32 research outputs found
Dynamic critical behavior of failure and plastic deformation in the random fiber bundle model
The random fiber bundle (RFB) model, with the strength of the fibers
distributed uniformly within a finite interval, is studied under the assumption
of global load sharing among all unbroken fibers of the bundle. At any fixed
value of the applied stress (load per fiber initially present in the bundle),
the fraction of fibers that remain unbroken at successive time steps is shown
to follow simple recurrence relations. The model is found to have stable fixed
point for applied stress in the range 0 and 1; beyond which total failure of
the bundle takes place discontinuously. The dynamic critical behavior near this
failure point has been studied for this model analysing the recurrence
relations. We also investigated the finite size scaling behavior. At the
critical point one finds strict power law decay (with time t) of the fraction
of unbroken fibers. The avalanche size distribution for this mean-field
dynamics of failure has been studied. The elastic response of the RFB model has
also been studied analytically for a specific probability distribution of fiber
strengths, where the bundle shows plastic behavior before complete failure,
following an initial linear response.Comment: 13 pages, 5 figures, extensively revised and accepted for publication
in Phys. Rev.
Precursors of catastrophe in the BTW, Manna and random fiber bundle models of failure
We have studied precursors of the global failure in some self-organised
critical models of sand-pile (in BTW and Manna models) and in the random fiber
bundle model (RFB). In both BTW and Manna model, as one adds a small but fixed
number of sand grains (heights) to any central site of the stable pile, the
local dynamics starts and continues for an average relaxation time (\tau) and
an average number of topplings (\Delta) spread over a radial distance (\xi). We
find that these quantities all depend on the average height (h_{av}) of the
pile and they all diverge as (h_{av}) approaches the critical height (h_{c})
from below: (\Delta) (\sim (h_{c}-h_{av}))(^{-\delta}), (\tau \sim
(h_{c}-h_{av})^{-\gamma}) and (\xi) (\sim) ((h_{c}-h_{av})^{-\nu}). Numerically
we find (\delta \simeq 2.0), (\gamma \simeq 1.2) and (\nu \simeq 1.0) for both
BTW and Manna model in two dimensions. In the strained RFB model we find that
the breakdown susceptibility (\chi) (giving the differential increment of the
number of broken fibers due to increase in external load) and the relaxation
time (\tau), both diverge as the applied load or stress (\sigma) approaches the
network failure threshold (\sigma_{c}) from below: (\chi) (\sim) ((\sigma_{c})
(-)(\sigma)^{-1/2}) and (\tau) (\sim) ((\sigma_{c}) (-)(\sigma)^{-1/2}). These
self-organised dynamical models of failure therefore show some definite
precursors with robust power laws long before the failure point. Such
well-characterised precursors should help predicting the global failure point
of the systems in advance.Comment: 13 pages, 9 figures (eps
Failure due to fatigue in fiber bundles and solids
We consider first a homogeneous fiber bundle model where all the fibers have
got the same stress threshold beyond which all fail simultaneously in absence
of noise. At finite noise, the bundle acquires a fatigue behavior due to the
noise-induced failure probability at any stress. We solve this dynamics of
failure analytically and show that the average failure time of the bundle
decreases exponentially as the stress increases. We also determine the
avalanche size distribution during such failure and find a power law decay. We
compare this fatigue behavior with that obtained phenomenologically for the
nucleation of Griffith cracks. Next we study numerically the fatigue behavior
of random fiber bundles having simple distributions of individual fiber
strengths, at stress less than the bundle's strength (beyond which it fails
instantly). The average failure time is again seen to decrease exponentially as
the stress increases and the avalanche size distribution shows similar power
law decay. These results are also in broad agreement with experimental
observations on fatigue in solids. We believe, these observations regarding the
failure time are useful for quantum breakdown phenomena in disordered systems.Comment: 13 pages, 4 figures, figures added and the text is revise
Simple Fluids with Complex Phase Behavior
We find that a system of particles interacting through a simple isotropic
potential with a softened core is able to exhibit a rich phase behavior
including: a liquid-liquid phase transition in the supercooled phase, as has
been suggested for water; a gas-liquid-liquid triple point; a freezing line
with anomalous reentrant behavior. The essential ingredient leading to these
features resides in that the potential investigated gives origin to two
effective core radii.Comment: 7 pages including 3 eps figures + 1 jpeg figur
Which mechanism underlies the water-like anomalies in core-softened potentials?
Using molecular dynamics simulations we investigate the thermodynamic of
particles interacting with a continuous and a discrete versions of a
core-softened (CS) intermolecular potential composed by a repulsive shoulder.
Dynamic and structural properties are also analyzed by the simulations. We show
that in the continuous version of the CS potential the density at constant
pressure has a maximum for a certain temperature. Similarly the diffusion
constant, , at a constant temperature has a maximum at a density
and a minimum at a density
, and structural properties are also
anomalous. For the discrete CS potential none of these anomalies are observed.
The absence of anomalies in the discrete case and its presence in the
continuous CS potential are discussed in the framework of the excess entropy.Comment: 8 page
The Casimir Problem of Spherical Dielectrics: Quantum Statistical and Field Theoretical Approaches
The Casimir free energy for a system of two dielectric concentric nonmagnetic
spherical bodies is calculated with use of a quantum statistical mechanical
method, at arbitrary temperature. By means of this rather novel method, which
turns out to be quite powerful (we have shown this to be true in other
situations also), we consider first an explicit evaluation of the free energy
for the static case, corresponding to zero Matsubara frequency ().
Thereafter, the time-dependent case is examined. For comparison we consider the
calculation of the free energy with use of the more commonly known field
theoretical method, assuming for simplicity metallic boundary surfaces.Comment: 31 pages, LaTeX, one new reference; version to appear in Phys. Rev.
A Simple Model of Liquid-liquid Phase Transitions
In recent years, a second fluid-fluid phase transition has been reported in
several materials at pressures far above the usual liquid-gas phase transition.
In this paper, we introduce a new model of this behavior based on the
Lennard-Jones interaction with a modification to mimic the different kinds of
short-range orientational order in complex materials. We have done Monte Carlo
studies of this model that clearly demonstrate the existence of a second
first-order fluid-fluid phase transition between high- and low-density liquid
phases
Time evolution of damage under variable ranges of load transfer
We study the time evolution of damage in a fiber bundle model in which the
range of interaction of fibers varies through an adjustable stress transfer
function recently introduced. We find that the lifetime of the material
exhibits a crossover from mean field to short range behavior as in the static
case. Numerical calculations showed that the value at which the transition
takes place depends on the system's disorder. Finally, we have performed a
microscopic analysis of the failure process. Our results confirm that the
growth dynamics of the largest crack is radically different in the two limiting
regimes of load transfer during the first stages of breaking.Comment: 8 pages, 7 figures, revtex4 styl
Phase diagrams of classical spin fluids: the influence of an external magnetic field on the liquid-gas transition
The influence of an external magnetic field on the liquid-gas phase
transition in Ising, XY, and Heisenberg spin fluid models is studied using a
modified mean field theory and Gibbs ensemble Monte Carlo simulations. It is
demonstrated that the theory is able to reproduce quantitatively all
characteristic features of the field dependence of the critical temperature
T_c(H) for all the three models. These features include a monotonic decrease of
T_c with rising H in the case of the Ising fluid as well as a more complicated
nonmonotonic behavior for the XY and Heisenberg models. The nonmonotonicity
consists in a decrease of T_c with increasing H at weak external fields, an
increase of T_c with rising H in the strong field regime, and the existence of
a minimum in T_c(H) at intermediate values of H. Analytical expressions for
T_c(H) in the large field limit are presented as well. The magnetic para-ferro
phase transition is also considered in simulations and described within the
mean field theory.Comment: 14 pages, 12 figures (to be submitted to Phys. Rev. E
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.