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Scaling in plasticity-induced cell-boundary microstructure: Fragmentation and rotational diffusion
We develop a simple computational model for cell-boundary evolution in plastic deformation. We study the cell-boundary size distribution and cell-boundary misorientation distribution that experimentally have been found to have scaling forms that are largely material independent. The cell division acts as a source term in the misorientation distribution which significantly alters the scaling form, giving it a linear slope at small misori- entation angles as observed in the experiments. We compare the results of our simulation with two closely related exactly solvable models that exhibit scaling behavior at late times: i fragmentation theory and ii a random walk in rotation space with a source term. We find that the scaling exponents in our simulation agree with those of the theories, and that the scaling collapses obey the same equations, but that the shape of the scaling functions depends upon the methods used to measure sizes and to weight averages and histograms.Physic
Scaling in Plasticity-Induced Cell-Boundary Microstructure: Fragmentation and Rotational Diffusion
We develop a simple computational model for cell boundary evolution in
plastic deformation. We study the cell boundary size distribution and cell
boundary misorientation distribution that experimentally have been found to
have scaling forms that are largely material independent. The cell division
acts as a source term in the misorientation distribution which significantly
alters the scaling form, giving it a linear slope at small misorientation
angles as observed in the experiments. We compare the results of our simulation
to two closely related exactly solvable models which exhibit scaling behavior
at late times: (i) fragmentation theory and (ii) a random walk in rotation
space with a source term. We find that the scaling exponents in our simulation
agree with those of the theories, and that the scaling collapses obey the same
equations, but that the shape of the scaling functions depend upon the methods
used to measure sizes and to weight averages and histograms
Grain boundary energies and cohesive strength as a function of geometry
Cohesive laws are stress-strain curves used in finite element calculations to
describe the debonding of interfaces such as grain boundaries. It would be
convenient to describe grain boundary cohesive laws as a function of the
parameters needed to describe the grain boundary geometry; two parameters in 2D
and 5 parameters in 3D. However, we find that the cohesive law is not a smooth
function of these parameters. In fact, it is discontinuous at geometries for
which the two grains have repeat distances that are rational with respect to
one another. Using atomistic simulations, we extract grain boundary energies
and cohesive laws of grain boundary fracture in 2D with a Lennard-Jones
potential for all possible geometries which can be simulated within periodic
boundary conditions with a maximum box size. We introduce a model where grain
boundaries are represented as high symmetry boundaries decorated by extra
dislocations. Using it, we develop a functional form for the symmetric grain
boundary energies, which have cusps at all high symmetry angles. We also find
the asymptotic form of the fracture toughness near the discontinuities at high
symmetry grain boundaries using our dislocation decoration model.Comment: 12 pages, 19 figures, changed titl
CENP-A exceeds microtubule attachment sites in centromere clusters of both budding and fission yeast
Current models of centromere/kinetochore architecture are not sufficient to explain the number of molecules of histone H3 variant CENP-A observed in quantitative microscopy