In situ TEM studies of metal-carbon reactions.

The reactions which occur between amorphous carbon and a number of first transition metals (Ti, Cr, Fe, Co, Ni, and Cu) have been studied by transmission electron microscopy (TEM). The materials are in thin-film form with the metal layer sandwiched between thicker carbon layers. In four cases, the predominant reaction is the graphitization of the amorphous carbon, at temperatures well below 800 degrees C. This is brought about by the elements themselves in the case of Co and Ni, and by metastable carbides in the case of Fe (Fe3C) and Cr (Cr3C2-x). The Ti-C and Cu-C systems do not exhibit graphitization. For the former, only TiC is produced up to 1000 degrees C, while the carbon does not react at all with copper. In situ TEM studies show the mechanism to be of the dissolution-precipitation type, which is equivalent to the metal-mediated crystallization process for amorphous silicon and germanium. The heat of graphitization is found to be 18-19 kcal/mol-C by differential scanning calorimetry.     

Energy dependence of the reaction mechanism of 11B induced single nucleon transfers on 26Mg

Angular distributions for elastic scattering and for single nucléon stripping reactions induced by a 31 MeV ¹¹B beam on ²⁶Mg have been measured. The DWBA calculations provide a good account of the shape and magnitude of the proton transfer data and of the neutron transition to the $\text{j-}\text{favoured}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ level in ²⁷Mg, but fail to reproduce the features of the $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ transitions to ²⁷Mg. The j-dependent effects and l-matching conditions are investigated as a function of beam energy and their role in determining the reaction mechanism is examined.     

Particle-hole multiplets in 40Ca observed in the 41Ca(τ, α) reaction

Energy levels in ⁴⁰Ca up to 10.2 MeV have been studied in the neutron pickup reaction ⁴¹Ca(τ, α)⁴⁰Ca with 20 MeV bombarding energy. Thirty excited states have been identified and angular distributions have been measured in the interval from 5° to 40° by means of a split-pole magnetic spectrometer. The angular distributions together with DW calculations have been used to extract l_n values and spectroscopic factors. The l_n = 2 strength distribution for the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ particle-hole levels is compared to the l_p = 3 strength distribution from pr stripping data.     

Comparing O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions to SU(N) gauge theories in 3 + 1 dimensions

We have computed the scale breaking Λ parameters of the euclidean and hamiltonian formulations of the lattice regulated O(N) and SU(N) × SU(N) spin systems in 1 + 1 dimensions in terms of the Λ_PV parameters of the Pauli-Villars regulated continuum models. Using lattice perturbation theory, the renormalized mass gap has been determined in terms of Λ_PV for each model. These results are compared to analogous calculations in SU(N) gauge theories.     

Thirty-five years of synthetic studies directed towards the histrionicotoxin family of alkaloids

This article brings together for the first time reviews of all the synthetic attempts towards the spirocyclic histrionicotoxin alkaloids published since the discovery of the group in 1971. This covers 5 total syntheses of the fully unsaturated parent alkaloid HTX-283A, 7 total syntheses of perhydrohistrionicotoxin, 15 total syntheses of other members of this alkaloid family, 25 formal syntheses, and 19 partial syntheses involving the successful formation of the core azaspirocyclic structure but lacking advancement towards the target structure.     

Computation of viability kernels: a case study of by-catch fisheries

Traditional means of studying environmental economics and management problems consist of optimal control and dynamic game models that are solved for optimal or equilibrium strategies. Notwithstanding the possibility of multiple equilibria, the models’ users—managers or planners—will usually be provided with a single optimal or equilibrium strategy no matter how reliable, or unreliable, the underlying models and their parameters are. In this paper we follow an alternative approach to policy making that is based on viability theory. It establishes “satisficing” (in the sense of Simon), or viable, policies that keep the dynamic system in a constraint set and are, generically, multiple and amenable to each manager’s own prioritisation. Moreover, they can depend on fewer parameters than the optimal or equilibrium strategies and hence be more robust. For the determination of these (viable) policies, computation of “viability kernels” is crucial. We introduce a MATLAB application, under the name of VIKAASA, which allows us to compute approximations to viability kernels. We discuss two algorithms implemented in VIKAASA. One approximates the viability kernel by the locus of state space positions for which solutions to an auxiliary cost-minimising optimal control problem can be found. The lack of any solution implies the infinite value function and indicates an evolution which leaves the constraint set in finite time, therefore defining the point from which the evolution originates as belonging to the kernel’s complement. The other algorithm accepts a point as viable if the system’s dynamics can be stabilised from this point. We comment on the pros and cons of each algorithm. We apply viability theory and the VIKAASA software to a problem of by-catch fisheries exploited by one or two fleets and provide rules concerning the proportion of fish biomass and the fishing effort that a sustainable fishery’s exploitation should follow.     

A solvable mixed charge ensemble on the line: global results

We consider an ensemble of interacting charged particles on the line consisting of two species of particles with charge ratio 2:1 in the presence of an external field. With the total charge fixed and the system held at temperature corresponding to β = 1, it is proved that the particles form a Pfaffian point process. When the external field is quadratic (the harmonic oscillator potential), we produce the explicit family of skew-orthogonal polynomials necessary to simplify the related matrix kernels. In this setting a variety of limit theorems are proved on the distribution of the number as well as the spatial density of each species of particle as the total charge increases to infinity. Connections to Ginibre’s real ensemble of random matrix theory are highlighted throughout.     

Sounds and pictures: dynamism and dualism in Dynamic Geometry

In this paper, we examine and evaluate several new mathematical representations developed for The Geometer’s Sketchpad v5 (GSP5) from the perspective of their dynamic mathematical and pedagogic utility or expressibility. We claim the primary contributions of Dynamic Geometry’s principle of dynamism to the emerging concept of “Dynamic Mathematics” to be twofold: first, the powerful, temporalized representation of continuity and continuous change (dynamism’s mathematical aspect), and second, the sensory immediacy of direct interaction with mathematical representations (dynamism’s pedagogic aspect). Seen from this perspective, the growth of “Dynamic Mathematics software,” beyond the initial conception of first-generation planar geometry systems, represents a tremendous diversification and expansion of the mathematical domain of the dynamic principle’s applicability (for example, to dynamic statistics, graphing and 3D geometry). But at the same time, this expansion has come at the cost of a decrease in the immediacy of sensory interactions with mathematical representations, as in so-called dynamic graphing, wherein users modify a graph “at a distance” (through slider-based manipulation of the coefficients of its symbolic equation), or in solid geometry tools, in which users’ interactions with represented solids are mediated and distanced by the inevitably-2D communication interfaces of the computer mouse and screen. Thus we focus on this second aspect–sensory interaction with mathematical representations—in evaluating how novel dynamic representations in GSP5 affect mathematical modeling opportunities, student activity and engagement.     

Microchip laser-pumped continuous-wave doubly resonant optical parametric oscillator

We report what we believe to be the first use of a multilongitudinal-mode frequency-doubled microchip laser to pump a doubly resonant optical parametric oscillator (OPO). This compact OPO is based on potassium titanyl phosphate (KTP) and operates with a low pump power threshold of 35 mW. The OPO output consists of a single pair of signal and idler modes even though it is pumped with a multilongitudinal-mode pump laser. We achieved smooth tuning (1.7 GHz) of the output frequencies by temperature tuning of the pump laser.