2,602 research outputs found
Percolation Systems away from the Critical Point
This article reviews some effects of disorder in percolation systems even
away from the critical density p_c. For densities below p_c, the statistics of
large clusters defines the animals problem. Its relation to the directed
animals problem and the Lee-Yang edge singularity problem is described. Rare
compact clusters give rise to Griffiths singuraties in the free energy of
diluted ferromagnets, and lead to a very slow relaxation of magnetization. In
biassed diffusion on percolation clusters, trapping in dead-end branches leads
to asymptotic drift velocity becoming zero for strong bias, and very slow
relaxation of velocity near the critical bias field.Comment: Minor typos fixed. Submitted to Praman
Algebraic Aspects of Abelian Sandpile Models
The abelian sandpile models feature a finite abelian group G generated by the
operators corresponding to particle addition at various sites. We study the
canonical decomposition of G as a product of cyclic groups G = Z_{d_1} X
Z_{d_2} X Z_{d_3}...X Z_{d_g}, where g is the least number of generators of G,
and d_i is a multiple of d_{i+1}. The structure of G is determined in terms of
toppling matrix. We construct scalar functions, linear in height variables of
the pile, that are invariant toppling at any site. These invariants provide
convenient coordinates to label the recurrent configurations of the sandpile.
For an L X L square lattice, we show that g = L. In this case, we observe that
the system has nontrivial symmetries coming from the action of the cyclotomic
Galois group of the (2L+2)th roots of unity which operates on the set of
eigenvalues of the toppling matrix. These eigenvalues are algebraic integers,
whose product is the order |G|. With the help of this Galois group, we obtain
an explicit factorizaration of |G|. We also use it to define other simpler,
though under-complete, sets of toppling invariants.Comment: 39 pages, TIFR/TH/94-3
Slow dynamics at the smeared phase transition of randomly layered magnets
We investigate a model for randomly layered magnets, viz. a three-dimensional
Ising model with planar defects. The magnetic phase transition in this system
is smeared because static long-range order can develop on isolated rare spatial
regions. Here, we report large-scale kinetic Monte Carlo simulations of the
dynamical behavior close to the smeared phase transition which we characterize
by the spin (time) autocorrelation function. In the paramagnetic phase, its
behavior is dominated by Griffiths effects similar to those in magnets with
point defects. In the tail region of the smeared transition the dynamics is
even slower: the autocorrelation function decays like a stretched exponential
at intermediate times before approaching the exponentially small asymptotic
value following a power law at late times. Our Monte-Carlo results are in good
agreement with recent theoretical predictions based on optimal fluctuation
theory.Comment: 7 pages, 6 eps figures, final version as publishe
Tailoring symmetry groups using external alternate fields
Macroscopic systems with continuous symmetries subjected to oscillatory
fields have phases and transitions that are qualitatively different from their
equilibrium ones. Depending on the amplitude and frequency of the fields
applied, Heisenberg ferromagnets can become XY or Ising-like -or, conversely,
anisotropies can be compensated -thus changing the nature of the ordered phase
and the topology of defects. The phenomena can be viewed as a dynamic form of
"order by disorder".Comment: 4 pages, 2 figures finite dimension and selection mechanism clarifie
Logarithmic corrections of the avalanche distributions of sandpile models at the upper critical dimension
We study numerically the dynamical properties of the BTW model on a square
lattice for various dimensions. The aim of this investigation is to determine
the value of the upper critical dimension where the avalanche distributions are
characterized by the mean-field exponents. Our results are consistent with the
assumption that the scaling behavior of the four-dimensional BTW model is
characterized by the mean-field exponents with additional logarithmic
corrections. We benefit in our analysis from the exact solution of the directed
BTW model at the upper critical dimension which allows to derive how
logarithmic corrections affect the scaling behavior at the upper critical
dimension. Similar logarithmic corrections forms fit the numerical data for the
four-dimensional BTW model, strongly suggesting that the value of the upper
critical dimension is four.Comment: 8 pages, including 9 figures, accepted for publication in Phys. Rev.
Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality
We discuss the role played by the Lyapunov exponents in the dynamics of
Zhang's model of Self-Organized Criticality. We show that a large part of the
spectrum (slowest modes) is associated with the energy transpor in the lattice.
In particular, we give bounds on the first negative Lyapunov exponent in terms
of the energy flux dissipated at the boundaries per unit of time. We then
establish an explicit formula for the transport modes that appear as diffusion
modes in a landscape where the metric is given by the density of active sites.
We use a finite size scaling ansatz for the Lyapunov spectrum and relate the
scaling exponent to the scaling of quantities like avalanche size, duration,
density of active sites, etc ...Comment: 33 pages, 6 figures, 1 table (to appear
The rs12255372(G/T) and rs7903146(C/T) polymorphisms of the TCF7L2 gene are associated with type 2 diabetes mellitus in Asian Indians
One thousand thirty-eight normal glucose-tolerant and 1031 type 2 diabetic subjects selected from the Chennai Urban Rural
Epidemiology Study were genotyped using polymerase chain reaction-restriction fragment length polymorphism assay to investigate the
association of rs12255372(G/T) and rs7903146(C/T) polymorphisms of the transcription factor 7–like 2 (TCF7L2) gene with type 2 diabetes
mellitus in Asian Indians. The frequency of the “T” allele of both rs12255372(G/T) and rs7903146(C/T) polymorphisms was significantly
higher in diabetic subjects (23% and 33%) compared to that in normal glucose-tolerant subjects (19% and 28%; P = .001 and P = .0001,
respectively). Logistic regression analysis of the rs12255372(G/T) polymorphism showed that the odds ratio (adjusted for age, sex, and body
mass index) was 1.56 (95% confidence interval [CI], 1.03-2.37; P = .034) for the TT genotype and 1.29 (95% CI, 1.06-1.58; P = .011) for the
TG genotype when compared with the GG genotype. Adjusted odds ratios for the TT and TC genotypes of the rs7903146(C/T)
polymorphism were found to be 1.50 (95% CI, 1.08-2.08; P = .013) and 1.44 (95% CI, 1.18-1.76; P = .0003), respectively, compared with
the CC genotype. Normal glucose-tolerant subjects with the TT genotype of rs12255372(G/T) had significantly higher 2-hour plasma glucose
levels (mean ± SD, 6.1 ± 1.4 mmol/L) than those with the GG genotype (5.6 ± 1.0 mmol/L, P = .011). Normal glucose-tolerant subjects with
the TT genotype of rs7903146(C/T) polymorphism had significantly higher 2-hour plasma glucose levels (mean ± SD, 6.0 ± 1.3 mmol/L)
than those with the CC genotype (5.6 ± 1.0 mmol/L, P = .004). In conclusion, the T allele of the rs12255372(G/T) and rs7903146(C/T)
polymorphisms of TCF7L2 gene confer susceptibility to type 2 diabetes mellitus in Asian Indians.
© 2007 Elsevier Inc. All rights reserved
The effect of additive noise on dynamical hysteresis
We investigate the properties of hysteresis cycles produced by a
one-dimensional, periodically forced Langevin equation. We show that depending
on amplitude and frequency of the forcing and on noise intensity, there are
three qualitatively different types of hysteresis cycles. Below a critical
noise intensity, the random area enclosed by hysteresis cycles is concentrated
near the deterministic area, which is different for small and large driving
amplitude. Above this threshold, the area of typical hysteresis cycles depends,
to leading order, only on the noise intensity. In all three regimes, we derive
mathematically rigorous estimates for expectation, variance, and the
probability of deviations of the hysteresis area from its typical value.Comment: 30 pages, 5 figure
Efficiency of the Incomplete Enumeration algorithm for Monte-Carlo simulation of linear and branched polymers
We study the efficiency of the incomplete enumeration algorithm for linear
and branched polymers. There is a qualitative difference in the efficiency in
these two cases. The average time to generate an independent sample of
sites for large varies as for linear polymers, but as for branched (undirected and directed) polymers, where
. On the binary tree, our numerical studies for of order
gives . We argue that exactly in this
case.Comment: replaced with published versio
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