Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves

In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal direction. The proof is based upon the classical variational principle that a solitary wave of this type is a critical point of the energy subject to the constraint that the momentum is fixed. We prove the existence of a minimiser of the energy subject to the constraint that the momentum is fixed and small. The existence of a small-amplitude solitary wave is thus assured, and since the energy and momentum are both conserved quantities a standard argument may be used to establish the stability of the set of minimisers as a whole. `Stability' is however understood in a qualified sense due to the lack of a global well-posedness theory for three-dimensional water waves.Comment: 83 pages, 1 figur

Interview with Lydia Groves

An interview with Lydia Groves regarding her experiences in a one-room school house.https://scholars.fhsu.edu/ors/1063/thumbnail.jp

A cortical potential reflecting cardiac function

Emotional trauma and psychological stress can precipitate cardiac arrhythmia and sudden death through arrhythmogenic effects of efferent sympathetic drive. Patients with preexisting heart disease are particularly at risk. Moreover, generation of proarrhythmic activity patterns within cerebral autonomic centers may be amplified by afferent feedback from a dysfunctional myocardium. An electrocortical potential reflecting afferent cardiac information has been described, reflecting individual differences in interoceptive sensitivity (awareness of one's own heartbeats). To inform our understanding of mechanisms underlying arrhythmogenesis, we extended this approach, identifying electrocortical potentials corresponding to the cortical expression of afferent information about the integrity of myocardial function during stress. We measured changes in cardiac response simultaneously with electroencephalography in patients with established ventricular dysfunction. Experimentally induced mental stress enhanced cardiovascular indices of sympathetic activity (systolic blood pressure, heart rate, ventricular ejection fraction, and skin conductance) across all patients. However, the functional response of the myocardium varied; some patients increased, whereas others decreased, cardiac output during stress. Across patients, heartbeat-evoked potential amplitude at left temporal and lateral frontal electrode locations correlated with stress-induced changes in cardiac output, consistent with an afferent cortical representation of myocardial function during stress. Moreover, the amplitude of the heartbeat-evoked potential in the left temporal region reflected the proarrhythmic status of the heart (inhomogeneity of left ventricular repolarization). These observations delineate a cortical representation of cardiac function predictive of proarrhythmic abnormalities in cardiac repolarization. Our findings highlight the dynamic interaction of heart and brain in stress-induced cardiovascular morbidity

Gravity travelling waves for two superposed fluid layers, one being of infinite depth: a new type of bifurcation

International audienceIn this paper, we study the travelling gravity waves in a system of two layers of perfect fluids, the bottom one being infinitely deep, the upper one having a finite thickness h. We assume that the flow is potential, and the dimensionless parameters are the ratio between densities ρ = ρ 2 /ρ 1 and λ = gh/c^2. We study special values of the parameters such that λ(1 − ρ) is near 1 − , where a bifurcation of a new type occurs. We formulate the problem as a spatial reversible dynamical system, where U = 0 corresponds to a uniform state (velocity c in a moving reference frame), and we consider the linearized operator around 0. We show that its spectrum contains the entire real axis (essential spectrum), with in addition a double eigenvalue in 0, a pair of simple imaginary eigenvalues ±iλ at a distance O(1) from 0, and for λ(1 − ρ) above 1, another pair of simple imaginary eigenvalues tending towards 0 as λ(1 − ρ) → 1 +. When λ(1 − ρ) ≤ 1 this pair disappears into the essential spectrum. The rest of the spectrum lies at a distance at least O(1) from the imaginary axis. We show in this paper that for λ(1 − ρ) close to 1 − , there is a family of periodic solutions like in the Lyapunov-Devaney theorem (despite the resonance due to the point 0 in the spectrum). Moreover, showing that the full system can be seen as a perturbation of the Benjamin-Ono equation, coupled with a nonlinear oscillation, we also prove the existence of a family of homoclinic connections to these periodic orbits, provided that these ones are not too small

Altimeter sampling characteristics using a single satellite

This is the published version. Copyright 1998 WileyAltimetric satellites have characteristic sampling patterns in both space and time based on their repeat period and orbit inclination. Aliased phenomena measured by altimetric measurements can appear as propagating waves with both wavelength and direction of propagation different from the underlying phenomena. All signals that contribute to the altimetric measurement can be aliased and produce such patterns, not just tidal signals. For example, mesoscale energy will be aliased as will unmodeled atmospheric variations. Past discussions of aliasing have only considered spatially homogeneous signals. This paper extends this work to phenomena with finite wavelengths and considers both the north-south and east-west components of the resulting aliases

Effect of reminders on mitigating participation bias in a case-control study

BACKGROUND: Researchers commonly employ strategies to increase participation in health studies. These include use of incentives and intensive reminders. There is, however, little evidence regarding the quantitative effect that such strategies have on study results. We present an analysis of data from a case-control study of Campylobacter enteritis in England to assess the usefulness of a two-reminder strategy for control recruitment. METHODS: We compared sociodemographic characteristics of participants and non-participants, and calculated odds ratio estimates for a wide range of risk factors by mailing wave. RESULTS: Non-participants were more often male, younger and from more deprived areas. Among participants, early responders were more likely to be female, older and live in less deprived areas, but despite these differences, we found little evidence of a systematic bias in the results when using data from early reponders only. CONCLUSIONS: We conclude that the main benefit of using reminders in our study was the gain in statistical power from a larger sample size

Satellite mapping in cities and below cities: how good is it now?

Global navigation satellite systems (GNSS) have existed since the launch of the US global positioning system constellation in 1978. There is an increasing need for better maps in the digital age, particularly for buried utilities. One of the most convenient methods for creating accurate maps is the use of navigation satellites for positioning. However, built-up urban areas are not ideal for the use of this positioning technology. This paper provides an update on the situation regarding GNSS and assesses how new satellites and signals are contributing to better positioning availability by carrying out a test in a controlled environment. The results show that using combined satellite systems improves availability in urban canyons in some cases, but not in all scenarios. In addition, pipeline mapping technology has been tested and been shown to be an effective means of mapping pipes deep under the ground over short distances

An atmospheric source of S in Mesoarchaean structurally-controlled gold mineralisation of the Barberton Greenstone Belt

The Barberton Greenstone Belt of southern Africa hosts several Mesoarchaean gold deposits. The ores were mostly formed in greenschist facies conditions, and occur as hydrothermal alteration zones around extensional faults that truncate and post-date the main compressional structures of the greenstone belt. Ore deposition was accompanied by the intrusion of porphyries, which has led to the hypothesis that gold may have been sourced from magmas. Because the transport of Au in the hydrothermal fluids is widely believed to have involved S complexes, tracing the origin of S may place strong constraints on the origin of Au. We measured multiple S isotopes in sulfide ore from Sheba and Fairview mines of the Barberton Greenstone Belt to distinguish “deep” S sources (e.g. magmas) from “surface” S sources (i.e. rocks of the volcano-sedimentary succession that contain S processed in the atmosphere preserved as sulfide and sulfate minerals). Ion probe (SIMS) analyses of pyrite from ore zones indicate mass-independent fractionation of S isotopes (Δ33S = −0.6‰ to +1.0‰) and the distribution of the analyses in the Δ33S–δ34S space matches the distribution peak of previously published analyses of pyrite from the entire volcano-sedimentary succession. Notwithstanding that the H2O–CO2 components of the fluids may have been introduced from a deep source external to the greenstone belt rocks, the fact that S bears an atmospheric signature suggests the hypothesis that the source of Au should also be identified in the supracrustal succession of the greenstone belt. Our findings differ from conclusions of previous studies of other Archaean shear-hosted Au deposits based on mineralogical and isotopic evidence, which suggested a magmatic or mantle source for Au, and imply that there is no single model that can be applied to this type of mineralisation in the Archaean