A posteriori error estimators for nonconforming finite element methods of the linear elasticity problem

AbstractIn this work we derive and analyze a posteriori error estimators for low-order nonconforming finite element methods of the linear elasticity problem on both triangular and quadrilateral meshes, with hanging nodes allowed for local mesh refinement. First, it is shown that equilibrated Neumann data on interelement boundaries are simply given by the local weak residuals of the numerical solution. The first error estimator is then obtained by applying the equilibrated residual method with this set of Neumann data. From this implicit estimator we also derive two explicit error estimators, one of which is similar to the one proposed by Dörfler and Ainsworth (2005) [24] for the Stokes problem. It is established that all these error estimators are reliable and efficient in a robust way with respect to the Lamé constants. The main advantage of our error estimators is that they yield guaranteed, i.e., constant-free upper bounds for the energy-like error (up to higher order terms due to data oscillation) when a good estimate for the inf–sup constant is available, which is confirmed by some numerical results

Dilute magnetic semiconductor and half metal behaviors in 3d transition-metal doped black and blue phosphorenes: a first-principles study

We present first-principles density-functional calculations for the structural, electronic, and magnetic properties of substitutional 3d transition metal (TM) impurities in two-dimensional black and blue phosphorenes. We find that the magnetic properties of such substitutional impurities can be understood in terms of a simple model based on the Hund's rule. The TM-doped black phosphorenes with Ti, V, Cr, Mn, Fe and Ni impurities show dilute magnetic semiconductor (DMS) properties while those with Sc and Co impurities show nonmagnetic properties. On the other hand, the TM-doped blue phosphorenes with V, Cr, Mn and Fe impurities show DMS properties, those with Ti and Ni impurities show half-metal properties, whereas Sc and Co doped systems show nonmagnetic properties. We identify two different regimes depending on the occupation of the hybridized electronic states of TM and phosphorous atoms: (i) bonding states are completely empty or filled for Sc- and Co-doped black and blue phosphorenes, leading to non-magnetic; (ii) non-bonding d states are partially occupied for Ti-, V-, Cr-, Mn-, Fe- and Ni-doped black and blue phosphorenes, giving rise to large and localized spin moments. These results provide a new route for the potential applications of dilute magnetic semiconductor and half-metal in spintronic devices by employing black and blue phosphorenes.Comment: 9 pages, 7 figure

Multimodality cardiovascular imaging in pulmonary embolism

Acute pulmonary embolism (APE) is one of the leading causes of cardiovascular (CV) morbidity andmortality. To select appropriate therapeutic strategy and/or to minimize the mortality and morbidity,rapid and correct identification of life-threatening APE is very important. Also, right ventricular (RV)failure usually precedes acute hemodynamic compromise or death, and thus the identification of RVfailure is another important step in risk stratification or treatment of APE. With advances in diagnosisand treatment, the prognosis of APE has been dramatically improving in most cases, but inadequatetherapy or recurrent episodes of pulmonary embolism (PE) may result in negative outcomes or, so called,chronic thromboembolic pulmonary hypertension (CTEPH). CTEPH is a condition characterized byremaining chronic thromboembolic material in the pulmonary vasculature and subsequent chronicpulmonary hypertension.Various imaging modalities include chest computed tomography pulmonary angiography (CTPA),echocardiography, magnetic resonance imaging, and nuclear imaging and each are used for the assessmentof varying status of PE. Assessment of thromboembolic burden by chest CTPA is the first step inthe diagnosis of PE. Hemodynamic assessment can be achieved by echocardiography and also by chestCTPA. Nuclear imaging is useful in discriminating CTEPH from APE.Better perspectives on diagnosis, risk stratification and decision making in PE can be provided bycombining multimodality CV imaging. Here, the advantages or pitfalls of each imaging modality indiagnosis, risk stratification, or management of PE will be discussed