Brou\'e's abelian defect group conjecture holds for the Harada-Norton sporadic simple group HNHN

In representation theory of finite groups, there is a well-known and important conjecture due to M. Brou\'e. He conjectures that, for any prime $p$, if a $p$-block $A$ of a finite group $G$ has an abelian defect group $P$, then $A$ and its Brauer corresponding block $B$ of the normaliser $N_G(P)$ of $P$ in $G$ are derived equivalent (Rickard equivalent). This conjecture is called Brou\'e's abelian defect group conjecture. We prove in this paper that Brou\'e's abelian defect group conjecture is true for a non-principal 3-block $A$ with an elementary abelian defect group $P$ of order 9 of the Harada-Norton simple group $HN$. It then turns out that Brou\'e's abelian defect group conjecture holds for all primes $p$ and for all $p$-blocks of the Harada-Norton simple group $HN$.Comment: 36 page

On narrowing coated conductor film: emergence of granularity-induced field hysteresis of transport critical current

Critical current density Jc in polycrystalline or granular superconducting material is known to be hysteretic with applied field H due to the focusing of field within the boundary between adjacent grains. This is of concern in the so-called coated conductors wherein superconducting film is grown on a granular, but textured surface of a metal substrate. While previous work has mainly been on Jc determined using induced or magnetization currents, the present work utilizes transport current via an applied potential in strip geometry. It is observed that the effect is not as pronounced using transport current, probably due to a large difference in criterion voltage between the two types of measurements. However, when the films are narrowed by patterning into 200-, 100-, or 80-micron, the hysteresis is clearly seen, because of the forcing of percolation across higher-angle grain boundaries. This effect is compared for films grown on ion-beam-assisted-deposited (IBAD) YSZ substrate and those grown on rolling-assisted-biaxially-textures substrates (RABiTS) which have grains that are about ten times larger. The hysteresis is more pronounced for the latter, which is more likely to have a weak grain boundary spanning the width of the microbridge. This is also of concern to applications in which coated conductors will be striated in order to reduce of AC losses.Comment: text-only: 10 pages, plus 5 figures on 5 page

Superconducting YBa2Cu3O7-δ nanocomposites using preformed ZrO2 nanocrystals : growth mechanisms and vortex pinning properties

Although high temperature superconductors are promising for power applications, the production of low-cost coated conductors with high current densitiesat high magnetic fieldsremains challenging. A superior superconducting YBa2Cu3O7- nanocomposite is fabricated via chemical solution deposition (CSD) using preformed nanocrystals (NCs). Preformed, colloidally stable ZrO2 NCs are added to the trifluoroacetic acid based precursor solution and the NCs' stability is confirmed up to 50 mol% for at least 2.5 months. These NCs tend to disrupt the epitaxial growth of YBa2Cu3O7-, unless a thin seed layer is applied. A 10 mol% ZrO2 NC addition proved to be optimal, yielding a critical current density J(C) of 5 MA cm(-2) at 77 K in self-field. Importantly, this new approach results in a smaller magnetic field decay of J(C)(H//c) for the nanocomposite compared to a pristine film. Furthermore, microstructural analysis of the YBa2Cu3O7- nanocomposite films reveals that different strain generation mechanisms may occur compared to the spontaneous segregation approach. Yet, the generated nanostrain in the YBa2Cu3O7- nanocomposite results in an improvement of the superconducting properties similar to the spontaneous segregation approach. This new approach, using preformed NCs in CSD coatings, can be of great potential for high magnetic field applications

Hybrid model for vascular tree structures

This paper proposes a new representation scheme of the cerebral blood vessels. This model provides information on the semantics of the vascular structure: the topological relationships between vessels and the labeling of vascular accidents such as aneurysms and stenoses. In addition, the model keeps information of the inner surface geometry as well as of the vascular map volume properties, i.e. the tissue density, the blood flow velocity and the vessel wall elasticity. The model can be constructed automatically in a pre-process from a set of segmented MRA images. Its memory requirements are optimized on the basis of the sparseness of the vascular structure. It allows fast queries and efficient traversals and navigations. The visualizations of the vessel surface can be performed at different levels of detail. The direct rendering of the volume is fast because the model provides a natural way to skip over empty data. The paper analyzes the memory requirements of the model along with the costs of the most important operations on it.Postprint (published version

Brou\'e's abelian defect group conjecture holds for the double cover of the Higman-Sims sporadic simple group

In the representation theory of finite groups, there is a well-known and important conjecture, due to Brou\'e saying that for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding block B of the normaliser N_G(P) of P in G are derived equivalent. We prove in this paper, that Brou\'e's abelian defect group conjecture, and even Rickard's splendid equivalence conjecture are true for the faithful 3-block A with an elementary abelian defect group P of order 9 of the double cover 2.HS of the Higman-Sims sporadic simple group. It then turns out that both conjectures hold for all primes p and for all p-blocks of 2.HS.Comment: 20 pages. arXiv admin note: substantial text overlap with arXiv:1011.442