Hierarchical error estimates for the energy functional in obstacle problems

We present a hierarchical a posteriori error analysis for the minimum value of the energy functional in symmetric obstacle problems. The main result is that the error in the energy minimum is, up to oscillation terms, equivalent to an appropriate hierarchical estimator. The proof does not invoke any saturation assumption. We even show that small oscillation implies a related saturation assumption. In addition, we prove efficiency and reliability of an a posteriori estimate of the discretization error and thereby cast some light on the theoretical understanding of previous hierarchical estimators. Finally, we illustrate our theoretical results by numerical computations

Multi-megagauss field-generation using capacitor banks

Design of a high-field (6 MG) production experiment on the Pegasus capacitor bank is presented. One and two dimensions MHD simulations are benchmarked against Alikhanov`s previous experiments and used to support the design for the Pegasus experiment. Possible extensions to the Atlas facility, where production of 20 Mg fields may be possible, are also discussed

Dirac: A campaign of experiments to study physics and chemistry at ultrahigh magnetic fields

We present an overview of the Dirac experimental campaign conducted at Los Alamos in spring of 1996. The name was chosen in recognition of P.A.M. Dirac`s monumental contributions to quantum theory, which affected every aspect of the science we planned to investigate. We show how the various collaborations were put together, discuss some of the difficulties of collecting data in rapidly changing magnetic fields, describe the motivation, packaging, and integration of experiments, and give an exceedingly preliminary discussion of some of the results

Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions

We introduce an iterative method for computing the first eigenpair $(\lambda_{p},e_{p})$ for the $p$-Laplacian operator with homogeneous Dirichlet data as the limit of $(\mu_{q,}u_{q})$ as $q\rightarrow p^{-}$, where $u_{q}$ is the positive solution of the sublinear Lane-Emden equation $-\Delta_{p}u_{q}=\mu_{q}u_{q}^{q-1}$ with same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained through inverse iteration of a super-solution which is derived from the solution to the torsional creep problem. Convergence of $u_{q}$ to $e_{p}$ is in the $C^{1}$-norm and the rate of convergence of $\mu_{q}$ to $\lambda_{p}$ is at least $O(p-q)$. Numerical evidence is presented.Comment: Section 5 was rewritten. Jed Brown was added as autho

Spallation reactions. A successful interplay between modeling and applications

The spallation reactions are a type of nuclear reaction which occur in space by interaction of the cosmic rays with interstellar bodies. The first spallation reactions induced with an accelerator took place in 1947 at the Berkeley cyclotron (University of California) with 200 MeV deuterons and 400 MeV alpha beams. They highlighted the multiple emission of neutrons and charged particles and the production of a large number of residual nuclei far different from the target nuclei. The same year R. Serber describes the reaction in two steps: a first and fast one with high-energy particle emission leading to an excited remnant nucleus, and a second one, much slower, the de-excitation of the remnant. In 2010 IAEA organized a worskhop to present the results of the most widely used spallation codes within a benchmark of spallation models. If one of the goals was to understand the deficiencies, if any, in each code, one remarkable outcome points out the overall high-quality level of some models and so the great improvements achieved since Serber. Particle transport codes can then rely on such spallation models to treat the reactions between a light particle and an atomic nucleus with energies spanning from few tens of MeV up to some GeV. An overview of the spallation reactions modeling is presented in order to point out the incomparable contribution of models based on basic physics to numerous applications where such reactions occur. Validations or benchmarks, which are necessary steps in the improvement process, are also addressed, as well as the potential future domains of development. Spallation reactions modeling is a representative case of continuous studies aiming at understanding a reaction mechanism and which end up in a powerful tool.Comment: 59 pages, 54 figures, Revie

A posteriori error estimates for the virtual element method

An a posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully computable as it relies only on quantities available from the VEM solution, namely its degrees of freedom and element-wise polynomial projection. Upper and lower bounds of the error estimator with respect to the VEM approximation error are proven. The error estimator is used to drive adaptive mesh refinement in a number of test problems. Mesh adaptation is particularly simple to implement since elements with consecutive co-planar edges/faces are allowed and, therefore, locally adapted meshes do not require any local mesh post-processing

Organizational innovation in the multinational enterprise: internalization theory and business history

This article engages in a methodological experiment by using historical evidence to challenge a common misperception about internalization theory. The theory has often been criticized for maintaining that it assumes a hierarchically organized MNE based on knowledge flowing from the home country. This is not an accurate description of how global firms operate in recent decades, but this article shows it has never been true historically. Using longitudinal data on individual firms from the nineteenth century onwards, it reveals evidence of how entrepreneurs and firms with multinational activity faced with market imperfections changed the design of their headquarters and their organizational structures

Convergence of Adaptive Finite Element Methods with Error-Dominated Oscillation

Recently, we devised an approach to a posteriori error analysis, which clarifies the role of oscillation and where oscillation is bounded in terms of the current approximation error. Basing upon this approach, we derive plain convergence of adaptive linear finite elements approximating the Poisson problem. The result covers arbritray $H^{-1}$-data and characterizes convergent marking strategies

Planar streak camera laser-driven shockwave studies

High pressure equation-of-state parameter determination is now possible using a high-energy laser to drive shock waves into a multiple foil target. Recent progress in the design of streak cameras and targets has reduced the errors and uncertainties in impedance-match measurements to about 5 to 10%, and further improvements are expected in the near future. Initial measurements are reported for pressures in the few-megabar region for gold and aluminum

Isentropic compression of argon

The compression was done in an MC-1 flux compression (explosive) generator, in order to study the transition from an insulator to a conductor. Since conductivity signals were observed in all the experiments (except when the probe is removed), both the Teflon and the argon are becoming conductive. The conductivity could not be determined (Teflon insulation properties unknown), but it could be bounded as being {sigma}=1/{rho}{le}8({Omega}cm){sub -1}, because when the Teflon breaks down, the dielectric constant is reduced. The Teflon insulator problem remains, and other ways to better insulate the probe or to measure the conductivity without a probe is being sought