59,137 research outputs found
Nonlinear Measures for Characterizing Rough Surface Morphologies
We develop a new approach to characterizing the morphology of rough surfaces
based on the analysis of the scaling properties of contour loops, i.e. loops of
constant height. Given a height profile of the surface we perform independent
measurements of the fractal dimension of contour loops, and the exponent that
characterizes their size distribution. Scaling formulas are derived and used to
relate these two geometrical exponents to the roughness exponent of a
self-affine surface, thus providing independent measurements of this important
quantity. Furthermore, we define the scale dependent curvature and demonstrate
that by measuring its third moment departures of the height fluctuations from
Gaussian behavior can be ascertained. These nonlinear measures are used to
characterize the morphology of computer generated Gaussian rough surfaces,
surfaces obtained in numerical simulations of a simple growth model, and
surfaces observed by scanning-tunneling-microscopes. For experimentally
realized surfaces the self-affine scaling is cut off by a correlation length,
and we generalize our theory of contour loops to take this into account.Comment: 39 pages and 18 figures included; comments to
[email protected]
Voronoi cell finite element modelling of the intergranular fracture mechanism in polycrystalline alumina
The mechanisms of fracture in polycrystalline alumina were investigated at the grain level using both the micromechanical tests and finite element (FE) model. First, the bending experiments were performed on the alumina microcantilever beams with a controlled displacement rate of 10 nm s–1 at the free end; it was observed that the intergranular fracture dominates the failure process. The full scale 3D Voronoi cell FE model of the microcantilever bending tests was then developed and experimentally validated to provide the insight into the cracking mechanisms in the intergranular fracture. It was found that the crystalline morphology and orientation of grains have a significant impact on the localised stress in polycrystalline alumina. The interaction of adjacent grains as well as their different orientations determines the localised tensile and shear stress state in grain boundaries. In the intergranular fracture process, the crack formation and propagation are predominantly governed by tensile opening (mode I) and shear sliding (mode II) along grain boundaries. Additionally, the parametric FE predictions reveal that the bulk failure load of the alumina microcantilever increases with the cohesive strength and total fracture energy of grain boundaries
Front Stability in Mean Field Models of Diffusion Limited Growth
We present calculations of the stability of planar fronts in two mean field
models of diffusion limited growth. The steady state solution for the front can
exist for a continuous family of velocities, we show that the selected velocity
is given by marginal stability theory. We find that naive mean field theory has
no instability to transverse perturbations, while a threshold mean field theory
has such a Mullins-Sekerka instability. These results place on firm theoretical
ground the observed lack of the dendritic morphology in naive mean field theory
and its presence in threshold models. The existence of a Mullins-Sekerka
instability is related to the behavior of the mean field theories in the
zero-undercooling limit.Comment: 26 pp. revtex, 7 uuencoded ps figures. submitted to PR
Microstructural enrichment functions based on stochastic Wang tilings
This paper presents an approach to constructing microstructural enrichment
functions to local fields in non-periodic heterogeneous materials with
applications in Partition of Unity and Hybrid Finite Element schemes. It is
based on a concept of aperiodic tilings by the Wang tiles, designed to produce
microstructures morphologically similar to original media and enrichment
functions that satisfy the underlying governing equations. An appealing feature
of this approach is that the enrichment functions are defined only on a small
set of square tiles and extended to larger domains by an inexpensive stochastic
tiling algorithm in a non-periodic manner. Feasibility of the proposed
methodology is demonstrated on constructions of stress enrichment functions for
two-dimensional mono-disperse particulate media.Comment: 27 pages, 12 figures; v2: completely re-written after the first
revie
Euler-Poincare' Characteristic and Phase Transition in the Potts Model
Recent results concerning the topological properties of random geometrical
sets have been successfully applied to the study of the morphology of clusters
in percolation theory. This approach provides an alternative way of inspecting
the critical behaviour of random systems in statistical mechanics. For the 2d
q-states Potts model with q <= 6, intensive and accurate numerics indicates
that the average of the Euler characteristic (taken with respect to the
Fortuin-Kasteleyn random cluster measure) is an order parameter of the phase
transition.Comment: 17 pages, 8 figures, 1 tabl
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