Nonlinear Preconditioning: How to use a Nonlinear Schwarz Method to Precondition Newton's Method

For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much better residual polynomial than the stationary iteration, and thus converges much faster. We show in this paper that also for non-linear problems, domain decomposition methods can either be used directly as iterative solvers, or one can use them as preconditioners for Newton's method. For the concrete case of the parallel Schwarz method, we show that we obtain a preconditioner we call RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) which is similar to ASPIN (Additive Schwarz Preconditioned Inexact Newton), but with all components directly defined by the iterative method. This has the advantage that RASPEN already converges when used as an iterative solver, in contrast to ASPIN, and we thus get a substantially better preconditioner for Newton's method. The iterative construction also allows us to naturally define a coarse correction using the multigrid full approximation scheme, which leads to a convergent two level non-linear iterative domain decomposition method and a two level RASPEN non-linear preconditioner. We illustrate our findings with numerical results on the Forchheimer equation and a non-linear diffusion problem

The relativistic solar particle event of 2005 January 20: origin of delayed particle acceleration

The highest energies of solar energetic nucleons detected in space or through gamma-ray emission in the solar atmosphere are in the GeV range. Where and how the particles are accelerated is still controversial. We search for observational information on the location and nature of the acceleration region(s) by comparing the timing of relativistic protons detected on Earth and radiative signatures in the solar atmosphere during the particularly well-observed 2005 Jan. 20 event. This investigation focuses on the post-impulsive flare phase, where a second peak was observed in the relativistic proton time profile by neutron monitors. This time profile is compared in detail with UV imaging and radio spectrography over a broad frequency band from the low corona to interplanetary space. It is shown that the late relativistic proton release to interplanetary space was accompanied by a distinct new episode of energy release and electron acceleration in the corona traced by the radio emission and by brightenings of UV kernels. These signatures are interpreted in terms of magnetic restructuring in the corona after the coronal mass ejection passage. We attribute the delayed relativistic proton acceleration to magnetic reconnection and possibly to turbulence in large-scale coronal loops. While Type II radio emission was observed in the high corona, no evidence of a temporal relationship with the relativistic proton acceleration was found

Experimental study of the turbulent structure of a boundary layer developing over a rough surface

National audienceNous avons analysé les caractéristiques turbulentes de la couche limite neutre se développant sur une surface rugueuse. Des expériences ont été réalisées dans un canal hydraulique pour mesurer les champs bidimensionnels de vitesse via la technique de Particle Image Velocimetry (PIV). Ces données expérimentales décrivent cette couche limite en termes de quantités moyennes et turbulentes avec un haut niveau de précision. Les termes des budgets d'énergie ont ainsi pu être estimés. Il apparait que le développement de la couche limite rugueuse ne modifie pas significativement la répartition entre les termes constitutifs des différents bilans. Les échelles de longueurs intégrales ont été estimées, de manière directe, à partir des corrélations spatiales. Ces échelles de longueurs verticales permettent alors de paramétrer les longueurs de mélange et de dissipation, utilisées dans des modèles 1D de prédiction. / We analysed the turbulent characteristics of the neutral boundary-layer developing over rough surfaces. A set of hydraulic flume experiments were carried out in order to measure two-dimensional velocity fields via a particle image velocimetry (PIV) technique. The resulting experimental data describe this boundary layer in terms of the mean and turbulent quantities with a high level of accuracy. These results enabled the terms of the energy budgets to be estimated and show that the development of the rough neutral boundary layer does not significantly modify the repartition between the constitutive terms of the different budget. Spatial correlation analysis permitted the longitudinal and vertical integral length also to be estimated directly. Theses vertical length scales are then used to parametrize the mixing and dissipative lengths, used in 1D prediction models

Examples of derivation-based differential calculi related to noncommutative gauge theories

Some derivation-based differential calculi which have been used to construct models of noncommutative gauge theories are presented and commented. Some comparisons between them are made.Comment: 22 pages, conference given at the "International Workshop in honour of Michel Dubois-Violette, Differential Geometry, Noncommutative Geometry, Homology and Fundamental Interactions". To appear in a special issue of International Journal of Geometric Methods in Modern Physic

Testing for stochastic dominance in social networks

Also can be found at https://ideas.repec.org/p/adl/wpaper/2017-02.htmlThis paper illustrates how stochastic dominance criteria can be used to rank social networks in terms of efficiency, and develops statistical inference procedures for as- sessing these criteria. The tests proposed can be viewed as extensions of a Pearson goodness-of-fit test and a studentized maximum modulus test often used to partially rank income distributions and inequality measures. We establish uniform convergence of the empirical size of the tests to the nominal level, and show their consistency under the usual conditions that guarantee the validity of the approximation of a multinomial distribution to a Gaussian distribution. Furthermore, we propose a bootstrap method that enhances the finite-sample properties of the tests. The performance of the tests is illustrated via Monte Carlo experiments and an empirical application to risk sharing networks in rural IndiaFirmin Doko Tchatoka, Robert Garrard and Virginie Masso

Enhanced software and platform for the Town Energy Balance (TEB) model

The Town Energy Balance (TEB) model (Masson, 2000) is a physically based single layer Urban Canopy Model (UCM) to calculate the urban surface energy balance at neighborhood scale assuming a simplified canyon geometry. It includes several capabilities (Table 1) that have been extensively evaluated offline with flux observations (Lemonsu, Grimmond, & Masson, 2004; Leroyer, Mailhot, Bélair, Lemonsu, & Strachan, 2010; Masson, Grimmond, & Oke, 2002; Pigeon, Moscicki, Voogt, & Masson, 2008) and online coupled to atmospheric models such as ALARO (Gerard, Piriou, Brožková, Geleyn, & Banciu, 2009) in ALARO-TEB (Hamdi, Degrauwe, & Termonia, 2012), the Global Environmental Multiscale (GEM; Côté et al. (1998)) in GEM-TEB (Lemonsu, Belair, & Mailhot, 2009), Meso-NH (Lac et al., 2018; Lafore et al., 1998) in TEB-MesoNH (Lemonsu & Masson, 2002), the Regional Atmospheric Modeling System (RAMS; Pielke et al. (1992)) in RAMS-TEB (Freitas, Rozoff, Cotton, & Dias, 2007), the Advanced Regional Prediction System (ARPS; Xue et al., (2000)) in ARPS-TEB (Rozoff, Cotton, & Adegoke, 2003), and the Weather Research and Forecasting (WRF; Skamarock et al. (2019)) in WRF-TEB (Meyer et al., 2020). Here, we present an enhanced software and platform for the TEB model to help scientists and practitioners wishing to use the TEB model in their research as a standalone software application or as a library in their own software. This includes several features such as crossplatform support for Windows, Linux, and macOS using CMake (Kitware Inc., 2020), static and dynamic library generation for integration with other software/models, namelist-based configuration, integration with MinimalDX (Meyer & Raustad, 2019) and PsychroLib (Meyer & Thevenard, 2019) to improve the modelling of air conditioners (AC) and psychrometric calculations respectively, a thin interface used in the coupling with WRF-CMake (Riechert & Meyer, 2019), helper functions for Python for pre- and post-processing inputs and outputs files, and a tutorial in Jupyter Notebook to allow users to quickly become familiar with the general TEB modeling workflow. In the new platform we implement testing at every code commit through continuous integration (CI) and automate the generation of documentation. The project is developed as a free, open source, community-driven project on GitHub (https://github.com/teb-model/teb) to support existing and new model applications with enhanced functionality. We welcome contributions and encourage users to provide feedback, bug reports and feature requests, via GitHub’s issue system at https://github.com/teb-model/teb/issue

High resolution modelling of aerosol dispersion regimes during the CAPITOUL field experiment: from regional to local scale interactions

High resolution simulation of complex aerosol particle evolution and gaseous chemistry over an atmospheric urban area is of great interest for understanding air quality and processes. In this context, the CAPITOUL (Canopy and Aerosol Particle Interactions in the Toulouse Urban Layer) field experiment aims at a better understanding of the interactions between the urban dynamics and the aerosol plumes. During a two-day Intensive Observational Period, a numerical model experiment was set up to reproduce the spatial distribution of specific particle pollutants, from the regional scales and the interactions between different cities, to the local scales with specific turbulent structures. Observations show that local dynamics depends on the day-regime, and may lead to different mesoscale dynamical structures. This study focuses on reproducing these fine scale dynamical structures, and investigate the impact on the aerosol plume dispersion. The 500-m resolution simulation manages to reproduce convective rolls at local scale, which concentrate most of the aerosol particles and can locally affect the pollutant dispersion and air quality

Synchronous Behavior of Two Coupled Electronic Neurons

We report on experimental studies of synchronization phenomena in a pair of analog electronic neurons (ENs). The ENs were designed to reproduce the observed membrane voltage oscillations of isolated biological neurons from the stomatogastric ganglion of the California spiny lobster Panulirus interruptus. The ENs are simple analog circuits which integrate four dimensional differential equations representing fast and slow subcellular mechanisms that produce the characteristic regular/chaotic spiking-bursting behavior of these cells. In this paper we study their dynamical behavior as we couple them in the same configurations as we have done for their counterpart biological neurons. The interconnections we use for these neural oscillators are both direct electrical connections and excitatory and inhibitory chemical connections: each realized by analog circuitry and suggested by biological examples. We provide here quantitative evidence that the ENs and the biological neurons behave similarly when coupled in the same manner. They each display well defined bifurcations in their mutual synchronization and regularization. We report briefly on an experiment on coupled biological neurons and four dimensional ENs which provides further ground for testing the validity of our numerical and electronic models of individual neural behavior. Our experiments as a whole present interesting new examples of regularization and synchronization in coupled nonlinear oscillators.Comment: 26 pages, 10 figure

Bio-Inspired Computer Vision: Towards a Synergistic Approach of Artificial and Biological Vision

To appear in CVIUStudies in biological vision have always been a great source of inspiration for design of computer vision algorithms. In the past, several successful methods were designed with varying degrees of correspondence with biological vision studies, ranging from purely functional inspiration to methods that utilise models that were primarily developed for explaining biological observations. Even though it seems well recognised that computational models of biological vision can help in design of computer vision algorithms, it is a non-trivial exercise for a computer vision researcher to mine relevant information from biological vision literature as very few studies in biology are organised at a task level. In this paper we aim to bridge this gap by providing a computer vision task centric presentation of models primarily originating in biological vision studies. Not only do we revisit some of the main features of biological vision and discuss the foundations of existing computational studies modelling biological vision, but also we consider three classical computer vision tasks from a biological perspective: image sensing, segmentation and optical flow. Using this task-centric approach, we discuss well-known biological functional principles and compare them with approaches taken by computer vision. Based on this comparative analysis of computer and biological vision, we present some recent models in biological vision and highlight a few models that we think are promising for future investigations in computer vision. To this extent, this paper provides new insights and a starting point for investigators interested in the design of biology-based computer vision algorithms and pave a way for much needed interaction between the two communities leading to the development of synergistic models of artificial and biological vision