3,392 research outputs found
Sandpile model on a quenched substrate generated by kinetic self-avoiding trails
Kinetic self-avoiding trails are introduced and used to generate a substrate
of randomly quenched flow vectors. Sandpile model is studied on such a
substrate with asymmetric toppling matrices where the precise balance between
the net outflow of grains from a toppling site and the total inflow of grains
to the same site when all its neighbors topple once is maintained at all sites.
Within numerical accuracy this model behaves in the same way as the
multiscaling BTW model.Comment: Four pages, five figure
Precise toppling balance, quenched disorder, and universality for sandpiles
A single sandpile model with quenched random toppling matrices captures the
crucial features of different models of self-organized criticality. With
symmetric matrices avalanche statistics falls in the multiscaling BTW
universality class. In the asymmetric case the simple scaling of the Manna
model is observed. The presence or absence of a precise toppling balance
between the amount of sand released by a toppling site and the total quantity
the same site receives when all its neighbors topple once determines the
appropriate universality class.Comment: 5 Revtex pages, 4 figure
Sandpile model on an optimized scale-free network on Euclidean space
Deterministic sandpile models are studied on a cost optimized
Barab\'asi-Albert (BA) scale-free network whose nodes are the sites of a square
lattice. For the optimized BA network, the sandpile model has the same critical
behaviour as the BTW sandpile, whereas for the un-optimized BA network the
critical behaviour is mean-field like.Comment: Five pages, four figure
Critical States in a Dissipative Sandpile Model
A directed dissipative sandpile model is studied in the two-dimension.
Numerical results indicate that the long time steady states of this model are
critical when grains are dropped only at the top or, everywhere. The critical
behaviour is mean-field like. We discuss the role of infinite avalanches of
dissipative models in periodic systems in determining the critical behaviour of
same models in open systems.Comment: 4 pages (Revtex), 5 ps figures (included
Proof by analogy in mural
One of the most important advantages of using a formal method of developing software is that one can prove that development steps are correct with respect to their specification.
Conducting proofs by hand, however,can be time consuming to the extent that designers have to judge whether a proof of a particular obligation is worth conducting.
Even if hand proofs are worth conducting, how do we know that they are correct?
One approach to overcoming this problem is to use an automatic theorem proving system to develop and check our proofs. However, in order to enable present day
theorem provers to check proofs, one has to conduct
them in much more detail than hand proofs. Carrying out more detailed proofs is of course more time consuming.
This paper describes the use of proof by analogy in an attempt to reduce the time spent on proofs.
We develop and implement a proof follower based on analogy and present two examples to illustrate its
characteristics. One example illustrates the successful use of the proof follower. The other example illustrates that the follower's failure can provide a hint that enables the user to complete a proof
High-resolution thermal expansion measurements under Helium-gas pressure
We report on the realization of a capacitive dilatometer, designed for
high-resolution measurements of length changes of a material for temperatures
1.4 K 300 K and hydrostatic pressure 250 MPa. Helium
(He) is used as a pressure-transmitting medium, ensuring
hydrostatic-pressure conditions. Special emphasis has been given to guarantee,
to a good approximation, constant-pressure conditions during temperature
sweeps. The performance of the dilatometer is demonstrated by measurements of
the coefficient of thermal expansion at pressures 0.1 MPa (ambient
pressure) and 104 MPa on a single crystal of azurite,
Cu(CO)(OH), a quasi-one-dimensional spin S = 1/2 Heisenberg
antiferromagnet. The results indicate a strong effect of pressure on the
magnetic interactions in this system.Comment: 8 pages, 7 figures, published in Rev. Sci. Instrum with minor change
Clustering properties of a generalised critical Euclidean network
Many real-world networks exhibit scale-free feature, have a small diameter
and a high clustering tendency. We have studied the properties of a growing
network, which has all these features, in which an incoming node is connected
to its th predecessor of degree with a link of length using a
probability proportional to . For , the
network is scale free at with the degree distribution and as in the Barab\'asi-Albert model (). We find a phase boundary in the plane along which
the network is scale-free. Interestingly, we find scale-free behaviour even for
for where the existence of a new universality class
is indicated from the behaviour of the degree distribution and the clustering
coefficients. The network has a small diameter in the entire scale-free region.
The clustering coefficients emulate the behaviour of most real networks for
increasing negative values of on the phase boundary.Comment: 4 pages REVTEX, 4 figure
Self-Structuring of Granular Media under Internal Avalanches
We study the phenomenon of internal avalanching within the context of
recently proposed ``Tetris'' lattice models for granular media. We define a
recycling dynamics under which the system reaches a steady state which is
self-structured, i.e. it shows a complex interplay between textured internal
structures and critical avalanche behavior. Furthermore we develop a general
mean-field theory for this class of systems and discuss possible scenarios for
the breakdown of universality.Comment: 4 pages RevTex, 3 eps figures, revised version to appear in Phys.
Rev. Let
Directed Fixed Energy Sandpile Model
We numerically study the directed version of the fixed energy sandpile. On a
closed square lattice, the dynamical evolution of a fixed density of sand
grains is studied. The activity of the system shows a continuous phase
transition around a critical density. While the deterministic version has the
set of nontrivial exponents, the stochastic model is characterized by mean
field like exponents.Comment: 5 pages, 6 figures, to be published in Phys. Rev.
Irreversible Deposition of Line Segment Mixtures on a Square Lattice: Monte Carlo Study
We have studied kinetics of random sequential adsorption of mixtures on a
square lattice using Monte Carlo method. Mixtures of linear short segments and
long segments were deposited with the probability and , respectively.
For fixed lengths of each segment in the mixture, the jamming limits decrease
when increases. The jamming limits of mixtures always are greater than
those of the pure short- or long-segment deposition.
For fixed and fixed length of the short segments, the jamming limits have
a maximum when the length of the long segment increases. We conjectured a
kinetic equation for the jamming coverage based on the data fitting.Comment: 7 pages, latex, 5 postscript figure
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