Calculations of the axial and azimuthal fluxes contained in a type II superconducting cylinder in a force-free configuration

The force free equation, J∧ B = 0, is expressed in an undimensionalized form for a reversible, Type II, superconducting cylinder carrying a transport current in a longitudinal magnetic field. Using a simple model, the form of the current distribution inside the specimen is varied, and this equation is solved to yield the total axial and azimuthal fluxes. For fixed values of the transport current and applied field it is shown that the total axial flux insensitive to the current distribution, whilst the total azimthal flux varies considerably. It is concluded, therefore, that measurements of the axial magnetization alone cannot discriminate between various force-free models.     

THE U.V. PHOTOCHEMISTRY OF CYTIDYLIC ACID

Abstract The ultraviolet (u.v.) irradiation of the 3' isomer of cytidylic acid (Cp) produces the hydrate (Cp*) with water added across the 5–6 double bond. The yield of this photo-product has been measured by, (a) separating the photoproduct by electrophoresis and (b) by observing the loss in absorbance. When corrections are made for reversal of the hydrate during the experiment, both methods gave the same result. Cross sections and quantum yields for the production of the hydrate were measured over the wavelength range 220 to 290 nm and over a pH range from 1 to 10. The quantum yield is markedly dependent on pH being higher by a factor of 6 to 10 for the neutral form. We have also demonstrated the existence of a very short lived photoproduct (half life 8–9 min) in both Cp3' and Cp5': The nature of this short lived product is not known.     

Spiral Anchoring in Media with Multiple Inhomogeneities: A Dynamical System Approach

The spiral is one of nature’s more ubiquitous shapes: It can be seen in various media, from galactic geometry to cardiac tissue. Mathematically, spiral waves arise as solutions to reaction–diffusion partial differential equations (RDS). In the literature, various experimentally observed dynamical states and bifurcations of spiral waves have been explained using the underlying Euclidean symmetry of the RDS—see for example (Barkley in Phys. Rev. Lett. 68:2090–2093, 1992; Phys. Rev. Lett. 76:164–167, 1994; Sandstede et al. in C. R. Acad. Sci. 324:153–158, 1997; J. Differ. Equ. 141:122–149, 1997; J. Nonlinear Sci. 9:439–478, 1999), or additionally using the concept of forced Euclidean symmetry-breaking for situations where an inhomogeneity or anisotropy is present—see (LeBlanc in Nonlinearity 15:1179–1203, 2002; LeBlanc and Wulff in J. Nonlinear Sci. 10:569–601, 2000). In this paper, we further investigate the role of medium inhomogeneities on spiral wave dynamics by considering the effects of several localized sites of inhomogeneity. Using a model-independent approach based on n>1 simultaneous translational symmetry-breaking perturbations of the dynamics near rotating waves, we fully characterize the local anchoring behavior of the spiral wave in the n-dimensional parameter space of relative “amplitudes” of the individual perturbations. For the case n=2, we supplement the local anchoring results with a classification of the generic one-parameter bifurcation diagrams of anchored states which can be obtained by circling the origin of the two-dimensional amplitude parameter space. Numerical examples are given to illustrate our various results.     

A Tutorial Program: Collaboration Between Preservice and Inservice Teachers

Many elementary school teachers face severe time constraints working individually with students who need extra help or attention in mathematics. Sometimes, children who need this attention do not receive it. At the same time, critics of teacher education programs contend that preservice teachers do not receive enough hands-on experience teaching children. The Mathematics Tutorial Program is one attempt to address both of these issues. In this program, elementary grade children are identified by their classroom teachers as needing extra help in mathematics. They are paired with preservice elementary school teachers. Each preservice teacher tutors one or more elementary children for two 30-minute sessions each week for 6 to 24 weeks. They use manipulatives and a hands-on approach. The tutors reported professional gains from their contacts with classroom teachers, mathematics educators, and elementary children. Classroom teachers involved with the program commented on the children's improved selfesteem and confidence in mathematics. The children eagerly looked forward to the time with their tutors.