6,113 research outputs found
Digraph Complexity Measures and Applications in Formal Language Theory
We investigate structural complexity measures on digraphs, in particular the
cycle rank. This concept is intimately related to a classical topic in formal
language theory, namely the star height of regular languages. We explore this
connection, and obtain several new algorithmic insights regarding both cycle
rank and star height. Among other results, we show that computing the cycle
rank is NP-complete, even for sparse digraphs of maximum outdegree 2.
Notwithstanding, we provide both a polynomial-time approximation algorithm and
an exponential-time exact algorithm for this problem. The former algorithm
yields an O((log n)^(3/2))- approximation in polynomial time, whereas the
latter yields the optimum solution, and runs in time and space O*(1.9129^n) on
digraphs of maximum outdegree at most two. Regarding the star height problem,
we identify a subclass of the regular languages for which we can precisely
determine the computational complexity of the star height problem. Namely, the
star height problem for bideterministic languages is NP-complete, and this
holds already for binary alphabets. Then we translate the algorithmic results
concerning cycle rank to the bideterministic star height problem, thus giving a
polynomial-time approximation as well as a reasonably fast exact exponential
algorithm for bideterministic star height.Comment: 19 pages, 1 figur
Micromechanics of creep fracture: simulation of intergranular crack growth
A computational model is presented to analyze intergranular creep crack growth in a polycrystalline aggregate in a discrete manner and based directly on the underlying physical micromechanisms. A crack tip process zone is used in which grains and their grain boundaries are represented discretely, while the surrounding undamaged material is described as a continuum. The constitutive description of the grain boundaries accounts for the relevant physical mechanisms, i.e. viscous grain boundary sliding, the nucleation and growth of grain boundary cavities, and microcracking by the coalescence of cavities. Discrete propagation of the main crack occurs by linking up of neighbouring facet microcracks. Assuming small-scale damage conditions, the model is used to simulate the initial stages of crack growth under C* controlled, model I loading conditions. Initially sharp or blunted cracks are considered. The emphasis in this study is on the effect of the grain microstructure on crack growth.
Numerical simulation of grain-size effects on creep crack growth by means of grain elements
The effect of grain size on creep crack growth is investigated by means of a numerical technique in which the actual crack growth process is simulated in a discrete manner by grain elements and grain boundary elements. The grain elements account for the creep deformation of individual grains, while grain boundary cavitation and sliding are accounted for by grain boundary elements between the grains. This grain-element technique allows for an independent study of multiple grain size effects: a (direct) size effect related to the specimen size/grain size ratio or an (indirect) effect related to the effect of grain size on nucleation rate and creep resistance. Preliminary numerical results are presented concerning the direct effect of grain size, which predict that the crack growth rate and brittleness increase with grain size.
Study of size effects in thin films by means of a crystal plasticity theory based on DiFT
In a recent publication, we derived the mesoscale continuum theory of
plasticity for multiple-slip systems of parallel edge dislocations, motivated
by the statistical-based nonlocal continuum crystal plasticity theory for
single-glide due to Yefimov et al. (2004b). In this dislocation field theory
(DiFT) the transport equations for both the total dislocation densities and
geometrically necessary dislocation densities on each slip system were obtained
from the Peach-Koehler interactions through both single and pair dislocation
correlations. The effect of pair correlation interactions manifested itself in
the form of a back stress in addition to the external shear and the
self-consistent internal stress. We here present the study of size effects in
single crystalline thin films with symmetric double slip using the novel
continuum theory. Two boundary value problems are analyzed: (1) stress
relaxation in thin films on substrates subject to thermal loading, and (2)
simple shear in constrained films. In these problems, earlier discrete
dislocation simulations had shown that size effects are born out of layers of
dislocations developing near constrained interfaces. These boundary layers
depend on slip orientations and applied loading but are insensitive to the film
thickness. We investigate stress response to changes in controlled parameters
in both problems. Comparisons with previous discrete dislocation simulations
are discussed.Comment: 20 pages, 11 figure
A fatigue crack initiation model incorporating discrete dislocation plasticity and surface roughness
Although a thorough understanding of fatigue crack initiation is lacking, experiments have shown that the evolution of distinct dislocation distributions and surface roughness are key ingredients. In the present study we introduce a computational framework that ties together dislocation dynamics, the fields due to crystallographic surface steps and cohesive surfaces to model near-atomic separation leading to fracture. Cyclic tension–compression simulations are carried out where a single plastically deforming grain at a free surface is surrounded by elastic material. While initially, the cycle-by-cycle maximum cohesive opening increases slowly, the growth rate at some instant increases rapidly, leading to fatigue crack initiation at the free surface and subsequent growth into the crystal. This study also sheds light on random local microstructural events which lead to premature fatigue crack initiation
Simple analytical expression for the peak-frequency shifts of plasmonic resonances for sensing
We derive a closed-form expression that accurately predicts the peak
frequency-shift and broadening induced by tiny perturbations of plasmonic
nanoresonators without critically relying on repeated electrodynamic
simulations of the spectral response of nanoresonator for various locations,
sizes or shapes of the perturbing objects. The force of the present approach,
in comparison with other approaches of the same kind, is that the derivation is
supported by a mathematical formalism based on a rigorous normalization of the
resonance modes of nanoresonators consisting of lossy and dispersive materials.
Accordingly, accurate predictions are obtained for a large range of
nanoparticle shapes and sizes, used in various plasmonic nanosensors, even
beyond the quasistatic limit. The expression gives quantitative insight, and
combined with an open-source code, provides accurate and fast predictions that
are ideally suited for preliminary designs or for interpretation of
experimental data. It is also valid for photonic resonators with large mode
volumes.Comment: 24 pages, 9 figures, journal pape
Microstructural modelling of creep crack growth from a blunted crack
The effect of crack tip blunting on the initial stages of creep crack growth is investigated by means of a planar microstructural model in which grains are represented discretely. The actual linking-up process of discrete microcracks with the macroscopic crack is simulated, with full account of the underlying physical mechanisms such as the nucleation, growth and coalescence of grain boundary cavities accompanied by grain boundary sliding. Results are presented for C*-controlled mode I crack growth under small-scale damage conditions. Particular attention is focused on creep constrained vs. unconstrained growth. Also the effect of grain boundary shear stresses on linking-up is investigated through shear-modified nucleation and growth models. The computations show a general trend that while an initially sharp crack tends to propagate away from the original crack plane, crack tip blunting reduces the crack growth direction. Under unconstrained conditions this can be partly rationalized by the strain rate and facet stress distribution corresponding to steady-state creep.
Density Functional Theory of a Curved Liquid-Vapour Interface: Evaluation of the rigidity constants
It is argued that to arrive at a quantitative description of the surface
tension of a liquid drop as a function of its inverse radius, it is necessary
to include the bending rigidity k and Gaussian rigidity k_bar in its
description. New formulas for k and k_bar in the context of density functional
theory with a non-local, integral expression for the interaction between
molecules are presented. These expressions are used to investigate the
influence of the choice of Gibbs dividing surface and it is shown that for a
one-component system, the equimolar surface has a special status in the sense
that both k and k_bar are then the least sensitive to a change in the location
of the dividing surface. Furthermore, the equimolar value for k corresponds to
its maximum value and the equimolar value for k_bar corresponds to its minimum
value. An explicit evaluation using a short-ranged interaction potential
between molecules, shows that k is negative with a value around minus 0.5-1.0
kT and that k_bar is positive with a value which is a bit more than half the
magnitude of k. Finally, for dispersion forces between molecules, we show that
a term proportional to log(R)/R^2 replaces the rigidity constants and we
determine the (universal) proportionality constants.Comment: 28 pages; 5 figures; accepted for publication in J. Phys.: Condens.
Matter (2013
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