1,515 research outputs found
Intermittency and roughening in the failure of brittle heterogeneous materials
Stress enhancement in the vicinity of brittle cracks makes the macro-scale
failure properties extremely sensitive to the micro-scale material disorder.
Therefore: (i) Fracturing systems often display a jerky dynamics, so-called
crackling noise, with seemingly random sudden energy release spanning over a
broad range of scales, reminiscent of earthquakes; (ii) Fracture surfaces
exhibit roughness at scales much larger than that of material micro-structure.
Here, I provide a critical review of experiments and simulations performed in
this context, highlighting the existence of universal scaling features,
independent of both the material and the loading conditions, reminiscent of
critical phenomena. I finally discuss recent stochastic descriptions of crack
growth in brittle disordered media that seem to capture qualitatively - and
sometimes quantitatively - these scaling features.Comment: 38 pages, invited review for J. Phys. D cluster issue on "Fracture:
from the Atomic to the Geophysics Scale
Recoloring graphs via tree decompositions
Let be an integer. Two vertex -colorings of a graph are
\emph{adjacent} if they differ on exactly one vertex. A graph is
\emph{-mixing} if any proper -coloring can be transformed into any other
through a sequence of adjacent proper -colorings. Jerrum proved that any
graph is -mixing if is at least the maximum degree plus two. We first
improve Jerrum's bound using the grundy number, which is the worst number of
colors in a greedy coloring.
Any graph is -mixing, where is the treewidth of the graph
(Cereceda 2006). We prove that the shortest sequence between any two
-colorings is at most quadratic (which is optimal up to a constant
factor), a problem left open in Bonamy et al. (2012).
We also prove that given any two -colorings of a cograph (resp.
distance-hereditary graph) , we can find a linear (resp. quadratic) sequence
between them. In both cases, the bounds cannot be improved by more than a
constant factor for a fixed . The graph classes are also optimal in
some sense: one of the smallest interesting superclass of distance-hereditary
graphs corresponds to comparability graphs, for which no such property holds
(even when relaxing the constraint on the length of the sequence). As for
cographs, they are equivalently the graphs with no induced , and there
exist -free graphs that admit no sequence between two of their
-colorings.
All the proofs are constructivist and lead to polynomial-time recoloring
algorithmComment: 20 pages, 8 figures, partial results already presented in
http://arxiv.org/abs/1302.348
Recoloring bounded treewidth graphs
Let be an integer. Two vertex -colorings of a graph are
\emph{adjacent} if they differ on exactly one vertex. A graph is
\emph{-mixing} if any proper -coloring can be transformed into any other
through a sequence of adjacent proper -colorings. Any graph is
-mixing, where is the treewidth of the graph (Cereceda 2006). We
prove that the shortest sequence between any two -colorings is at most
quadratic, a problem left open in Bonamy et al. (2012).
Jerrum proved that any graph is -mixing if is at least the maximum
degree plus two. We improve Jerrum's bound using the grundy number, which is
the worst number of colors in a greedy coloring.Comment: 11 pages, 5 figure
On the neighbour sum distinguishing index of planar graphs
Let be a proper edge colouring of a graph with integers
. Then , while by Vizing's theorem, no more than
is necessary for constructing such . On the course of
investigating irregularities in graphs, it has been moreover conjectured that
only slightly larger , i.e., enables enforcing additional
strong feature of , namely that it attributes distinct sums of incident
colours to adjacent vertices in if only this graph has no isolated edges
and is not isomorphic to . We prove the conjecture is valid for planar
graphs of sufficiently large maximum degree. In fact even stronger statement
holds, as the necessary number of colours stemming from the result of Vizing is
proved to be sufficient for this family of graphs. Specifically, our main
result states that every planar graph of maximum degree at least which
contains no isolated edges admits a proper edge colouring
such that for every edge of .Comment: 22 page
The interactive sum choice number of graphs
We introduce a variant of the well-studied sum choice number of graphs, which we call the interactive sum choice number. In this variant, we request colours to be added to the vertices' colour-lists one at a time, and so we are able to make use of information about the colours assigned so far to determine our future choices. The interactive sum choice number cannot exceed the sum choice number and we conjecture that, except in the case of complete graphs, the interactive sum choice number is always strictly smaller than the sum choice number. In this paper we provide evidence in support of this conjecture, demonstrating that it holds for a number of graph classes, and indeed that in many cases the difference between the two quantities grows as a linear function of the number of vertices
Brooks' theorem on powers of graphs
We prove that for , the bound given by Brooks' theorem on the
chromatic number of -th powers of graphs of maximum degree
can be lowered by 1, even in the case of online list coloring.Comment: 7 pages, no figure, submitte
Crackling vs. continuum-like dynamics in brittle failure
We study how the loading rate, specimen geometry and microstructural texture
select the dynamics of a crack moving through an heterogeneous elastic material
in the quasi-static approximation. We find a transition, fully controlled by
two dimensionless variables, between dynamics ruled by continuum fracture
mechanics and crackling dynamics. Selection of the latter by the loading,
microstructure and specimen parameters is formulated in terms of scaling laws
on the power spectrum of crack velocity. This analysis defines the experimental
conditions required to observe crackling in fracture. Beyond failure problems,
the results extend to a variety of situations described by models of the same
universality class, e.g. the dynamics in wetting or of domain walls in
amorphous ferromagnets.Comment: 5 pages, 4 figures, accepted in Phys. Rev. Let
Local Care Services : Reflection on the Conditions of their Emergence and Development
Local care services are making a comeback in the headlines (with the Borloo plan, CAE report). The development of this market (or markets) and the policies linked with them nonetheless give rise to problems.This article seeks to identify the levers on which current policy can rely to become effective and emphasises the shortcomings that need to be resolved to ensure impetus. It attempts to specify certain macrosociological and macroeconomic conditions, and analyse the conditions specific to demand and the constraints in building efficient supply that may explain the failures of the policies implemented so far.local care services; innovation; supply of services
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