A note on the calculation of the effective range

The closed form of the first order non-linear differential equation that is satisfied by the effective range within the variable phase formulation of scattering theory is discussed. It is shown that the conventional method of determining the effective range, by fitting a numerical solution of the Schr\"odinger equation to known asymptotic boundary conditions, can be modified to include the first order contribution of a long range interaction.Comment: 4 page

PREPARATION AND CHARACTERIZATION OF AN IMMUNOELECTRON MICROSCOPE TRACER CONSISTING OF A HEME-OCTAPEPTIDE COUPLED TO Fab

A heme-octapeptide (mol wt 1,550) has been obtained from cytochrome c by successive pepsin and trypsin hydrolysis and purified by gel filtration and countercurrent distribution. It possesses peroxidatic activity characterized by an apparent Km of 0.2 M, an apparent vmax of 4 mmol/min per mg of peptide, and a pH optimum of 7.0. Using a novel two-step conjugation procedure, the heme-octapeptide was coupled to rabbit Fab antibody fragments by first derivatizing it with the N-hydroxysuccinimide ester of p-formylbenzoic acid and subsequently allowing it to form a Schiff base with the amino groups of Fab. Stable covalent linkages were then obtained by reduction of the Schiff bases with sodium borohydride. The conjugate consists of ∼2 heme-octapeptides attached to each Fab molecule. The molecular weight is 45,000 daltons when coupled to sheep Fab and 50,000 daltons with a Stokes radius of 32 Å, when conjugated to rabbit Fab. Its peroxidatic activity is characterized by an apparent Km of 0.4 M, an apparent vmax of 0.4 mmol/min and per mg of attached heme-octapeptide and a pH optimum of 7.0. The conjugate has been used for the localization at the electron microscope level of secretory immunoglobulins in the mammary gland of lactating rabbits

Self-aligned fabrication process for silicon quantum computer devices

We describe a fabrication process for devices with few quantum bits (qubits), which are suitable for proof-of-principle demonstrations of silicon-based quantum computation. The devices follow the Kane proposal to use the nuclear spins of 31P donors in 28Si as qubits, controlled by metal surface gates and measured using single electron transistors (SETs). The accurate registration of 31P donors to control gates and read-out SETs is achieved through the use of a self-aligned process which incorporates electron beam patterning, ion implantation and triple-angle shadow-mask metal evaporation

Structural and Stratigraphic Evolution of the Mid North Sea High Region of the UK Continental Shelf

This research was undertaken as part of a 2-year Post-Doctoral Research Associate (PDRA) project undertaken at the Applied Geoscience Unit in the Centre of Exploration Geoscience at Heriot Watt University. The project was funded by the UK Oil and Gas Authority (OGA) as part of their Frontier Basins Research program. We extend our gratitude Jo Bagguley, Malcolm Gall and Nick Richardson for their support of the work and technical discussions. All research outputs are available for download on the Oil and Gas Authority’s National Data Repository (NDR) website, and we thank the OGA’s data management and Arc GIS team for their work to make this publicly available. The work has benefitted from technical discussion with Matthew Booth, Ross Grant and Richard McKeen, who have undertaken complementary studies in neighbouring parts of the basin.Peer reviewedPostprin

Fractal-like Distributions over the Rational Numbers in High-throughput Biological and Clinical Data

Recent developments in extracting and processing biological and clinical data are allowing quantitative approaches to studying living systems. High-throughput sequencing, expression profiles, proteomics, and electronic health records are some examples of such technologies. Extracting meaningful information from those technologies requires careful analysis of the large volumes of data they produce. In this note, we present a set of distributions that commonly appear in the analysis of such data. These distributions present some interesting features: they are discontinuous in the rational numbers, but continuous in the irrational numbers, and possess a certain self-similar (fractal-like) structure. The first set of examples which we present here are drawn from a high-throughput sequencing experiment. Here, the self-similar distributions appear as part of the evaluation of the error rate of the sequencing technology and the identification of tumorogenic genomic alterations. The other examples are obtained from risk factor evaluation and analysis of relative disease prevalence and co-mordbidity as these appear in electronic clinical data. The distributions are also relevant to identification of subclonal populations in tumors and the study of the evolution of infectious diseases, and more precisely the study of quasi-species and intrahost diversity of viral populations

Bias spectroscopy and simultaneous SET charge state detection of Si:P double dots

We report a detailed study of low-temperature (mK) transport properties of a silicon double-dot system fabricated by phosphorous ion implantation. The device under study consists of two phosphorous nanoscale islands doped to above the metal-insulator transition, separated from each other and the source and drain reservoirs by nominally undoped (intrinsic) silicon tunnel barriers. Metallic control gates, together with an Al-AlOx single-electron transistor, were positioned on the substrate surface, capacitively coupled to the buried dots. The individual double-dot charge states were probed using source-drain bias spectroscopy combined with non-invasive SET charge sensing. The system was measured in linear (VSD = 0) and non-linear (VSD 0) regimes allowing calculations of the relevant capacitances. Simultaneous detection using both SET sensing and source-drain current measurements was demonstrated, providing a valuable combination for the analysis of the system. Evolution of the triple points with applied bias was observed using both charge and current sensing. Coulomb diamonds, showing the interplay between the Coulomb charging effects of the two dots, were measured using simultaneous detection and compared with numerical simulations.Comment: 7 pages, 6 figure

The variable phase method used to calculate and correct scattering lengths

It is shown that the scattering length can be obtained by solving a Riccati equation derived from variable phase theory. Two methods of solving it are presented. The equation is used to predict how long-range interactions influence the scattering length, and upper and lower bounds on the scattering length are determined. The predictions are compared with others and it is shown how they may be obtained from secular perturbation theory.Comment: 7 pages including 3 figure

Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page