An introduction to Multitrace Formulations and Associated Domain Decomposition Solvers

Multitrace formulations (MTFs) are based on a decomposition of the problem domain into subdomains, and thus domain decomposition solvers are of interest. The fully rigorous mathematical MTF can however be daunting for the non-specialist. We introduce in this paper MTFs on a simple model problem using concepts familiar to researchers in domain decomposition. This allows us to get a new understanding of MTFs and a natural block Jacobi iteration, for which we determine optimal relaxation parameters. We then show how iterative multitrace formulation solvers are related to a well known domain decomposition method called optimal Schwarz method: a method which used Dirichlet to Neumann maps in the transmission condition. We finally show that the insight gained from the simple model problem leads to remarkable identities for Calderon projectors and related operators, and the convergence results and optimal choice of the relaxation parameter we obtained is independent of the geometry, the space dimension of the problem{\color{black}, and the precise form of the spatial elliptic operator, like for optimal Schwarz methods. We illustrate our analysis with numerical experiments

Progenitors of Supernovae Type Ia

Despite the significance of Type Ia supernovae (SNeIa) in many fields in astrophysics, SNeIa lack a theoretical explanation. The standard scenarios involve thermonuclear explosions of carbon/oxygen white dwarfs approaching the Chandrasekhar mass; either by accretion from a companion or by a merger of two white dwarfs. We investigate the contribution from both channels to the SNIa rate with the binary population synthesis (BPS) code SeBa in order to constrain binary processes such as the mass retention efficiency of WD accretion and common envelope evolution. We determine the theoretical rates and delay time distribution of SNIa progenitors and in particular study how assumptions affect the predicted rates.Comment: 6 pages, 6 figures, appeared in proceedings for "The 18th European White Dwarf Workshop

Asymptotics for a special solution to the second member of the Painleve I hierarchy

We study the asymptotic behavior of a special smooth solution y(x,t) to the second member of the Painleve I hierarchy. This solution arises in random matrix theory and in the study of Hamiltonian perturbations of hyperbolic equations. The asymptotic behavior of y(x,t) if x\to \pm\infty (for fixed t) is known and relatively simple, but it turns out to be more subtle when x and t tend to infinity simultaneously. We distinguish a region of algebraic asymptotic behavior and a region of elliptic asymptotic behavior, and we obtain rigorous asymptotics in both regions. We also discuss two critical transitional asymptotic regimes.Comment: 19 page

Astronomical component estimation (ACE v.1) by time-variant sinusoidal modeling

Accurately deciphering periodic variations in paleoclimate proxy signals is essential for cyclostratigraphy. Classical spectral analysis often relies on methods based on (fast) Fourier transformation. This technique has no unique solution separating variations in amplitude and frequency. This characteristic can make it difficult to correctly interpret a proxy's power spectrum or to accurately evaluate simultaneous changes in amplitude and frequency in evolutionary analyses. This drawback is circumvented by using a polynomial approach to estimate instantaneous amplitude and frequency in orbital components. This approach was proven useful to characterize audio signals (music and speech), which are non-stationary in nature. Paleoclimate proxy signals and audio signals share similar dynamics; the only difference is the frequency relationship between the different components. A harmonic-frequency relationship exists in audio signals, whereas this relation is non-harmonic in paleoclimate signals. However, this difference is irrelevant for the problem of separating simultaneous changes in amplitude and frequency. Using an approach with overlapping analysis frames, the model (Astronomical Component Estimation, version 1: ACE v.1) captures time variations of an orbital component by modulating a stationary sinusoid centered at its mean frequency, with a single polynomial. Hence, the parameters that determine the model are the mean frequency of the orbital component and the polynomial coefficients. The first parameter depends on geologic interpretations, whereas the latter are estimated by means of linear least-squares. As output, the model provides the orbital component waveform, either in the depth or time domain. Uncertainty analyses of the model estimates are performed using Monte Carlo simulations. Furthermore, it allows for a unique decomposition of the signal into its instantaneous amplitude and frequency. Frequency modulation patterns reconstruct changes in accumulation rate, whereas amplitude modulation identifies eccentricity-modulated precession. The functioning of the time-variant sinusoidal model is illustrated and validated using a synthetic insolation signal. The new modeling approach is tested on two case studies: (1) a Pliocene-Pleistocene benthic delta O-18 record from Ocean Drilling Program (ODP) Site 846 and (2) a Danian magnetic susceptibility record from the Contessa Highway section, Gubbio, Italy

Scholar-activists in an expanding European food sovereignty movement

This article analyzes the roles, relations, and positions of scholar-activists in the European food sovereignty movement. In doing so, we document, make visible and question the political dimensions of researchers' participation in the movement. We argue that scholar-activists are part of the movement, but are distinct from the affected constituencies, put in place to ensure adequate representation of key movement actors. This is because scholar-activists lack a collective identity, have no processes to formulate collective demands, and no mechanisms for inter-researcher and researchers-movement communication. We reflect on whether and how scholar-activists could organize, and discuss possible pathways for a more cohesive and stronger researcher engagement in the movement.</p

Presence of peritrophic-like membranes in the intestine of three bacteriophagous nematodes (Nematoda : Rhabditida)

Chez trois nématodes Rhabdities, #Caenorhabditis elegans, Panagrolaimus superbus et #Acrobeloides maximus, les analyses ultrastructurales ont démontré la présence d'une membrane prenant naissance à l'extrémité des microvillosités intestinales, et ce sur l'entière longueur de l'intestin. Ces membranes permettent le passage de l'isothiocyanate de fluorescéine, du rouge de méthyle, du rouge neutre et de l'orange d'acridine, mais un passage très limité des molécules de ferritine. Après introduction d'une dose subléthale d'azide de sodium, la lumière intestinale est le siège d'une augmentation de la sécrétion des couches de la membrane. Des colorations #in toto des nématodes avec des lectines provenant de #Solanum tuberosum et #Triticum vulgare$, connues pour leur grande affinité avec la chitine, ont seulement montré une liaison spécifique de la première avec la frange en brosse, et ce chez tous les stades des trois nématodes considérés. Ces résultats révèlent dans l'intestin de trois espèces appartenant à un des plus anciens phylums de métazoaire, la présence de membranes possédant des caractéristiques morphologiques et fonctionnelles rappelant les membranes péritrophiques des insectes. (Résumé d'auteur

Something interacting and solvable in 1D

We present a two-parameter family of exactly solvable quantum many-body systems in one spatial dimension containing the Lieb-Liniger model of interacting bosons as a particular case. The principal building block of this construction is the previously-introduced (arXiv:1712.09375) family of two-particle scattering matrices. We discuss an $SL(2)$ transformation connecting the models within this family and make a correspondence with generalized point interactions. The Bethe equations for the ground state are discussed with a special emphasis on "non-interacting modes" connected by the modular subgroup of $SL(2)$. The bound state solutions are discussed and are conjectured to follow some correlated version of the string hypothesis. The excitation spectrum of the new models in this family is derived in analogy to the Lieb-Liniger model and we show that for certain choices of parameters a spectrum inversion occurs such that the Umklapp solutions become the new ground state.Comment: 11 pages, 6 figure