Invasion fronts with variable motility: phenotype selection, spatial sorting and wave acceleration

Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena of front acceleration (when the motility is unbounded) as well as other quantitative results, such as the selection of the most motile individuals (when the motility is bounded). The key argument for the construction and analysis of traveling fronts is the derivation of the dispersion relation linking the speed of the wave and the spatial decay. When the motility is unbounded we show that the position of the front scales as $t^{3/2}$. When the mutation rate is low we show that the canonical equation for the dynamics of the fittest trait should be stated as a PDE in our context. It turns out to be a type of Burgers equation with source term.Comment: 7 page

Influence of power take-off modelling on the far-field effects of wave energy converter farms

The study of the potential impact of wave energy converter (WEC) farms on the surrounding wave field at long distances from the WEC farm location (also know as “far field” effects) has been a topic of great interest in the past decade. Typically, “far-field” effects have been studied using phase average or phase resolving numerical models using a parametrization of the WEC power absorption using wave transmission coefficients. Most recent studies have focused on using coupled models between a wave-structure interaction solver and a wave-propagation model, which offer a more complex and accurate representation of the WEC hydrodynamics and PTO behaviour. The difference in the results between the two aforementioned approaches has not been studied yet, nor how different ways of modelling the PTO system can affect wave propagation in the lee of the WEC farm. The Coastal Engineering Research Group of Ghent University has developed both a parameterized model using the sponge layer technique in the mild slope wave propagation model MILDwave and a coupled model MILDwave-NEMOH (NEMOH is a boundary element method-based wave-structure interaction solver), for studying the “far-field” effects of WEC farms. The objective of the present study is to perform a comparison between both numerical approaches in terms of performance for obtaining the “far-field” effects of two WEC farms. Results are given for a series of regular wave conditions, demonstrating a better accuracy of the MILDwave-NEMOH coupled model in obtaining the wave disturbance coefficient (Kd) values around the considered WEC farms. Subsequently, the analysis is extended to study the influence of the PTO system modelling technique on the “far-field” effects by considering: (i) a linear optimal, (ii) a linear sub-optimal and (iii) a non-linear hydraulic PTO system. It is shown that modelling a linear optimal PTO system can lead to an unrealistic overestimation of the WEC motions than can heavily affect the wave height at a large distance in the lee of the WEC farm. On the contrary, modelling of a sub-optimal PTO system and of a hydraulic PTO system leads to a similar, yet reduced impact on the “far-field” effects on wave height. The comparison of the PTO systems’ modelling technique shows that when using coupled models, it is necessary to carefully model the WEC hydrodynamics and PTO behaviour as they can introduce substantial inaccuracies into the WECs’ motions and the WEC farm “far-field” effects

Analyzing the near-field effects and the power production of an array of heaving cylindrical WECs and OSWECs using a coupled hydrodynamic-PTO model

The Power Take-Off (PTO) system is the key component of a Wave Energy Converter (WEC) that distinguishes it from a simple floating body because the uptake of the energy by the PTO system modifies the wave field surrounding the WEC. Consequently, the choice of a proper PTO model of a WEC is a key factor in the accuracy of a numerical model that serves to validate the economic impact of a wave energy project. Simultaneously, the given numerical model needs to simulate many WEC units operating in close proximity in a WEC farm, as such conglomerations are seen by the wave energy industry as the path to economic viability. A balance must therefore be struck between an accurate PTO model and the numerical cost of running it for various WEC farm configurations to test the viability of any given WEC farm project. Because hydrodynamic interaction between the WECs in a farm modifies the incoming wave field, both the power output of a WEC farm and the surface elevations in the ‘near field’ area will be affected. For certain types of WECs, namely heaving cylindrical WECs, the PTO system strongly modifies the motion of the WECs. Consequently, the choice of a PTO system affects both the power production and the surface elevations in the ‘near field’ of a WEC farm. In this paper, we investigate the effect of a PTO system for a small wave farm that we term ‘WEC array’ of 5 WECs of two types: a heaving cylindrical WEC and an Oscillating Surge Wave Energy Converter (OSWEC). These WECs are positioned in a staggered array configuration designed to extract the maximum power from the incident waves. The PTO system is modelled in WEC-Sim, a purpose-built WEC dynamics simulator. The PTO system is coupled to the open-source wave structure interaction solver NEMOH to calculate the average wave field η in the ‘near-field’. Using a WEC-specific novel PTO system model, the effect of a hydraulic PTO system on the WEC array power production and the near-field is compared to that of a linear PTO system. Results are given for a series of regular wave conditions for a single WEC and subsequently extended to a 5-WEC array. We demonstrate the quantitative and qualitative differences in the power and the ‘near-field’ effects between a 5-heaving cylindrical WEC array and a 5-OSWEC array. Furthermore, we show that modeling a hydraulic PTO system as a linear PTO system in the case of a heaving cylindrical WEC leads to considerable inaccuracies in the calculation of average absorbed power, but not in the near-field surface elevations. Yet, in the case of an OSWEC, a hydraulic PTO system cannot be reduced to a linear PTO coefficient without introducing substantial inaccuracies into both the array power output and the near-field effects. We discuss the implications of our results compared to previous research on WEC arrays which used simplified linear coefficients as a proxy for PTO systems

Un cadre pour la réduction de modèle dans la simulation de structures assemblées

Les assemblages boulonnés influencent fortement l'amortissement et la rigidité des structures. Malheureusement, leur comportement mécanique reste difficile à prédire, principalement parce que les phénomènes physiques impliqués se produisent avec des échelles très différentes, taille des zones du contact réel et longueur d'onde des modes de vibration. Cela rend la méthode des éléments finis classiques difficile à utiliser parce que dans les zones de contact, le maillage doit être fin, alors qu'il peut être grossier ailleurs. Pour surmonter ces difficultés, le but de cet article est d'utiliser une décomposition en deux sous-domaines qui permet de travailler avec deux niveaux de discrétisation spatiale différents. La première idée consiste à résoudre alternativement les problèmes écrits sur les deux sous-domaines jusqu'à convergence. Ceci est fortement inspiré de la méthode LATIN mais adapté à l'étude des vibrations périodiques en utilisant la méthode de l'équilibrage harmonique (HBM) couplée à celle de l'algorithme ""alternating frequency time"" (AFT). La deuxième idée de ce travail est de réduire l'ordre du modèle en utilisant une projection sur base réduite (méthode de Ritz) et des méta-modèles couvrant le sous-espace qui contient les solutions

Linear Mixing Models for Active Listening of Music Productions in Realistic Studio Conditions

International audienceThe mixing/demixing of audio signals as addressed in the signal processing literature (the "source separation" problem) and the music production in studio remain quite separated worlds. Scienti c audio scene analysis rather focuses on "natural" mixtures and most often uses linear (convolutive) models of point sources placed in the same acoustic space. In contrast, the sound engineer can mix musical signals of very di erent nature and belonging to di erent acoustic spaces, and exploits many audio e ects including non-linear processes. In the present paper we discuss these di erences within the strongly emerging framework of active music listening, which is precisely at the crossroads of these two worlds: it consists in giving to the listener the ability to manipulate the di erent musical sources while listening to a musical piece. We propose a model that allows the description of a general studio mixing process as a linear stationary process of "generalized source image signals" considered as individual tracks. Such a model can be used to allow the recovery of the isolated tracks while preserving the professional sound quality of the mixture. A simple addition of these recovered tracks enables the end-user to recover the full-quality stereo mix, while these tracks can also be used for, e.g., basic remix / karaoke / soloing and re-orchestration applications

Optical surface waves on one-dimensional photonic crystals: investigation of loss mechanisms and demonstration of centimeter-scale propagation

It has been predicted that optical surface waves at interfaces that separate purely dielectric media should be able to propagate over long distances, particularly over distances greater than possible with surface plasmon polaritons. Despite numerous studies, there has been no report of such an observation, and an estimate of the propagation length achievable with dielectric optical surface waves is yet to be provided. In this work, we focus on the propagation properties of optical modes supported at the free surface of a one-dimensional photonic crystal. The contributions of intrinsic and extrinsic loss mechanisms are discussed. The developed understanding is applied to the design of structures that are optimized to support long propagating optical surface waves. We experimentally demonstrate, for the first time, the existence of optical surface waves capable of propagating over centimeter-scale distances in the visible spectral range. This result opens new perspectives for the use of optical surface waves in integrated optics and for light-matter interactions at interfaces.Comment: 11 pages, 4 figure

A Context-Driven Modelling Framework for Dynamic Authentication Decisions

International audienceNowadays, many mechanisms exist to perform authentication, such as text passwords and biometrics. However, reasoning about their relevance (e.g., the appropriateness for security and usability) regarding the contextual situation is challenging for authentication system designers. In this paper, we present a Context-driven Modelling Framework for dynamic Authentication decisions (COFRA), where the context information specifies the relevance of authentication mechanisms. COFRA is based on a precise metamodel that reveals framework abstractions and a set of constraints that specify their meaning. Therefore, it provides a language to determine the relevant authentication mechanisms (characterized by properties that ensure their appropriateness) in a given context. The framework supports the adaptive authentication system designers in the complex trade-off analysis between context information, risks and authentication mechanisms, according to usability, deployability, security, and privacy. We validate the proposed framework through case studies and extensive exchanges with authentication and modelling experts. We show that model instances describing real-world use cases and authentication approaches proposed in the literature can be instantiated validly according to our metamodel. This validation highlights the necessity, sufficiency, and soundness of our framework