Piling and avalanches of magnetized particles

We performed computer simulations based on a two-dimensional Distinct Element Method to study granular systems of magnetized spherical particles. We measured the angle of repose and the surface roughness of particle piles, and we studied the effect of magnetization on avalanching. We report linear dependence of both angle of repose and surface roughness on the ratio $f$ of the magnetic dipole interaction and the gravitational force (\emph{interparticle force ratio}). There is a difference in avalanche formation at small and at large interparticle force ratios. The transition is at $f_c \approx 7$. For $f < f_c$ the particles forming the avalanches leave the system in a quasi-continuous granular flow (\emph{granular regime}), while for $f > f_c$ the avalanches are formed by long particle clusters (\emph{correlated regime}). The transition is not sharp. We give plausible estimates for $f_c$ based on stability criteria.Comment: 9 pages, 7 figure

Reconstructing Surfaces Using Anisotropic Basis Functions

Point sets obtained from computer vision techniques are often noisy and non-uniform. We present a new method of surface reconstruction that can handle such data sets using anisotropic basis functions. Our reconstruction algorithm draws upon the work in variational implicit surfaces for constructing smooth and seamless 3D surfaces. Implicit functions are often formulated as a sum of weighted basis functions that are radially symmetric. Using radially symmetric basis functions inherently assumes, however that the surface to be reconstructed is, everywhere, locally symmetric. Such an assumption is true only at planar regions, and hence, reconstruction using isotropic basis is insufficient to recover objects that exhibit sharp features. We preserve sharp features using anisotropic basis that allow the surface to vary locally. The reconstructed surface is sharper along edges and at corner points. We determine the direction of anisotropy at a point by performing principal component analysis of the data points in a small neighborhood. The resulting field of principle directions across the surface is smoothed through tensor filtering. We have applied the anisotropic basis functions to reconstruct surfaces from noisy synthetic 3D data and from real range data obtained from space carving

Doctor of Philosophy

dissertationOne of the fundamental building blocks of many computational sciences is the construction and use of a discretized, geometric representation of a problem domain, often referred to as a mesh. Such a discretization enables an otherwise complex domain to be represented simply, and computation to be performed over that domain with a finite number of basis elements. As mesh generation techniques have become more sophisticated over the years, focus has largely shifted to quality mesh generation techniques that guarantee or empirically generate numerically well-behaved elements. In this dissertation, the two complementary meshing subproblems of vertex placement and element creation are analyzed, both separately and together. First, a dynamic particle system achieves adaptivity over domains by inferring feature size through a new information passing algorithm. Second, a new tetrahedral algorithm is constructed that carefully combines lattice-based stenciling and mesh warping to produce guaranteed quality meshes on multimaterial volumetric domains. Finally, the ideas of lattice cleaving and dynamic particle systems are merged into a unified framework for producing guaranteed quality, unstructured and adaptive meshing of multimaterial volumetric domains

Indium growth and island height control on Si submonolayer phases

The quantum size effects (QSE) make it possible to control the dimensions of self-assembled nanostructures. An important goal in present day surface science is to grow uniform sized self-assembled nanostructures. One system which has displayed a number of interesting surface structures is Pb/In grown on a Si(111) substrate. The first part of the thesis discussed Pb islands grown on the anisotropic Si(111)-In(4x1) substrate. In addition to a preferred height of 4 monolayers due to QSE, these islands grow as nanowires with a preferred width of 660nm due to strain driven growth from the anisotropic substrate. Islands grown on the In(4x1) substrate also retain their preferred height to room temperature in contrast to previously observed critical temperatures of 250 K or less for islands grown on other substrates. Then In islands were grown on Si(111)-Pb-alpha-sqrt3 x sqrt3 substrate. The In islands in face-centered cubic (FCC) structure were found to have a preferred height of 4 monolayers due to QSE. With further depositions, an FCC to body-centered tetragonal(BCT) structure transition is observed. The In bct islands was found to have unexpected fast growth rate compared to FCC structure, which indicate the extra high mobility of In atoms. In the last part In islands were grown on varies of In phases at low temperature. Conversion between submonolayer In phases are observed. Due to the highly mobility of In atoms, the QSE effects observed on the Pb alpha phase is not observed

Efficient Reconstruction From Scattered Points

Most algorithms that reconstruct surface from sample points rely on computationally demanding operations to derive the reconstruction, beside this, most of the classical algorithm use a kind of three-dimensional structure to derive a two-dimensional one. In this paper we introduce an innovative approach for generating two-dimensional piecewise linear approximations from sample points in R3 that simplify significantly the numerical calculation and the memory usage in the reconstruction process. The approach proposed here is an advancing front approach that uses rigid movements in the three-dimensional space and a bidimensional Delaunay triangulation as the main tools for the algorithm. The principal idea is to use a combination of rotations and translations in order to simplify the calculations and avoid the three-dimensional structure used by the most of the algorithms. Avoiding those structures, this approach can reduce the computational cost and numerical instabilities typically associated with the classical algorithm reconstructions

Elastic wave scattering by shelled spherical scatterers in a focused field

Embrittlement of many important metal alloys has been related to the accumulation of undesirable materials at grain boundaries, a condition which may be detectable through measurement of ultrasonic scattering from the material’s microstructure. Grains with decorated grain boundaries are modeled as shelled microspheres embedded in an isotropic elastic host, and a practical means of predicting scattering from these particles is developed. The incident field often used for measuring backscattered grain noise is focused; both plane and focused incident fields are treated. Theoretical predictions of scattering from isolated scatterers are compared with experimental measurements on metal microspheres embedded in plastic to validate the computational procedure, then predictions of scattering from similar spherical structures embedded in a metal host are presented. In the former case theoretical predictions are found consistent with observations, although differences between shelled and nonshelled scatterers are obscured by the great contrast between host and scatterer. In the latter case, where host and core are quite similar, even thin shells can produce scattering readily distinguishable from the weak scattering in polycrystals that may be due to locally inhomogeneous properties. Results of this study can be used to calculate a backscattering coefficient for calculations of grain noise in metals containing, or composed of, numerous shelled scatterers