Working group report: Collider Physics

This is summary of the activities of the working group on collider physics in the IXth Workshop on High Energy Physics Phenomenology (WHEPP-9) held at the Institute of Physics, Bhubaneswar, India in January 2006. Some of the work subsequently done on these problems by the subgroups formed during the workshop is included in this report.     

On the singularity of Green's tensor for a perfectly conducting semi-infinite cone

This paper is intended to clarify a misunderstanding concerningthe source singularity of the electric Green's tensor for aperfectly conducting semi-infinite cone of circular cross-section.Tai's series expansion of the Green's tensor is known to lacka singular term at the source region. Jones has reconstructedthe solution to this problem and has pointed out the differencebetween his result and that of Tai. The aim of our paper isto demonstrate that, although Jones's closed-form solution iscorrect, there is a mistake in his comparison with Tai's seriessolution. We conclude that one of the two additional singularterms that Jones claims as missing from Tai's formula must beomitted. Besides, we compare Jones's closed-form solution withSmyshlyaev's solution to the very same problem. We concludethat the magnetic field expressions given by Jones and Smyshlyaevcoincide, but a singular term is missing from Smyshlyaev's expressionfor the electric field.     

Superconvergence of the iterated collocation methods for Hammerstein equations

In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [16] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also discuss the discrete collocation method for weakly singular Hammerstein equations. Some discrete collocation methods for Hammerstein equations with smooth kernels were given previously in [3, 18].     

Coupled In/Te and Ni/vacancy ordering and the modulated crystal structure of a B8 type, Ni3±xIn1−yTe2+y solid solution phase

The commensurate superstructures of a NiAs/Ni₂In type parent structure, Ni_3.32InTe₂ and Ni_3.12In_0.86Te_2.14 (q=γ[0 0 1]^*, γ=2/3) as well as one dimensionally incommensurate structure of Ni₃InTe₂ (γ=0.71) were refined from neutron powder diffraction data (R_wp=4.77%, 4.53% and 4.91% for the three structures, respectively, at 298 K). The commensurate structures were refined in the P6₃/mmc space group (c=3c_NiAs). The stacking sequence at the hcp array is -In/Te/Te/- and the trigonal bipyramidal site within the In layer, Ni(2), is partially occupied while it is empty in the Te layers. The octahedral position in between the In and Te layers, Ni(1a), is fully occupied while the octahedral position in between two adjacent Te layers, Ni(1b), is partially occupied. With decreasing In and Ni content, the modulation wave vector, γ, was found to increase continuously until γ=1. From this, crenel functions to describe the whole homogeneity range of the solid solution were constructed with the length of the atomic domains Δ^Te=γ (and hence Δ^In=Δ^Ni=1−γ) and Δ^Ni(1b)=γ/2 (and hence Δ^Ni(1a)=1−γ/2) which were then used for the refinement of the incommensurate structure of Ni₃InTe₂. The corresponding effect in real space is that the single In layers separating double layers of Te occur less frequent when γ in increasing until at γ=1 the CdI₂ type structure of Ni_1+xTe₂ is reached.     

Alternating copolymers of styrene with tricyanoethylene and ethyl 2,3-dicyanoacrylate

Ethyl 2,3-dicyanoacrylate was prepared from ethyl 2,3-dicyanopropionate. High molecular weight, 1:1 alternating copolymers of styrene with tricyanoethylene and ethyl 2,3-dicyanoacrylate were prepared by bulk polymerization with the use of free-radical initiators. Solution polymerization of styrene with ethyl 2,3-dicyanoacrylate in acetonitrile gave the highest molecular weight copolymer (η_inh = 0.74). The copolymers showed unusual thermal properties, i.e., an initial break that was 50–75°C lower than that of polystyrene followed by the formation of an intermediate product that was fairly stable to approximately 500°C.     

Dissecting the Chemistry of Protein Splicing and Its Applications

Protein splicing, the protein equivalent of RNA splicing, is a newly discovered posttranslational process that proceeds through a branched protein intermediate and produces two separate polypeptides from one gene. The experimental data used to distinguish among the proposed protein-splicing mechanisms are presented along with the progress made towards fully describing the mechanism. Numerous protein engineering applications using modified inteins have been developed, including the generation of alpha-thioesters in proteins, which circumvent the limits of solid-phase peptide synthesis.     

Scattering by small defects in the neighbourhood of a fluid-solid interface

The scattering of incident plane elastic waves by a varietyof different defects that lie upon a fluid-solid interface isconsidered here using matched asymptotic expansions. The expansionscheme is developed in terms of a parameter , the ratio of typicaldefect length scale to a typical wavelength of the incidentfield, taken to be small. Three different canonical situations occur and these are illustratedvia three specific examples treated here: a rigid strut, anedge crack, and a rigid strip. In each case the leading-ordermatching is performed to identify the leading-order contributionof the defect to the acoustic field in the far field. In particular,each defect is identified with a source of dipole response ininterfacial stress of displacement. It is shown in the limit as s<<s1 that in the inner problemsthe fluid and solid pieces uncouple in a particularly convenientmanner allowing analytical solutions to be deduced. These arethen matched with appropriate outer solutions.