High-Q spectral peaks and nonstationarity in the deep ocean infragravity wave band: Tidal harmonics and solar normal modes

Author Posting. © American Geophysical Union, 2019. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research-Oceans 124(3), (2019):2072-2087, doi:10.1029/2018JC014586.Infragravity waves have received the least study of any class of waves in the deep ocean. This paper analyzes a 389‐day‐long deep ocean pressure record from the Hawaii Ocean Mixing Experiment for the presence of narrowband (≲2 μHz) components and nonstationarity over 400–4,000 μHz using a combination of fitting a mixture noncentral/central χ2 model to spectral estimates, high‐resolution multitaper spectral estimation, and computation of the offset coherence between distinct frequencies for a given data segment. In the frequency band 400–1,000 μHz there is a noncentral fraction of 0.67 ± 0.07 that decreases with increasing frequency. Evidence is presented for the presence of tidal harmonics in the data over the 400‐ to 1,400‐μHz bands. Above ~2,000 μHz the noncentral fraction rises with frequency, comprising about one third of the spectral estimates over 3,000–4,000 μHz. The power spectrum exhibits frequent narrowband peaks at 6–11 standard deviations above the noise level. The widths of the peaks correspond to a Q of at least 1,000, vastly exceeding that of any oceanic or atmospheric process. The offset coherence shows that the spectral peaks have substantial (p = 0.99–0.9999) interfrequency correlation, both locally and between distinct peaks within a given analysis band. Many of the peak frequencies correspond to the known values for solar pressure modes that have previously been observed in solar wind and terrestrial data, while others are the result of nonstationarity that distributes power across frequency. Overall, this paper documents the existence of two previously unrecognized sources of infragravity wave variability in the deep ocean.This work was supported at WHOI by an Independent Research and Development award and the Walter A. and Hope Noyes Smith Chair for Excellence in Oceanography. At the University of Hawaii, Martin Guiles provided a number of consequential data analyses, and work was supported by NSF‐OCE1460022. D. J. T. acknowledges support from Queen's University and NSERC. The data used in this study are available from the supporting information.2019-08-2

Finite time and asymptotic behaviour of the maximal excursion of a random walk

We evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self-similar supports under the assumption of spherical symmetry. This distribution is obtained in closed form and is an approximation of the exact distribution comparable to that obtained by real space renormalization methods. Then we focus on the early time behaviour of this quantity. The instantaneous diffusion exponent $\nu_n$ exhibits a systematic overshooting of the long time exponent. Exact results are obtained in one dimension up to third order in $n^{-1/2}$. In two dimensions, on a regular lattice and on the Sierpi\'nski gasket we find numerically that the analytic scaling $\nu_n \simeq \nu+A n^{-\nu}$ holds.Comment: 9 pages, 4 figures, accepted J. Phys.

Ecological equivalence: a realistic assumption for niche theory as a testable alternative to neutral theory

Hubbell's 2001 neutral theory unifies biodiversity and biogeography by modelling steady-state distributions of species richness and abundances across spatio-temporal scales. Accurate predictions have issued from its core premise that all species have identical vital rates. Yet no ecologist believes that species are identical in reality. Here I explain this paradox in terms of the ecological equivalence that species must achieve at their coexistence equilibrium, defined by zero net fitness for all regardless of intrinsic differences between them. I show that the distinction of realised from intrinsic vital rates is crucial to evaluating community resilience. An analysis of competitive interactions reveals how zero-sum patterns of abundance emerge for species with contrasting life-history traits as for identical species. I develop a stochastic model to simulate community assembly from a random drift of invasions sustaining the dynamics of recruitment following deaths and extinctions. Species are allocated identical intrinsic vital rates for neutral dynamics, or random intrinsic vital rates and competitive abilities for niche dynamics either on a continuous scale or between dominant-fugitive extremes. Resulting communities have steady-state distributions of the same type for more or less extremely differentiated species as for identical species. All produce negatively skewed log-normal distributions of species abundance, zero-sum relationships of total abundance to area, and Arrhenius relationships of species to area. Intrinsically identical species nevertheless support fewer total individuals, because their densities impact as strongly on each other as on themselves. Truly neutral communities have measurably lower abundance/area and higher species/abundance ratios. Neutral scenarios can be parameterized as null hypotheses for testing competitive release, which is a sure signal of niche dynamics. Ignoring the true strength of interactions between and within species risks a substantial misrepresentation of community resilience to habitat los

Contact spheres and hyperk\"ahler geometry

A taut contact sphere on a 3-manifold is a linear 2-sphere of contact forms, all defining the same volume form. In the present paper we completely determine the moduli of taut contact spheres on compact left-quotients of SU(2) (the only closed manifolds admitting such structures). We also show that the moduli space of taut contact spheres embeds into the moduli space of taut contact circles. This moduli problem leads to a new viewpoint on the Gibbons-Hawking ansatz in hyperkahler geometry. The classification of taut contact spheres on closed 3-manifolds includes the known classification of 3-Sasakian 3-manifolds, but the local Riemannian geometry of contact spheres is much richer. We construct two examples of taut contact spheres on open subsets of 3-space with nontrivial local geometry; one from the Helmholtz equation on the 2-sphere, and one from the Gibbons-Hawking ansatz. We address the Bernstein problem whether such examples can give rise to complete metrics.Comment: 29 pages, v2: Large parts have been rewritten; previous Section 6 has been removed; new Section 5.2 on the Gibbons-Hawking ansatz; new Sections 6 and

Spatial effects on species persistence and implications for biodiversity

Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance distributions are examples of emerging patterns irrespective of the details of the underlying ecosystem functions. Here we present empirical and theoretical evidence for a new macroecological pattern related to the distributions of local species persistence times, defined as the timespans between local colonizations and extinctions in a given geographic region. Empirical distributions pertaining to two different taxa, breeding birds and herbaceous plants, analyzed in a new framework that accounts for the finiteness of the observational period, exhibit power-law scaling limited by a cut-off determined by the rate of emergence of new species. In spite of the differences between taxa and spatial scales of analysis, the scaling exponents are statistically indistinguishable from each other and significantly different from those predicted by existing models. We theoretically investigate how the scaling features depend on the structure of the spatial interaction network and show that the empirical scaling exponents are reproduced once a two-dimensional isotropic texture is used, regardless of the details of the ecological interactions. The framework developed here also allows to link the cut-off timescale with the spatial scale of analysis, and the persistence-time distribution to the species-area relationship. We conclude that the inherent coherence obtained between spatial and temporal macroecological patterns points at a seemingly general feature of the dynamical evolution of ecosystems.Comment: 5 pages, 5 figures. Supplementary materials avaliable on http://www.pnas.org/content/108/11/434

Concerted changes in tropical forest structure and dynamics: evidence from 50 South American long-term plots

Several widespread changes in the ecology of old-growth tropical forests have recently been documented for the late twentieth century, in particular an increase in stem turnover (pan-tropical), and an increase in above-ground biomass (neotropical). Whether these changes are synchronous and whether changes in growth are also occurring is not known. We analysed stand-level changes within 50 long-term. monitoring plots from across South America spanning 1971-2002. We show that: (i) basal area (BA: sum of the cross-sectional areas of all trees in a plot) increased significantly over time (by 0.10 +/- 0.04 m(2) ha(-1) yr(-1), mean +/- 95% CI); as did both (ii) stand-level BA growth rates (sum of the increments of BA of surviving trees and BA of new trees that recruited into a plot); and (iii) stand-level BA mortality rates (sum of the cross-sectional areas of all trees that died in a plot). Similar patterns were observed on a per-stem basis: (i) stem density (number of stems per hectare; 1 hectare is 10(4) m(2)) increased significantly over time (0.94 +/- 0.63 stems ha(-1) yr(-1)); as did both (ii) stem recruitment rates; and (iii) stem mortality rates. In relative terms, the pools of BA and stem density increased by 0.38 +/- 0.15% and 0.18 +/- 0.12% yr(-1), respectively. The fluxes into and out of these pools-stand-level BA growth, stand-level BA mortality, stem recruitment and stem mortality rates-increased, in relative terms, by an order of magnitude more. The gain terms (BA growth, stem recruitment) consistently exceeded the loss terms (BA loss, stem mortality) throughout the period, suggesting that whatever process is driving these changes was already acting before the plot network was established. Large long-term increases in stand-level BA growth and simultaneous increases in stand BA and stem density imply a continent-wide increase in resource availability which is increasing net primary productivity and altering forest dynamics. Continent-wide changes in incoming solar radiation, and increases in atmospheric concentrations of CO2 and air temperatures may have increased resource supply over recent decades, thus causing accelerated growth and increased dynamism across the world's largest tract of tropical forest

Localization of thermal packets and metastable states in Sinai model

We consider the Sinai model describing a particle diffusing in a 1D random force field. As shown by Golosov, this model exhibits a strong localization phenomenon for the thermal packet: the disorder average of the thermal distribution of the relative distance y=x-m(t), with respect to the (disorder-dependent) most probable position m(t), converges in the limit of infinite time towards a distribution P(y). In this paper, we revisit this question of the localization of the thermal packet. We first generalize the result of Golosov by computing explicitly the joint asymptotic distribution of relative position y=x(t)-m(t) and relative energy u=U(x(t))-U(m(t)) for the thermal packet. Next, we compute in the infinite-time limit the localization parameters Y_k, representing the disorder-averaged probabilities that k particles of the thermal packet are at the same place, and the correlation function C(l) representing the disorder-averaged probability that two particles of the thermal packet are at a distance l from each other. We moreover prove that our results for Y_k and C(l) exactly coincide with the thermodynamic limit of the analog quantities computed for independent particles at equilibrium in a finite sample of length L. Finally, we discuss the properties of the finite-time metastable states that are responsible for the localization phenomenon and compare with the general theory of metastable states in glassy systems, in particular as a test of the Edwards conjecture.Comment: 17 page

Pliocene Te Aute limestones, New Zealand: Expanding concepts for cool-water shelf carbonates

Acceptance of a spectrum of warm- through cold-water shallow-marine carbonate facies has become of fundamental importance for correctly interpreting the origin and significance of all ancient platform limestones. Among other attributes, properties that have become a hallmark for characterising many Cenozoic non-tropical occurrences include: (1) the presence of common bryozoan and epifaunal bivalve skeletons; (2) a calcite-dominated mineralogy; (3) relatively thin deposits exhibiting low rates of sediment accumulation; (4) an overall destructive early diagenetic regime; and (5) that major porosity destruction and lithification occur mainly in response to chemical compaction of calcitic skeletons during moderate to deep burial. The Pliocene Te Aute limestones are non-tropical skeletal carbonates formed at paleolatitudes near 40-42°S under the influence of commonly strong tidal flows along the margins of an actively deforming and differentially uplifting forearc basin seaway, immediately inboard of the convergent Pacific-Australian plate boundary off eastern North Island, New Zealand. This dynamic depositional and tectonic setting strongly influenced both the style and subsequent diagenetic evolution of the limestones. Some of the Te Aute limestones exhibit the above kinds of "normal" non-tropical characteristics, but others do not. For example, many are barnacle and/or bivalve dominated, and several include attributes that at least superficially resemble properties of certain tropical carbonates. In this regard, a number of the limestones are infaunal bivalve rich and dominated by an aragonite over a calcite primary mineralogy, with consequently relatively high diagenetic potential. Individual limestone units are also often rather thick (e.g., up to 50-300 m), with accumulation rates from 0.2 to 0.5 m/ka, and locally as high as 1 m/ka. Moreover, there can be a remarkable array of diagenetic features in the limestones, involving grain alteration and/or cementation to widely varying extents within any, or some combination of, the marine phreatic, burial, and meteoric diagenetic environments, including locally widespread development of meteoric cement sourced from aragonite dissolution. The message is that non-tropical shelf carbonates include a more diverse array of geological settings, of skeletal and mineralogical facies, and of diagenetic features than current sedimentary models mainly advocate. While several attributes positively distinguish tropical from non-tropical limestones, continued detailed documentation of the wide spectrum of shallow-marine carbonate deposits formed outside tropical regions remains an important challenge in carbonate sedimentology

Anomalous diffusion, Localization, Aging and Sub-aging effects in trap models at very low temperature

We study in details the dynamics of the one dimensional symmetric trap model, via a real-space renormalization procedure which becomes exact in the limit of zero temperature. In this limit, the diffusion front in each sample consists in two delta peaks, which are completely out of equilibrium with each other. The statistics of the positions and weights of these delta peaks over the samples allows to obtain explicit results for all observables in the limit $T \to 0$. We first compute disorder averages of one-time observables, such as the diffusion front, the thermal width, the localization parameters, the two-particle correlation function, and the generating function of thermal cumulants of the position. We then study aging and sub-aging effects : our approach reproduces very simply the two different aging exponents and yields explicit forms for scaling functions of the various two-time correlations. We also extend the RSRG method to include systematic corrections to the previous zero temperature procedure via a series expansion in $T$. We then consider the generalized trap model with parameter $\alpha \in [0,1]$ and obtain that the large scale effective model at low temperature does not depend on $\alpha$ in any dimension, so that the only observables sensitive to $\alpha$ are those that measure the `local persistence', such as the probability to remain exactly in the same trap during a time interval. Finally, we extend our approach at a scaling level for the trap model in $d=2$ and obtain the two relevant time scales for aging properties.Comment: 33 pages, 3 eps figure