18,161 research outputs found
Non-Local Product Rules for Percolation
Despite original claims of a first-order transition in the product rule model
proposed by Achlioptas et al. [Science 323, 1453 (2009)], recent studies
indicate that this percolation model, in fact, displays a continuous
transition. The distinctive scaling properties of the model at criticality,
however, strongly suggest that it should belong to a different universality
class than ordinary percolation. Here we introduce a generalization of the
product rule that reveals the effect of non-locality on the critical behavior
of the percolation process. Precisely, pairs of unoccupied bonds are chosen
according to a probability that decays as a power-law of their Manhattan
distance, and only that bond connecting clusters whose product of their sizes
is the smallest, becomes occupied. Interestingly, our results for
two-dimensional lattices at criticality shows that the power-law exponent of
the product rule has a significant influence on the finite-size scaling
exponents for the spanning cluster, the conducting backbone, and the cutting
bonds of the system. In all three cases, we observe a continuous variation from
ordinary to (non-local) explosive percolation exponents.Comment: 5 pages, 4 figure
Magnetic models on Apollonian networks
Thermodynamic and magnetic properties of Ising models defined on the
triangular Apollonian network are investigated. This and other similar networks
are inspired by the problem of covering an Euclidian domain with circles of
maximal radii. Maps for the thermodynamic functions in two subsequent
generations of the construction of the network are obtained by formulating the
problem in terms of transfer matrices. Numerical iteration of this set of maps
leads to exact values for the thermodynamic properties of the model. Different
choices for the coupling constants between only nearest neighbors along the
lattice are taken into account. For both ferromagnetic and anti-ferromagnetic
constants, long range magnetic ordering is obtained. With exception of a size
dependent effective critical behavior of the correlation length, no evidence of
asymptotic criticality was detected.Comment: 21 pages, 5 figure
From Heavy Menstrual Bleeding to Amenorrhoea and Reversal of Anaemia - Novel, Effective, Intrauterine Levonorgestrel-Releasing Systems for Contraception and Treatment
Local Physical Coodinates from Symplectic Projector Method
The basic arguments underlying the symplectic projector method are presented.
By this method, local free coordinates on the constrait surface can be obtained
for a broader class of constrained systems. Some interesting examples are
analyzed.Comment: 8 page
SAMplus: adaptive optics at optical wavelengths for SOAR
Adaptive Optics (AO) is an innovative technique that substantially improves
the optical performance of ground-based telescopes. The SOAR Adaptive Module
(SAM) is a laser-assisted AO instrument, designed to compensate ground-layer
atmospheric turbulence in near-IR and visible wavelengths over a large Field of
View. Here we detail our proposal to upgrade SAM, dubbed SAMplus, that is
focused on enhancing its performance in visible wavelengths and increasing the
instrument reliability. As an illustration, for a seeing of 0.62 arcsec at 500
nm and a typical turbulence profile, current SAM improves the PSF FWHM to 0.40
arcsec, and with the upgrade we expect to deliver images with a FWHM of
arcsec -- up to 0.23 arcsec FWHM PSF under good seeing
conditions. Such capabilities will be fully integrated with the latest SAM
instruments, putting SOAR in an unique position as observatory facility.Comment: To appear in Proc. SPIE 10703 (Ground-based and Airborne
Instrumentation for Astronomy VII; SPIEastro18
Multiple Invaded Consolidating Materials
We study a multiple invasion model to simulate corrosion or intrusion
processes. Estimated values for the fractal dimension of the invaded region
reveal that the critical exponents vary as function of the generation number
, i.e., with the number of times the invasion process takes place. The
averaged mass of the invaded region decreases with a power-law as a
function of , , where the exponent . We
also find that the fractal dimension of the invaded cluster changes from
to . This result confirms that the
multiple invasion process follows a continuous transition from one universality
class (NTIP) to another (optimal path). In addition, we report extensive
numerical simulations that indicate that the mass distribution of avalanches
has a power-law behavior and we find that the exponent
governing the power-law changes continuously as a
function of the parameter . We propose a scaling law for the mass
distribution of avalanches for different number of generations .Comment: 8 pages and 16 figure
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