195 research outputs found
Geometric origin of mechanical properties of granular materials
Some remarkable generic properties, related to isostaticity and potential
energy minimization, of equilibrium configurations of assemblies of rigid,
frictionless grains are studied. Isostaticity -the uniqueness of the forces,
once the list of contacts is known- is established in a quite general context,
and the important distinction between isostatic problems under given external
loads and isostatic (rigid) structures is presented. Complete rigidity is only
guaranteed, on stability grounds, in the case of spherical cohesionless grains.
Otherwise, the network of contacts might deform elastically in response to load
increments, even though grains are rigid. This sets an uuper bound on the
contact coordination number. The approximation of small displacements (ASD)
allows to draw analogies with other model systems studied in statistical
mechanics, such as minimum paths on a lattice. It also entails the uniqueness
of the equilibrium state (the list of contacts itself is geometrically
determined) for cohesionless grains, and thus the absence of plastic
dissipation. Plasticity and hysteresis are due to the lack of such uniqueness
and may stem, apart from intergranular friction, from small, but finite,
rearrangements, in which the system jumps between two distinct potential energy
minima, or from bounded tensile contact forces. The response to load increments
is discussed. On the basis of past numerical studies, we argue that, if the ASD
is valid, the macroscopic displacement field is the solution to an elliptic
boundary value problem (akin to the Stokes problem).Comment: RevTex, 40 pages, 26 figures. Close to published paper. Misprints and
minor errors correcte
From dynamical scaling to local scale-invariance: a tutorial
Dynamical scaling arises naturally in various many-body systems far from
equilibrium. After a short historical overview, the elements of possible
extensions of dynamical scaling to a local scale-invariance will be introduced.
Schr\"odinger-invariance, the most simple example of local scale-invariance,
will be introduced as a dynamical symmetry in the Edwards-Wilkinson
universality class of interface growth. The Lie algebra construction, its
representations and the Bargman superselection rules will be combined with
non-equilibrium Janssen-de Dominicis field-theory to produce explicit
predictions for responses and correlators, which can be compared to the results
of explicit model studies.
At the next level, the study of non-stationary states requires to go over,
from Schr\"odinger-invariance, to ageing-invariance. The ageing algebra admits
new representations, which acts as dynamical symmetries on more general
equations, and imply that each non-equilibrium scaling operator is
characterised by two distinct, independent scaling dimensions. Tests of
ageing-invariance are described, in the Glauber-Ising and spherical models of a
phase-ordering ferromagnet and the Arcetri model of interface growth.Comment: 1+ 23 pages, 2 figures, final for
Critical behavior of a one-dimensional fixed-energy stochastic sandpile
We study a one-dimensional fixed-energy version (that is, with no input or
loss of particles), of Manna's stochastic sandpile model. The system has a
continuous transition to an absorbing state at a critical value of
the particle density. Critical exponents are obtained from extensive
simulations, which treat both stationary and transient properties. In contrast
with other one-dimensional sandpiles, the model appears to exhibit finite-size
scaling, though anomalies exist in the scaling of relaxation times and in the
approach to the stationary state. The latter appear to depend strongly on the
nature of the initial configuration. The critical exponents differ from those
expected at a linear interface depinning transition in a medium with point
disorder, and from those of directed percolation.Comment: 15 pages, 11 figure
Endpoint distribution of directed polymers in 1+1 dimensions
We give an explicit formula for the joint density of the max and argmax of
the Airy process minus a parabola. The argmax has a universal distribution
which governs the rescaled endpoint for large time or temperature of directed
polymers in 1+1 dimensions.Comment: Expanded introductio
Airy processes and variational problems
We review the Airy processes; their formulation and how they are conjectured
to govern the large time, large distance spatial fluctuations of one
dimensional random growth models. We also describe formulas which express the
probabilities that they lie below a given curve as Fredholm determinants of
certain boundary value operators, and the several applications of these
formulas to variational problems involving Airy processes that arise in
physical problems, as well as to their local behaviour.Comment: Minor corrections. 41 pages, 4 figures. To appear as chapter in "PASI
Proceedings: Topics in percolative and disordered systems
Random walks and polymers in the presence of quenched disorder
After a general introduction to the field, we describe some recent results
concerning disorder effects on both `random walk models', where the random walk
is a dynamical process generated by local transition rules, and on `polymer
models', where each random walk trajectory representing the configuration of a
polymer chain is associated to a global Boltzmann weight. For random walk
models, we explain, on the specific examples of the Sinai model and of the trap
model, how disorder induces anomalous diffusion, aging behaviours and Golosov
localization, and how these properties can be understood via a strong disorder
renormalization approach. For polymer models, we discuss the critical
properties of various delocalization transitions involving random polymers. We
first summarize some recent progresses in the general theory of random critical
points : thermodynamic observables are not self-averaging at criticality
whenever disorder is relevant, and this lack of self-averaging is directly
related to the probability distribution of pseudo-critical temperatures
over the ensemble of samples of size . We describe the
results of this analysis for the bidimensional wetting and for the
Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S.,
France, November 200
Roughness distributions for 1/f^alpha signals
The probability density function (PDF) of the roughness, i.e., of the
temporal variance, of 1/f^alpha noise signals is studied. Our starting point is
the generalization of the model of Gaussian, time-periodic, 1/f noise,
discussed in our recent Letter [T. Antal et al., PRL, vol. 87, 240601 (2001)],
to arbitrary power law. We investigate three main scaling regions,
distinguished by the scaling of the cumulants in terms of the microscopic scale
and the total length of the period. Various analytical representations of the
PDF allow for a precise numerical evaluation of the scaling function of the PDF
for any alpha. A simulation of the periodic process makes it possible to study
also non-periodic signals on short intervals embedded in the full period. We
find that for alpha=<1/2 the scaled PDF-s in both the periodic and the
non-periodic cases are Gaussian, but for alpha>1/2 they differ from the
Gaussian and from each other. Both deviations increase with growing alpha. That
conclusion, based on numerics, is reinforced by analytic results for alpha=2
and alpha->infinity. We suggest that our theoretical and numerical results open
a new perspective on the data analysis of 1/f^alpha processes.Comment: 12 pages incl. 6 figures, with RevTex4, for A4 paper, in v2 some
references were correcte
Anisotropy studies around the galactic centre at EeV energies with the Auger Observatory
Data from the Pierre Auger Observatory are analyzed to search for
anisotropies near the direction of the Galactic Centre at EeV energies. The
exposure of the surface array in this part of the sky is already significantly
larger than that of the fore-runner experiments. Our results do not support
previous findings of localized excesses in the AGASA and SUGAR data. We set an
upper bound on a point-like flux of cosmic rays arriving from the Galactic
Centre which excludes several scenarios predicting sources of EeV neutrons from
Sagittarius . Also the events detected simultaneously by the surface and
fluorescence detectors (the `hybrid' data set), which have better pointing
accuracy but are less numerous than those of the surface array alone, do not
show any significant localized excess from this direction.Comment: Matches published versio
Search for gravitational waves from Scorpius X-1 in the second Advanced LIGO observing run with an improved hidden Markov model
We present results from a semicoherent search for continuous gravitational waves from the low-mass x-ray binary Scorpius X-1, using a hidden Markov model (HMM) to track spin wandering. This search improves on previous HMM-based searches of LIGO data by using an improved frequency domain matched filter, the J-statistic, and by analyzing data from Advanced LIGO's second observing run. In the frequency range searched, from 60 to 650 Hz, we find no evidence of gravitational radiation. At 194.6 Hz, the most sensitive search frequency, we report an upper limit on gravitational wave strain (at 95% confidence) of h095%=3.47×10-25 when marginalizing over source inclination angle. This is the most sensitive search for Scorpius X-1, to date, that is specifically designed to be robust in the presence of spin wandering. © 2019 American Physical Society
Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)
[no abstract available
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