Convergence of a linearly transformed particle method for aggregation equations

We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the regularity of the initial data. Moreover, we give convergence estimates in bounded Lipschitz distance for measure valued solutions. For singular interaction forces, we establish the convergence of the error between the approximated and exact flows up to the existence time of the solutions in $L^1 \cap L^p$ norm

MATHEMATICAL AND NUMERICAL STUDY OF A DUSTY KNUDSEN GAS MIXTURE

We consider a mixture composed of a gas and dust particles in a very rarefied setting. Whereas the dust particles are individually described, the surrounding gas is treated as a Knudsen gas, in such a way that interactions occur only between gas particles and dust by means of diffuse reflection phenomena. After introducing the model, we prove existence and uniqueness of the solution and provide a numerical strategy for the study of the equations. At the numerical level, we focus our attention on the phenomenon of energy transfer between the gas and the moving dust particles

Uniform convergence of a linearly transformed particle method for the Vlasov-Poisson system

International audienceA particle method with linear transformation of the particle shape functions is studied for the 1d-1v Vlasov-Poisson equation, and a priori error estimates are proven which show that the approximated densities converge in the uniform norm. When compared to standard fixed-shape particle methods, the present approach can be seen as a way to gain one order in the convergence rate of the particle trajectories at the cost of linearly transforming each particle shape. It also allows to compute strongly convergent densities with particles that overlap in a bounded way

Bayesian inference of petrophysical properties with generative spectral induced polarization models

Mechanistic induced polarization (IP) models describe the relationships between the intrinsic properties of geomaterials and their frequency-dependent complex conductivity spectra. However, the uncertainties associated with estimating petrophysical properties from IP data are still poorly understood. Therefore, practitioners rarely use mechanistic models to interpret actual IP data. We propose a framework for critically assessing any IP model's sensitivity and parameter estimation limitations. The framework consists of a conditional variational autoencoder (CVAE), an unsupervised Bayesian neural network specializing in data dimension reduction and generative modeling. We train the CVAE on the IP signatures of synthetic mixtures of metallic mineral inclusions in electrolyte-filled host geomaterials and describe the effect of data transformations on the model. First, the CVAE's Jacobian reveals the relative importance of each petrophysical property for generating spectral IP data. The most critical parameters are the conductivity of the host, the volumetric content of the inclusions, the characteristic length of the inclusions, and the permittivity of the host. The inclusions' diffusion coefficient, permittivity, and conductivity, as well as the host's diffusion coefficient, only have marginal importance for generative IP modeling. A parameter estimation experiment yields the standardized accuracy of petrophysical properties using various model constraints scenarios and corroborates the sensitivity analysis results. Finally, we visualize the effects of data transformations and model constraints on the petrophysical parameter space. We conclude that a common logarithm data transformation yields optimal parameter estimation results and that constraining the electrochemical properties of the geomaterial improves estimates of the characteristic length of its metallic inclusions and vice versa.Comment: 31 pages, 12 figures, 1 table. Original manuscript submitted to SEG Geophysics for review. For associated code, see https://doi.org/10.5281/zenodo.694865

Experimental and survey-based evidences for effective biotic resistance by predators in ports

International audienc

Nonlinear stability of a Vlasov equation for magnetic plasmas

The mathematical description of laboratory fusion plasmas produced in Tokamaks is still challenging. Complete models for electrons and ions, as Vlasov-Maxwell systems, are computationally too expensive because they take into account all details and scales of magneto-hydrodynamics. In particular, for most of the relevant studies, the mass electron is negligible and the velocity of material waves is much smaller than the speed of light. Therefore it is useful to understand simplified models. Here we propose and study one of those which keeps both the complexity of the Vlasov equation for ions and the Hall effect in Maxwell's equation. Based on energy dissipation, a fundamental physical property, we show that the model is nonlinear stable and consequently prove existence

Does a Carbonatite Deposit Influence Its Surrounding Ecosystem?

Carbonatites are unusual alkaline rocks with diverse compositions. Although previous work has characterized the effects these rocks have on soils and plants, little is known about their impacts on local ecosystems. Using a deposit within the Great Lakes–St. Lawrence forest in northern Ontario, Canada, we investigated the effect of a carbonatite on soil chemistry and on the structure of plant and soil microbial communities. This was done using a vegetation survey conducted above and around the deposit, with corresponding soil samples collected for determining soil nutrient composition and for assessing microbial community structure using 16S/ITS Illumina Mi-Seq sequencing. In some soils above the deposit a soil chemical signature of the carbonatite was found, with the most important effect being an increase in soil pH compared with the non-deposit soils. Both plants and microorganisms responded to the altered soil chemistry: the plant communities present in carbonatite-impacted soils were dominated by ruderal species, and although differences in microbial communities across the surveyed areas were not obvious, the abundances of specific bacteria and fungi were reduced in response to the carbonatite. Overall, the deposit seems to have created microenvironments of relatively basic soil in an otherwise acidic forest soil. This study demonstrates for the first time how carbonatites can alter ecosystems in situ

Numerical simulation by a random particle method of Deuterium-Tritium fusion reactions in a plasma.

We propose and we justify a Monte-Carlo algorithm which solves a spatially homogeneous kinetic equation of Boltzmann type that models the fusion reaction between a deuterium ion and a tritium ion, and giving an α particle and a neutron. The proposed algorithm is validated with the use of explicit solutions of the kinetic model obtained by replacing the fusion cross-section by a Maxwellian cross section

WEIRD: Wide-orbit Exoplanet search with InfraRed Direct imaging

We report results from the Wide-orbit Exoplanet search with InfraRed Direct imaging (WEIRD), a survey designed to search for Jupiter-like companions on very wide orbits (1000 to 5000 AU) around young stars ($<$120 Myr) that are known members of moving groups in the solar neighborhood ($<$70 pc). Sharing the same age, distance, and metallicity as their host while being on large enough orbits to be studied as "isolated" objects make such companions prime targets for spectroscopic observations and valuable benchmark objects for exoplanet atmosphere models. The search strategy is based on deep imaging in multiple bands across the near-infrared domain. For all 177 objects of our sample, $z_{ab}^\prime$, $J$, [3.6] and [4.5] images were obtained with CFHT/MegaCam, GEMINI/GMOS, CFHT/WIRCam, GEMINI/Flamingos-2, and $Spitzer$/IRAC. Using this set of 4 images per target, we searched for sources with red $z_{ab}^\prime$ and $[3.6]-[4.5]$ colors, typically reaching good completeness down to 2Mjup companions, while going down to 1Mjup for some targets, at separations of $1000-5000$ AU. The search yielded 4 candidate companions with the expected colors, but they were all rejected through follow-up proper motion observations. Our results constrain the occurrence of 1-13 Mjup planetary-mass companions on orbits with a semi-major axis between 1000 and 5000 AU at less than 0.03, with a 95\% confidence level.Comment: 55 pages, 16 figures, accepted to A