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, $P_{\text c}(G)$, with very high accuracy. The RG flow of $P(G)$ at energies away from the transition yielded the value of the critical exponent, $\nu$, 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 $\nu=2.37\pm0.02$ 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

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