Brown University -
Joint Materials/Solid Mechanics Seminar Series
Abstract: A unique "6-degree of freedom" (6DOF) deformation experiment has been fully developed specifically for the purpose of validation of dislocation dynamics simulations of plastic flow up to strains on the order of 1%. The experiment has been designed so that a compressive uniaxial stress field is essentially super imposed on the test sample, and the crystal is free to deform with 3 orthogonal translation directions, and 3 rotation/tilt axes of freedom. The rotation, tilt and translation of the crystal are monitored by 5 laser displacement gages and 3 extensometers. Experiments are being performed on high purity Mo single crystals orientated for "single slip". All of the experiments are performed in pairs, with one test sample having highly polished surfaces for optical light and AFM slip-trace analyses, and the other having 4 strain gage rosettes mounted on the sides for measurement of the bi-axial surface strains during testing. All of the experimental data is used together to determine the slip activity of the orientated single crystal during deformation. The experimentally observed slip activity during deformation can be correlated directly with that predicted by dislocation dynamics simulations that use realistic initial conditions (i.e., natural sources), thereby validating the simulation results.
Brown Analysis Seminar
Special Scientific Computing Seminar
Abstract: Although it has long been recognized that simulations of most physical systems are fundamentally stochastic, this fact remains overlooked in most practical applications. Even essentially deterministic systemsmust be treated stochastically when their parameters, boundary and initial conditions, or forcing functions are under-specified by data. The method of random domain decomposition (RDD) provides a powerful tool for dealing with the kinds of spatially heterogeneous random processes that typically appear in realistic simulations of physical systems. RDD is based on a doubly stochastic model in which the problem domain is decomposed according to stochastic geometries into disjoint random fields. The stochastic decomposition is determined by variations in the parameter space based on additional (uncertain) geometric information that can be derived from new characterization techniques and also from expert knowledge. Previous work has tended to concentrate on spatially homogeneous parametrizations, or at most on heterogeneous parameter fields whose geometry is assumed known with certainty. This is almost never the case in natural systems. On the other hand, random domain decomposition allows us to estimate system states when heterogeneous parameterizations depend on realistic geometric uncertainty.
Scientific Computing Seminar
Old Dominion University, Norfolk, VA | |
Abstract: The discontinuous Galerkin method is a finite element method that allows discontinuities at element interfaces. In most Fourier analyses of discontinuous Galerkin schemes for hyperbolic systems, a spatial wavenumber is specified and the corresponding temporal frequency is computed as an eigenvalue of the semi-discrete equations. The relation of the two yields the numerical dispersion relation. In the present study, we reverse this process by specifying the temporal frequency and compute the corresponding spatial wavenumber. There are two advantages in this approach. First, due to compactness of the scheme, the eigenvalue problem is simplified and reduced to a quadratic algebraic equation, for any given order of the basis functions. This allows the numerical dispersion relation be solved analytically, which will subsequently be shown to be super-accurate for discontinuous Galerkin schemes. Second, the wave reflection and transmission at an interface of grid stretching, or other forms of grid variation, can be analyzed analytically using the eigensolutions so formed. Expressions of numerical reflection and transmission coefficients will be derived and analyzed for various flux formulas. All the findings of the study will be illustrated through numerical examples.
Special Scientific Computing Seminar
Abstract: We shall discuss the class of adaptive grid methods often called moving mesh methods (or dynamic methods -- in contrast to the static methods) for solving time dependent PDEs. These methods involve the solution of the underlying PDE for the physical problem solution in conjunction with a so-called moving mesh PDE for the mesh itself. This talk will describe some recent developments on moving mesh methods for computational fluid dynamics. Our moving mesh schemes are based on a fractional step approach. At each time level, the mesh will be adjusted based on the regularity of the solution, and then proper interpolation step is used to update the numerical solutions on the new grid. Special attention has to be taken to make sure that the overall scheme preserves some physical properties such as divergence free for the incompressible flow and conservation of mass for hyperbolic conservation laws. In this talk, we will also discuss some preliminary results on the theoretical aspects of this approach.
PDE Seminar
Department of Mathematics Colloquium
<--- 2003 Index