3,180 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
Numerical Diagonalisation Study of the Trimer Deposition-Evaporation Model in One Dimension
We study the model of deposition-evaporation of trimers on a line recently
introduced by Barma, Grynberg and Stinchcombe. The stochastic matrix of the
model can be written in the form of the Hamiltonian of a quantum spin-1/2 chain
with three-spin couplings given by H= \sum\displaylimits_i [(1 -
\sigma_i^-\sigma_{i+1}^-\sigma_{i+2}^-) \sigma_i^+\sigma_{i+1}^+\sigma_{i+2}^+
+ h.c]. We study by exact numerical diagonalization of the variation of
the gap in the eigenvalue spectrum with the system size for rings of size up to
30. For the sector corresponding to the initial condition in which all sites
are empty, we find that the gap vanishes as where the gap exponent
is approximately . This model is equivalent to an interfacial
roughening model where the dynamical variables at each site are matrices. From
our estimate for the gap exponent we conclude that the model belongs to a new
universality class, distinct from that studied by Kardar, Parisi and Zhang.Comment: 11 pages, 2 figures (included
The Irreducible String and an Infinity of Additional Constants of Motion in a Deposition-Evaporation Model on a Line
We study a model of stochastic deposition-evaporation with recombination, of
three species of dimers on a line. This model is a generalization of the model
recently introduced by Barma {\it et. al.} (1993 {\it Phys. Rev. Lett.} {\bf
70} 1033) to states per site. It has an infinite number of constants
of motion, in addition to the infinity of conservation laws of the original
model which are encoded as the conservation of the irreducible string. We
determine the number of dynamically disconnected sectors and their sizes in
this model exactly. Using the additional symmetry we construct a class of exact
eigenvectors of the stochastic matrix. The autocorrelation function decays with
different powers of in different sectors. We find that the spatial
correlation function has an algebraic decay with exponent 3/2, in the sector
corresponding to the initial state in which all sites are in the same state.
The dynamical exponent is nontrivial in this sector, and we estimate it
numerically by exact diagonalization of the stochastic matrix for small sizes.
We find that in this case .Comment: Some minor errors in the first version has been correcte
Nonequilibrium Phase Transitions in a Driven Sandpile Model
We construct a driven sandpile slope model and study it by numerical
simulations in one dimension. The model is specified by a threshold slope
\sigma_c\/, a parameter \alpha\/, governing the local current-slope
relation (beyond threshold), and , the mean input current of sand.
A nonequilibrium phase diagram is obtained in the \alpha\, -\, j_{\rm in}\/
plane. We find an infinity of phases, characterized by different mean slopes
and separated by continuous or first-order boundaries, some of which we obtain
analytically. Extensions to two dimensions are discussed.Comment: 11 pages, RevTeX (preprint format), 4 figures available upon requs
Charge and Statistics of Quasiparticles in Fractional Quantum Hall Effec
We have studied here the charge and statistics of quasiparticle excitations
in FQH states on the basis of the Berry phase approach incorporating the fact
that even number of flux quanta can be gauged away when the Berry phase is
removed to the dynamical phase. It is observed that the charge and
statistical parameter of a quasiparticle at filling factor
are given by and
, with the fact that the charge of the quasihole is
opposite to that of the quasielectron. Using Laughlin wave function for
quasiparticles, numerical studies have been done following the work of
Kj{\o}nsberg and Myrheim \cite{KM} for FQH states at and it is
pointed out that as in case of quasiholes, the statistics parameter can be well
defined for quasielectrons having the value .Comment: 12 pages, 4 figure
Quenched Averages for self-avoiding walks and polygons on deterministic fractals
We study rooted self avoiding polygons and self avoiding walks on
deterministic fractal lattices of finite ramification index. Different sites on
such lattices are not equivalent, and the number of rooted open walks W_n(S),
and rooted self-avoiding polygons P_n(S) of n steps depend on the root S. We
use exact recursion equations on the fractal to determine the generating
functions for P_n(S), and W_n(S) for an arbitrary point S on the lattice. These
are used to compute the averages and over different positions of S. We find that the connectivity constant
, and the radius of gyration exponent are the same for the annealed
and quenched averages. However, , and , where the exponents
and take values different from the annealed case. These
are expressed as the Lyapunov exponents of random product of finite-dimensional
matrices. For the 3-simplex lattice, our numerical estimation gives ; and , to be
compared with the annealed values and .Comment: 17 pages, 10 figures, submitted to Journal of Statistical Physic
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
Heat conduction in one dimensional systems: Fourier law, chaos, and heat control
In this paper we give a brief review of the relation between microscopic
dynamical properties and the Fourier law of heat conduction as well as the
connection between anomalous conduction and anomalous diffusion. We then
discuss the possibility to control the heat flow.Comment: 15 pages, 11 figures. To be published in the Proceedings of the NATO
Advanced Research Workshop on Nonlinear Dynamics and Fundamental
Interactions, Tashkent, Uzbekistan, Octo. 11-16, 200
Crossover phenomenon in self-organized critical sandpile models
We consider a stochastic sandpile where the sand-grains of unstable sites are
randomly distributed to the nearest neighbors. Increasing the value of the
threshold condition the stochastic character of the distribution is lost and a
crossover to the scaling behavior of a different sandpile model takes place
where the sand-grains are equally transferred to the nearest neighbors. The
crossover behavior is numerically analyzed in detail, especially we consider
the exponents which determine the scaling behavior.Comment: 6 pages, 9 figures, accepted for publication in Physical Review
Randmoness and Step-like Distribution of Pile Heights in Avalanche Models
The paper develops one-parametric family of the sand-piles dealing with the
grains' local losses on the fixed amount. The family exhibits the crossover
between the models with deterministic and stochastic relaxation. The mean
height of the pile is destined to describe the crossover. The height's
densities corresponding to the models with relaxation of the both types tend
one to another as the parameter increases. These densities follow a step-like
behaviour in contrast to the peaked shape found in the models with the local
loss of the grains down to the fixed level [S. Lubeck, Phys. Rev. E, 62, 6149,
(2000)]. A spectral approach based on the long-run properties of the pile
height considers the models with deterministic and random relaxation more
accurately and distinguishes the both cases up to admissible parameter values.Comment: 5 pages, 5 figure
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