216 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
Fracture precursors in disordered systems
A two-dimensional lattice model with bond disorder is used to investigate the
fracture behaviour under stress-controlled conditions. Although the cumulative
energy of precursors does not diverge at the critical point, its derivative
with respect to the control parameter (reduced stress) exhibits a singular
behaviour. Our results are nevertheless compatible with previous experimental
findings, if one restricts the comparison to the (limited) range accessible in
the experiment. A power-law avalanche distribution is also found with an
exponent close to the experimental values.Comment: 4 pages, 5 figures. Submitted to Europhysics Letter
Spatio-temporal trends in stock mixing of eastern and western Baltic cod in the Arkona Basin and the implications for recruitment
In the Baltic Sea, two genetically distinct cod populations occur, the eastern and the western Baltic cod. Since 2006, cod abundance has increased substantially in the Arkona Basin (SD 24), the potential mixing area between the two stocks management areas, presumably due to spill-over from the eastern stock. In this study, the spatio-temporal dynamics of stock mixing were analysed using shape analysis of archived otoliths. Further, the impact of eastern cod immigration on recruitment in the western Baltic Sea was investigated using hydrographic drift modelling. The percentage of eastern Baltic cod in the Arkona Basin increased from ca. 30% before 2005 to >80% in recent years. Geographic patterns in stock mixing with a pronounced east–west trend suggest that immigration occurs north of Bornholm, but propagates throughout the Arkona Basin. The immigration cannot be attributed to spawning migration, as no seasonal trend in stock mixing was observed. Based on environmental threshold levels for egg survival and time-series of hydrography data, the habitat suitable for successful spawning of eastern cod was estimated to range between 20 and 50% of the maximum possible habitat size, limited by primarily low salinity. Best conditions occurred irregularly in May–end June, interspersed with years where successful spawning was virtually impossible. Using a coupled hydrodynamic modelling and particle-tracking approach, the drift and survival of drifters representing eastern cod eggs was estimated. On average, 19% of the drifters in the Arkona Basin survive to the end of the yolk-sac stage, with mortality primarily after bottom contact due to low salinity. The general drift direction of the surviving larvae was towards the east. Therefore, it is the immigration of eastern cod, rather than larval transport, that contributes to cod recruitment in the western Baltic Sea
Conditions for abrupt failure in the democratic fiber bundle model
We argue that the existence of abrupt failure in the democratic fiber bundle
model is more general than concluded by da Silveira in his comment
(cond-mat/9709327). We refute his claim that the nature of the rupture process
in the DFBM depends on the ``disorder distribution only via its large failure
strength behavior''.Comment: 1 page in revtex, reply to the comment to our letter J.V. Andersen,
D. Sornette and K.-T. Leung, Phys. Rev. Lett. 78, 2140 (1997
Failure Processes in Elastic Fiber Bundles
The fiber bundle model describes a collection of elastic fibers under load.
the fibers fail successively and for each failure, the load distribution among
the surviving fibers change. Even though very simple, the model captures the
essentials of failure processes in a large number of materials and settings. We
present here a review of fiber bundle model with different load redistribution
mechanism from the point of view of statistics and statistical physics rather
than materials science, with a focus on concepts such as criticality,
universality and fluctuations. We discuss the fiber bundle model as a tool for
understanding phenomena such as creep, and fatigue, how it is used to describe
the behavior of fiber reinforced composites as well as modelling e.g. network
failure, traffic jams and earthquake dynamics.Comment: This article has been Editorially approved for publication in Reviews
of Modern Physic
Fracture of disordered solids in compression as a critical phenomenon: I. Statistical mechanics formalism
This is the first of a series of three articles that treats fracture
localization as a critical phenomenon. This first article establishes a
statistical mechanics based on ensemble averages when fluctuations through time
play no role in defining the ensemble. Ensembles are obtained by dividing a
huge rock sample into many mesoscopic volumes. Because rocks are a disordered
collection of grains in cohesive contact, we expect that once shear strain is
applied and cracks begin to arrive in the system, the mesoscopic volumes will
have a wide distribution of different crack states. These mesoscopic volumes
are the members of our ensembles. We determine the probability of observing a
mesoscopic volume to be in a given crack state by maximizing Shannon's measure
of the emergent crack disorder subject to constraints coming from the
energy-balance of brittle fracture. The laws of thermodynamics, the partition
function, and the quantification of temperature are obtained for such cracking
systems.Comment: 11 pages, 2 figure
Liquid-liquid equilibrium for monodisperse spherical particles
A system of identical particles interacting through an isotropic potential
that allows for two preferred interparticle distances is numerically studied.
When the parameters of the interaction potential are adequately chosen, the
system exhibits coexistence between two different liquid phases (in addition to
the usual liquid-gas coexistence). It is shown that this coexistence can occur
at equilibrium, namely, in the region where the liquid is thermodynamically
stable.Comment: 6 pages, 8 figures. Published versio
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Homomorphisms and Higher Extensions for Schur algebras and symmetric groups
This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext groups in the two categories, and discuss those cases where explicit results have been determined
Fracture model with variable range of interaction
We introduce a fiber bundle model where the interaction among fibers is
modeled by an adjustable stress-transfer function which can interpolate between
the two limiting cases of load redistribution, the global and the local load
sharing schemes. By varying the range of interaction several features of the
model are numerically studied and a crossover from mean field to short range
behavior is obtained. The properties of the two regimes and the emergence of
the crossover in between are explored by numerically studying the dependence of
the ultimate strength of the material on the system size, the distribution of
avalanches of breakings, and of the cluster sizes of broken fibers. Finally, we
analyze the moments of the cluster size distributions to accurately determine
the value at which the crossover is observed.Comment: 8 pages, 8 figures. Two columns revtex format. Final version to be
published in Phys. Rev.
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