Magnetic Relaxation of a Voigt-MHD System

We construct solutions of the magnetohydrostatic (MHS) equations in bounded domains and on the torus in three spatial dimensions, as infinite time limits of Voigt approximations of viscous, non-resistive incompressible magnetohydrodynamics equations. The Voigt approximations modify the time evolution without introducing artificial viscosity. We show that the obtained MHS solutions are regular, nontrivial, and are not Beltrami fields.Comment: 16 page

From Instability to Singularity Formation in Incompressible Fluids

We establish finite-time singularity formation for $C^{1,\alpha}$ solutions to the Boussinesq system that are compactly supported on $\mathbb{R}^2$ and infinitely smooth except in the radial direction at the origin. The solutions are smooth in the angular variable at the blow-up point, which was a fundamental obstruction in previous works. This is done by exploiting a second-order effect, related to the classical Rayleigh--B\'enard instability, that overcomes the regularizing effect of transport. A similar result is established for the 3d Euler system based on the Taylor--Couette instability

Invertibility of a linearized Boussinesq flow: a symbolic approach

We develop a computer-assisted symbolic method to show that a linearized Boussinesq flow in self-similar coordinates gives rise to an invertible operator.Comment: The argument involves 7 Matlab files, which are attached to this submissio

The asymptotics of massive fields on stationary spherically symmetric black holes for all angular momenta

We study the massive scalar field equation $\Box_g \phi = m^2 \phi$ on a stationary and spherically symmetric black hole $g$ (including in particular the Schwarzschild and Reissner--Nordstr\"om black holes in the full sub-extremal range) for solutions $\phi$ projected on a fixed spherical harmonic. Our problem involves the scattering of an attractive long-range potential (Coulomb-like) and thus cannot be treated perturbatively. We prove precise (point-wise) asymptotic tails of the form $t^{-5/6} f(t)+ O(t^{-1+\delta})$, where $f(t)$ is an explicit oscillating profile. Our asymptotics appear to be the first rigorous decay result for a massive scalar field on a black hole. Establishing these asymptotics is also an important step in retrieving the assumptions used in work of the third author regarding the interior of dynamical black holes and Strong Cosmic Censorship.Comment: 40 page

Nonlinear waves in general relativity and fluid dynamics

This thesis deals with the analysis of partial differential equations describing nonlinear wave-like phenomena in three different settings: general relativity, the compressible Navier--Stokes equations, and magnetohydrodynamics. Many results on the global dynamics of hyperbolic equations, particularly in the case of the Einstein equations, rely on the use of the vector field method. This method requires the initial data to be highly localized around a single point in space. In this first part of the dissertation, we extend the classical vector field method of Klainerman to deal with initial data localized around several points whose pairwise distances are assumed to be large. We are therefore able to prove global stability for solutions to quasilinear wave equations satisfying the null condition when the initial data are not required to be localized around a single point. This probes a regime which was not accessible by previous physical-space methods. This part is based on joint work with John Anderson. The second chapter of this thesis deals with the global dynamics of the compressible Navier—Stokes equations in one and two space dimensions. A particular case of these equations arises in geophysical fluid dynamics as the viscous shallow water equations. Concerning the one-dimensional model, we introduce a quantity, called the active potential, which allows us to control the dynamics for a large range of pressure and viscosity laws. As a byproduct, we are able to prove a conjecture formulated in 1994 by Peter Constantin. This part is based on joint work with Peter Constantin, Theodore Drivas, and Huy Nguyen. Finally, the third chapter deals with the equations of magnetohydrodynamics (MHD). We prove that a suitably regularized Voigt—MHD model admits a global-in-time solution, which moreover converges, in the infinite time limit, to a solution of the steady three-dimensional incompressible Euler equations. This can be regarded as a rigorous construction of an MHD equilibrium by means of a process known in the physics literature as magnetic relaxation: the magnetic field is drawn towards equilibrium by an MHD-type system. This part is based on joint work with Peter Constantin

Design and Development of a Diagnostic System for a Non-Intercepting Direct Measure of the SPIDER Ion Source Beamlet Current

Stable and uniform beams with low divergence are required in particle accelerators; therefore, beyond the accelerated current, measuring the beam current spatial uniformity and stability over time is necessary to assess the beam performance, since these parameters affect the perveance and thus the beam optics. For high-power beams operating with long pulses, it is convenient to directly measure these current parameters with a non-intercepting system due to the heat management requirement. Such a system needs to be capable of operating in a vacuum in the presence of strong electromagnetic fields and overvoltages, due to electrical breakdowns in the accelerator. Finally, the measure of the beam current needs to be efficiently integrated into a pulse file with the other relevant plant parameters to allow the data analyses required for beam optimization. This paper describes the development, design and commissioning of such a non-intercepting system, the so-called beamlet current monitor (BCM), aimed to directly measure the electric current of a particle beam. In particular, the layout of the system was adapted to the SPIDER experiment, the ion source (IS) prototype of the heating neutral beam injectors (HNB) for the ITER fusion reactor. The diagnostic is suitable to provide the electric current of five beamlets from DC up to 10 MHz

NEOTROPICAL XENARTHRANS: a data set of occurrence of xenarthran species in the Neotropics

Xenarthrans—anteaters, sloths, and armadillos—have essential functions for ecosystem maintenance, such as insect control and nutrient cycling, playing key roles as ecosystem engineers. Because of habitat loss and fragmentation, hunting pressure, and conflicts with domestic dogs, these species have been threatened locally, regionally, or even across their full distribution ranges. The Neotropics harbor 21 species of armadillos, 10 anteaters, and 6 sloths. Our data set includes the families Chlamyphoridae (13), Dasypodidae (7), Myrmecophagidae (3), Bradypodidae (4), and Megalonychidae (2). We have no occurrence data on Dasypus pilosus (Dasypodidae). Regarding Cyclopedidae, until recently, only one species was recognized, but new genetic studies have revealed that the group is represented by seven species. In this data paper, we compiled a total of 42,528 records of 31 species, represented by occurrence and quantitative data, totaling 24,847 unique georeferenced records. The geographic range is from the southern United States, Mexico, and Caribbean countries at the northern portion of the Neotropics, to the austral distribution in Argentina, Paraguay, Chile, and Uruguay. Regarding anteaters, Myrmecophaga tridactyla has the most records (n = 5,941), and Cyclopes sp. have the fewest (n = 240). The armadillo species with the most data is Dasypus novemcinctus (n = 11,588), and the fewest data are recorded for Calyptophractus retusus (n = 33). With regard to sloth species, Bradypus variegatus has the most records (n = 962), and Bradypus pygmaeus has the fewest (n = 12). Our main objective with Neotropical Xenarthrans is to make occurrence and quantitative data available to facilitate more ecological research, particularly if we integrate the xenarthran data with other data sets of Neotropical Series that will become available very soon (i.e., Neotropical Carnivores, Neotropical Invasive Mammals, and Neotropical Hunters and Dogs). Therefore, studies on trophic cascades, hunting pressure, habitat loss, fragmentation effects, species invasion, and climate change effects will be possible with the Neotropical Xenarthrans data set. Please cite this data paper when using its data in publications. We also request that researchers and teachers inform us of how they are using these data