Investigations of radiative lifetimes in the 3p5p configuration of neutral silicon

Lifetimes for the³ S ₁,³ P _{0, 1, 2} and³ D _{1, 2, 3} states in the 3s ²3p5p configuration of silicon have been determined using stepwise dye laser excitation and time resolved detection. A comparison is made with theoretical values, calculated using multi-configuration Hartree-Fock wavefunctions. Laser-evaporation was used to produce free silicon atoms by focusing a Nd: YAG laser on a rotating silicon target.     

Modeling of hydrogen ground state rotational and vibrational temperatures in kinetic plasmas

A dipole-quadrupole electron-impact excitation model, consistent with molecular symmetry rules, is presented to fit ro-vibronic spectra of the hydrogen Fulcher-α Q-branch line emissions for passively measuring the rotational temperature of hydrogen neutral molecules in kinetic plasmas with the coronal equilibrium approximation. A quasi-rotational temperature and quadrupole contribution factor are adjustable parameters in the model. Quadrupole excitation is possible due to a violation of the 1st Born approximation for low to medium energy electrons (up to several hundred eV). The Born-Oppenheimer and Franck-Condon approximations are implicitly shown to hold. A quadrupole contribution of 10% is shown to fit experimental data at several temperatures from different experiments with electron energies from several to 100 eV. A convenient chart is produced to graphically determine the vibrational temperature of the hydrogen molecules from diagonal band intensities, if the ground state distribution is Boltzmann. Hydrogen vibrational modes are long-lived, surviving up to thousands of wall collisions, consistent with multiple other molecular dynamics computational results. The importance of inter-molecular collisions during a plasma pulse is also discussed.     

Modeling the motion of the internal tongue from tagged cine-MRI images.

A new technique, tagged Cine-Magnetic Resonance Imaging (tMRI), was used to develop a mechanical model that represented local, homogeneous, internal tongue deformation during speech. The goal was to infer muscle activity within the tongue from tissue deformations seen on tMRI. Measurements were made in three sagittal slices (left, middle, right) during production of the syllable /ka/. Each slice was superimposed with a grid of tag lines, and the approximately 40 tag line intersections were tracked at 7 time-phases during the syllable. A local model, similar to a finite element analysis, represented planar stretch and shear between the consonant and vowel at 110 probed locations within the tongue. Principal strains were calculated at these locations and revealed internal compression and extension patterns from which inferences could be drawn about the activities of the Verticalis, Hyoglossus, and Superior Longitudinal muscles, among others.     

Transcendental Harmonic Mappings and Gravitational Lensing by Isothermal Galaxies

Using the Schwarz function of an ellipse, it was recently shown that galaxies with density constant on confocal ellipses can produce at most four “bright” images of a single source. The more physically interesting example of an isothermal galaxy has density that is constant on homothetic ellipses. In that case bright images can be seen to correspond to zeros of a certain transcendental harmonic mapping. We use complex dynamics to give an upper bound on the total number of such zeros.     

Ruthenium‐Catalyzed Tandem‐Isomerization/Asymmetric Transfer Hydrogenation of Allylic Alcohols

A one‐pot procedure for the direct conversion of racemic allylic alcohols to enantiomerically enriched saturated alcohols is presented. The tandem‐isomerization/asymmetric transfer hydrogenation process is efficiently catalyzed by [{Ru(p‐cymene)Cl₂}₂] in combination with the α‐amino acid hydroxyamide ligand 1 , and performed under mild conditions in a mixture of ethanol and THF. The saturated alcohol products are isolated in good to excellent chemical yields and in enantiomeric excess up to 93 %.     

Almost all orbit types imply period-3

A special case of Sarkovskii's theorem says that if a continuous function has a period-3 point then it has periodic points of every order. In this note we will investigate how often orbit types of period-n guarantee a period-3 point. An informal statement of our result is that as n goes to infinity the probability that a period-n orbit guarantees a period-3 point converges to 1.