Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner

We investigate the eigenvalue problem $-\text{div}(\sigma \nabla u) = \lambda u\ (\mathscr{P})$ in a 2D domain $\Omega$ divided into two regions $\Omega_{\pm}$. We are interested in situations where $\sigma$ takes positive values on $\Omega_{+}$ and negative ones on $\Omega_{-}$. Such problems appear in time harmonic electromagnetics in the modeling of plasmonic technologies. In a recent work [15], we highlighted an unusual instability phenomenon for the source term problem associated with $(\mathscr{P})$: for certain configurations, when the interface between the subdomains $\Omega_{\pm}$ presents a rounded corner, the solution may depend critically on the value of the rounding parameter. In the present article, we explain this property studying the eigenvalue problem $(\mathscr{P})$. We provide an asymptotic expansion of the eigenvalues and prove error estimates. We establish an oscillatory behaviour of the eigenvalues as the rounding parameter of the corner tends to zero. We end the paper illustrating this phenomenon with numerical experiments.Comment: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 09/12/2016. arXiv admin note: text overlap with arXiv:1304.478

On the Convergence of Population Protocols When Population Goes to Infinity

Population protocols have been introduced as a model of sensor networks consisting of very limited mobile agents with no control over their own movement. A population protocol corresponds to a collection of anonymous agents, modeled by finite automata, that interact with one another to carry out computations, by updating their states, using some rules. Their computational power has been investigated under several hypotheses but always when restricted to finite size populations. In particular, predicates stably computable in the original model have been characterized as those definable in Presburger arithmetic. We study mathematically the convergence of population protocols when the size of the population goes to infinity. We do so by giving general results, that we illustrate through the example of a particular population protocol for which we even obtain an asymptotic development. This example shows in particular that these protocols seem to have a rather different computational power when a huge population hypothesis is considered.Comment: Submitted to Applied Mathematics and Computation. 200

Efficacy of herbicide spray droplet size, flooding period, and seed burial depth on Palmer amaranth (Amaranthus palmeri S. Wats.) control

The continued spread of Palmer amaranth (Amaranthus palmeri S. Wats.) throughout the southern and midwestern United States is a result of herbicide-resistant populations. Besides being the most troublesome weed specie in several agronomic crops, Palmer amaranth is also host to economically important pests such as tarnished plant bug (Lygus lineolaris Palisot de Beauvois). Pesticide application methodology that maximizes efficacy while reducing selection pressure is needed to combat herbicide-resistant Palmer amaranth. Pulse width modulation (PWM) sprayers are used for pesticide application with the goal of maintaining product efficacy while mitigating spray drift. Additionally, alternative off-season weed management practices such as flooding could be adopted to optimize soil seedbank depletion. Therefore, evaluation of spray droplet size and flooding period on Palmer amaranth control and seed germination was conducted. The objectives of this research were to: (1) evaluate the influence of spray droplet size on lactofen and acifluorfen efficacy on Palmer amaranth using a PWM sprayer, (2) develop prediction models to determine spray droplet size that provides the greatest level of Palmer amaranth control, (3) evaluate the impact of flooding period and seed burial depth on Palmer amaranth seed germination in different soil textures, and (4) analyze the impact of nitrogen fertilizer application rate on the attractiveness of Palmer amaranth to tarnished plant bug. Results show that spray droplet size does not affect lactofen efficacy on Palmer amaranth, thus, coarser spray droplets are recommended to increase spray drift mitigation efforts. In contrast, acifluorfen applied with 300 μm (medium) spray droplets provided the greatest Palmer amaranth control. Furthermore, prediction models indicated that greater model accuracy was obtained when adopting a location-specific weed management approach. Flooding periods of 3, 4, and 5 months reduced Palmer amaranth seed germination across burial depths and soil textures. Therefore, fall-winter flooding may be adopted as an effective practice for soil seedbank depletion. Results also demonstrated that nitrogen fertilizer application rate does not consistently impact Palmer amaranth attractiveness to tarnished plant bug

Contact Lie systems

We define and analyse the properties of contact Lie systems, namely systems of first-order differential equations describing the integral curves of a $t$-dependent vector field taking values in a finite-dimensional Lie algebra of Hamiltonian vector fields relative to a contact structure. As a particular example, we study families of conservative contact Lie systems. Liouville theorems, contact reductions, and Gromov non-squeezing theorems are developed and applied to contact Lie systems. Our results are illustrated by examples with relevant physical and mathematical applications, e.g. Schwarz equations, Brockett systems, etcetera.Comment: 29 pp, 4 figures. New version of the manuscript with Sections 4, 5.4, and 6 added. Many new results included and typos correcte

On Darboux theorems for geometric structures induced by closed forms

This work reviews the classical Darboux theorem for symplectic, presymplectic, and cosymplectic manifolds (which are used to describe regular and singular mechanical systems), and certain cases of multisymplectic manifolds, and extends it in new ways to k-symplectic and k-cosymplectic manifolds (all these structures appear in the geometric formulation of first-order classical field theories). Moreover, we discuss the existence of Darboux theorems for classes of precosymplectic, k-presymplectic, k-precosymplectic, and premultisymplectic manifolds, which are the geometrical structures underlying some kinds of singular field theories. Approaches to Darboux theorems based on flat connections associated with geometric structures are given, while new results on polarisations for (k-)(pre)(co)symplectic structures arise.Comment: improved and extended proofs. 33 p

Semantic and Visual Similarities for Efficient Knowledge Transfer in CNN Training

International audienceIn recent years, representation learning approaches have disrupted many multimedia computing tasks. Among those approaches, deep convolutional neural networks (CNNs) have notably reached human level expertise on some constrained image classification tasks. Nonetheless, training CNNs from scratch for new task or simply new data turns out to be complex and time-consuming. Recently, transfer learning has emerged as an effective methodology for adapting pre-trained CNNs to new data and classes, by only retraining the last classification layer. This paper focuses on improving this process, in order to better transfer knowledge between CNN architectures for faster trainings in the case of fine tuning for image classification. This is achieved by combining and transfering supplementary weights, based on similarity considerations between source and target classes. The study includes a comparison between semantic and content-based similarities, and highlights increased initial performances and training speed, along with superior long term performances when limited training samples are available