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A limiting technique for scalar transport equations is presented. The originality of the method is that it does not require solving nonlinear optimization problems nor does it rely on the construction of a low-order approximation. The method has minimal complexity and is numerically demonstrated to maintain high-order accuracy. The performance of the method is illustrated on the radiation transport equation. 

The paper compares standard iterative methods for solving the generalized Stokes problem arising from the time and space approximation of the time-dependent incompressible Navier-Stokes equations. Various preconditioning techniques are considered: (1) pressure Schur complement; (2) fully coupled system using an exact factorization as a basis for the preconditioner; (3) fully coupled system using norm equivalence considerations as a basis for the preconditioner; (4) in all the cases we also investigate the benefits of the augmented Lagrangian formulation. Our objective is to see whether one of these methods can compete with traditional pressure-correction and velocity-correction methods in terms of throughput (the throughput is the ratio of the number of degrees of freedom of the problem divided by the number of cores and the wall-clock time in second). Numerical tests on fine unstructured meshes (68 millions degrees of freedoms) demonstrate GMRES/CG convergence rates that are independent of the mesh size and improve with the Reynolds number for most methods. Three conclusions are drawn: (1) The throughputs of all the methods tested in the paper are similar up to mesh-independent multiplicative constants (see Fig. 6). (2) Although very good parallel scalability is observed for the augmented Lagrangian version of the generalized Stokes problem, the best throughputs are achieved without the augmented Lagrangian term. (3) The throughput of all the methods tested in the paper is on average 5 to 25 times slower than that of traditional pressure-correction and velocity-correction methods (on average 5 for the best one). Hence, although all these methods are very efficient for solving steady state problems, pressure- 

We design pairs of six-stage, third-order, alternating implicit Runge–Kutta (RK) schemes that can be used to integrate in time two stiff operators by an operator-splitting technique. We also design for each pair a companion explicit RK scheme to be used for a third, nonstiff oper- ator in an implicit-explicit (IMEX) fashion. The main application we have in mind is (non)linear parabolic problems, where the two stiff operators represent diffusion processes (for instance, in two spatial directions) and the nonstiff operator represents (non)linear transport. We identify necessary conditions for linear sectorial A( )-stability by considering a scalar ODE with two (complex) ei- genvalues lying in some fixed cone of the half-complex plane with nonpositive real part. We show numerically that it is possible to achieve A(0)-stability when combining two operators with negative eigenvalues, irrespective of their relative magnitude. Finally, we show by numerical examples includ- ing two-dimensional nonlinear transport problems discretized in space using finite elements that the proposed schemes behave well. 

Despite their versatile synthetic utility, vinyl azides have complex and poorly understood photochemistry. To address this, we investigated the photoreactivity of 1-azidostyrene 1 and 3-phenyl-2H-azirine 2 in solution and cryogenic matrices. In argon matrices, irradiation of 1 at 254 nm yielded 2, phenyl nitrile ylide 3, and N-phenyl ketenimine 4, whereas irradiation at wavelengths above 300 nm produced only 2 and 4. Similarly, irradiation of 1 in 2-methyltetrahydrofuran (mTHF) glass at 77 K mainly yielded absorption corresponding to the formation of 2 (λmax ~ 252 nm). In contrast, irradiation of 2 at wavelengths above 300 nm in Argon matrices yielded no photoproducts, whereas irradiation at 254 nm resulted in the formation of 3. Furthermore, femto- and nanosecond transient absorption and laser flash photolysis were performed to ascertain the transient species and reactive intermediates formed during the photochemical transformations of 1 and 2. The ultrafast transient absorption spectroscopy of 1 resulted in a transient absorption band centered at ca. 472 nm with a time constant τ ~ 22 ps, which was assigned to the first singlet excited state (S1) of 1. The nano-second flash photolysis of 1 (308 nm laser) generated 2 within the laser pulse (~17 ns), and subsequently 2 is excited to yield triplet vinylnitrene 31N with an absorption centered at ~ 440 nm. In contrast, the nano-second laser flash photolysis of 2 with 266 nm laser produced a weak absorption corresponding to 3, whereas 308 nm laser yielded absorption due to triplet vinylnitrene 31N (λmax ~ 440 nm). These findings demonstrate that the direct irradiation of 1 populates S1 of 1, which does not intersystem cross to form 31N, but instead decays to yield 2. Density functional theory calculations supported the characteristics of the excited states and reactive intermediates formed upon irradiation of 1 and 2. 

Jupiter's icy moon Europa is currently seen as the most habitable world closest to Earth. Data from the space mission Galileo supported the presence of a global subsurface water ocean in direct contact with a rocky mantle, implying possible rock-water processes similar to those occurring on Earth's ocean floor, which is teeming with life. Although Juno can provide occasional glimpses of the Galilean satellites, close-up observations are not expected until the arrival of Europa Clipper and JUICE in the Jovian system. In the meantime, radar astronomy can help expand our understanding of this intriguing ocean world.There are ongoing efforts to determine Europa's obliquity from radar echoes observed with the Goldstone Solar System Radar and the Green Bank Telescope [1]. In this contribution, we will present our latest models for icy moon obliquity and nutations, and demonstrate the need for precise modelling of elastic deformation in the ice shell. We will also investigate possible resonant amplification of the obliquity due to ocean dynamics.This work is financially supported by the Belgian Science Policy Office (BELSPO) through the BRAIN.be-2.0 programme.[1] Margot J.-L., Spin states of Europa and Ganymede, European Geosciences Union General Assembly 2025 

In this paper we construct an explicit approximation for the Lagrangian hydrodynamics equations equipped with an arbitrary equation of state. The approximation of the state variable is done with piecewise constant finite elements and the approximation of the mesh motion is done with higher-order continuous finite elements. The method is invariant-domain preserving and locally mass conservative. The purpose of this method is to be used in combination with higher-order methods to make them invariant domain preserving as well. 

The paper analyzes the discontinuous Galerkin approximation of Maxwell’s equations written in first-order form and with nonhomogeneous magnetic permeability and electric permittivity. Although the Sobolev smoothness index of the solution may be smaller than 1 2 , it is shown that the approximation converges strongly and is therefore spectrally correct. The convergence proof uses the notion of involution and is based on a deflated inf-sup condition and a duality argument. One essential idea is that the smoothness index of the dual solution is always larger than 1 2 irrespective of the regularity of the material properties. 

Radar speckle tracking observations of Europa and Ganymede with the Goldstone Solar System Radar and the Green Bank Telescope in 2011-2023 yield estimates of their spin axis orientations to ~0.01 degrees. These measurements conform to the expected 30-year precessional cycle and provide insights into the moons' Cassini States. I will describe the latest results and discuss new scientific prospects associated with these observations. First, the spin state can reveal the presence of a subsurface ocean: a decoupling between the icy shell and the interior results in a different obliquity than that of a solid body. Second, an angular deviation from the strict Cassini state enables estimates of energy dissipation. Third, a measurement of librations, if detectable, would enable a measurement of the shell's moment of inertia and provide bounds on the rheology and thickness of the shell. Fourth, the obliquity may explain remarkable surface features, such as the distribution and orientation of cycloids, strike-slip faults, and lineaments on Europa. Fifth, knowledge of the obliquity is required to enable tidal heating calculations. Finally, these measurements are expected to facilitate Clipper and JUICE operations and prevent initial, large mapping errors in spacecraft data products.