Transfer measurements for the Ti+Ni systems at near barrier energies

Large enhancements have been observed in the sub-barrier fusion cross sections for Ti+Ni systems in our previous studies. Coupled channel calculations incorporating couplings to 2⁺ and 3⁻ states failed to explain these enhancements completely. A possibilty of transfer channels contributing to the residual enhancements had been suggested. In order to investigate the role of relevant transfer channels, measurements of one- and two-nucleon transfer were carried out for ^46,48Ti+⁶¹Ni systems. The present paper gives the results of these studies.     

An unsteady MHD duct flow

An exact solution is presented for unsteady laminar flow of a viscous, incompressible, electrically conducting fluid between nonconducting, parallel, flat plates. A constant magnetic field is suddenly applied perpendicular to the plates and the motion is modified by the induced current. Numerical results are given which show how the velocity profile changes from the parabolic profile of hydrodynamics to the Hartmann profile of magnetohydrodynamics.     

A variational characterisation of spherical designs

In this paper we first establish a new variational characterisation of spherical designs: it is shown that a set , where , is a spherical L-design if and only if a certain non-negative quantity A_L,N(X_N) vanishes. By combining this result with a known “sampling theorem” for the sphere, we obtain the main result, which is that if is a stationary point set of A_L,N whose “mesh norm” satisfies h_XN<1/(L+1), then X_N is a spherical L-design. The latter result seems to open a pathway to the elusive problem of proving (for fixed d) the existence of a spherical L-design with a number of points N of order (L+1)^d. A numerical example with d=2 and L=19 suggests that computational minimisation of A_L,N can be a valuable tool for the discovery of new spherical designs for moderate and large values of L.     

Lanthanide reagents in solid phase synthesis

From solid-supported ytterbium(III) catalysts to linkers cleaved by electron transfer from samarium(II) species, lanthanide reagents are beginning to find widespread application in solid phase organic synthesis. This tutorial review introduces the use of lanthanide(III) Lewis acids and lanthanide(IV) oxidants in solid phase chemistry before concentrating on the growing use of lanthanide(II) reagents in the area.     

Electronic switching of single silicon atoms by molecular field effects

We have observed on-off switching of scanning tunneling microscope current flow to silicon adatoms of the Si(111)-(7 x 7) surface that are enclosed within a bistable dimeric corral of self-assembled chlorododecane molecules. These thermally activated oscillations amounted to an order of magnitude change in the current. Theory showed that small changes in molecular configuration could cause alterations in the corralled adatom's electronic energy by as much as 1 eV due to local field effects, accounting for the observed current switching.     

Preparing and regulating a bi-stable molecular switch by atomic manipulation

We present a scanning tunneling microscopy (STM) investigation into the influence of the STM tip on the adsorption site switching of polychlorinatedbiphenyl (PCB) molecules on the Si(111)-7?×?7 surface at room temperature. From an initially stable adsorption configuration, atomic manipulation by charge injection from the STM tip prepared a new bi-stable configuration that switched between two bonding arrangements. No switching rate bias dependence was found for +?1.0 to +?2.2?V. Assuming a thermally driven switching process we find that the measured energy barriers to switching are influenced by the exact location of the STM tip by more than 10%. We propose that this energy difference is due the dispersion interaction between the tip and the molecule.     

Tractability of Multivariate Integration for Weighted Korobov Classes

We study the worst-case error of multivariate integration in weighted Korobov classes of periodic functions of d coordinates. This class is defined in terms of weights γ_j which moderate the behavior of functions with respect to successive coordinates. We study two classes of quadrature rules. They are quasi-Monte Carlo rules which use n function values and in which all quadrature weights are 1/n and rules for which all quadrature weights are non-negative. Tractability for these two classes of quadrature rules means that the minimal number of function values needed to guarantee error in the worst-case setting is bounded by a polynomial in d and ⁻¹. Strong tractability means that the bound does not depend on d and depends polynomially on ⁻¹. We prove that strong tractability holds iff ∑^∞_j=1 γ_j<∞, and tractability holds iff lim sup_d→∞ ∑^d_j=1 γ_j/log d<∞. Furthermore, strong tractability or tractability results are achieved by the relatively small class of lattice rules. We also prove that if ∑^∞_j=1 γ^1/α_j<∞, where α measures the decay of Fourier coefficients in the weighted Korobov class, then for d1, n prime and δ>0 there exist lattice rules that satisfy an error bound independent of d and of order n^−α/2+δ. This is almost the best possible result, since the order n^−α/2 cannot be improved upon even for d=1. A corresponding result is deduced for weighted non-periodic Sobolev spaces: if ∑^∞_j=1 γ^1/2_j<∞, then for d1, n prime and δ>0 there exist shifted lattice rules that satisfy an error bound independent of d and of order n^−1+δ. We also check how the randomized error of the (classical) Monte Carlo algorithm depends on d for weighted Korobov classes. It turns out that Monte Carlo is strongly tractable iff ∑^∞_j=1 log γ_j<∞ and tractable iff lim sup_d→∞ ∑^d_j=1 log γ_j/log d<∞. Hence, in particular, for γ_j=1 we have the usual Korobov space in which integration is intractable for the two classes of quadrature rules in the worst-case setting, whereas Monte Carlo is strongly tractable in the randomized setting.     

Purification of Single-walled Carbon Nanotubes Grown by a Chemical Vapour Deposition (CVD) Method

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Time discretization via Laplace transformation of an integro-differential equation of parabolic type

We consider the discretization in time of an inhomogeneous parabolic integro-differential equation, with a memory term of convolution type, in a Banach space setting. The method is based on representing the solution as an integral along a smooth curve in the complex plane which is evaluated to high accuracy by quadrature, using the approach in recent work of López-Fernández and Palencia. This reduces the problem to a finite set of elliptic equations with complex coefficients, which may be solved in parallel. The method is combined with finite element discretization in the spatial variables to yield a fully discrete method. The paper is a further development of earlier work by the authors, which on the one hand treated purely parabolic equations and, on the other, an evolution equation with a positive type memory term. The authors acknowledge the support of the Australian Research Council.     

Self-assembled molecular corrals on a semiconductor surface

Nano-corrals for capturing surface electrons are of interest in molecular electronics. Here we show that haloalkane molecules, e.g., 1-chlorododecane, physisorbed on Si(1 1 1)-(7 × 7) self-assemble to form dimers stable to 100 °C which corral silicon adatoms. Corral size is shown to be governed by the haloalkane chain-length. Spectroscopic and theoretical evidence shows that the haloalkane dimer induces electron transfer to the corralled adatom, shifting its energy levels by ∼1 eV. Isolation of a labile pre-cursor points to a model for corral formation which combines mobility with immobility; monomers diffusing in a mobile vertical state meet and convert to the immobile horizontal dimers constituting the corrals.