37,165 research outputs found

### Universality in survivor distributions: Characterising the winners of competitive dynamics

We investigate the survivor distributions of a spatially extended model of
competitive dynamics in different geometries. The model consists of a
deterministic dynamical system of individual agents at specified nodes, which
might or might not survive the predatory dynamics: all stochasticity is brought
in by the initial state. Every such initial state leads to a unique and
extended pattern of survivors and non-survivors, which is known as an attractor
of the dynamics. We show that the number of such attractors grows exponentially
with system size, so that their exact characterisation is limited to only very
small systems. Given this, we construct an analytical approach based on
inhomogeneous mean-field theory to calculate survival probabilities for
arbitrary networks. This powerful (albeit approximate) approach shows how
universality arises in survivor distributions via a key concept -- the {\it
dynamical fugacity}. Remarkably, in the large-mass limit, the survival
probability of a node becomes independent of network geometry, and assumes a
simple form which depends only on its mass and degree.Comment: 12 pages, 6 figures, 2 table

### Slow synaptic dynamics in a network: from exponential to power-law forgetting

We investigate a mean-field model of interacting synapses on a directed
neural network. Our interest lies in the slow adaptive dynamics of synapses,
which are driven by the fast dynamics of the neurons they connect. Cooperation
is modelled from the usual Hebbian perspective, while competition is modelled
by an original polarity-driven rule. The emergence of a critical manifold
culminating in a tricritical point is crucially dependent on the presence of
synaptic competition. This leads to a universal $1/t$ power-law relaxation of
the mean synaptic strength along the critical manifold and an equally universal
$1/\sqrt{t}$ relaxation at the tricritical point, to be contrasted with the
exponential relaxation that is otherwise generic. In turn, this leads to the
natural emergence of long- and short-term memory from different parts of
parameter space in a synaptic network, which is the most novel and important
result of our present investigations.Comment: 12 pages, 8 figures. Phys. Rev. E (2014) to appea

### A two-species model of a two-dimensional sandpile surface: a case of asymptotic roughening

We present and analyze a model of an evolving sandpile surface in (2 + 1)
dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile
clusters (h(x, t)) are coupled. Our coupling models the situation where the
sandpile is flat on average, so that there is no bias due to gravity. We find
anomalous scaling: the expected logarithmic smoothing at short length and time
scales gives way to roughening in the asymptotic limit, where novel and
non-trivial exponents are found.Comment: 7 Pages, 6 Figures; Granular Matter, 2012 (Online

### Glassy dynamics in granular compaction

Two models are presented to study the influence of slow dynamics on granular
compaction. It is found in both cases that high values of packing fraction are
achieved only by the slow relaxation of cooperative structures. Ongoing work to
study the full implications of these results is discussed.Comment: 12 pages, 9 figures; accepted in J. Phys: Condensed Matter,
proceedings of the Trieste workshop on 'Unifying concepts in glass physics

### 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

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### Determination of machinable volume for finish cuts in CAPP

Identification of machinable volume for finish cut is a complex task as it involves the details not only of the final product but also the intermediate part obtained from rough machining of the blank. A feature recognition technique that adopts a rule-based methodology is required for calculating this small, complex shaped finish cut volume. This paper presents the feature recognition module in a CAPP system that calculates the intermediate finish cut volume by adopting a rule based syntactic pattern recognition approach. In this module, the interfacer uses STEP AP203/214, a CAD neutral format, to trace the coordinate point information and to calculate the machinable volume. Two illustrative examples are given to explain the proposed syntactic pattern approach for prismatic parts

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