Poisson Groups and Differential Galois Theory of Schroedinger Equation on the Circle

We combine the projective geometry approach to Schroedinger equations on the circle and differential Galois theory with the theory of Poisson Lie groups to construct a natural Poisson structure on the space of wave functions (at the zero energy level). Applications to KdV-like nonlinear equations are discussed. The same approach is applied to 2^nd order difference operators on a one-dimensional lattice, yielding an extension of the lattice Poisson Virasoro algebra.     

Simultaneous detection of ultraviolet and infrared radiation in a single GaN/GaAlN heterojunction

Results are presented for a dual-band detector that simultaneously detects UV radiation in the 250-360 nm and IR radiation in the 5-14 microm regions with near zero spectral cross talk. In this detector having separate UV- and IR-active regions with three contacts (one common contact for both regions) allows the separation of the UV and IR generated photocurrent components, identifying the relative strength of each component. This will be an important development in UV-IR dual-band applications such as fire-flame detection, solar astronomy, and military sensing, eliminating the difficulties of employing several individual detectors with separate electronics-cooling mechanisms.     

Base‐dependent selectivity of an SNAr reaction

A detailed kinetic analysis and computational study of an S_NAr reaction between 2,5,6‐trifluoronicotinonitrile, 2 , and the ambident 3‐isopropoxy‐1H‐pyrazol‐5‐amine, 3 , is presented. The selectivity with respect to the reaction at the primary amino group of 2 , to give the desired product, 2,5‐difluoro‐6‐[(3‐isopropoxy‐1H‐pyrazol‐5‐yl)amino]nicotinonitrile, 1 , is strongly dependent upon reaction conditions. Reaction is found to proceed via both uncatalysed and base catalysed routes, and selectivity towards 1 is strongly enhanced in the presence of the base diazabicyclo[2,2,2]octane (DABCO). Computational studies in tetrahydrofuran solution at the B3LYP/6‐31G* level of theory have provided valuable insight into alternative kinetically indistinguishable reaction pathways. The results suggest that for reaction at the primary amino group, proton removal by DABCO accompanying amine addition allows avoidance of a high‐energy, zwitterionic Meisenheimer intermediate. Reactions at the alternative pyrazole nitrogen atoms are less sensitive to the presence of base because of stabilisation of the Meisenheimer zwitterions by intramolecular hydrogen bonding. Copyright © 2010 John Wiley & Sons, Ltd.     

White matter maturation in the brains of Long Evans shaker myelin mutant rats by ex-vivo QSI and DTI

The brains of Long Evans shaker (les) rats, a model of dysmyelination, and their age- matched controls were studied by ex-vivo q-space diffusion imaging (QSI) and diffusion tensor imaging (DTI). The QSI and DTI indices were computed from the same acquisition. The les and the control brains were studied at different stages of maturation and disease progression. The mean displacement, the probability for zero displacement and kurtosis were computed from QSI data while the fractional anisotropy (FA) and the eigenvalues were computed from DTI. It was found that all QSI indices detect the les pathology, at all stages of maturation, while only some of the DTI indices could detect the les pathology. The QSI mean displacement was larger in the les group as compared with their age-matched controls while the probability for zero displacement and the kurtosis were both lower all indicating higher degree of restriction in the control brains. Since all the DTI eigenvalues were higher in the les brains as compared to controls, the less efficient DTI measure for discerning the les pathology was found to be the FA. Clearly, the most sensitive DTI parameter to the les pathology is λ₃, i.e. the minimal diffusivity. Since the QSI and DTI data were obtained from the same acquisition, despite the somewhat higher SNR of the QSI data compared to the DTI data, it seems that the higher diagnostic capacity of the QSI data in this experimental model of dysmyelination, originates mainly from the higher diffusing weighting of the QSI data.     

Higgs boson cosmology

The discovery of the Standard Model Higgs boson opens up a range of speculative cosmological scenarios, from the formation of structure in the early universe immediately after the big bang, to relics from the electroweak phase transition one nanosecond after the big bang, on to the end of the present-day universe through vacuum decay. Higgs physics is wide ranging, and gives an impetus to go beyond the Standard Models of particle physics and cosmology to explore the physics of ultra-high energies and quantum gravity.     

On the photoelectron spectrum of sulphur trioxide

He(I), He(II) and variable temperature Ne(I) photoelectron spectra of sulphur trioxide are reported. All six of the expected ionic states have been detected and assigned; the assignment differs from a previous one. Ab initio calculations in a medium basis set have been carried out and spectral intensities have been calculated; agreement between the calculations and the spectra is good. The calculations show a substantial S(3d) character in the S-O bond, and the spectra are consistent with this.     

Binary-black-hole encounters, gravitational bursts, and maximum final spin

The spin of the final black hole in the coalescence of nonspinning black holes is determined by the "residual" orbital angular momentum of the binary. This residual momentum consists of the orbital angular momentum that the binary is not able to shed in the process of merging. We study the angular momentum radiated, the spin of the final black hole, and the gravitational bursts in a sequence of equal mass encounters. The initial orbital configurations range from those producing an almost direct infall to others leading to numerous orbits before infall, with multiple bursts of radiation. Our sequence consists of orbits with fixed impact parameter. What varies is the initial linear momentum of the black holes. For this sequence, the final black hole of mass M_{h} gets a maximum spin parameter a/M_{h} approximately 0.823, with this maximum occurring for initial orbital angular momentum L/M_{h};{2} approximately 1.176.     

Instabilities in quantum-dot spin-VCSELs

A modified spin-flip model is used to investigate the stability of optically-pumped quantum-dot spin-vertical cavity surface-emitting lasers. in terms of pump intensity and polarization. The stability maps exhibit pronounced polarization switching in the stable regions. Periodic oscillations in unstable regions are attributed to competition between spin relaxation and birefringence.