Asymptotic expansions for high-contrast elliptic equations

In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in \cite{ge09_1} where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high and low conductivity inclusions

Magnetic and superconducting phase diagrams in ErNi2B2C

We present measurements of the superconducting upper critical field Hc2(T) and the magnetic phase diagram of the superconductor ErNi2B2C made with a scanning tunneling microscope (STM). The magnetic field was applied in the basal plane of the tetragonal crystal structure. We have found large gapless regions in the superconducting phase diagram of ErNi2B2C, extending between different magnetic transitions. A close correlation between magnetic transitions and Hc2(T) is found, showing that superconductivity is strongly linked to magnetism.Comment: 5 pages, 4 figure

Cataract Surgery in Anterior Megalophthalmos: A Review

Anterior megalophthalmos is characterized by megalocornea associated with a very broad anterior chamber and ciliary ring elongation. It is also known as X-linked megalocornea. It is accompanied by the early development of cataracts, zonular anomalies, and rarely vitreoretinal disorders. Cataract surgery involves the risk of subluxation of the cataract because zonular weakness. In addition, in most cases, standard IOL decentration is a danger due to the enlargement of the sulcus and capsular bag. Cataract surgery is challenging because of these unique circumstances. Several approaches have been performed to date. Implantation of a retropupillary iris-claw aphakic intraocular lens might be a good option, since it is easier than suturing the IOL and could have better and more stable anatomic and visual outcomes compared with the other techniques

On the first South American species of the genus Anasaitis Bryant, 1950 (Aranei: Salticidae: Salticinae: Euophryini) from Cartagena, Colombia

A new species - Anasaitis champetera sp.n. (Salticidae: Salticinae: Euophryini), the first species of the genus Anasaitis Bryant, 1950 from South America - is described of the basis of both sexes collected from Cano del Oro, Tierra Bomba island, Cartagena (Bolivar), Colombia.Peer reviewe

Global-local nonlinear model reduction for flows in heterogeneous porous media

In this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media