Boundary conditions and stability of a perfectly matched layer for the elastic wave equation in first order form

The article of record as published by be found at http://dx.doi.org/10.1016/j.jcp.2015.09.048In computations, it is now common to surround artificial boundaries of a computational domain with a perfectly matched layer (PML) of finite thickness in order to prevent artificially reflected waves from contaminating a numerical simulation. Unfortunately, the PML does not give us an indication about appropriate boundary conditions needed to close the edges of the PML, or how those boundary conditions should be enforced in a numerical setting. Terminating the PML with an inappropriate boundary condition or an unstable numerical boundary procedure can lead to exponential growth in the PML which will eventually destroy the accuracy of a numerical simulation everywhere. In this paper, we analyze the stability and the well-posedness of boundary conditions terminating the PML for the elastic wave equation in first order form. First, we consider a vertical modal PML truncating a two space dimensional computational domain in the horizontal direction. We freeze all coefficients and consider a left half-plane problem with linear boundary conditions terminating the PML. The normal mode analysis is used to study the stability and well-posedness of the resulting initial boundary value problem (IBVP). The result is that any linear well-posed boundary condition yielding an energy estimate for the elastic wave equation, without the PML, will also lead to a well-posed IBVP for the PML. Second, we extend the analysis to the PML corner region where both a horizontal and vertical PML are simultaneously active. The challenge lies in constructing accurate and stable numerical approximations for the PML and the boundary conditions. Third, we develop a high order accurate finite difference approximation of the PML subject to the boundary conditions. To enable accurate and stable numerical boundary treatments for the PML we construct continuous energy estimates in the Laplace space for a one space dimensional problem and two space dimensional PML corner problem. We use summation-by-parts finite difference operators to approximate the spatial derivatives and impose boundary conditions weakly using penalties. In order to ensure numerical stability of the discrete PML, it is necessary to extend the numerical boundary procedure to the auxiliary differential equations. This is crucial for deriving discrete energy estimates analogous to the continuous energy estimates. Numerical experiments are presented corroborating the theoretical results. Moreover, in order to ensure longtime numerical stability, the boundary condition closing the PML, or its corresponding discrete implementation, must be dissipative. Furthermore, the numerical experiments demonstrate the stable and robust treatment of PML corners

Variational solution of the Yang-Mills Schr\"odinger equation in Coulomb gauge

The Yang-Mills Schr\"odinger equation is solved in Coulomb gauge for the vacuum by the variational principle using an ansatz for the wave functional, which is strongly peaked at the Gribov horizon. A coupled set of Schwinger-Dyson equations for the gluon and ghost propagators in the Yang-Mills vacuum as well as for the curvature of gauge orbit space is derived and solved in one-loop approximation. We find an infrared suppressed gluon propagator, an infrared singular ghost propagator and a almost linearly rising confinement potential.Comment: 24 pages, revtex, 13 figure

Coarse-grained computations of demixing in dense gas-fluidized beds

We use an "equation-free", coarse-grained computational approach to accelerate molecular dynamics-based computations of demixing (segregation) of dissimilar particles subject to an upward gas flow (gas-fluidized beds). We explore the coarse-grained dynamics of these phenomena in gently fluidized beds of solid mixtures of different densities, typically a slow process for which reasonable continuum models are currently unavailable

Use of oregano (Origanum onites L.) essential oil as hatching egg disinfectant

This study was carried out to determine whether oregano (Origanum onites) essential oil works as a disinfectant for hatching egg obtained from broiler breeder flock. Oregano essential oil was applied at two doses 0.55 and 0.75 ìl/cm3 and two exposure times, 3 and 6 h. The formaldehyde treated eggs were used as positive control and untreated eggs used as negative control. After chemical analysis, the main constituents of oregano essential oil were carvacrol, linalool, para-cymene and -terpinene. Thelowest microbial counts on eggs were obtained from oregano essential oil. Microbial inhibition increased with the increasing essential oil concentrations. Essential oil exposure times had no significant effects on microbial counts. Essential oil fumigation lowered middle embryonic mortality and discarded chick rate, but increased early and late embryonic mortalities compared to formaldehyde treatment. Essential oil doses significantly affected late embryonic mortality, discarded chicks rate,contamination rate, hatchability of fertile egg, body weight at 21 and 42 days, body weight gain and total feed consumption. But, early and middle embryonic mortality were not significantly affected by treatments. These results imply that oregano essential oil had great potential for hatching egg disinfectant and it could be used as natural egg disinfectant

Boundary Shape and Casimir Energy

Casimir energy changes are investigated for geometries obtained by small but arbitrary deformations of a given geometry for which the vacuum energy is already known for the massless scalar field. As a specific case, deformation of a spherical shell is studied. From the deformation of the sphere we show that the Casimir energy is a decreasing function of the surface to volume ratio. The decreasing rate is higher for less smooth deformations.Comment: 12 page

PRM14 European Assessment of the Validity of the QALY Outcome Measure: Results From the Experiment Conducted by the Echoutcome Project

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