Higher-order finite element methods for elliptic problems with interfaces

We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of the problem. We prove optimal error estimates of the methods on general quasi-uniform and shape regular meshes in maximum norms. In addition, we apply the method to a Stokes interface problem, adding correction terms for the velocity and the pressure, obtaining optimal convergence results.Comment: 26 pages, 6 figures. An earlier version of this paper appeared on November 13, 2014 in http://www.brown.edu/research/projects/scientific-computing/reports/201

The diffuse Nitsche method: Dirichlet constraints on phase-field boundaries

We explore diffuse formulations of Nitsche's method for consistently imposing Dirichlet boundary conditions on phase-field approximations of sharp domains. Leveraging the properties of the phase-field gradient, we derive the variational formulation of the diffuse Nitsche method by transferring all integrals associated with the Dirichlet boundary from a geometrically sharp surface format in the standard Nitsche method to a geometrically diffuse volumetric format. We also derive conditions for the stability of the discrete system and formulate a diffuse local eigenvalue problem, from which the stabilization parameter can be estimated automatically in each element. We advertise metastable phase-field solutions of the Allen-Cahn problem for transferring complex imaging data into diffuse geometric models. In particular, we discuss the use of mixed meshes, that is, an adaptively refined mesh for the phase-field in the diffuse boundary region and a uniform mesh for the representation of the physics-based solution fields. We illustrate accuracy and convergence properties of the diffuse Nitsche method and demonstrate its advantages over diffuse penalty-type methods. In the context of imaging based analysis, we show that the diffuse Nitsche method achieves the same accuracy as the standard Nitsche method with sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human vertebral body

Factores determinantes del salario del sector privado en el Ecuador para el año 2014: Un caso de estudio en la ciudad de Guayaquil

In Ecuador, wage compensation for private sector workers has become a difficult problem to deal with and conciliate throughout history. The current Ecuadorean Constitution approved in Montecristi in 2008 strongly protects labour rights; however, many companies do not obey the law. This study investigates the variables that are significant to address private-sector wages in Guayaquil city. An analysis of the results in the previous literature and a review by Mincer (1974) suggest these variables: years of work experience, education, gender of the employee, position, seniority in the company, and marital status. Interactive and quadratic variables were also included. The inference methodology selected was ordinary least squares (OLS) with robust standard errors of White, and taking into account the sample bias correction proposed by Heckman (1979). The results show that the significant variables concerning human capital depend on the type of company they are working for and its interaction with other variables. Thus, empirical evidence was found to support that small companies are not paying their labour force in terms of productivity, specifically to new employees.En Ecuador, la remuneración salarial de los trabajadores del sector privado se ha convertido en un problema difícil de tratar y armonizar a lo largo de la historia. La actual Constitución del Ecuador, aprobada en Montecristi en 2008, protege los derechos laborales de los empleados; sin embargo, muchas empresas no actúan apegadas a la ley. El presente trabajo se desarrolla con la finalidad de encontrar las variables que están influyendo de manera significativa al salario de los trabajadores del sector privado en la ciudad de Guayaquil. Dada la revisión previa de literatura, y tomando como base los estudios realizados por Mincer (1974), las variables analizadas fueron: años de experiencia laboral, nivel de educación, sexo del empleado, tipo de cargo, antigüedad en la compañía y estado civil. Además, se incluyeron variables interactivas y cuadráticas. Por otro lado, la metodología de inferencia utilizada es la de mínimos cuadrados ordinarios con errores estándar robustos de White tomando en cuenta la corrección por sesgo muestral propuesta por Heckman (1979). Según los resultados obtenidos, la significación de las variables que conforma el capital humano depende del tipo de empresa en la que laboran los empleados y de su interacción con otras variables. Es así que se encontró evidencia empírica para afirmar que las compañías pequeñas no están remunerando a sus dependientes en función de su productividad, específicamente a los empleados nuevo

What's at Stake for the State: Undocumented Californians, Immigration Reform, and Our Future Together

Building off a methodology originally pioneered by co-author Enrico A.Marcelli (Demographer, Department ofSociology, San Diego State University) to estimate the unauthorized, this is the first report to estimate undocumented Californians at this breadth and level of detail. One in six California children has at least one undocumented parent and 81% of those children are citizens. Nearly half (49%) of undocumented Californians have lived here more than 10 years. Undocumented Californians comprise nearly 7% of the state's total population, 8% of all adults and 9% of the state's workforce.However, achievement of these gains will require a clear and quick roadmap to citizenship. To succeed, federal immigration reform needs to take immigrant integration seriously, and the state and local governments will need to invest in programs to raise education levels, increase English fluency and improve job skills as a way to maximize the potential of undocumented Californians and build a stronger state

Spin-polarized current oscillations in diluted magnetic semiconductor multiple quantum wells

We study the spin and charge dynamics of electrons in n-doped II--VI semiconductor multiple quantum wells when one or more quantum wells are doped with Mn. The interplay between strongly nonlinear inter-well charge transport and the large tunable spin-splitting induced by exchange interactions with spin-polarized Mn ions produces interesting new spin dependent features. The tunneling current between quantum wells can be strongly spin polarized and, under certain conditions, can develop self sustained oscillations under a finite dc voltage. The spin polarization oscillates in both magnetic and nonmagnetic quantum wells and the time average in magnetic wells can differ from its zero-voltage value. Our numerical simulations demonstrate that the amplitude of the spin polarization oscillations depends on the distribution of magnetic wells within the sample. We discuss how the spin polarized current and the spin polarization of the quantum wells can be tailored experimentally.Comment: 5 pages, 5 figures; to be published in Phys. Rev.