Random walks with ‘spontaneous emission’ on lattices with periodically distributed imperfect traps

We study random walks on d-dimensional lattices with periodically distributed traps in which the walker has a finite probability per step of disappearing from the lattice and a finite probability of escaping from a trap. General expressions are derived for the total probability that the walk ends in a trap and for the moments of the number of steps made before this happens if it does happen. The analysis is extended to lattices with more types of traps and to a model where the trapping occurs during special steps. Finally, the Green's function at the origin G(0; z) for a finite lattice with periodic boundary conditions, which enters into the main expressions, is studied more closely. A generalization of an expression for G(0; 1) for the square lattice given by Montroll to values of z different from, but close to, 1 is derived.     

Dependence of the spectral width of the self-absorbed Sr 4607.33Åresonance line on Sr atomic density in a flame

Using a pressure-scanned Fabry-Pérot interferometer, we measured spectral profiles of the self-absorbed Sr resonance line at 4607.33Åemitted in a pre-mixed, laminar, shielded air-C₂H₂ flame at 1 atm for various Sr-solution concentrations. The dependence of the full width at one-half maximum (FWHM) on Sr atomic density in the flame was found to agree with a calculation based on the Voigt expression and Beer's law. It appears that one can derive the FWHM under optically thin conditions (i.e. at vanishing Sr atomic density) by linear extrapolation from measurements made at higher concentrations where the signal-to-noise ratio is good, but broadening due to self-absorption plays a role.     

Some observations on small-size electrodeless discharge lamps for strontium used for Zeeman scanning of absorption line profiles in flames

Microwave-excited electrodeless discharge lamps (EDL) for Sr were produced and a technique was developed for stabilizing the microwave power. Some characteristics of the EDL were investigated. The lamps were compared with a normal (= non-boosted) commercial hollow cathode lamp (HCL).Half-intensity widths of the Sr-line at 4607.33 Å were determined by interferometry for EDL and HCL sources under various operating conditions. Moreover, with both sources peak absorption measurements were carried out in a flame with Sr vapor; the results obtained by either technique were partially mutually consistent. Selected samples of EDL gave half-intensity widths of about 7–10 mÅ, independent of microwave power.The line width of the HCL increased from about 7 to 20 mÅ with increasing current up to 26 mÅ (= maximum rating). The radiance of the EDL's (at 50 W) was about the same as that of the HCL, when the latter was operated at 10 mA to give a comparable half-intensity width of 10 mÅ. At maximum microwave power the radiance of the EDL appeared to be 15–20 % of that of the HCL at maximum current, but the EDL line width remains only 7–10 mÅ, whereas that of the HCL line is about 20 mÅ and the HCL line is heavily self-reversed. EDL's with radiance values 10–100 × higher than that of the HCL at 25 mA were also produced; the high radiance value is obtained by increasing the Sr content in the EDL drastically. The profile of the EDL line has then a width of about 60 mÅ and the line is heavily self-reversed. Some tentative results on stability and life of the EDL's are reported.     

Quenching of excited strontium atomic state measured in H2- and CO-flames

The efficiency of resonance fluorescence, Y, of the strontium resonance line (¹P₁→¹S₀ transition) at 4607.33 Å was measured in CO/N₂O, CO/O₂/Ar, and H₂/O₂/CO₂/N₂ flames at atmospheric pressure. From these data, the specific quenching cross sections, σ_qu, for CO₂ and CO were found to be (60 ± 10) Ų and  (300 ± 60) Ų, respectively. The experimental cross sections were confronted with the intermediate ionic-state curve-crossing model and chemical quenching model, respectively.     

Assessment of the regioselectivity in the condensation reaction of unsymmetrical o-phthaldialdehydes with alanine

One approach for the synthesis of isoindolinones, a privileged bioactive heterocyclic core structure, involves a condensation reaction of o-phthaldialdehydes with a suitable nitrogen-containing nucleophile. This fascinating reaction is revisited here in the context of the use of o-phthaldialdehydes that contain additional substituents in the aromatic ring leading to a detailed analysis of the regioselectivity of the reaction. Eleven monosubstituted o-phthaldialdehydes were synthesised and reacted with alanine. The regioselectivity observed across the eleven substrates led to the design of a disubstituted substrate that reacted with very high control. A gram-scale reaction followed by esterification gave one major regioisomer in high yield. In addition, the regioselectivity observed on reaction of two novel monodeuterated substrates led to an increased mechanistic understanding.     

Chemically induced dynamic nuclear polarization. Decarboxylation of photochemically generated benzoyloxy radicals

CIDNP has been studied during thermal decomposition, photolysis, and sensitized photolysis of benzoyl chloroacetyl peroxide. The ratio of the CIDNP intensities for the recombination products benzyl chloride and chloromethyl benzoate is dependent on the mode of decomposition, reflecting the extent of rapid decarboxylation of the primary formed benzoyloxy radicals.     

Bifurcation phenomena of a biphasic compressible hyperelastic spherical continuum

A basic linear bifurcation problem is solved for a representative biphasic composite spherical cell. Setting is that of an internal inclusion that expends with an external shell made of a different material. Exact rate equations are derived in the framework of hyperelastic continuum mechanics. Sample examples are solved numerically revealing sensitivity of critical strain levels and bifurcated mode pattern to strength differential between both phases. Mathematical framework can be adapted to other types of constitutive responses.