5,662 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
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
Two non-commutative parameters and regular cosmological phase transition in the semi-classical dilaton cosmology
We study cosmological phase transitions from modified equations of motion by
introducing two non-commutative parameters in the Poisson brackets, which
describes the initial- and future-singularity-free phase transition in the
soluble semi-classical dilaton gravity with a non-vanishing cosmological
constant. Accelerated expansion and decelerated expansion corresponding to the
FRW phase appear alternatively, and then it ends up with the second accelerated
expansion. The final stage of the universe approaches the flat spacetime
independent of the initial state of the curvature scalar as long as the product
of the two non-commutative parameters is less than one. Finally, we show that
the initial-singularity-free condition is related to the second accelerated
expansion of the universe.Comment: 13 pages, 4 figures; v2. to appear in Mod. Phys. Lett.
The Master Equation for Large Population Equilibriums
We use a simple N-player stochastic game with idiosyncratic and common noises
to introduce the concept of Master Equation originally proposed by Lions in his
lectures at the Coll\`ege de France. Controlling the limit N tends to the
infinity of the explicit solution of the N-player game, we highlight the
stochastic nature of the limit distributions of the states of the players due
to the fact that the random environment does not average out in the limit, and
we recast the Mean Field Game (MFG) paradigm in a set of coupled Stochastic
Partial Differential Equations (SPDEs). The first one is a forward stochastic
Kolmogorov equation giving the evolution of the conditional distributions of
the states of the players given the common noise. The second is a form of
stochastic Hamilton Jacobi Bellman (HJB) equation providing the solution of the
optimization problem when the flow of conditional distributions is given. Being
highly coupled, the system reads as an infinite dimensional Forward Backward
Stochastic Differential Equation (FBSDE). Uniqueness of a solution and its
Markov property lead to the representation of the solution of the backward
equation (i.e. the value function of the stochastic HJB equation) as a
deterministic function of the solution of the forward Kolmogorov equation,
function which is usually called the decoupling field of the FBSDE. The
(infinite dimensional) PDE satisfied by this decoupling field is identified
with the \textit{master equation}. We also show that this equation can be
derived for other large populations equilibriums like those given by the
optimal control of McKean-Vlasov stochastic differential equations. The paper
is written more in the style of a review than a technical paper, and we spend
more time and energy motivating and explaining the probabilistic interpretation
of the Master Equation, than identifying the most general set of assumptions
under which our claims are true
Color confinement and dual superconductivity in full QCD
We report on evidence that confinement is related to dual superconductivity
of the vacuum in full QCD, as in quenched QCD. The vacuum is a dual
superconductor in the confining phase, whilst the U(1) magnetic symmetry is
realized a la Wigner in the deconfined phase.Comment: 4 pages, 4 eps figure
Breaking a Chaotic Cryptographic Scheme Based on Composition Maps
Recently, a chaotic cryptographic scheme based on composition maps was
proposed. This paper studies the security of the scheme and reports the
following findings: 1) the scheme can be broken by a differential attack with
chosen-plaintext, where is the size of
plaintext and is the number of different elements in plain-text; 2) the
scheme is not sensitive to the changes of plaintext; 3) the two composition
maps do not work well as a secure and efficient random number source.Comment: 9 pages, 7 figure
Noncommutative fields in three dimensions and mass generation
We apply the noncommutative fields method for gauge theory in three
dimensions where the Chern-Simons term is generated in the three-dimensional
electrodynamics. Under the same procedure, the Chern-Simons term is shown to be
cancelled in the Maxwell-Chern-Simons theory for the appropriate value of the
noncommutativity parameter. Hence the mutual interchange between
Maxwell-Chern-Simons theory and pure Maxwell theory turns out to be generated
within this method.Comment: Comments 5 pages, epl, version accepted for publication in
Europhysics Letter
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