ML is a multigrid preconditioning package intended to solve linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package or to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the Aztec 2.1 and AztecOO iterative package [16]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and nonsymmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.
This paper presents solution verification studies applicable to a class of problems involving wave propagation, frictional contact, geometrical complexity, and localized incompressibility. The studies are in support of a validation exercise of a phenomenological screw failure model. The numerical simulations are performed using a fully explicit transient dynamics finite element code, employing both standard four-node tetrahedral and eight-node mean quadrature hexahedral elements. It is demonstrated that verifying the accuracy of the simulation involves not only consideration of the mesh discretization error, but also the effect of the hourglass control and the contact enforcement. In particular, the proper amount of hourglass control and the behavior of the contact search and enforcement algorithms depend greatly on the mesh resolution. We carry out the solution verification exercise using mesh refinement studies and describe our systematic approach to handling the complicating issues. It is shown that hourglassing and contact must both be carefully monitored as the mesh is refined, and it is often necessary to make adjustments to the hourglass and contact user input parameters to accommodate finer meshes. We introduce in this paper the hourglass energy, which is used as an 'error indicator' for the hourglass control. If the hourglass energy does not tend to zero with mesh refinement, then an hourglass control parameter is changed and the calculation is repeated.
An important challenge encountered during post-processing of finite element analyses is the visualizing of three-dimensional fields of real-valued second-order tensors. Namely, as finite element meshes become more complex and detailed, evaluation and presentation of the principal stresses becomes correspondingly problematic. In this paper, we describe techniques used to visualize simulations of perturbed in-situ stress fields associated with hypothetical salt bodies in the Gulf of Mexico. We present an adaptation of the Mohr diagram, a graphical paper and pencil method used by the material mechanics community for estimating coordinate transformations for stress tensors, as a new tensor glyph for dynamically exploring tensor variables within three-dimensional finite element models. This interactive glyph can be used as either a probe or a filter through brushing and linking.
The purpose of the present work is to increase our understanding of which properties of geomaterials most influence the penetration process with a goal of improving our predictive ability. Two primary approaches were followed: development of a realistic, constitutive model for geomaterials and designing an experimental approach to study penetration from the target's point of view. A realistic constitutive model, with parameters based on measurable properties, can be used for sensitivity analysis to determine the properties that are most important in influencing the penetration process. An immense literature exists that is devoted to the problem of predicting penetration into geomaterials or similar man-made materials such as concrete. Various formulations have been developed that use an analytic or more commonly, numerical, solution for the spherical or cylindrical cavity expansion as a sort of Green's function to establish the forces acting on a penetrator. This approach has had considerable success in modeling the behavior of penetrators, both as to path and depth of penetration. However the approach is not well adapted to the problem of understanding what is happening to the material being penetrated. Without a picture of the stress and strain state imposed on the highly deformed target material, it is not easy to determine what properties of the target are important in influencing the penetration process. We developed an experimental arrangement that allows greater control of the deformation than is possible in actual penetrator tests, yet approximates the deformation processes imposed by a penetrator. Using explosive line charges placed in a central borehole, we loaded cylindrical specimens in a manner equivalent to an increment of penetration, allowing the measurement of the associated strains and accelerations and the retrieval of specimens from the more-or-less intact cylinder. Results show clearly that the deformation zone is highly concentrated near the borehole, with almost no damage occurring beyond 1/2 a borehole diameter. This implies penetration is not strongly influenced by anything but the material within a diameter or so of the penetration. For penetrator tests, target size should not matter strongly once target diameters exceed some small multiple of the penetrator diameter. Penetration into jointed rock should not be much affected unless a discontinuity is within a similar range. Accelerations measured at several points along a radius from the borehole are consistent with highly-concentrated damage and energy absorption; At the borehole wall, accelerations were an order of magnitude higher than at 1/2 a diameter, but at the outer surface, 8 diameters away, accelerations were as expected for propagation through an elastic medium. Accelerations measured at the outer surface of the cylinders increased significantly with cure time for the concrete. As strength increased, less damage was observed near the explosively-driven borehole wall consistent with the lower energy absorption expected and observed for stronger concrete. As it is the energy absorbing properties of a target that ultimately stop a penetrator, we believe this may point the way to a more readily determined equivalent of the S number.
Biosecurity must be implemented without impeding biomedical and bioscience research. Existing security literature and regulatory requirements do not present a comprehensive approach or clear model for biosecurity, nor do they wholly recognize the operational issues within laboratory environments. To help address these issues, the concept of Biosecurity Levels should be developed. Biosecurity Levels would have increasing levels of security protections depending on the attractiveness of the pathogens to adversaries. Pathogens and toxins would be placed in a Biosecurity Level based on their security risk. Specifically, the security risk would be a function of an agent's weaponization potential and consequences of use. To demonstrate the concept, examples of security risk assessments for several human, animal, and plant pathogens will be presented. Higher security than that currently mandated by federal regulations would be applied for those very few agents that represent true weapons threats and lower levels for the remainder.
We explore stability of Random Boolean Networks as a model of biological interaction networks. We introduce surface-to-volume ratio as a measure of stability of the network. Surface is defined as the set of states within a basin of attraction that maps outside the basin by a bit-flip operation. Volume is defined as the total number of states in the basin. We report development of an object-oriented Boolean network analysis code (Attract) to investigate the structure of stable vs. unstable networks. We find two distinct types of stable networks. The first type is the nearly trivial stable network with a few basins of attraction. The second type contains many basins. We conclude that second type stable networks are extremely rare.
The efficiency of neuronal encoding in sensory and motor systems has been proposed as a first principle governing response properties within the central nervous system. We present a continuation of a theoretical study presented by Zhang and Sejnowski, where the influence of neuronal tuning properties on encoding accuracy is analyzed using information theory. When a finite stimulus space is considered, we show that the encoding accuracy improves with narrow tuning for one- and two-dimensional stimuli. For three dimensions and higher, there is an optimal tuning width.
