17 research outputs found
Statistical modeling of the long-range dependent structure of barrier island framework geology and surface geomorphology
Shorelines exhibit long-range dependence (LRD) and have been shown in some environments to be described in the wavenumber domain by a power law characteristic of scale-independence. Recent evidence suggests that the geomorphology of barrier islands can, however, exhibit scale dependence as a result of systematic variations of the underlying framework geology. The LRD of framework geology, which influences island geomorphology and its response to storms and sea level rise, has not been previously examined. Electromagnetic induction (EMI) surveys conducted along Padre Island National Seashore (PAIS), Texas, USA, reveal that the EMI apparent conductivity σa signal and, by inference, the framework geology exhibits LRD at scales up to 101 to 102 km. Our study demonstrates the utility of describing EMI σa and LiDAR spatial series by a fractional auto-regressive integrated moving average process that specifically models LRD. This method offers a robust and compact way for quantifying the geological variations along a barrier island shoreline using three parameters (p,d,q). We discuss how ARIMA (0,d,0) models that use a single parameter d provide a quantitative measure for determining free and forced barrier island evolutionary behavior across different scales. Statistical analyses at regional, intermediate, and local scales suggest that the geologic framework within an area of paleo-channels exhibits a first order control on dune height. The exchange of sediment amongst nearshore, beach and dune in areas outside this region are scale-independent, implying that barrier islands like PAIS exhibit a combination of free and forced behaviors that affect the response of the island to sea level rise
Fluctuating Hall resistance defeats the quantized Hall insulator
Using the Chalker-Coddington network model as a drastically simplified, but
universal model of integer quantum Hall physics, we investigate the
plateau-to-insulator transition at strong magnetic field by means of a
real-space renormalization approach. Our results suggest that for a fully
quantum coherent situation, the quantized Hall insulator with R_H approx. h/e^2
is observed up to R_L ~25 h/e^2 when studying the most probable value of the
distribution function P(R_H). Upon further increasing R_L ->\infty the Hall
insulator with diverging Hall resistance R_H \propto R_L^kappa is seen. The
crossover between these two regimes depends on the precise nature of the
averaging procedure.Comment: major revision, discussion of averaging improved; 8 pages, 7 figures;
accepted for publication in EP
Localization in non-chiral network models for two-dimensional disordered wave mechanical systems
Scattering theoretical network models for general coherent wave mechanical
systems with quenched disorder are investigated. We focus on universality
classes for two dimensional systems with no preferred orientation: Systems of
spinless waves undergoing scattering events with broken or unbroken time
reversal symmetry and systems of spin 1/2 waves with time reversal symmetric
scattering. The phase diagram in the parameter space of scattering strengths is
determined. The model breaking time reversal symmetry contains the critical
point of quantum Hall systems but, like the model with unbroken time reversal
symmetry, only one attractive fixed point, namely that of strong localization.
Multifractal exponents and quasi-one-dimensional localization lengths are
calculated numerically and found to be related by conformal invariance.
Furthermore, they agree quantitatively with theoretical predictions. For
non-vanishing spin scattering strength the spin 1/2 systems show
localization-delocalization transitions.Comment: 4 pages, REVTeX, 4 figures (postscript
Renormalization group approach to energy level statistics at the integer quantum Hall transition
We extend the real-space renormalization group (RG) approach to the study of
the energy level statistics at the integer quantum Hall (QH) transition.
Previously it was demonstrated that the RG approach reproduces the critical
distribution of the {\em power} transmission coefficients, i.e., two-terminal
conductances, , with very high accuracy. The RG flow of
at energies away from the transition yielded the value of the critical
exponent, , that agreed with most accurate large-size lattice simulations.
To obtain the information about the level statistics from the RG approach, we
analyze the evolution of the distribution of {\em phases} of the {\em
amplitude} transmission coefficient upon a step of the RG transformation. From
the fixed point of this transformation we extract the critical level spacing
distribution (LSD). This distribution is close, but distinctively different
from the earlier large-scale simulations. We find that away from the transition
the LSD crosses over towards the Poisson distribution. Studying the change of
the LSD around the QH transition, we check that it indeed obeys scaling
behavior. This enables us to use the alternative approach to extracting the
critical exponent, based on the LSD, and to find very close
to the value established in the literature. This provides additional evidence
for the surprising fact that a small RG unit, containing only five nodes,
accurately captures most of the correlations responsible for the
localization-delocalization transition.Comment: 10 pages, 11 figure
Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder
We theoretically study the effect of long-ranged inhomogeneities on the
critical properties of the integer quantum Hall transition. For this purpose we
employ the real-space renormalization-group (RG) approach to the network model
of the transition. We start by testing the accuracy of the RG approach in the
absence of inhomogeneities, and infer the correlation length exponent nu=2.39
from a broad conductance distribution. We then incorporate macroscopic
inhomogeneities into the RG procedure. Inhomogeneities are modeled by a smooth
random potential with a correlator which falls off with distance as a power
law, r^{-alpha}. Similar to the classical percolation, we observe an
enhancement of nu with decreasing alpha. Although the attainable system sizes
are large, they do not allow one to unambiguously identify a cusp in the
nu(alpha) dependence at alpha_c=2/nu, as might be expected from the extended
Harris criterion. We argue that the fundamental obstacle for the numerical
detection of a cusp in the quantum percolation is the implicit randomness in
the Aharonov-Bohm phases of the wave functions. This randomness emulates the
presence of a short-range disorder alongside the smooth potential.Comment: 10 pages including 6 figures, revised version as accepted for
publication in PR
An illustrated key to male Actinote from Southeastern Brazil (Lepidoptera, Nymphalidae)
How Offshore Groundwater Shapes the Seafloor
The MARCAN project, launched last January, is working to fill a gap in our knowledge of how freshwater flowing underground shapes and alters the continental margins