34,427 research outputs found
Corrections to Finite Size Scaling in Percolation
A 1/L-expansion for percolation problems is proposed, where L is the lattice
finite length. The square lattice with 27 different sizes L = 18, 22 ... 1594
is considered. Certain spanning probabilities were determined by Monte Carlo
simulations, as continuous functions of the site occupation probability p. We
estimate the critical threshold pc by applying the quoted expansion to these
data. Also, the universal spanning probability at pc for an annulus with aspect
ratio r=1/2 is estimated as C = 0.876657(45)
Line-strength indices and velocity dispersions for 148 early-type galaxies in different environments
We have derived high quality line-strength indices and velocity
dispersions for a sample of 148 early-type galaxies in different
environments. The wavelength region covered by the observations
( to 6600 Å) includes the Lick/IDS indices
H, Mg1, Mg2, Mgb, Fe5015, Fe5270, Fe5335, Fe5406,
Fe5709, Fe5782, NaD, TiO1 and TiO2. The data are intended to
address possible differences of the stellar populations of early-type
galaxies in low- and high-density environments. This paper describes
the sample properties, explains the data reduction and presents the
complete list of all the measurements. Most galaxies of the sample
(85%) had no previous measurements of any Lick/IDS indices and for
30% of the galaxies we present first-time determinations of their
velocity dispersions. Special care is taken to identify galaxies with
emission lines. We found that 62 per cent of the galaxies in the
sample have emission lines, as measured by the equivalent width of the
[OIII] 5007Å line, EW[OIII] > 0.3 Å
Scaling behavior of explosive percolation on the square lattice
Clusters generated by the product-rule growth model of Achlioptas, D'Souza,
and Spencer on a two-dimensional square lattice are shown to obey qualitatively
different scaling behavior than standard (random growth) percolation. The
threshold with unrestricted bond placement (allowing loops) is found precisely
using several different criteria based upon both moments and wrapping
probabilities, yielding p_c = 0.526565 +/- 0.000005, consistent with the recent
result of Radicchi and Fortunato. The correlation-length exponent nu is found
to be close to 1. The qualitative difference from regular percolation is shown
dramatically in the behavior of the percolation probability P_(infinity) (size
of largest cluster), the susceptibility, and of the second moment of finite
clusters, where discontinuities appears at the threshold. The critical
cluster-size distribution does not follow a consistent power-law for the range
of system sizes we study L 2
for larger L.Comment: v2: Updated results in original version with new data; expanded
discussion. v3: Resubmitted version. New figures, reference
Optimization of hierarchical structures of information flow
The efficiency of a large hierarchical organisation is simulated on
Barabasi-Albert networks, when each needed link leads to a loss of information.
The optimum is found at a finite network size, corresponding to about five
hierarchical layers, provided a cost for building the network is included in
our optimization.Comment: Draft of 6 pages including all figure
Hermitian Dirac Hamiltonian in time dependent gravitational field
It is shown by a straightforward argument that the Hamiltonian generating the
time evolution of the Dirac wave function in relativistic quantum mechanics is
not hermitian with respect to the covariantly defined inner product whenever
the background metric is time dependent. An alternative, hermitian, Hamiltonian
is found and is shown to be directly related to the canonical field Hamiltonian
used in quantum field theory.Comment: 9 pages, final version, to appear in Class. Quant. Gra
Broad Histogram Method for Continuous Systems: the XY-Model
We propose a way of implementing the Broad Histogram Monte Carlo method to
systems with continuous degrees of freedom, and we apply these ideas to
investigate the three-dimensional XY-model with periodic boundary conditions.
We have found an excellent agreement between our method and traditional
Metropolis results for the energy, the magnetization, the specific heat and the
magnetic susceptibility on a very large temperature range. For the calculation
of these quantities in the temperature range 0.7<T<4.7 our method took less CPU
time than the Metropolis simulations for 16 temperature points in that
temperature range. Furthermore, it calculates the whole temperature range
1.2<T<4.7 using only 2.2 times more computer effort than the Histogram Monte
Carlo method for the range 2.1<T<2.2. Our way of treatment is general, it can
also be applied to other systems with continuous degrees of freedom.Comment: 23 pages, 10 Postscript figures, to be published in Int. J. Mod.
Phys.
- …