Spontaneous Surgery on the Borromean Rings

We study the cone-manifolds whose singular sets are obtained by orbifold and spontaneous surgeries on components of the Borromean rings. We establish existence of geometric structures on these manifolds. For manifolds with hyperbolic structure we obtain an integral representation for volumes.     

关于AP-内射环的一个注记

本文的主要目的是讨论AP-内射环中的两个问题:(1)环R是正则的当且仅当R是左AP-内射的左PP-环;(2)如果R是左AP-内射环,那么R是内射环当且仅当R是弱内射环.因此我们推广了内射环的一些结果,与此同时我们还取得了一些新的结果.     

The p-chain Spectral Sequence

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the corresponding Atiyah–Hirzebruch-type spectral sequence. It can be used in combination with the Isomorphism Conjectures of Baum and Connes and Farrell and Jones to compute algebraic K- and L-groups of group rings and topological K-groups of reduced group C*-algebras.     

on submicron rings and their application for coherent nanoelectronic devices

Electron-phase modulation in magnetic and electric fields will be presented in In_0.75Ga_0.25As Aharonov–Bohm (AB) rings. The zero Schottky barrier of this material made it possible to nanofabricate devices with radii down to below 200 nm without carrier depletion. We shall present a fabrication scheme based on wet and dry etching that yielded excellent reproducibility, very high contrast of the oscillations and good electrical gating. The operation of these structures is compatible with closed-cycle refrigeration and suggests that this process can yield coherent electronic circuits that do not require cryogenic liquids. The InGaAs/AlInAs heterostructure was grown by MBE on a GaAs substrate [F. Capotondi, G. Biasiol, D. Ercolani, V. Grillo, E. Carlino, F. Romanato, L. Sorba, Thin Solid Films 484 (2005) 400], and in light of the large effective g-factor and the absence of the Schottky barrier is a material system of interest for the investigation of spin-related effects [W. Desrat, F. Giazotto, V. Pellegrini, F. Beltram, F. Capotondi, G. Biasiol, L. Sorba, D.K. Maude, Phys. Rev. B 69 (2004) 245324; W. Desrat, F. Giazotto, V. Pellegrini, M. Governale, F. Beltram, F. Capotondi, G. Biasiol, L. Sorba, Phys. Rev. B 71 (2005) 153314; J. Nitta, T. Akazaki, H. Takayanagi, T. Enoki, Phys. Rev. Lett. 78 (1997) 1335] and the realization of hybrid superconductor/semiconductor devices [Th. Schäpers, A. Kaluza, K. Neurohr, J. Malindretos, G. Crecelius, A. van der Hart, H. Hardtdegen, H. Lüth, Appl. Phys. Lett. 71 (1997) 3575].     

Impurity effects in the optical absorption of quantum rings

We study the interplay between impurity scattering and Coulomb interaction effects in the absorption spectrum of neutral bound magnetoexcitons confined in quantum-ring structures. Impurity scattering breaks the rotational symmetry of the ring system, introducing characteristic features in the optical emission. Signatures of the optical Aharonov–Bohm effect are still present for weak scattering and strong Coulomb screening. Furthermore, an impurity-induced modulation of the absorption strength is present even for a strong impurity potential and low screening. This behavior is likely responsible of recent experimental observations in quantum-ring structures.     

Hydrodynamics of a particle impact on a wall

The problem of a particle impacting on a wall, a common phenomenon in particle-laden flows in the minerals and process industries, is investigated computationally using a spectral-element method with the grid adjusting to the movement of the particle towards the wall. Remeshing is required at regular intervals to avoid problems associated with mesh distortion and the constantly reducing maximum time-step associated with integration of the non-linear convective terms of the Navier–Stokes equations. Accurate interpolation between meshes is achieved using the same high-order interpolation employed by the spectral-element flow solver. This approach allows the full flow evolution to be followed from the initial approach, through impact and afterwards as the flow relaxes. The method is applied to the generic two-dimensional and three-dimensional bluff body geometries, the circular cylinder and the sphere. The principal case reported here is that of a particle colliding normally with a wall and sticking. For the circular cylinder, non-normal collisions are also considered. The impacts are studied for moderate Reynolds numbers up to approximately 1200. A cylindrical body impacting on a wall produces two vortices from its wake that convect away from the cylinder along the wall before stalling while lifting induced wall vorticity into the main flow. The situation for a sphere impact is similar, except in this case a vortex ring is formed from the wake vorticity. Again, secondary vorticity from the wall and particle plays a role. At higher Reynolds number, the secondary vorticity tends to form a semi-annular structure encircling the primary vortex core. At even higher Reynolds numbers, the secondary annular structure fragments into semi-discrete structures, which again encircle and orbit the primary core. Vorticity fields and passive tracer particles are used to characterize the interaction of the vortical structures. The evolution of the pressure and viscous drag coefficients during a collision are provided for a typical sphere impact. For a Reynolds number greater than approximately 1000 for a sphere and 400 for a cylinder, the primary vortex core produced by the impacting body undergoes a short-wavelength instability in the azimuthal/spanwise direction. Experimental visualisation using dye carried out in water is presented to validate the predictions.     

Rhythmic pattern formations in gels and Matalon—Packter law: A fresh perspective

The periodic precipitation pattern formation in gelatinous media is interpreted as a moving boundary problem. The time law, spacing law and width law are revisited on the basis of the new scenario. The explicit dependence of the geometric structure on the initial concentrations of the reactants is derived. Matalon—Packter law, which relates the spacing coefficient with the initial concentrations is reformulated removing many ambiguities and impractical parameters. Experimental results are discussed to establish the significance of moving boundary concept in the diffusion controlled pattern forming systems     

Multimode squeezed states produced by a confocal parametric oscillator

We investigate the spatial behaviour of the quantum-noise-reduction spectrum of the vacuum state emitted by a degenerate optical parametric oscillator below threshold. In view of possible experimental implementations, we consider a mode-degenerate resonator and two matching lenses and show that, for the realistic case of a finite-width pump, significant level of squeezing can be observed in a very small region of the beam. Received 25 September 2002 Published online 11 February 2003     

T拟内射模与TQI环

本文定义并刻划了Ｔ拟内射模与Ｔ拟内射包，证明了ＷＧ－ｃｏｃｒｉｔｉｃａｌＴ拟内射模的自同态环为正则非奇异右自内射环．最后讨论了Ｔ拟内射模与Ｔ内射模一致的环，即ＴＱＩ环．还给出了Ｇａｂｒｉｅｌ拓扑Ｇ中每个右理想Ｔ拟内射的几个等价条件     

VUV photoionisation of free azabenzenes: Pyridine, pyrazine, pyrimidine, pyridazine and s-triazine

Photoionisation mass spectrometry was used to obtain the fragmentation pathways of pyridine, pyridazine, pyrimidine, pyrazine and s-triazine molecules upon absorption of 23.0, 15.7 and 13.8 eV synchrotron photons. The ionic fragments observed vary from molecule to molecule, however C₂H₂⁺, HCN⁺and HCNH⁺ are common to all five molecules at the three photon energies. Furthermore, the presence of C₂H₂N₂⁺, C₃H₃N⁺ and C₄H₄⁺ in the spectra of some of the molecules suggests dissociation pathways via loss of HCN moieties. The respective parent cations, m/q=79, 80 and 81 have a greater yield at low photon energies when compared to the most intense fragment peak in each spectra. We recorded two of the fragment cation yields, as well as the parent photoion yield curves of pyridine, pyridazine, and pyrimidine in the 8–30 eV range. The formation of abundant cation fragments show a strong propensity of the molecules for dissociation after the absorption of VUV photons higher than 14 eV. The differences in relative fragment yields from molecule to molecule, and when changing the excitation energy, suggest significant bond rearrangements and nuclear motion during the dissociation time. Thus, bond cleavage is dependent on the photon energy deposited in the molecule and on intramolecular reactivity. With the aid of photoion yield curves and energy estimations we have assigned major peaks in the spectra and discussed their fragmentation pathways.