2,527 research outputs found
Crossover Behavior in Burst Avalanches of Fiber Bundles: Signature of Imminent Failure
Bundles of many fibers, with statistically distributed thresholds for
breakdown of individual fibers and where the load carried by a bursting fiber
is equally distributed among the surviving members, are considered. During the
breakdown process, avalanches consisting of simultaneous rupture of several
fibers occur, with a distribution D(Delta) of the magnitude Delta of such
avalanches. We show that there is, for certain threshold distributions, a
crossover behavior of D(Delta) between two power laws D(Delta) proportional to
Delta^(-xi), with xi=3/2 or xi=5/2. The latter is known to be the generic
behavior, and we give the condition for which the D(Delta) proportional to
Delta^(-3/2) behavior is seen. This crossover is a signal of imminent
catastrophic failure in the fiber bundle. We find the same crossover behavior
in the fuse model.Comment: 4 pages, 4 figure
Energy bursts in fiber bundle models of composite materials
As a model of composite materials, a bundle of many fibers with
stochastically distributed breaking thresholds for the individual fibers is
considered. The bundle is loaded until complete failure to capture the failure
scenario of composite materials under external load. The fibers are assumed to
share the load equally, and to obey Hookean elasticity right up to the breaking
point. We determine the distribution of bursts in which an amount of energy
is released. The energy distribution follows asymptotically a universal power
law , for any statistical distribution of fiber strengths. A similar
power law dependence is found in some experimental acoustic emission studies of
loaded composite materials.Comment: 5 pages, 4 fig
Failure avalanches in fiber bundles for discrete load increase
The statistics of burst avalanche sizes during failure processes in a
fiber bundle follows a power law, , for large avalanches.
The exponent depends upon how the avalanches are provoked. While it is
known that when the load on the bundle is increased in a continuous manner, the
exponent takes the value , we show that when the external load is
increased in discrete and not too small steps, the exponent value is
relevant. Our analytic treatment applies to bundles with a general probability
distribution of the breakdown thresholds for the individual fibers. The
pre-asymptotic size distribution of avalanches is also considered.Comment: 4 pages 2 figure
Coherent Population Trapping of Single Spins in Diamond Under Optical Excitation
Coherent population trapping is demonstrated in single nitrogen-vacancy
centers in diamond under optical excitation. For sufficient excitation power,
the fluorescence intensity drops almost to the background level when the laser
modulation frequency matches the 2.88 GHz splitting of the ground states. The
results are well described theoretically by a four-level model, allowing the
relative transition strengths to be determined for individual centers. The
results show that all-optical control of single spins is possible in diamond.Comment: minor correction
The Continuous 1.5{D} Terrain Guarding Problem: {D}iscretization, Optimal Solutions, and {PTAS}
In the NP-hard continuous 1.5D Terrain Guarding Problem (TGP) we are given an x-monotone chain of line segments in the plain (the terrain ), and ask for the minimum number of guards (located anywhere on ) required to guard all of . We construct guard candidate and witness sets of polynomial size, such that any feasible (optimal) guard cover for is also feasible (optimal) for the continuous TGP. This discretization allows us to: (1) settle NP-completeness for the continuous TGP; (2) provide a Polynomial Time Approximation Scheme (PTAS) for the continuous TGP using the existing PTAS for the discrete TGP by Gibson et al.; (3) formulate the continuous TGP as an Integer Linear Program (IP). Furthermore, we propose several filtering techniques reducing the size of our discretization, allowing us to devise an efficient IP-based algorithm that reliably provides optimal guard placements for terrains with up to 1000000 vertices within minutes on a standard desktop computer
Discrete Fracture Model with Anisotropic Load Sharing
A two-dimensional fracture model where the interaction among elements is
modeled by an anisotropic stress-transfer function is presented. The influence
of anisotropy on the macroscopic properties of the samples is clarified, by
interpolating between several limiting cases of load sharing. Furthermore, the
critical stress and the distribution of failure avalanches are obtained
numerically for different values of the anisotropy parameter and as a
function of the interaction exponent . From numerical results, one can
certainly conclude that the anisotropy does not change the crossover point
in 2D. Hence, in the limit of infinite system size, the crossover
value between local and global load sharing is the same as the one
obtained in the isotropic case. In the case of finite systems, however, for
, the global load sharing behavior is approached very slowly
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