84 research outputs found
Localization phase diagram of two-dimensional quantum percolation
We examine quantum percolation on a square lattice with random dilution up to
and energy (measured in units of the hopping
matrix element), using numerical calculations of the transmission coefficient
at a much larger scale than previously. Our results confirm the previous
finding that the two dimensional quantum percolation model exhibits
localization-delocalization transitions, where the localized region splits into
an exponentially localized region and a power-law localization region. We
determine a fuller phase diagram confirming all three regions for energies as
low as , and the delocalized and exponentially localized regions for
energies down to . We also examine the scaling behavior of the
residual transmission coefficient in the delocalized region, the power law
exponent in the power-law localized region, and the localization length in the
exponentially localized region. Our results suggest that the residual
transmission at the delocalized to power-law localized phase boundary may be
discontinuous, and that the localization length is likely not to diverge with a
power-law at the exponentially localized to power-law localized phase boundary.
However, further work is needed to definitively assess the characters of the
two phase transitions as well as the nature of the intermediate power-law
regime
Fractal Properties of the Distribution of Earthquake Hypocenters
We investigate a recent suggestion that the spatial distribution of
earthquake hypocenters makes a fractal set with a structure and fractal
dimensionality close to those of the backbone of critical percolation clusters,
by analyzing four different sets of data for the hypocenter distributions and
calculating the dynamical properties of the geometrical distribution such as
the spectral dimension . We find that the value of is consistent
with that of the backbone, thus supporting further the identification of the
hypocenter distribution as having the structure of the percolation backbone.Comment: 11 pages, LaTeX, HLRZ 68/9
Effect of Loops on the Vibrational Spectrum of Percolation Network
We study the effects of adding loops to a critical percolation cluster on the
diffusional, and equivalently, (scalar) elastic properties of the fractal
network. From the numerical calculations of the eigenspectrum of the transition
probability matrix, we find that the spectral dimension and the walk
dimension change suddenly as soon as the floppy ends of a critical
percolation cluster are connected together to form relatively large loops, and
that the additional inclusion of successively smaller loops only change these
exponents little if at all. This suggests that there is a new universality
class associated with the loop-enhanced percolation problem.Comment: 12 pages, LaTeX, HLRZ 107/9
Markov chain analysis of random walks on disordered medium
We study the dynamical exponents and for a particle diffusing
in a disordered medium (modeled by a percolation cluster), from the regime of
extreme disorder (i.e., when the percolation cluster is a fractal at )
to the Lorentz gas regime when the cluster has weak disorder at and
the leading behavior is standard diffusion. A new technique of relating the
velocity autocorrelation function and the return to the starting point
probability to the asymptotic spectral properties of the hopping transition
probability matrix of the diffusing particle is used, and the latter is
numerically analyzed using the Arnoldi-Saad algorithm. We also present evidence
for a new scaling relation for the second largest eigenvalue in terms of the
size of the cluster, , which provides a
very efficient and accurate method of extracting the spectral dimension
where .Comment: 34 pages, REVTEX 3.
Incorporation rate measurements of 10Be, 230Th, 231Pa, and 239,240Pu radionuclides in manganese crust in the Pacific Ocean: A search for extraterrestrial material
高エネルギー加速器研究機構 共通基盤研究施設・放射線科学センター金沢大学大学院自然科学研究科物質情報解析金沢大学理学部In order to estimate the deposition rate of extraterrestrial material onto a manganese crust in a search for supernova debris, we analyzed the contents of 10Be, 230Th, 231Pa, and 239,240Pu in a sample of manganese crust collected from the North Pacific Ocean. On the basis of the depth profile of 10Be, the growth rate of the manganese crust was determined to be 2.3 mm Myr-1. The uptake rates of 10Be, 230Th, and 231Pa onto the manganese crust were estimated to be 0.22-0.44%, 0.11-0.73%, and 1.4-4.5%, respectively, as compared to the deposition rates onto the deep-sea sediments near the sampling station, while that for 239,240Pu was 0.14% as compared to the total inventory of seawater and sediment column. Assuming that sinking particles represent 0.11-4.5% of the uptake rates, the deposition rate of extraterrestrial material onto the manganese crust was estimated to be 2-800 μ g cm-2Myr-1 according to the uptake of 10Be onto the manganese crust. Further, our estimate is similar to the value of 9-90 μ g cm-2Myr-1 obtained using the integrated global production rate of 10Be and the deposition rate of 10Be onto the manganese crust. © The Oceanographic Society of Japan/TERRAPUB/Springer 2007
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