5,315 research outputs found
Computer simulation of fatigue under diametrical compression
We study the fatigue fracture of disordered materials by means of computer
simulations of a discrete element model. We extend a two-dimensional fracture
model to capture the microscopic mechanisms relevant for fatigue, and we
simulate the diametric compression of a disc shape specimen under a constant
external force. The model allows to follow the development of the fracture
process on the macro- and micro-level varying the relative influence of the
mechanisms of damage accumulation over the load history and healing of
microcracks. As a specific example we consider recent experimental results on
the fatigue fracture of asphalt. Our numerical simulations show that for
intermediate applied loads the lifetime of the specimen presents a power law
behavior. Under the effect of healing, more prominent for small loads compared
to the tensile strength of the material, the lifetime of the sample increases
and a fatigue limit emerges below which no macroscopic failure occurs. The
numerical results are in a good qualitative agreement with the experimental
findings.Comment: 7 pages, 8 figures, RevTex forma
Antiferromagnetic O(N) models in four dimensions
We study the antiferromagnetic O(N) model in the F_4 lattice. Monte Carlo
simulations are applied for investigating the behavior of the transition for
N=2,3. The numerical results show a first order nature but with a large
correlation length. The limit is also considered with analytical
methods.Comment: 14 pages, 3 postscript figure
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Approachability with Discounting
We establish a version of Blackwell’s (1956) approachability result with discounting. Our main result shows that, for convex sets, our notion of approachability with discounting is equivalent to Blackwell’s (1956) approachability. Our proofs are based on a concentration result for probability measures and on the minmax theorem for two-person, zero-sum games
Singular diffusion and criticality in a confined sandpile
We investigate the behavior of a two-state sandpile model subjected to a
confining potential in one and two dimensions. From the microdynamical
description of this simple model with its intrinsic exclusion mechanism, it is
possible to derive a continuum nonlinear diffusion equation that displays
singularities in both the diffusion and drift terms. The stationary-state
solutions of this equation, which maximizes the Fermi-Dirac entropy, are in
perfect agreement with the spatial profiles of time-averaged occupancy obtained
from model numerical simulations in one as well as in two dimensions.
Surprisingly, our results also show that, regardless of dimensionality, the
presence of a confining potential can lead to the emergence of typical
attributes of critical behavior in the two-state sandpile model, namely, a
power-law tail in the distribution of avalanche sizes.Comment: 5 pages, 5 figure
Localization for a matrix-valued Anderson model
We study localization properties for a class of one-dimensional,
matrix-valued, continuous, random Schr\"odinger operators, acting on
L^2(\R)\otimes \C^N, for arbitrary . We prove that, under suitable
assumptions on the F\"urstenberg group of these operators, valid on an interval
, they exhibit localization properties on , both in the
spectral and dynamical sense. After looking at the regularity properties of the
Lyapunov exponents and of the integrated density of states, we prove a Wegner
estimate and apply a multiscale analysis scheme to prove localization for these
operators. We also study an example in this class of operators, for which we
can prove the required assumptions on the F\"urstenberg group. This group being
the one generated by the transfer matrices, we can use, to prove these
assumptions, an algebraic result on generating dense Lie subgroups in
semisimple real connected Lie groups, due to Breuillard and Gelander. The
algebraic methods used here allow us to handle with singular distributions of
the random parameters
Vortices, Infrared effects and Lorentz Invariance Violation
The Yang-Mills theory with noncommutative fields is constructed following
Hamiltonian and lagrangean methods. This modification of the standard
Yang-Mills theory shed light on the confinement mechanism viewed as a Lorentz
invariance violation (LIV) effect. The modified Yang-Mills theory contain in
addition to the standard contribution, the term where
is a given space-like constant vector with canonical dimension of
energy. The field rescaling and the choice ,
one can show that the modified Yang-Mills theory in 3+1 dimensions can be made
equivalent to a Yang-Mills-Chern-Simons theory in 2+1 dimensions if one
consider only heavy fermionic excitations. Thus, the Yang-Mills-Chern-Simons
theory in 2+1 dimensions is a codified way of that include only heavy
quarks. The classical solutions of the modified Yang-Mills theory for the SU(2)
gauge group are confining ones.Comment: Title changed and comments added. To appear in PL
Mechanisms in impact fragmentation
The brittle fragmentation of spheres is studied numerically by a 3D Discrete Element Model. Large scale computer simulations are performed with models that consist of agglomerates of many spherical particles, interconnected by beam-truss elements. We focus on a detailed description of the fragmentation process and study several fragmentation mechanisms involved. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasi-periodic angular distribution and give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. The results prove to be independent of the degree of disorder in the model, but mean fragment sizes scale with velocity. Our results reproduce many experimental observations of fragment shapes, impact energy dependence or mass distribution, and significantly improve the understanding of the fragmentation process for impact fracture since we have full access to the failure conditions and evolutio
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