Hypernormal form theory: foundations and algorithms

Hypernormal forms (unique normal forms, simplest normal forms) are investigated both from the standpoint of foundational theory and algorithms suitable for use with computer algebra. The Baider theory of the Campbell-Hausdorff group is refined, by a study of its subgroups, to determine the smallest substages into which the hypernormalization process can be divided. This leads to a linear algebra algorithm to compute the generators needed for each substage with the least amount of work. A concrete interpretation of Jan Sanders’ spectral sequence for hypernormal forms is presented. Examples are given, and a proof is given for a little-known theorem of Belitskii expressing the hypernormal form space (in the inner product style) as the kernel of a higher-order differential operator.     

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.     

RNAi for Insect Control: Current Perspective and Future Challenges

The research on the RNA interference (RNAi) for the control of insect pests has made significant growth in recent years. The availability of the genomic sequences of insects has further widened the horizons for the testing of this technology to various insect groups. Different modes of application of double-stranded RNA (dsRNA) have been tested; however, the practicability of delivery of dsRNA in insects still remains the biggest challenge. Till date, the oral delivery of dsRNA in insects is one of the efficient approaches for the practical application of this technique. The uptake of dsRNA from the insect gut is mediated either by SID-1/SID-2 transmembrane proteins or by endocytosis; however, the systemic RNAi machinery still remains to be revealed in insect species. The RNAi-mediated gene knockdown has shown striking results in different insect groups, pointing it to be the upcoming technique for insect control. However, before the successful application of this technique for insect control, some potential issues need to be resolved. This review presents the account of prospects and challenges for the use of this technology for insect control.     

Stationary-fiber rotary probe with unobstructed 360° view for optical coherence tomography

A side-scanning fiber probe is a critical component for optical coherence tomography in medical imaging and diagnosis. We propose and fabricate an on-axis rotating probe that performs in situ, circumferential scanning that is shadow-free (not susceptible to shadow effects caused by the motor's wires). A miniature motor that incorporates a bored-out shaft for the optical fiber is located at the distal end of the probe, which results in a more stable and uniform circumferential scan, free from wire-shadow interference effects. More importantly, this design, novel to our knowledge, compared to other probes avoids the insertion losses introduced by optical coupling components and the multitude of optical interfaces, which is very important for sensing weak signals backscattered from structures deep in the tissue.     

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.     

Conformer specific dissociation dynamics of iodocyclohexane studied by velocity map imaging

The photodissociation dynamics of iodocyclohexane has been studied using velocity map imaging following excitation at many wavelengths within its A-band (230 ≤ λ ≤ 305 nm). This molecule exists in two conformations (axial and equatorial), and one aim of the present experiment was to explore the extent to which conformer-specific fragmentation dynamics could be distinguished. Ground (I) and spin-orbit excited (I?) state iodine atom products were monitored by 2 + 1 resonance enhanced multiphoton ionization, and total kinetic energy release (TKER) spectra and angular distributions derived from analysis of images recorded at all wavelengths studied. TKER spectra obtained at the longer excitation wavelengths show two distinct components, which can be attributed to the two conformers and the different ways in which these partition the excess energy upon C-I bond fission. Companion calculations based on a simple impulsive model suggest that dissociation of the equatorial (axial) conformer preferentially yields vibrationally (rotationally) excited cyclohexyl co-fragments. Both I and I? products are detected at the longest parent absorption wavelength (λ ～ 305 nm), and both sets of products show recoil anisotropy parameters, β > 1, implying prompt dissociation following excitation via a transition whose dipole moment is aligned parallel to the C-I bond. The quantum yield for forming I? products, Φ(I?), has been determined by time resolved infrared diode laser absorption methods to be 0.14 ± 0.02 (at λ = 248 nm) and 0.22 ± 0.05 (at λ = 266 nm). Electronic structure calculations indicate that the bulk of the A-band absorption is associated with transition to the 4A(') state, and that the (majority) I atom products arise via non-adiabatic transfer from the 4A(') potential energy surface (PES) via conical intersection(s) with one or more PESs correlating with ground state products.     

New, unexpected, and dominant mechanisms in the hydrogen exchange reaction

A quasiclassical trajectory study of the state specific H+D(2)(upsilon = 0,j = 0) --> HD(upsilon' = 0,j' = 0) + D reaction at a collision energy of 1.85 eV (total energy of 2.04 eV) found that the scattering is governed by two unexpected and dominant new mechanisms, and not by direct recoil as is generally assumed. The new mechanisms involve strong interaction with the sloping potential around the conical intersection, an area of the potential energy surface not previously considered to have much effect upon reactive scattering. Initial investigations indicate that more than 50% of reactive scattering could be the result of these new mechanisms at this collision energy. Features in the corresponding quantum mechanical results can be attributed to these new (classical) reaction mechanisms.