Kinetics of grafting acrylonitrile onto starch

Acrylonitrile (AN) was graft copolymerized onto gelatinized and granular wheat starch in aqueous media in the presence of ceric ammonium nitrate initiator at 91-364 anhydroglucose units (AGU) per cerium (IV) and at 1.08-4.33 AN to AGU ratios. Molecular weights and dispersities of polyacrylonitrile side chains were determined by gel-permeation chromatography. Conversion-time plots of AN polymerizations in both gelatinized and granular starch systems show characteristics common to heterogeneous polymerizations that could be explained on the basis of buried polymer radicals. The rates of polymerizations were directly related to the square root of the corrected cerium(IV) concentration and to the 1.3 power of the AN concentration. Graft copolymerization of AN onto starch, at least during initial stages, is not suitably explained by a kinetic scheme involving termination by polymer radical with cerium(IV) ion.     

Computer simulation of liquid metal ion source optics

A numerical calculation of the electric field and current density distribution for a liquid metal ion (LMI) source has been carried out. If a field evaporation mechanism for ion formation is assumed an elongated Taylor cone shape emitter is required to account for the observed total currents. Trajectory calculations including the effect of uniform space charge have been carried out as a function of total current and particle mass. The predicted emission characteristics compare favorably with experimental results for Ga, however the homogeneous space charge model is unable to account for all of the experimentally observed increase in beam divergence with increasing mass and current.     

Normal cones of monomial primes

We explicitly calculate the normal cones of all monomial primes which define the curves of the form , where . All of these normal cones are reduced and Cohen-Macaulay, and their reduction numbers are independent of the reduction. These monomial primes are new examples of integrally closed ideals for which the product with the maximal homogeneous ideal is also integrally closed.

Substantial use was made of the computer algebra packages Maple and Macaulay2.

     

The effect of a coriolis force on Taylor-Couette flow

Taylor-Couette flow subject to a Coriolis force is studied experimentally and numerically. In the experiment, the Couette apparatus is mounted on a turntable with the axis of the cylinders orthogonal to the rotation vector of the turntable. The Coriolis force stabilizes the fluid against the onset of Taylor vortices and alters the velocity fields, both above and below the transition from the initial flow. At small dimensionless turntable frequencies, the transition yields time-independent Taylor vortices which are tilted with respect to the cylinder axis. At larger there is a direct transition to turbulence. We determine the first-order correction to the classical Couette initial flow, to account for the effects of the Coriolis force, by expanding in powers of. We present numerical results for the axial velocity (the only nonvanishing correction term to order) in the infinite-cylinder approximation.     

Quantum mechanics: cleaning up metaphysical baggage

The dynamic electronic structure of atoms and molecules can be directly observed by means of the (e, 2e) reaction, which measures the distribution of energies and momenta of two electrons in coincidence after a knockout reaction initiated by an electron beam of known momentum incident on a molecular gas target. The molecular state for each event is identified by the electron separation energy. The recoil momentum for each event is known from the difference of measured initial and final momenta. It has been verified that values of this momentum are equal under suitable conditions to the momentum of the electron in the target immediately before knockout. Thus the spherically-averaged electron momentum distribution for each molecular orbital is measured. This is directly related to molecular orbitals calculated by the methods of quantum chemistry. Properties obtained by this method for different types of molecules are discussed.