2,196 research outputs found
Effects of the oceans on polar motion: Continued investigations
Data on the pole tide, the oceanic response to the Chandler wobble were presented. Observed North Sea pole tide enhancement (i.e., larger amplitudes than a static tide would possess) resulted from bottom friction, with the drag coefficient, in combination with the depth of the North Sea decreasing southward. Computer programs were written for the boundary conditions. Dissipation of the energy by North Sea pole tide currents was also computed; preliminary results indicate that such dissipation may explain a significant fraction of Chandler wobble energy loss
Path-integral representation for a stochastic sandpile
We introduce an operator description for a stochastic sandpile model with a
conserved particle density, and develop a path-integral representation for its
evolution. The resulting (exact) expression for the effective action highlights
certain interesting features of the model, for example, that it is nominally
massless, and that the dynamics is via cooperative diffusion. Using the
path-integral formalism, we construct a diagrammatic perturbation theory,
yielding a series expansion for the activity density in powers of the time.Comment: 22 pages, 6 figure
Series expansion for a stochastic sandpile
Using operator algebra, we extend the series for the activity density in a
one-dimensional stochastic sandpile with fixed particle density p, the first
terms of which were obtained via perturbation theory [R. Dickman and R.
Vidigal, J. Phys. A35, 7269 (2002)]. The expansion is in powers of the time;
the coefficients are polynomials in p. We devise an algorithm for evaluating
expectations of operator products and extend the series to O(t^{16}).
Constructing Pade approximants to a suitably transformed series, we obtain
predictions for the activity that compare well against simulations, in the
supercritical regime.Comment: Extended series and improved analysi
Asymptotic behavior of the order parameter in a stochastic sandpile
We derive the first four terms in a series for the order paramater (the
stationary activity density rho) in the supercritical regime of a
one-dimensional stochastic sandpile; in the two-dimensional case the first
three terms are reported. We reorganize the pertubation theory for the model,
recently derived using a path-integral formalism [R. Dickman e R. Vidigal, J.
Phys. A 35, 7269 (2002)], to obtain an expansion for stationary properties.
Since the process has a strictly conserved particle density p, the Fourier mode
N^{-1} psi_{k=0} -> p, when the number of sites N -> infinity, and so is not a
random variable. Isolating this mode, we obtain a new effective action leading
to an expansion for rho in the parameter kappa = 1/(1+4p). This requires
enumeration and numerical evaluation of more than 200 000 diagrams, for which
task we develop a computational algorithm. Predictions derived from this series
are in good accord with simulation results. We also discuss the nature of
correlation functions and one-site reduced densities in the small-kappa
(large-p) limit.Comment: 18 pages, 5 figure
Diffusive epidemic process: theory and simulation
We study the continuous absorbing-state phase transition in the
one-dimensional diffusive epidemic process via mean-field theory and Monte
Carlo simulation. In this model, particles of two species (A and B) hop on a
lattice and undergo reactions B -> A and A + B -> 2B; the total particle number
is conserved. We formulate the model as a continuous-time Markov process
described by a master equation. A phase transition between the (absorbing)
B-free state and an active state is observed as the parameters (reaction and
diffusion rates, and total particle density) are varied. Mean-field theory
reveals a surprising, nonmonotonic dependence of the critical recovery rate on
the diffusion rate of B particles. A computational realization of the process
that is faithful to the transition rates defining the model is devised,
allowing for direct comparison with theory. Using the quasi-stationary
simulation method we determine the order parameter and the survival time in
systems of up to 4000 sites. Due to strong finite-size effects, the results
converge only for large system sizes. We find no evidence for a discontinuous
transition. Our results are consistent with the existence of three distinct
universality classes, depending on whether A particles diffusive more rapidly,
less rapidly, or at the same rate as B particles.Comment: 19 pages, 5 figure
Scaling behavior of the conserved transfer threshold process
We analyze numerically the critical behavior of an absorbing phase transition
in the conserved transfer threshold process. We determined the steady state
scaling behavior of the order parameter as a function of both, the control
parameter and an external field, conjugated to the order parameter. The
external field is realized as a spontaneous creation of active particles which
drives the system away from criticality. The obtained results yields that the
conserved transfers threshold process belongs to the universality class of
absorbing phase transitions in a conserved field.Comment: 6 pages, 8 figures, accepted for publication in Phys. Rev.
Contact process on a Voronoi triangulation
We study the continuous absorbing-state phase transition in the contact
process on the Voronoi-Delaunay lattice. The Voronoi construction is a natural
way to introduce quenched coordination disorder in lattice models. We simulate
the disordered system using the quasistationary simulation method and determine
its critical exponents and moment ratios. Our results suggest that the critical
behavior of the disordered system is unchanged with respect to that on a
regular lattice, i.e., that of directed percolation
Sandpiles with height restrictions
We study stochastic sandpile models with a height restriction in one and two
dimensions. A site can topple if it has a height of two, as in Manna's model,
but, in contrast to previously studied sandpiles, here the height (or number of
particles per site), cannot exceed two. This yields a considerable
simplification over the unrestricted case, in which the number of states per
site is unbounded. Two toppling rules are considered: in one, the particles are
redistributed independently, while the other involves some cooperativity. We
study the fixed-energy system (no input or loss of particles) using cluster
approximations and extensive simulations, and find that it exhibits a
continuous phase transition to an absorbing state at a critical value zeta_c of
the particle density. The critical exponents agree with those of the
unrestricted Manna sandpile.Comment: 10 pages, 14 figure
Activated Random Walkers: Facts, Conjectures and Challenges
We study a particle system with hopping (random walk) dynamics on the integer
lattice . The particles can exist in two states, active or
inactive (sleeping); only the former can hop. The dynamics conserves the number
of particles; there is no limit on the number of particles at a given site.
Isolated active particles fall asleep at rate , and then remain
asleep until joined by another particle at the same site. The state in which
all particles are inactive is absorbing. Whether activity continues at long
times depends on the relation between the particle density and the
sleeping rate . We discuss the general case, and then, for the
one-dimensional totally asymmetric case, study the phase transition between an
active phase (for sufficiently large particle densities and/or small )
and an absorbing one. We also present arguments regarding the asymptotic mean
hopping velocity in the active phase, the rate of fixation in the absorbing
phase, and survival of the infinite system at criticality. Using mean-field
theory and Monte Carlo simulation, we locate the phase boundary. The phase
transition appears to be continuous in both the symmetric and asymmetric
versions of the process, but the critical behavior is very different. The
former case is characterized by simple integer or rational values for critical
exponents (, for example), and the phase diagram is in accord with
the prediction of mean-field theory. We present evidence that the symmetric
version belongs to the universality class of conserved stochastic sandpiles,
also known as conserved directed percolation. Simulations also reveal an
interesting transient phenomenon of damped oscillations in the activity
density
N-Site approximations and CAM analysis for a stochastic sandpile
I develop n-site cluster approximations for a stochastic sandpile in one
dimension. A height restriction is imposed to limit the number of states: each
site can harbor at most two particles (height z_i \leq 2). (This yields a
considerable simplification over the unrestricted case, in which the number of
states per site is unbounded.) On the basis of results for n \leq 11 sites, I
estimate the critical particle density as zeta_c = 0.930(1), in good agreement
with simulations. A coherent anomaly analysis yields estimates for the order
parameter exponent [beta = 0.41(1)] and the relaxation time exponent (nu_||
\simeq 2.5).Comment: 12 pages, 7 figure
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