An extended finite element method with smooth nodal stress

The enrichment formulation of double-interpolation finite element method (DFEM) is developed in this paper. DFEM is first proposed by Zheng \emph{et al} (2011) and it requires two stages of interpolation to construct the trial function. The first stage of interpolation is the same as the standard finite element interpolation. Then the interpolation is reproduced by an additional procedure using the nodal values and nodal gradients which are derived from the first stage as interpolants. The re-constructed trial functions are now able to produce continuous nodal gradients, smooth nodal stress without post-processing and higher order basis without increasing the total degrees of freedom. Several benchmark numerical examples are performed to investigate accuracy and efficiency of DFEM and enriched DFEM. When compared with standard FEM, super-convergence rate and better accuracy are obtained by DFEM. For the numerical simulation of crack propagation, better accuracy is obtained in the evaluation of displacement norm, energy norm and the stress intensity factor

Multiple G-It\^{o} integral in the G-expectation space

In this paper, motivated by mathematic finance we introduce the multiple G-It\^{o} integral in the G-expectation space, then investigate how to calculate. We get the the relationship between Hermite polynomials and multiple G-It\^{o} integrals which is a natural extension of the classical result obtained by It\^{o} in 1951.Comment: 9 page

An Invariance Principle of G-Brownian Motion for the Law of the Iterated Logarithm under G-expectation

The classical law of the iterated logarithm (LIL for short)as fundamental limit theorems in probability theory play an important role in the development of probability theory and its applications. Strassen (1964) extended LIL to large classes of functional random variables, it is well known as the invariance principle for LIL which provide an extremely powerful tool in probability and statistical inference. But recently many phenomena show that the linearity of probability is a limit for applications, for example in finance, statistics. As while a nonlinear expectation--- G-expectation has attracted extensive attentions of mathematicians and economists, more and more people began to study the nature of the G-expectation space. A natural question is: Can the classical invariance principle for LIL be generalized under G-expectation space? This paper gives a positive answer. We present the invariance principle of G-Brownian motion for the law of the iterated logarithm under G-expectation

Ferromagnetism in 2p Light Element-Doped II-oxide and III-nitride Semiconductors

II-oxide and III-nitride semiconductors doped by nonmagnetic 2p light elements are investigated as potential dilute magnetic semiconductors (DMS). Based on our first-principle calculations, nitrogen doped ZnO, carbon doped ZnO, and carbon doped AlN are predicted to be ferromagnetic. The ferromagnetism of such DMS materials can be attributed to a p-d exchange-like p-p coupling interaction which is derived from the similar symmetry and wave function between the impurity (p-like t_2) and valence (p) states. We also propose a co-doping mechanism, using beryllium and nitrogen as dopants in ZnO, to enhance the ferromagnetic coupling and to increase the solubility and activity

Nickel-catalysed carbonylative homologation of aryl iodides

Homologation is an important organic transformation which extends the carbon chain of a parent molecule, and many procedures have been established. However, although carbonylation reactions are now well developed as valuable methods for the synthesis of carbonyl-containing compounds, studies of carbonylative homologation are limited. Here we report a nickel-catalysed carbonylative homologation of aryl iodides. With molybdenum hexacarbonyl as the solid carbon monoxide source and silane as the deoxygenation reagent, benzylic units can be effectively produced. Various (hetero)arenes can be successfully benzylated and give the corresponding products in moderate to excellent yields

Graphitic-BN Based Metal-free Molecular Magnets From A First Principle Study

We perform a first principle calculation on the electronic properties of carbon doped graphitic boron nitride graphitic BN. It was found that carbon substitution for either boron or nitrogen atom in graphitic BN can induce spontaneous magnetization. Calculations based on density functional theory with the local spin density approximation on the electronic band structure revealed a spin polarized, dispersionless band near the Fermi energy. Spin density contours showed that the magnetization density originates from the carbon atom. The magnetization can be attributed to the carbon 2p electron. Charge density distribution shows that the carbon atom forms covalent bonds with its three nearest neighbourhood. The spontaneous magnetization survives the curvature effect in BN nanotubes, suggesting the possibility of molecular magnets made from BN. Compared to other theoretical models of light-element or metal-free magnetic materials, the carbon-doped BN are more experimentally accessible and can be potentially useful.Comment: 8 pages, 4 figure

Parkinson\u27s disease-related spatial covariance pattern identified with resting-state functional MRI

In this study, we sought to identify a disease-related spatial covariance pattern of spontaneous neural activity in Parkinson\u27s disease using resting-state functional magnetic resonance imaging (MRI). Time-series data were acquired in 58 patients with early to moderate stage Parkinson\u27s disease and 54 healthy controls, and analyzed by Scaled Subprofile Model Principal Component Analysis toolbox. A split-sample analysis was also performed in a derivation sample of 28 patients and 28 control subjects and validated in a prospective testing sample of 30 patients and 26 control subjects. The topographic pattern of neural activity in Parkinson\u27s disease was characterized by decreased activity in the striatum, supplementary motor area, middle frontal gyrus, and occipital cortex, and increased activity in the thalamus, cerebellum, precuneus, superior parietal lobule, and temporal cortex. Pattern expression was elevated in the patients compared with the controls, with a high accuracy (90%) to discriminate the patients from the controls. The split-sample analysis produced a similar pattern but with a lower accuracy for group discrimination in both the derivation (80%) and the validation (73%) samples. Our results showed that resting-state functional MRI can be potentially useful for identification of Parkinson\u27s disease-related spatial covariance patterns, and for differentiation of Parkinson\u27s disease patients from healthy controls at an individual level.Journal of Cerebral Blood Flow & Metabolism advance online publication, 3 June 2015; doi:10.1038/jcbfm.2015.118

Environmental Effect on the Associations of Background Quasars with Foreground Objects: II. Numerical Simulations

Using numerical simulations of cluster formation in the standard CDM model (SCDM) and in a low-density, flat CDM model with a cosmological constant (LCDM), we investigate the gravitational lensing explanation for the reported associations between background quasars and foreground clusters. Under the thin-lens approximation and the unaffected background hypothesis , we show that the recently detected quasar overdensity around clusters of galaxies on scales of $\sim10$ arcminutes cannot be interpreted as a result of the gravitational lensing by cluster matter and/or by their environmental and projected matter along the line of sight, which is consistent with the analytical result based on the observed cluster and galaxy correlations (Wu, et al. 1996). It appears very unlikely that uncertainties in the modeling of the gravitational lensing can account for the disagreement between the theoretical predictions and the observations. We conclude that either the detected signal of the quasar-cluster associations is a statistical fluke or the associations are are generated by mechanisms other than the magnification bias.Comment: 15 pages, 5 figures, accepted for publication in Ap