer. Moreover, the elution behaviour of toluene at different buffer salt concentrations in the mobile phase, confirmed the preferential partition of salt ions into the stagnant layer, as ACN content was increased. The results from the fitting of partitioning and surface adsorption models indicated differences in the contribution of the two retention mechanisms to both neutral and charged compounds. The occurrence of surface adsorption and the retentivity differences for neutral WSVs depend on the hydration degree and the hydrogen bonding properties of the solutes and the column surface, respectively. For charged solutes experiencing electrostatic repulsion, the contribution of the adsorption mechanism at highly organic mobile phases, emanates from both the weak effect of buffer salt ions on the electrostatic interaction and the strong effect of hydrophilic interactions. On the other hand, the chromatographic retention of electrostatically attracted solutes indicates that the surface adsorption dominates, even at mobile phases rich in water.     

Kinetic-spectrophotometric determination of molybdenum (VI) and tungsten (VI) in mixtures

A simple kinetic-spectrophotometric method is described for the determination of molybdenum(VI) and tungsten(VI) in mixtures, without prior separation. The method is based on the catalytic effect of molybdenum(VI) and tungsten(VI) on the oxidation of 2,4-diaminophenol dihydrochloride (DAP) by hydrogen peroxide in acidic medium. The reaction was followed spectrophotometrically by measuring the rate of change in absorbance with time at 500 nm. A partial inhibition in the catalytic activity of each catalyst, when the other one is present, at all ratios of Mo(VI) W(VI) mixtures studied was observed. On the other hand, the catalytic activity of tungsten(VI) dropped to zero whilst that of molybdenum(VI) decreased slightly, in the presence of citrate ions. Two sets of experiments were carried out, the first in the absence and the other in the presence of citrate, and the resolution of Mo(VI)/W(VI) mixtures was achieved by solving two simultaneous equations. Various molar ratios of Mo(VI) W(VI), at the 10^–6 M level, from 0.2 1 to 5 1 can be determined with satisfactory precision and accuracy. The selectivity of the method was investigated and the method was applied successfully to the determination of molybdenum and tungsten in each other's presence in steel.     

Comparison of topological, shape, and docking methods in virtual screening

Virtual screening benchmarking studies were carried out on 11 targets to evaluate the performance of three commonly used approaches: 2D ligand similarity (Daylight, TOPOSIM), 3D ligand similarity (SQW, ROCS), and protein structure-based docking (FLOG, FRED, Glide). Active and decoy compound sets were assembled from both the MDDR and the Merck compound databases. Averaged over multiple targets, ligand-based methods outperformed docking algorithms. This was true for 3D ligand-based methods only when chemical typing was included. Using mean enrichment factor as a performance metric, Glide appears to be the best docking method among the three with FRED a close second. Results for all virtual screening methods are database dependent and can vary greatly for particular targets.