2,115 research outputs found
Surface Properties of Aperiodic Ising Quantum Chains
We consider Ising quantum chains with quenched aperiodic disorder of the
coupling constants given through general substitution rules. The critical
scaling behaviour of several bulk and surface quantities is obtained by exact
real space renormalization.Comment: 4 pages, RevTex, reference update
Competition and cooperation:aspects of dynamics in sandpiles
In this article, we review some of our approaches to granular dynamics, now
well known to consist of both fast and slow relaxational processes. In the
first case, grains typically compete with each other, while in the second, they
cooperate. A typical result of {\it cooperation} is the formation of stable
bridges, signatures of spatiotemporal inhomogeneities; we review their
geometrical characteristics and compare theoretical results with those of
independent simulations. {\it Cooperative} excitations due to local density
fluctuations are also responsible for relaxation at the angle of repose; the
{\it competition} between these fluctuations and external driving forces, can,
on the other hand, result in a (rare) collapse of the sandpile to the
horizontal. Both these features are present in a theory reviewed here. An arena
where the effects of cooperation versus competition are felt most keenly is
granular compaction; we review here a random graph model, where three-spin
interactions are used to model compaction under tapping. The compaction curve
shows distinct regions where 'fast' and 'slow' dynamics apply, separated by
what we have called the {\it single-particle relaxation threshold}. In the
final section of this paper, we explore the effect of shape -- jagged vs.
regular -- on the compaction of packings near their jamming limit. One of our
major results is an entropic landscape that, while microscopically rough,
manifests {\it Edwards' flatness} at a macroscopic level. Another major result
is that of surface intermittency under low-intensity shaking.Comment: 36 pages, 23 figures, minor correction
Latent space policy search for robotics
Learning motor skills for robots is a hard
task. In particular, a high number of degrees-of-freedom
in the robot can pose serious challenges to existing reinforcement
learning methods, since it leads to a highdimensional
search space. However, complex robots are
often intrinsically redundant systems and, therefore, can
be controlled using a latent manifold of much smaller
dimensionality. In this paper, we present a novel policy
search method that performs efficient reinforcement learning
by uncovering the low-dimensional latent space of
actuator redundancies. In contrast to previous attempts
at combining reinforcement learning and dimensionality
reduction, our approach does not perform dimensionality
reduction as a preprocessing step but naturally combines
it with policy search. Our evaluations show that the new
approach outperforms existing algorithms for learning
motor skills with high-dimensional robots
Os isotopes in SNC meteorites and their implications to the early evolution of Mars and Earth
A new development on the measurement of the Os isotopic composition by mass spectrometry using negative ions opened a new field of applications. The Re-Os systematic provides time information on the differentiation of the nobel metals. The nobel metals are strongly partitioned into metal and sulphide phases, but also the generation of silicate melts might fractionate the Re-Os system. Compared to the other isotopic systems which are mainly dating the fractionation of the alkalis and alkali-earth elements, the Re-Os system is expected to disclose entirely new information about the geochemistry. Especially the differentiation and early evolution of the planets such as the formation of the core will be elucidated with this method
Growth and Structure of Stochastic Sequences
We introduce a class of stochastic integer sequences. In these sequences,
every element is a sum of two previous elements, at least one of which is
chosen randomly. The interplay between randomness and memory underlying these
sequences leads to a wide variety of behaviors ranging from stretched
exponential to log-normal to algebraic growth. Interestingly, the set of all
possible sequence values has an intricate structure.Comment: 4 pages, 4 figure
Aperiodic Ising Quantum Chains
Some years ago, Luck proposed a relevance criterion for the effect of
aperiodic disorder on the critical behaviour of ferromagnetic Ising systems. In
this article, we show how Luck's criterion can be derived within an exact
renormalisation scheme for Ising quantum chains with coupling constants
modulated according to substitution rules. Luck's conjectures for this case are
confirmed and refined. Among other outcomes, we give an exact formula for the
correlation length critical exponent for arbitrary two-letter substitution
sequences with marginal fluctuations of the coupling constants.Comment: 27 pages, LaTeX, 1 Postscript figure included, using epsf.sty and
amssymb.sty (one error corrected, some minor changes
Statistics of leaders and lead changes in growing networks
We investigate various aspects of the statistics of leaders in growing
network models defined by stochastic attachment rules. The leader is the node
with highest degree at a given time (or the node which reached that degree
first if there are co-leaders). This comprehensive study includes the full
distribution of the degree of the leader, its identity, the number of
co-leaders, as well as several observables characterizing the whole history of
lead changes: number of lead changes, number of distinct leaders, lead
persistence probability. We successively consider the following network models:
uniform attachment, linear attachment (the Barabasi-Albert model), and
generalized preferential attachment with initial attractiveness.Comment: 28 pages, 14 figures, 1 tabl
Random Geometric Series
Integer sequences where each element is determined by a previous randomly
chosen element are investigated analytically. In particular, the random
geometric series x_n=2x_p with 0<=p<=n-1 is studied. At large n, the moments
grow algebraically, n^beta(s) with beta(s)=2^s-1, while the typical
behavior is x_n n^ln 2. The probability distribution is obtained explicitly in
terms of the Stirling numbers of the first kind and it approaches a log-normal
distribution asymptotically.Comment: 6 pages, 2 figure
On the statistics of superlocalized states in self-affine disordered potentials
We investigate the statistics of eigenstates in a weak self-affine disordered
potential in one dimension, whose Gaussian fluctuations grow with distance with
a positive Hurst exponent . Typical eigenstates are superlocalized on
samples much larger than a well-defined crossover length, which diverges in the
weak-disorder regime. We present a parallel analytical investigation of the
statistics of these superlocalized states in the discrete and the continuum
formalisms. For the discrete tight-binding model, the effective localization
length decays logarithmically with the sample size, and the logarithm of the
transmission is marginally self-averaging. For the continuum Schr\"odinger
equation, the superlocalization phenomenon has more drastic effects. The
effective localization length decays as a power of the sample length, and the
logarithm of the transmission is fully non-self-averaging.Comment: 21 pages, 6 figure
Metastability in zero-temperature dynamics: Statistics of attractors
The zero-temperature dynamics of simple models such as Ising ferromagnets
provides, as an alternative to the mean-field situation, interesting examples
of dynamical systems with many attractors (absorbing configurations, blocked
configurations, zero-temperature metastable states). After a brief review of
metastability in the mean-field ferromagnet and of the droplet picture, we
focus our attention onto zero-temperature single-spin-flip dynamics of
ferromagnetic Ising models. The situations leading to metastability are
characterized. The statistics and the spatial structure of the attractors thus
obtained are investigated, and put in perspective with uniform a priori
ensembles. We review the vast amount of exact results available in one
dimension, and present original results on the square and honeycomb lattices.Comment: 21 pages, 6 figures. To appear in special issue of JPCM on Granular
Matter edited by M. Nicodem
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