Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, we improve Conti's results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions.Comment: 29 pages, 3 figure

Ultrasound elastographic techniques in focal liver lesions

Elastographic techniques are new ultrasound-based imaging techniques developed to estimate tissue deformability/stiffness. Several ultrasound elastographic approaches have been developed, such as static elastography, transient elastography and acoustic radiation force imaging methods, which include point shear wave and shear wave imaging elastography. The application of these methods in clinical practice aims at estimating the mechanical tissues properties. One of the main settings for the application of these tools has been liver stiffness assessment in chronic liver disease, which has been studied mainly using transient elastography. Another field of application for these techniques is the assessment of focal lesions, detected by ultrasound in organs such as pancreas, prostate, breast, thyroid, lymph nodes. Considering the frequency and importance of the detection of focal liver lesions through routine ultrasound, some studies have also aimed to assess the role that elestography can play in studying the stiffness of different types of liver lesions, in order to predict their nature and thus offer valuable non-invasive methods for the diagnosis of liver masses

The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ imposed by the contracted Codazzi equations. We use this fact to study the Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in B\"ar, Gauduchon, Moroianu (2005). We also answer negatively the corresponding questions in the smooth category.Comment: 28 pages; final versio

The Role of Spleen and Liver Elastography and Color-Doppler Ultrasound in the Assessment of Transjugular Intrahepatic Portosystemic Shunt Function

The reference standard for assessing transjugular intrahepatic portosystemic shunt (TIPS) function is venography with portosystemic pressure gradient (PPG) measurement. This procedure is invasive and expensive; thus, we assessed the feasibility, reproducibility and diagnostic accuracy of color-Doppler ultrasound (CDUS) and spleen and liver stiffness (LS) measurements for identifying TIPS dysfunction. Twenty-four patients (15 undergoing TIPS placement and nine undergoing TIPS revision) consecutively underwent CDUS examination and LS and spleen stiffness (SS) determination by transient elastography (TE) and point shear-wave elastography (pSWE). All parameters were taken before TIPS placement/revision (1\u201315 d before) and 24 h after, just before revision by venography. pSWE inter-observer agreement was assessed by intra-class correlation coefficient (ICC). CDUS and elastographic data were correlated (Pearson coefficient) with pressure gradients (hepatic venous pressure gradient [HVPG], PPG). Main determinants of TIPS dysfunction were investigated by linear regression. Forty-nine paired examinations were performed in total: 49 (100%) SS reliable measurements by pSWE and 38 (88%) by TE. The ICC for pSWE values was 0.90 (95% confidence interval [CI] 0.81\u20120.94). SS values significantly correlated with HVPG and PPG (R = 0.51, p = 0.01). The area under the Receiver-Operating Characteristic (AUROC) curve of SS for diagnosing TIPS dysfunction was 0.86 (95% CI 0.70\u20120.96) using a 25 kPa cutoff. At multivariate analysis, the flow direction of the intrahepatic portal vein branches and SS values were independently associated to TIPS dysfunction. The intrahepatic portal vein branches flow direction and SS value are two simple, highly sensitive parameters accurately excluding TIPS dysfunction. SS measurement by pSWE is feasible, reproducible and both positively and significantly correlates with HVPG and PPG values

Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones

We apply the averaging theory of first order for discontinuous differential systems to study the bifurcation of limit cycles from the periodic orbits of the uniform isochronous center of the differential systems ẋ = -y+x, y = x + xy, and ẋ = -y + xy, y = x + xy, when they are perturbed inside the class of all discontinuous quadratic and cubic polynomials differential systems with four zones separately by the axes of coordinates, respectively. Using averaging theory of first order the maximum number of limit cycles that we can obtain is twice the maximum number of limit cycles obtained in a previous work for discontinuous quadratic differential systems perturbing the same uniform isochronous quadratic center at origin perturbed with two zones separately by a straight line, and 5 more limit cycles than those achieved in a prior result for discontinuous cubic differential systems with the same uniform isochronous cubic center at the origin perturbed with two zones separately by a straight line. Comparing our results with those obtained perturbing the mentioned centers by the continuous quadratic and cubic differential systems we obtain 8 and 9 more limit cycles respectively

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC

Measurements of inclusive jet suppression in heavy ion collisions at the LHC provide direct sensitivity to the physics of jet quenching. In a sample of lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the anti-kt algorithm with values for the distance parameter that determines the nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp. Jet production is found to be suppressed by approximately a factor of two in the 10% most central collisions relative to peripheral collisions. Rcp varies smoothly with centrality as characterized by the number of participating nucleons. The observed suppression is only weakly dependent on jet radius and transverse momentum. These results provide the first direct measurement of inclusive jet suppression in heavy ion collisions and complement previous measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables, submitted to Physics Letters B. All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02

Measurement of the cross section for isolated-photon plus jet production in pp collisions at √s=13 TeV using the ATLAS detector

The dynamics of isolated-photon production in association with a jet in proton–proton collisions at a centre-of-mass energy of 13 TeV are studied with the ATLAS detector at the LHC using a dataset with an integrated luminosity of 3.2 fb−1. Photons are required to have transverse energies above 125 GeV. Jets are identified using the anti- algorithm with radius parameter and required to have transverse momenta above 100 GeV. Measurements of isolated-photon plus jet cross sections are presented as functions of the leading-photon transverse energy, the leading-jet transverse momentum, the azimuthal angular separation between the photon and the jet, the photon–jet invariant mass and the scattering angle in the photon–jet centre-of-mass system. Tree-level plus parton-shower predictions from Sherpa and Pythia as well as next-to-leading-order QCD predictions from Jetphox and Sherpa are compared to the measurements