379 research outputs found
Electrical conductance of a 2D packing of metallic beads under thermal perturbation
Electrical conductivity measurements on a 2D packing of metallic beads have
been performed to study internal rearrangements in weakly pertubed granular
materials. Small thermal perturbations lead to large non gaussian conductance
fluctuations. These fluctuations are found to be intermittent and gathered in
bursts. The distributions of the waiting time between to peaks is found to be a
power law inside bursts. The exponent is independent of the bead network, the
intensity of the perturbation and external stress. these bursts are interpreted
as the signature of individual bead creep rather than collective vaults
reorganisations. We propose a simple model linking the exponent of the waiting
time distribution to the roughness exponent of the surface of the beads.Comment: 7 pages, 6 figure
Scaling exponents for fracture surfaces in homogenous glass and glassy ceramics
We investigate the scaling properties of post-mortem fracture surfaces in
silica glass and glassy ceramics. In both cases, the 2D height-height
correlation function is found to obey Family-Viseck scaling properties, but
with two sets of critical exponents, in particular a roughness exponent
in homogeneous glass and in glassy
ceramics. The ranges of length-scales over which these two scalings are
observed are shown to be below and above the size of process zone respectively.
A model derived from Linear Elastic Fracture Mechanics (LEFM) in the
quasistatic approximation succeeds to reproduce the scaling exponents observed
in glassy ceramics. The critical exponents observed in homogeneous glass are
conjectured to reflect damage screening occurring for length-scales below the
size of the process zone
Fracture through cavitation in a metallic glass
The fracture surfaces of a Zr-based bulk metallic glass exhibit exotic multi-affine isotropic scaling properties. The study of the mismatch between the two facing fracture surfaces as a function of their distance shows that fracture occurs mostly through the growth and coalescence of damage cavities. The fractal nature of these damage cavities is shown to control the roughness of the fracture surfaces
Atomic-scale avalanche along a dislocation in a random alloy
International audienceThe propagation of dislocations in random crystals is evidenced to be governed by atomic-scale avalanches whose the extension in space and the time intermittency characterizingly diverge at the critical threshold. Our work is the very first atomic-scale evidence that the paradigm of second order phase transitions applies to the depinning of elastic interfaces in random media
Reconfiguring Independent Sets in Claw-Free Graphs
We present a polynomial-time algorithm that, given two independent sets in a
claw-free graph , decides whether one can be transformed into the other by a
sequence of elementary steps. Each elementary step is to remove a vertex
from the current independent set and to add a new vertex (not in )
such that the result is again an independent set. We also consider the more
restricted model where and have to be adjacent
Experimental study of granular surface flows via a fast camera: a continuous description
Depth averaged conservation equations are written for granular surface flows.
Their application to the study of steady surface flows in a rotating drum
allows to find experimentally the constitutive relations needed to close these
equations from measurements of the velocity profile in the flowing layer at the
center of the drum and from the flowing layer thickness and the static/flowing
boundary profiles. The velocity varies linearly with depth, with a gradient
independent of both the flowing layer thickness and the static/flowing boundary
local slope. The first two closure relations relating the flow rate and the
momentum flux to the flowing layer thickness and the slope are then deduced.
Measurements of the profile of the flowing layer thickness and the
static/flowing boundary in the whole drum explicitly give the last relation
concerning the force acting on the flowing layer. Finally, these closure
relations are compared to existing continuous models of surface flows.Comment: 20 pages, 11 figures, submitted to Phys. FLuid
Cleaved surface of i-AlPdMn quasicrystals: Influence of the local temperature elevation at the crack tip on the fracture surface roughness
Roughness of i-AlPdMn cleaved surfaces are presently analysed. From the
atomic scale to 2-3 nm, they are shown to exhibit scaling properties hiding the
cluster (0.45 nm) aperiodic structure. These properties are quantitatively
similar to those observed on various disordered materials, albeit on other
ranges of length scales. These properties are interpreted as the signature of
damage mechanisms occurring within a 2-3 nm wide zone at the crack tip. The
size of this process zone finds its origin in the local temperature elevation
at the crack tip. For the very first time, this effect is reported to be
responsible for a transition from a perfectly brittle behavior to a nanoductile
one.Comment: 8 page
A reconfigurations analogue of Brooks’ theorem.
Let G be a simple undirected graph on n vertices with maximum degree Δ. Brooks’ Theorem states that G has a Δ-colouring unless G is a complete graph, or a cycle with an odd number of vertices. To recolour G is to obtain a new proper colouring by changing the colour of one vertex. We show that from a k-colouring, k > Δ, a Δ-colouring of G can be obtained by a sequence of O(n 2) recolourings using only the original k colours unless
G is a complete graph or a cycle with an odd number of vertices, or
k = Δ + 1, G is Δ-regular and, for each vertex v in G, no two neighbours of v are coloured alike.
We use this result to study the reconfiguration graph R k (G) of the k-colourings of G. The vertex set of R k (G) is the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. It is known that
if k ≤ Δ(G), then R k (G) might not be connected and it is possible that its connected components have superpolynomial diameter,
if k ≥ Δ(G) + 2, then R k (G) is connected and has diameter O(n 2).
We complete this structural classification by settling the missing case:
if k = Δ(G) + 1, then R k (G) consists of isolated vertices and at most one further component which has diameter O(n 2).
We also describe completely the computational complexity classification of the problem of deciding whether two k-colourings of a graph G of maximum degree Δ belong to the same component of R k (G) by settling the case k = Δ(G) + 1. The problem is
O(n 2) time solvable for k = 3,
PSPACE-complete for 4 ≤ k ≤ Δ(G),
O(n) time solvable for k = Δ(G) + 1,
O(1) time solvable for k ≥ Δ(G) + 2 (the answer is always yes)
Independent Set Reconfiguration in Cographs
We study the following independent set reconfiguration problem, called
TAR-Reachability: given two independent sets and of a graph , both
of size at least , is it possible to transform into by adding and
removing vertices one-by-one, while maintaining an independent set of size at
least throughout? This problem is known to be PSPACE-hard in general. For
the case that is a cograph (i.e. -free graph) on vertices, we show
that it can be solved in time , and that the length of a shortest
reconfiguration sequence from to is bounded by , if such a
sequence exists.
More generally, we show that if is a graph class for which (i)
TAR-Reachability can be solved efficiently, (ii) maximum independent sets can
be computed efficiently, and which satisfies a certain additional property,
then the problem can be solved efficiently for any graph that can be obtained
from a collection of graphs in using disjoint union and complete join
operations. Chordal graphs are given as an example of such a class
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