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

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

Magnetostrictive hysteresis of TbCo/CoFe multilayers and magnetic domains

Magnetic and magnetostrictive hysteresis loops of TbCo/CoFe multilayers under field applied along the hard magnetization axis are studied using vectorial magnetization measurements, optical deflectometry and magneto optical Kerr microscopy. Even a very small angle misalignment between hard axis and magnetic field direction is shown to drastically change the shape of magnetization and magnetostrictive torsion hysteresis loops. Two kinds of magnetic domains are revealed during the magnetization: big regions with opposite rotation of spontaneous magnetization vector and spontaneous magnetic domains which appear in a narrow field interval and provide an inversion of this rotation. We show that the details of the hysteresis loops of our exchange-coupled films can be described using the classical model of homogeneous magnetization rotation of single uniaxial films and the configuration of observed domains. The understanding of these features is crucial for applications (for MEMS or microactuators) which benefit from the greatly enhanced sensitivity near the point of magnetic saturation at the transverse applied field.Comment: 10 pages, 11 figure

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

Vortex in Maxwell-Chern-Simons models coupled to external backgrounds

We consider Maxwell-Chern-Simons models involving different non-minimal coupling terms to a non relativistic massive scalar and further coupled to an external uniform background charge. We study how these models can be constrained to support static radially symmetric vortex configurations saturating the lower bound for the energy. Models involving Zeeman-type coupling support such vortices provided the potential has a "symmetry breaking" form and a relation between parameters holds. In models where minimal coupling is supplemented by magnetic and electric field dependant coupling terms, non trivial vortex configurations minimizing the energy occur only when a non linear potential is introduced. The corresponding vortices are studied numericallyComment: LaTeX file, 2 figure

ETS-1 and ETS-2 are upregulated in a transgenic mouse model of pigmented ocular neoplasm

Purpose: Choroidal melanoma is the most common primary malignant ocular tumor in human adults. Relevant mouse models of human uveal melanoma still remain to be developed. We have studied the transgenic mouse strain, Tyrp-1-TAg, to try to gain insight into possible molecular mechanisms common to pigmented ocular neoplasms occurring spontaneously in the eyes of these mice and human choroidal melanoma. The role of two members of the ETS (E26 avian leukemia oncogene) family of transcription factors, ETS-1 and ETS-2, has been investigated in many cancers but has not yet been studied in ocular tumors. Methods: This is the first study describing the production and distribution of ETS-1 and ETS-2 mRNAs and proteins using in situ hybridization and immunohistochemistry in murine ocular tissue sections of normal control eyes and tumoral eyes from mice of the same age. Using semi-quantitative reverse-transcription polymerase chain reaction (RT–PCR) and western blots experiments, we compared changes in ETS-1 and ETS-2 expression, their protein levels, and the regulation of some of their target gene expressions at different stages of the ocular tumoral progression in the transgenic mouse model, Tyrp-1-TAg, with those in normal eyes from control mice of the same age. Results: In normal control adult mouse eyes, ETS-1 was mostly present in the nuclei of all neuroretinal layers whereas ETS-2 was mostly localized in the cytosol of the cell bodies of these layers with a smaller amount present in the nuclei. Both were found in the retinal pigmentary epithelium (RPE). ETS-1 and ETS-2 mRNA and protein levels were much higher in the ocular tissues of Tyrp-1-TAg mice than in control ocular tissues from wild-type mice. This upregulation was correlated with tumor progression. We also demonstrated upregulation of ETS-1 and ETS-2 target expressions in Tyrp-1-TAg mice when comparing with the same target expressions in control mice. Conclusions: Our findings suggest that ETS-1 and ETS-2 are upregulated in ocular tumors derived from the retinal epithelium and may be involved in one or several signaling pathways that activate the expression of a set of genes involved in ocular tumor progression such as those encoding ICAM-1 (intercellular adhesion molecule-1), PAI-1 (Plasminogen activator inhibitor-1), MCP-1 (monocyte chemoattractant protein-1) and p16 (Cyclin dependent kinase inhibitor 2A)

Developing a western Siberia reference site for tropospheric water vapour isotopologue observations obtained by different techniques (in situ and remote sensing)

Water stable isotopologues provide integrated tracers of the atmospheric water cycle, affected by changes in air mass origin, non-convective and convective processes and continental recycling. Novel remote sensing and in situ measuring techniques have recently offered opportunities for monitoring atmospheric water vapour isotopic composition. Recently developed infrared laser spectrometers allow for continuous in situ measurements of surface water vapour δD_v and δ¹⁸O_v. So far, very few intercomparisons of measurements conducted using different techniques have been achieved at a given location, due to difficulties intrinsic to the comparison of integrated with local measurements. Nudged simulations conducted with high-resolution isotopically enabled general circulation models (GCMs) provide a consistent framework for comparison with the different types of observations. Here, we compare simulations conducted with the ECHAM5-wiso model with two types of water vapour isotopic data obtained during summer 2012 at the forest site of Kourovka, western Siberia: hourly ground-based FTIR total atmospheric columnar δD_v amounts, and in situ hourly Picarro δD_v measurements. There is an excellent correlation between observed and predicted δD_v at surface while the comparison between water column values derived from the model compares well with FTIR estimates

WRF‐TEB: implementation and evaluation of the coupled Weather Research and Forecasting (WRF) and Town Energy Balance (TEB) model

Urban land surface processes need to be represented to inform future urban‐climate and building‐energy projections. Here, the single layer urban canopy model Town Energy Balance (TEB) is coupled to the Weather Research and Forecasting (WRF) model to create WRF‐TEB. The coupling method is described generically, implemented into software, and the issue of scientific reproducibility is addressed by releasing all code and data with a Singularity image. The coupling is implemented modularly and verified by an integration test. Results show no detectable errors in the coupling. Separately, a meteorological evaluation is undertaken using observations from Toulouse, France. The latter evaluation, during an urban canopy layer heat island episode, shows reasonable ability to estimate turbulent heat flux densities and other meteorological quantities. We conclude that new model couplings should make use of integration tests as meteorological evaluations by themselves are insufficient, given that errors are difficult to attribute because of the interplay between observational errors and multiple parameterization schemes (e.g. radiation, microphysics, boundary layer)

Symmetry breaking, conformal geometry and gauge invariance

When the electroweak action is rewritten in terms of SU(2) gauge invariant variables, the Higgs can be interpreted as a conformal metric factor. We show that asymptotic flatness of the metric is required to avoid a Gribov problem: without it, the new variables fail to be nonperturbatively gauge invariant. We also clarify the relations between this approach and unitary gauge fixing, and the existence of similar transformations in other gauge theories.Comment: 11 pages. Version 2: typos corrected, discussion of Elitzur's theorem added. Version to appear in J.Phys.

A late medieval warm period in the Southern Ocean as a delayed response to external forcing?

International audienceOn the basis of long simulations performed with a three‐dimensional climate model, we propose an interhemispheric climate lag mechanism, involving the long‐term memory of deepwater masses. Warm anomalies, formed in the North Atlantic when warm conditions prevail at surface, are transported by the deep ocean circulation towards the Southern Ocean. There, the heat is released because of large scale upwelling, maintaining warm conditions and inducing a lagged response of about 150 years compared to the Northern Hemisphere. Model results and observations covering the first half of the second millenium suggest a delay between the temperature evolution in the Northern Hemisphere and in the Southern Ocean. The mechanism described here provides a reasonable hypothesis to explain such an interhemipsheric lag