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.     

Triflic acid-catalyzed additions of 2-alkoxycarbonyl allylboronates to aldehydes. Study of scope and mechanistic investigation of the reaction stereochemistry

The substrate scope and the effect of substrate on the observed inversion of stereoselectivity in the triflic acid-catalyzed allylboration reaction between 2-alkoxycarbonyl allylboronates and aldehydes are presented. A mechanistic investigation is described so as to confirm the involvement of a carbocation intermediate as the source of stereochemical inversion. This methodology allows a facile access to beta,gamma-disubstituted five-membered ring lactones with an exo-methylene at the alpha-position.     

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.     

B and collider physics: Working group report

This report summarises the work done during WHEPP-6 (Institute of Mathematical Sciences, Chennai, India, Jan 3–15, 2000) in Working group on ‘B and collider physics’.     

Matryoshka locally resonant sonic crystal

The results of numerical modeling of sonic crystals with resonant array elements are reported. The investigated resonant elements include plain slotted cylinders as well as their various combinations, in particular, Russian doll or Matryoshka configurations. The acoustic band structure and transmission characteristics of such systems have been computed with the use of finite element methods. The general concept of a locally resonant sonic crystal is proposed that utilizes acoustic resonances to form additional band gaps that are decoupled from Bragg gaps. An existence of a separate attenuation mechanism associated with the resonant elements that increases performance in the lower frequency regime has been identified. The results show a formation of broad band gaps positioned significantly below the first Bragg frequency. For low frequency broadband attenuation, a most optimal configuration is the Matryoshka sonic crystal, where each scattering unit is composed of multiple concentric slotted cylinders. This system forms numerous gaps in the lower frequency regime, below Bragg bands, while maintaining a reduced crystal size viable for noise barrier technology. The finding opens alternative perspectives for the construction of sound barriers in the low frequency range usually inaccessible by traditional means including conventional sonic crystals.