Quantification and prediction of extreme events in a one-dimensional nonlinear dispersive wave model

The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional non- linear model with deep-water waves dispersion relation, the Majda-McLaughlin-Tabak (MMT) model, in a dynamical regime that is characterized by broadband spectrum and strong non- linear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A stochastic analysis of the Gabor coefficients reveals i) the low-dimensionality of the intermittent structures, ii) the interplay between non-Gaussian statis- tical properties and nonlinear energy transfers between modes, as well as iii) the critical scales (or critical Gabor coefficients) where a critical amount of energy can trigger the formation of an extreme event. We analyze the unstable character of these special localized modes directly through the system equation and show that these intermittent events are due to the interplay of the system nonlinearity, the wave dispersion, and the wave dissipation which mimics wave breaking. These localized instabilities are triggered by random localizations of energy in space, created by the dispersive propagation of low-amplitude waves with random phase. Based on these properties, we design low-dimensional functionals of these Gabor coefficients that allow for the prediction of the extreme event well before the nonlinear interactions begin to occur.Comment: 21 pages, 14 figure

Reduced-order precursors of rare events in unidirectional nonlinear water waves

We consider the problem of short-term prediction of rare, extreme water waves in irregular unidirectional fields, a critical topic for ocean structures and naval operations. One possible mechanism for the occurrence of such rare, unusually intense waves is nonlinear wave focusing. Recent results have demonstrated that random localizations of energy, induced by the linear dispersive mixing of different harmonics, can grow significantly due to modulation instability. Here we show how the interplay between (i) modulation instability properties of localized wave groups and (ii) statistical properties of wave groups that follow a given spectrum defines a critical length scale associated with the formation of extreme events. The energy that is locally concentrated over this length scale acts as the ‘trigger’ of nonlinear focusing for wave groups and the formation of subsequent rare events. We use this property to develop inexpensive, short-term predictors of large water waves, circumventing the need for solving the governing equations. Specifically, we show that by merely tracking the energy of the wave field over the critical length scale allows for the robust, inexpensive prediction of the location of intense waves with a prediction window of 25 wave periods. We demonstrate our results in numerical experiments of unidirectional water wave fields described by the modified nonlinear Schrödinger equation. The presented approach introduces a new paradigm for understanding and predicting intermittent and localized events in dynamical systems characterized by uncertainty and potentially strong nonlinear mechanisms.Naval Engineering Education Center (Grant 3002883706)United States. Office of Naval Research (Grant ONR N00014-14-1-0520

Unsteady evolution of localized unidirectional deep-water wave groups

We study the evolution of localized wave groups in unidirectional water wave envelope equations [the nonlinear Schrodinger (NLSE) and the modified NLSE (MNLSE)]. These localizations of energy can lead to disastrous extreme responses (rogue waves). We analytically quantify the role of such spatial localization, introducing a technique to reduce the underlying partial differential equation dynamics to a simple ordinary differential equation for the wave packet amplitude. We use this reduced model to show how the scale-invariant symmetries of the NLSE break down when the additional terms in the MNLSE are included, inducing a critical scale for the occurrence of extreme waves.Naval Engineering Education Center (Grant 3002883706)United States. Office of Naval Research (Grant N00014-14-1-0520

A probabilistic decomposition-synthesis method for the quantification of rare events due to internal instabilities

We consider the problem of the probabilistic quantification of dynamical systems that have heavy-tailed characteristics. These heavy-tailed features are associated with rare transient responses due to the occurrence of internal instabilities. Systems with these properties can be found in a variety of areas including mechanics, fluids, and waves. Here we develop a computational method, a probabilistic decomposition-synthesis technique, that takes into account the nature of internal instabilities to inexpensively determine the non-Gaussian probability density function for any arbitrary quantity of interest. Our approach relies on the decomposition of the statistics into a 'non-extreme core', typically Gaussian, and a heavy-tailed component. This decomposition is in full correspondence with a partition of the phase space into a 'stable' region where we have no internal instabilities, and a region where non-linear instabilities lead to rare transitions with high probability. We quantify the statistics in the stable region using a Gaussian approximation approach, while the non-Gaussian distribution associated with the intermittently unstable regions of phase space is inexpensively computed through order-reduction methods that take into account the strongly nonlinear character of the dynamics. The probabilistic information in the two domains is analytically synthesized through a total probability argument. The proposed approach allows for the accurate quantification of non-Gaussian tails at more than 10 standard deviations, at a fraction of the cost associated with the direct Monte-Carlo simulations. We demonstrate the probabilistic decomposition-synthesis method for rare events for two dynamical systems exhibiting extreme events: a twodegree-of-freedom system of nonlinearly coupled oscillators, and in a nonlinear envelope equation characterizing the propagation of unidirectional water waves

Training future generations to deliver evidence-based conservation and ecosystem management

1. To be effective, the next generation of conservation practitioners and managers need to be critical thinkers with a deep understanding of how to make evidence-based decisions and of the value of evidence synthesis. 2. If, as educators, we do not make these priorities a core part of what we teach, we are failing to prepare our students to make an effective contribution to conservation practice. 3. To help overcome this problem we have created open access online teaching materials in multiple languages that are stored in Applied Ecology Resources. So far, 117 educators from 23 countries have acknowledged the importance of this and are already teaching or about to teach skills in appraising or using evidence in conservation decision-making. This includes 145 undergraduate, postgraduate or professional development courses. 4. We call for wider teaching of the tools and skills that facilitate evidence-based conservation and also suggest that providing online teaching materials in multiple languages could be beneficial for improving global understanding of other subject areas.Peer reviewe

Liberty County Strategic Plan 2016 - 2036

In the fall of 2015, the County of Liberty and Texas Target Communities partnered to create a task force to represent the community. The task force was integral to the planning process, contributing the thoughts, desires, and opinions of community members—as well as their enthusiasm about Liberty’s future. This fourteen-month planning process ended in August 2016. The result of this collaboration is the County of Liberty Strategic Plan, which is the official policy guide for the community’s growth over the next twenty years.Liberty Strategic Plan 2036 provides a guide for the future growth of the county. This document was developed by Texas Target Communities in partnership with the County of Liberty

Differential cross section measurements for the production of a W boson in association with jets in proton–proton collisions at √s = 7 TeV

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pT) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 fb[superscript −1]. The measured cross sections are compared to predictions from Monte Carlo generators, MadGraph + pythia and sherpa, and to next-to-leading-order calculations from BlackHat + sherpa. The differential cross sections are found to be in agreement with the predictions, apart from the pT distributions of the leading jets at high pT values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.United States. Dept. of EnergyNational Science Foundation (U.S.)Alfred P. Sloan Foundatio