Optimal rank matrix algebras preconditioners

When a linear system Ax = y is solved by means of iterative methods (mainly CG and GMRES) and the convergence rate is slow, one may consider a preconditioner P and move to the preconditioned system P-1 Ax = P(-1)y. The use of such preconditioner changes the spectrum of the matrix defining the system and could result into a great acceleration of the convergence rate. The construction of optimal rank preconditioners is strongly related to the possibility of splitting A as A = P R E. where E is a small perturbation and R is of low rank (Tyrtyshnikov, 1996) [1]. In the present work we extend the black-dot algorithm for the computation of such splitting for P circulant (see Oseledets and Tyrtyshnikov, 2006 [2]), to the case where P is in A, for several known low-complexity matrix algebras A. The algorithm so obtained is particularly efficient when A is Toeplitz plus Hankel like. We finally discuss in detail the existence and the properties of the decomposition A = P+R+E when A is Toeplitz, also extending to the phi-circulant and Hartley-type cases some results previously known for P circulant

Generalized modularity matrices

Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In this paper we put in evidence certain common traits of various modularity matrices and shed light on their spectral properties that are at the basis of various theoretical results and practical spectral-type algorithms for community detection

Effect of a high forage: Concentrate ratio on milk yield, blood parameters and oxidative status in lactating cows

A feeding strategy that requires a forage: concentrate ratio equal to 70: 30, with at least five different herbs in the forage and the use of silages prohibited, has recently been introduced in Italy. Despite the benefits in terms of human health (lower ω6: ω3 ratio, higher conjugated linoleic acid level) of the obtained milk, little information regarding the possible effects on cows' health is available. The aim of this study was to evaluate the effects of such a feeding strategy in dairy cows (90 days in milk at the beginning of the trial) on milk yield and composition, and blood metabolic profile, including the evaluation of oxidative stress. The proposed feeding strategy, compared with a semi-intensive strategy, resulted in an improvement of animal oxidative status (lower levels of reactive oxygen metabolites, higher levels of antioxidant potential and anti-reactive oxygen metabolites) and a significant increase of milk urea only in the first part of the trial. No differences in milk yield and composition were detected throughout the trial

Single-row vs. double-row arthroscopic rotator cuff repair: clinical and 3 Tesla MR arthrography results.

Background Arthroscopic rotator cuff repair has become popular in the last few years because it avoids large skin incisions and deltoid detachment and dysfunction. Earlier arthroscopic single-row (SR) repair methods achieved only partial restoration of the original footprint of the tendons of the rotator cuff, while double-row (DR) repair methods presented many biomechanical advantages and higher rates of tendon-to-bone healing. However, DR repair failed to demonstrate better clinical results than SR repair in clinical trials. MR imaging at 3 Tesla, especially with intra-articular contrast medium (MRA), showed a better diagnostic performance than 1.5 Tesla in the musculoskeletal setting. The objective of this study was to retrospectively evaluate the clinical and 3 Tesla MRA results in two groups of patients operated on for a medium-sized full-thickness rotator cuff tear with two different techniques. Methods The first group consisted of 20 patients operated on with the SR technique; the second group consisted of 20 patients operated on with the DR technique. All patients were evaluated at a minimum of 3 years after surgery. The primary end point was the re-tear rate at 3 Tesla MRA. The secondary end points were the Constant-Murley Scale (CMS), the Simple Shoulder Test (SST) scores, surgical time and implant expense. Results The mean follow-up was 40 months in the SR group and 38.9 months in the DR group. The mean postoperative CMS was 70 in the SR group and 68 in the DR group. The mean SST score was 9.4 in the SR group and 10.1 in the DR group. The re-tear rate was 60% in the SR group and 25% in the DR group. Leakage of the contrast medium was observed in all patients. Conclusions To the best of our knowledge, this is the first report on 3 Tesla MRA in the evaluation of two different techniques of rotator cuff repair. DR repair resulted in a statistically significant lower re-tear rate, with longer surgical time and higher implant expense, despite no difference in clinical outcomes. We think that leakage of the contrast medium is due to an incomplete tendon-to-bone sealing, which is not a re-tear. This phenomenon could have important medicolegal implications. Level of evidence III. Treatment study: Case–control study

4D analysis of the microstructural evolution of Si-based electrodes during lithiation: Time-lapse X-ray imaging and digital volume correlation

Silicon is a promising candidate to substitute or complement graphite as anode material in Li-ion batteries due, mainly, to its high energy density. However, the lithiation/delithiation processes of silicon particles are inherently related to drastic volume changes which, within a battery's physically constrained case, can induce significant deformation of the fundamental components of the battery that can eventually cause it to fail. In this work, we use non-destructive time-lapse X-ray imaging techniques to study the coupled electrochemo-mechanical phenomena in Li-ion batteries. We present X-ray computed tomography data acquired at different times during the first lithiation of custom-built silicon-lithium battery cells. Microstructural volume changes have been quantified using full 3D strain field measurements from digital volume correlation analysis. Furthermore, the extent of lithiation of silicon particles has been quantified in 3D from the grey-scale of the tomography images. Correlation of the volume expansion and grey-scale changes over the silicon-based electrode volume indicates that the process of lithiation is kinetically affected by the reaction at the Si/LixSi interface

Full-field measurements of strain localisation in sandstone by neutron tomography and 3D-volumetric Digital Image Correlation

AbstractRecent studies have demonstrated that the combination of x-ray tomography during triaxial tests (“in-situ” tests) and 3D- volumetric Digital Image Correlation (3D-DIC) can provide important insight into the mechanical behaviour and deformation processes of granular materials such as sand. The application of these tools to investigate the mechanisms of failure in rocks is also of obvious interest. However, the relevant applied confining pressures for triaxial testing on rocks are higher than those on sands and therefore stronger pressure containment vessels, i.e., made of thick metal walls, are required. This makes in-situ x-ray imaging of rock deformation during triaxial tests a challenge. One possible solution to overcome this problem is to use neutrons, which should better penetrate the metal-walls of the pressure vessels. In this perspective, this work assesses the capability of neutron tomography with 3D-DIC to measure deformation fields in rock samples. Results from pre- and post-deformation neutron tomography of a Bentheim sandstone sample deformed ex-situ at 40MPa show that clear images of the internal structure can be achieved and utilised for 3D-DIC analysis to reveal the details of the 3D strain field. From these results the character of the localised deformation in the study sample can thus be described. Furthermore, comparison with analyses based on equivalent x-ray tomography imaging of the same sample confirms the effectiveness of the method in relation to the more established x-ray based approach

Evidence of a thermo-diffusion pinch on particle transport in FTU discharges close to density limit

Abstract In FTU, the density profile in the presence of large MARFE becomes more and more peaked with increasing density, forming strong density gradients close to the radial region affected by the MARFE. The temperature at the edge drops to few eV, driving a drop of the whole profile. The estimated particle source cannot justify the change of the density gradient, which instead is well-explained by a change of the pinch. A thermo-diffusion term well-describes the pinch evolution and the experimental behavior of the density at those radii where temperature measurements are reliable

dynamic and frequency behaviour of the marfe instability on ftu

The Frascati Tokamak Upgrade (FTU) device can operate at high electron density regimes of the order of 1020m−3, where the MARFE instability is present at various plasma current and magnetic field values. When the MARFE is well developed and oscillating, its movement causes continuous density fluctuation, contaminating the integral density measurements. The amplitude and frequency of these density fluctuations are well revealed by the high resolution interferometer available on FTU, the dependence of the frequency versus basic plasma parameters is investigated in this paper.A specific experimental session on FTU, including some discharges with reversed toroidal magnetic field, and pushing the plasma column towards the internal or external side of the vacuum chamber, respectively, has shown that, when the plasma column is distant from the toroidal limiter, the MARFE is stable and does not oscillate around the mid plane. For these last cases the MARFE localization with respect to the ion drift direction, which can influence the stable and unstable positions, is also discussed. Keywords: Tokamak, MARFE, Greenwald limit, Single particle motion, Ion drift, Plasma radiatio

ALERT Doctoral School 2012: advanced experimental techniques in geomechanics

The twenty-second session of the European Graduate School 2012 (called usually ALERT Doctoral School) entitled Advanced experimental techniques in geomechanics is organized by Cino Viggiani, Steve Hall and Enrique Romero.Postprint (published version