Hole burning—EIT studies of the NV centre in diamond

The negative nitrogen-vacancy centre in diamond is used to illustrate electromagnetically induced transparency features within a coherent hole. A hole is created in an inhomogeneously broadened electron spin transition and its spectrum modified by driving hyperfine transitions. The modified spectrum is discussed in terms of dressed states of the system, and the spectrum is shown to be in good correspondence with numerical solutions of the density matrix for the doubly driven system.     

Particle pinch in gyrokinetic simulations of closed field-line systems

Gyrokinetic simulations of small-scale turbulent transport in a closed magnetic field-line plasma geometry are presented. The simulations are potentially applicable to dipolar systems such as the levitated dipole experiment (LDX) [J. Kesner, Plasma Phys. Rep. 23, 742 (1997).] and planetary magnetospheres, as well as simpler systems such as the Z pinch. We report here for the first time the existence of a robust particle (and weaker temperature) pinch regime, in which the particles are transported up the density gradient. The particle pinch is driven by non-MHD entropy-mode turbulence at k(⊥) ρ(i) ～ 1 and particle pinch appears at larger η ≡ L(n)/L(T) ? 0.7, consistent with quasilinear theory. Our results suggest that entropy-mode transport will drive the LDX plasma profiles toward a state with η ～ 0.7 and pressure gradients that are near marginal ideal MHD interchange-mode stability.     

Controlling the passage of light through metal microchannels by nanocoatings of phospholipids

The flow of polarized light through a metal film with an array of microchannels is controlled by the phase of an optically active, phospholipid nanocoating, even though the coating does not cover the open area of the microchannels. The molecular details of the assembly (DPPC phospholipid monolayer/bilayer on a hexadecanethiol monolayer on a copper- or nickel-coated microarray) were determined using the infrared, surface-plasmon-mediated, extraordinary transmission of the metal microarrays. Infrared absorption spectra with greatly enhanced absorptions by comparison to literature were recorded and used as a diagnostic for the phase, composition, and molecular geometry of these nanocoatings. This approach presents new tools for nanoscale construction in constricted microspaces, which may ultimately be useful with individual microchannels.     

Neutron and proton transverse emission ratio measurements and the density dependence of the asymmetry term of the nuclear equation of state

Recent measurements of preequilibrium neutron and proton transverse emission from (112,124)Sn+(112,124)Sn reactions at 50 MeV/A have been completed at the National Superconducting Cyclotron Laboratory. Free nucleon transverse emission ratios are compared to those of A=3 mirror nuclei. Comparisons are made to Boltzmann-Uehling-Uhlenbeck (BUU) transport calculations and conclusions concerning the density dependence of the asymmetry term of the nuclear equation of state at subnuclear densities are made. Comparison to BUU model predictions indicate a density dependence of the asymmetry energy that is closer to a form in which the asymmetry energy increases as the square root of the density for the density region studied. A coalescent-invariant analysis is introduced as a means of reducing suggested difficulties with cluster emission in total nucleon emission.     

THE BIOGENETIC LAW AND ITS INFLUENCE ON THEORIES OF LEARNING MATHEMATICS

Reference to the history of mathematics has been widely used in discussions of the development of curricula, the problems students have in learning mathematics, and the development of concepts in the individual. This paper examines the background to the "Biogenetic Law" [1] which has influenced so much thinking in educational theory, and the use of the "principle of parallelism" where individual development is claimed to mirror the historical development of the subject matter. Interpretations of the history of mathematics which are used to justify these claims are examined, and the universality of the supposed concepts is challenged. Questions are raised about some of the fundamental tenets of Piagetian epistemology.     

The measurement of solid–liquid interfacial energy in colloidal suspensions using grain boundary grooves

Interfacial energy is a fundamental physiochemical property of any multi-phase system. Among the most direct approaches for determining solid–liquid interfacial energy is a technique based on measuring the shape of grain boundary grooves in specimens subjected to a linear temperature gradient. This technique was adapted to crystallizing colloids in a gravitational field. Such colloids exhibit a freezing–melting phase transition and are important not only as self-assembling precursors to photonic crystals, but also as physical models of atomic and molecular systems. The grain boundary groove technique was tested using suspensions of sterically stabilized poly(methyl methacrylate) spheres, which have been shown to closely approximate the hard sphere potential. Whereas isotropic models did not fit grain boundary groove data well, the capillary vector model, which is suitable for both isotropic and anisotropic surface energies, produced γ₁₁₀?=?0.58?±?0.05 k _B T/σ². This value of interfacial energy is in agreement with many of the published values for hard spheres, supporting the validity of our grain boundary groove technique adaptations to colloidal systems in a gravitational field. Finally, kinks observed in groove profiles suggest a minimum anisotropy parameter of ε?=?0.029 for hard spheres.     

Identities for the Ramanujan zeta function

We prove formulas for special values of the Ramanujan tau zeta function. Our formulas show that L(Δ,k)$L(\mathrm{\Delta },k)$ is a period in the sense of Kontsevich and Zagier when k?12$k?12$. As an illustration, we reduce L(Δ,k)$L(\mathrm{\Delta },k)$ to explicit integrals of hypergeometric and algebraic functions when k∈{12,13,14,15}$k\in \{12,13,14,15\}$.     

High- and low-confinement modes in simple magnetized toroidal plasmas

Three-field simulations of interchange turbulence are presented for a simple magnetized toroidal plasma with a vertical magnetic field. The simulations show the presence of two turbulent regimes characterized by low (L) and high (H) confinement properties. We evaluate analytically the properties of the L regime, obtaining expressions for the plasma gradients and for the density and heat fluxes that agree well with the simulations. By increasing the plasma source strength or reducing the vertical magnetic field, a transition to a H regime occurs, in which a strong velocity shear limits the perpendicular transport with respect to the L scaling and the plasma profiles steepen. The analytic estimate of the transition condition is in accord with the simulations.