3,370 research outputs found
Effect of Noise on Patterns Formed by Growing Sandpiles
We consider patterns generated by adding large number of sand grains at a
single site in an abelian sandpile model with a periodic initial configuration,
and relaxing. The patterns show proportionate growth. We study the robustness
of these patterns against different types of noise, \textit{viz.}, randomness
in the point of addition, disorder in the initial periodic configuration, and
disorder in the connectivity of the underlying lattice. We find that the
patterns show a varying degree of robustness to addition of a small amount of
noise in each case. However, introducing stochasticity in the toppling rules
seems to destroy the asymptotic patterns completely, even for a weak noise. We
also discuss a variational formulation of the pattern selection problem in
growing abelian sandpiles.Comment: 15 pages,16 figure
Effect of phonon-phonon interactions on localization
We study the heat current J in a classical one-dimensional disordered chain
with on-site pinning and with ends connected to stochastic thermal reservoirs
at different temperatures. In the absence of anharmonicity all modes are
localized and there is a gap in the spectrum. Consequently J decays
exponentially with system size N. Using simulations we find that even a small
amount of anharmonicity leads to a J~1/N dependence, implying diffusive
transport of energy.Comment: 4 pages, 2 figures, Published versio
Heat conduction in disordered harmonic lattices with energy conserving noise
We study heat conduction in a harmonic crystal whose bulk dynamics is
supplemented by random reversals (flips) of the velocity of each particle at a
rate . The system is maintained in a nonequilibrium stationary
state(NESS) by contacts with Langevin reservoirs at different temperatures. We
show that the one-body and pair correlations in this system are the same (after
an appropriate mapping of parameters) as those obtained for a model with
self-consistent reservoirs. This is true both for the case of equal and
random(quenched) masses. While the heat conductivity in the NESS of the ordered
system is known explicitly, much less is known about the random mass case. Here
we investigate the random system, with velocity flips. We improve the bounds on
the Green-Kubo conductivity obtained by C.Bernardin. The conductivity of the 1D
system is then studied both numerically and analytically. This sheds some light
on the effect of noise on the transport properties of systems with localized
states caused by quenched disorder.Comment: 19 pages, 8 figure
Local Temperature and Universal Heat Conduction in FPU chains
It is shown numerically that for Fermi Pasta Ulam (FPU) chains with
alternating masses and heat baths at slightly different temperatures at the
ends, the local temperature (LT) on small scales behaves paradoxically in
steady state. This expands the long established problem of equilibration of FPU
chains. A well-behaved LT appears to be achieved for equal mass chains; the
thermal conductivity is shown to diverge with chain length N as N^(1/3),
relevant for the much debated question of the universality of one dimensional
heat conduction. The reason why earlier simulations have obtained
systematically higher exponents is explained.Comment: 4 pages, 3 figures, revised published versio
A universal form of slow dynamics in zero-temperature random-field Ising model
The zero-temperature Glauber dynamics of the random-field Ising model
describes various ubiquitous phenomena such as avalanches, hysteresis, and
related critical phenomena. Here, for a model on a random graph with a special
initial condition, we derive exactly an evolution equation for an order
parameter. Through a bifurcation analysis of the obtained equation, we reveal a
new class of cooperative slow dynamics with the determination of critical
exponents.Comment: 4 pages, 2 figure
Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
We derive the Bethe ansatz equations describing the complete spectrum of the
transition matrix of the partially asymmetric exclusion process with the most
general open boundary conditions. For totally asymmetric diffusion we calculate
the spectral gap, which characterizes the approach to stationarity at large
times. We observe boundary induced crossovers in and between massive, diffusive
and KPZ scaling regimes.Comment: 4 pages, 2 figures, published versio
Particle-hole symmetry in a sandpile model
In a sandpile model addition of a hole is defined as the removal of a grain
from the sandpile. We show that hole avalanches can be defined very similar to
particle avalanches. A combined particle-hole sandpile model is then defined
where particle avalanches are created with probability and hole avalanches
are created with the probability . It is observed that the system is
critical with respect to either particle or hole avalanches for all values of
except at the symmetric point of . However at the
fluctuating mass density is having non-trivial correlations characterized by
type of power spectrum.Comment: Four pages, our figure
Determinant solution for the Totally Asymmetric Exclusion Process with parallel update
We consider the totally asymmetric exclusion process in discrete time with
the parallel update. Constructing an appropriate transformation of the
evolution operator, we reduce the problem to that solvable by the Bethe ansatz.
The non-stationary solution of the master equation for the infinite 1D lattice
is obtained in a determinant form. Using a modified combinatorial treatment of
the Bethe ansatz, we give an alternative derivation of the resulting
determinant expression.Comment: 34 pages, 5 figures, final versio
Polyphenolic compounds as spray reagents in inorganic paper chromatography Part I
A study of 10 members of o-hydroxybenzoyl and isopentenylated o-hydroxybenzoyl group of compounds, as spray reagents in inorganic paper chromatography, for the detection of metal ions, shows, that resacetophenone, phloroacetophenone, gallacetophenone and 5-C-prenyl gallacetophenone can act as very useful and often universal reagents. Comparative sensitivity limits with respect to Ti(IV), V(V), Mn(II), Fe(II), Fe(III), Co(II), Ni(II), Cu(II), Ce(IV) and U(VI) have been determined for these four reagents
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