Descent of Equivalences and Character Bijections

Categorical equivalences between block algebras of finite groups—such as Morita and derived equivalences—are well known to induce character bijections which commute with the Galois groups of field extensions. This is the motivation for attempting to realise known Morita and derived equivalences over non-splitting fields. This article presents various results on the theme of descent to appropriate subfields and subrings. We start with the observation that perfect isometries induced by a virtual Morita equivalence induce isomorphisms of centres in non-split situations and explain connections with Navarro’s generalisation of the Alperin–McKay conjecture. We show that Rouquier’s splendid Rickard complex for blocks with cyclic defect groups descends to the non-split case. We also prove a descent theorem for Morita equivalences with endopermutation source

A New Model of Biodosimetry to Integrate Low and High Doses

Biological dosimetry, that is the estimation of the dose of an exposure to ionizing radiation by a biological parameter, is a very important tool in cases of radiation accidents. The score of dicentric chromosomes, considered to be the most accurate method for biological dosimetry, for low LET radiation and up to 5 Gy, fits very well to a linear-quadratic model of dose-effect curve assuming the Poisson distribution. The accuracy of this estimation raises difficulties for doses over 5 Gy,the highest dose of the majority of dose-effect curves used in biological dosimetry. At doses over 5 Gy most cells show difficulties in reaching mitosis and cannot be used to score dicentric chromosomes. In the present study with the treatment of lymphocyte cultures with caffeine and the standardization of the culture time, metaphases for doses up to 25 Gy have been analyzed. Here we present a new model for biological dosimetry, which includes a Gompertz-type function as the dose response, and also takes into account the underdispersion of aberrationamong-cell distribution. The new model allows the estimation of doses of exposures to ionizing radiation of up to 25 Gy. Moreover, the model is more effective in estimating whole and partial body exposures than the classical method based on linear and linear-quadratic functions, suggesting their effectiveness and great potential to be used after high dose exposures of radiation

Confinement and Quantization Effects in Mesoscopic Superconducting Structures

We have studied quantization and confinement effects in nanostructured superconductors. Three different types of nanostructured samples were investigated: individual structures (line, loop, dot), 1-dimensional (1D) clusters of loops and 2D clusters of antidots, and finally large lattices of antidots. Hereby, a crossover from individual elementary "plaquettes", via clusters, to huge arrays of these elements, is realized. The main idea of our study was to vary the boundary conditions for confinement of the superconducting condensate by taking samples of different topology and, through that, modifying the lowest Landau level E_LLL(H). Since the critical temperature versus applied magnetic field T_c(H) is, in fact, E_LLL(H) measured in temperature units, it is varied as well when the sample topology is changed through nanostructuring. We demonstrate that in all studied nanostructured superconductors the shape of the T_c(H) phase boundary is determined by the confinement topology in a unique way.Comment: 28 pages, 19 EPS figures, uses LaTeX's aipproc.sty, contribution to Euroschool on "Superconductivity in Networks and Mesoscopic Systems", held in Siena, Italy (8-20 september 1997

Comparative study of TIG and SMAW root welding passes on ductile iron cast weldability

This work compares the weldability of ductile iron when: (I) a root weld is applied with a tungsten inert gas (TIG) process using an Inconel 625 source rod and filler welds are subsequently applied using coated electrodes with 97,6%Ni; and (II) welds on ductile iron exclusively made using the manual shielded metal arc welding technique (SMAW). Both types of welds are performed on ductile iron specimen test plates that are subjected to preheat and post-weld annealing treatments. Samples with TIG root-welding pass shown higher hardness but slightly lower ductility and strength. Both types of welding achieved better ductile and strength properties than ones found in literature

Can we always get the entanglement entropy from the Kadanoff-Baym equations? The case of the T-matrix approximation

We study the time-dependent transmission of entanglement entropy through an out-of-equilibrium model interacting device in a quantum transport set-up. The dynamics is performed via the Kadanoff-Baym equations within many-body perturbation theory. The double occupancy $< \hat{n}_{R \uparrow} \hat{n}_{R \downarrow} >$, needed to determine the entanglement entropy, is obtained from the equations of motion of the single-particle Green's function. A remarkable result of our calculations is that $< \hat{n}_{R \uparrow} \hat{n}_{R \downarrow} >$ can become negative, thus not permitting to evaluate the entanglement entropy. This is a shortcoming of approximate, and yet conserving, many-body self-energies. Among the tested perturbation schemes, the $T$-matrix approximation stands out for two reasons: it compares well to exact results in the low density regime and it always provides a non-negative $< \hat{n}_{R \uparrow} \hat{n}_{R \downarrow} >$. For the second part of this statement, we give an analytical proof. Finally, the transmission of entanglement across the device is diminished by interactions but can be amplified by a current flowing through the system.Comment: 6 pages, 6 figure