Resonance ionization mass spectrometry for precise measurements of isotope ratios

Resonance ionization mass spectrometry offers extremely high sensitivity and elemental selectivity in microanalysis, but the isotopic precision attainable by this technique has been limited. Measured isotope ratios are sensitive to small fluctuations in the pointing, pulse timing, and wavelength of the resonance lasers. We show that, by minimizing these fluctuations using feedback controls and by power-broadening the optical transitions, we are able to measure chromium isotope ratios with statistics-limited precision better than 1%. Small additional improvements in reproducibility come from careful shaping of the electric field in the region where atoms are photoionized and from minimizing pulse-to-pulse variations in the time-of-flight mass spectrometer through which the photoions travel. The increased reproducibility of isotopic measurements on standard materials has enabled us to detect anomalous chromium isotopic abundances in presolar SiC grains extracted from primitive meteorites.     

A Special Topics Course in Perturbation Methods

A special topics course dealing with perturbation methods in applied mathematics which was recently taught at Stevens Institute of Technology is described. Since the course enrolment was comprised of undergraduate and graduate mathematics students as well as graduate students in engineering, an unusual course philosophy had to be developed and implemented. The approach taken to achieve this in both teaching techniques and selection of subject matter is discussed in detail. Finally, conclusions are drawn from the students’ and the instructor's experiences with the course which hopefully will be of value to those considering offering special topics courses in the future.     

On critical exponents for some quasilinear parabolic equations

We study the Cauchy problem for the quasilinear parabolic equation where p > 1 is a parameter and ψ is a smooth, bounded function on (1, ∞) with ? ? sψ′(s)/ψ(s) ? θ for some θ > 0. If 1 < p < 1 + 2/N, there are no global positive solutions, whereas if p > 1 + 2/N, there are global, positive solutions for small initial data.     

Some remarks on Saint-Venant's principle

We consider a three-dimensional hyperelastic cylinder in Ω = D × [0, ∞]. We study the asymptotic behaviour of the deformations of the cross-sections in an equilibrium state. In this case we show that the solutions either have exponential decay or exponential growth. We give some initial conditions such that the latter case occurs.     

Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity

Lower bounds for the eigenvalues of some elliptic equations and elliptic systems over bounded regions are obtained. The bounds are universal in that they depend only upon the volume of the region. Specific applications include the clamped plate, the buckling problem for the clamped plate and the equations of linear elasticity. Our results are consequences of extensions of the methods of Li and Yau (Comm. Mat. Phys. 88 (1983) 309–318) who obtained such results for the eigenvalues of the fixed membrane problem.     

Stereocontrol of attosecond time-scale electron dynamics in ABCU using ultrafast laser pulses: a computational study

The attosecond time-scale electronic dynamics induced by an ultrashort laser pulse is computed using a multi configuration time dependent approach in ABCU (C(10)H(19)N), a medium size polyatomic molecule with a rigid cage geometry. The coupling between the electronic states induced by the strong pulse is included in the many electron Hamiltonian used to compute the electron dynamics. We show that it is possible to implement control of the electron density stereodynamics in this medium size molecule by varying the characteristics of the laser pulse, for example by polarizing the electric field either along the N-C axis of the cage, or in the plane perpendicular to it. The excitation produces an oscillatory, non-stationary, electronic state that exhibits localization of the electron density in different parts of the molecule both during and after the pulse. The coherent oscillations of the non-stationary electronic state are also demonstrated through the alternation of the dipole moment of the molecule.