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

Discrete scale invariance and complex dimensions

We discuss the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group equations in the seventies, complex exponents have been studied in the eighties in relation to various problems of physics embedded in hierarchical systems. Only recently has it been realized that discrete scale invariance and its associated complex exponents may appear ``spontaneously'' in euclidean systems, i.e. without the need for a pre-existing hierarchy. Examples are diffusion-limited-aggregation clusters, rupture in heterogeneous systems, earthquakes, animals (a generalization of percolation) among many other systems. We review the known mechanisms for the spontaneous generation of discrete scale invariance and provide an extensive list of situations where complex exponents have been found. This is done in order to provide a basis for a better fundamental understanding of discrete scale invariance. The main motivation to study discrete scale invariance and its signatures is that it provides new insights in the underlying mechanisms of scale invariance. It may also be very interesting for prediction purposes.Comment: significantly extended version (Oct. 27, 1998) with new examples in several domains of the review paper with the same title published in Physics Reports 297, 239-270 (1998

Boolean Delay Equations: A simple way of looking at complex systems

Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the classification of ordinary or partial differential equations. Solutions to certain conservative BDEs exhibit growth of complexity in time. They represent therewith metaphors for biological evolution or human history. Dissipative BDEs are structurally stable and exhibit multiple equilibria and limit cycles, as well as more complex, fractal solution sets, such as Devil's staircases and ``fractal sunbursts``. All known solutions of dissipative BDEs have stationary variance. BDE systems of this type, both free and forced, have been used as highly idealized models of climate change on interannual, interdecadal and paleoclimatic time scales. BDEs are also being used as flexible, highly efficient models of colliding cascades in earthquake modeling and prediction, as well as in genetics. In this paper we review the theory of systems of BDEs and illustrate their applications to climatic and solid earth problems. The former have used small systems of BDEs, while the latter have used large networks of BDEs. We moreover introduce BDEs with an infinite number of variables distributed in space (``partial BDEs``) and discuss connections with other types of dynamical systems, including cellular automata and Boolean networks. This research-and-review paper concludes with a set of open questions.Comment: Latex, 67 pages with 15 eps figures. Revised version, in particular the discussion on partial BDEs is updated and enlarge

Sizing hybrid green hydrogen energy generation and storage systems (HGHES) to enable an increase in renewable penetration for stabilising the grid.

A problem that has become apparently growing in the deployment of renewable energy systems is the power grids inability to accept the forecasted growth in renewable energy generation integration. To support forecasted growth in renewable generation integration, it is now recognised that Energy Storage Technologies (EST) must be utilised. Recent advances in Hydrogen Energy Storage Technologies (HEST) have unlocked their potential for use with constrained renewable generation. HEST combines Hydrogen production, storage and end use technologies with renewable generation in either a directly connected configuration, or indirectly via existing power networks. A levelised cost (LC) model has been developed within this thesis to identify the financial competitiveness of the different HEST application scenarios when used with grid constrained renewable energy. Five HEST scenarios have been investigated to demonstrate the most financially competitive configuration and the benefit that the by-product oxygen from renewable electrolysis can have on financial competitiveness. Furthermore, to address the lack in commercial software tools available to size an energy system incorporating HEST with limited data, a deterministic modelling approach has been developed to enable the initial automatic sizing of a hybrid renewable hydrogen energy system (HRHES) for a specified consumer demand. Within this approach, a worst-case scenario from the financial competitiveness analysis has been used to demonstrate that initial sizing of a HRHES can be achieved with only two input data, namely “ the available renewable resource and the load profile. The effect of the electrolyser thermal transients at start-up on the overall quantity of hydrogen produced (and accordingly the energy stored), when operated in conjunction with an intermittent renewable generation source, has also been modelled. Finally, a mass-transfer simulation model has been developed to investigate the suitability of constrained renewable generation in creating hydrogen for a hydrogen refuelling station

A variational approach to probing extreme events in turbulent dynamical systems

Extreme events are ubiquitous in a wide range of dynamical systems, including turbulent fluid flows, nonlinear waves, large scale networks and biological systems. Here, we propose a variational framework for probing conditions that trigger intermittent extreme events in high-dimensional nonlinear dynamical systems. We seek the triggers as the probabilistically feasible solutions of an appropriately constrained optimization problem, where the function to be maximized is a system observable exhibiting intermittent extreme bursts. The constraints are imposed to ensure the physical admissibility of the optimal solutions, i.e., significant probability for their occurrence under the natural flow of the dynamical system. We apply the method to a body-forced incompressible Navier--Stokes equation, known as the Kolmogorov flow. We find that the intermittent bursts of the energy dissipation are independent of the external forcing and are instead caused by the spontaneous transfer of energy from large scales to the mean flow via nonlinear triad interactions. The global maximizer of the corresponding variational problem identifies the responsible triad, hence providing a precursor for the occurrence of extreme dissipation events. Specifically, monitoring the energy transfers within this triad, allows us to develop a data-driven short-term predictor for the intermittent bursts of energy dissipation. We assess the performance of this predictor through direct numerical simulations.Comment: Minor revisions, generalized the constraints in Eq. (2

Models of turbulent dissipation regions in the diffuse interstellar medium

Supersonic turbulence is a large reservoir of suprathermal energy in the interstellar medium. Its dissipation, because it is intermittent in space and time, can deeply modify the chemistry of the gas. We further explore a hybrid method to compute the chemical and thermal evolution of a magnetized dissipative structure, under the energetic constraints provided by the observed properties of turbulence in the cold neutral medium. For the first time, we model a random line of sight by taking into account the relative duration of the bursts with respect to the thermal and chemical relaxation timescales of the gas. The key parameter is the turbulent rate of strain "a" due to the ambient turbulence. With the gas density, it controls the size of the dissipative structures, therefore the strength of the burst. For a large range of rates of strain and densities, the models of turbulent dissipation regions (TDR) reproduce the CH+ column densities observed in the diffuse medium and their correlation with highly excited H2. They do so without producing an excess of CH. As a natural consequence, they reproduce the abundance ratios of HCO+/OH and HCO+/H2O, and their dynamic range of about one order of magnitude observed in diffuse gas. Large C2H and CO abundances, also related to those of HCO+, are another outcome of the TDR models that compare well with observed values. The abundances and column densities computed for CN, HCN and HNC are one order of magnitude above PDR model predictions, although still significantly smaller than observed values

An agent-driven semantical identifier using radial basis neural networks and reinforcement learning

Due to the huge availability of documents in digital form, and the deception possibility raise bound to the essence of digital documents and the way they are spread, the authorship attribution problem has constantly increased its relevance. Nowadays, authorship attribution,for both information retrieval and analysis, has gained great importance in the context of security, trust and copyright preservation. This work proposes an innovative multi-agent driven machine learning technique that has been developed for authorship attribution. By means of a preprocessing for word-grouping and time-period related analysis of the common lexicon, we determine a bias reference level for the recurrence frequency of the words within analysed texts, and then train a Radial Basis Neural Networks (RBPNN)-based classifier to identify the correct author. The main advantage of the proposed approach lies in the generality of the semantic analysis, which can be applied to different contexts and lexical domains, without requiring any modification. Moreover, the proposed system is able to incorporate an external input, meant to tune the classifier, and then self-adjust by means of continuous learning reinforcement.Comment: Published on: Proceedings of the XV Workshop "Dagli Oggetti agli Agenti" (WOA 2014), Catania, Italy, Sepember. 25-26, 201

Optimization of stochastic lossy transport networks and applications to power grids

Motivated by developments in renewable energy and smart grids, we formulate a stylized mathematical model of a transport network with stochastic load fluctuations. Using an affine control rule, we explore the trade-off between the number of controllable resources in a lossy transport network and the performance gain they yield in terms of expected power losses. Our results are explicit and reveal the interaction between the level of flexibility, the intrinsic load uncertainty and the network structure.Comment: 30 pages, 10 figure