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Geometric flux-based Volume-of-Fluid (VOF) methods are widely considered consistent in handling two-phase flows with high density ratios. However, although the conservation of mass and momentum is consistent for two-phase incompressible single-field Navier-Stokes equations without phase-change, discretization may easily introduce small inconsistencies that result in very large errors or catastrophic failure. We apply the consistency conditions derived for the unstructured Level Set / Front Tracking method to flux-based geometric VOF methods, and implement our discretization into the plicRDF-isoAdvector geometrical VOF method. We find that computing the mass flux by scaling the geometrically computed fluxed phase-specific volume destroys the equivalence between the scaled volume fraction equation and the mass conservation equation, depending on the choice for the temporal and convective term discretization schemes. We propose two solutions. First, based on the analysis of discretization errors, we suggest a consistent combination of the temporal discretization scheme and the interpolation scheme for the momentum convection term. Second, similar to our previous work on the unstructured Level Set / Front Tracking method, we solve an auxiliary mass conservation equation with a geometrical calculation of the face-centered density. We prove the equivalence between these two approaches mathematically and verify and validate their numerical stability for density ratios in the range $[1,10^6]$ and viscosity ratios in the range $[10^2,10^5]$.

A comprehensive numerical investigation has been conducted on the angular distribution and spectrum of radiation emitted by 855 MeV electron and positron beams while traversing a 'quasi-mosaic' bent silicon (111) crystal. This interaction of charged particles with a bent crystal gives rise to various phenomena such as channeling, dechanneling, volume reflection, and volume capture. The crystal's geometry, emittance of the collimated particle beams, as well as their alignment with respect to the crystal, have been taken into account as they are essential for an accurate quantitative description of the processes. The simulations have been performed using a specialized relativistic molecular dynamics module implemented in the MBN Explorer package. The angular distribution of the particles after traversing the crystal has been calculated for beams of different emittances as well as for different anticlastic curvatures of the bent crystals. For the electron beam, the angular distributions of the deflected particles and the spectrum of radiation obtained in the simulations are compared with the experimental data collected at the Mainz Microtron facility. For the positron beam such calculations have been performed for the first time. We predict significant differences in the angular distributions and the radiation spectra for positrons versus electrons., Comment: 17 pages, 9 figures. Submitted to: J. Phys. B: At. Mol. Opt. Phys

Dusty star-forming galaxies emit most of their light at far-IR to mm wavelengths as their star formation is highly obscured. Far-IR and mm observations have revealed their dust, neutral and molecular gas properties. The sensitivity of JWST at rest-frame optical and near-infrared wavelengths now allows the study of the stellar and ionized gas content. We investigate the spatially resolved distribution and kinematics of the ionized gas in GN20, a dusty star forming galaxy at $z$=4.0548. We present deep MIRI/MRS integral field spectroscopy of the near-infrared rest-frame emission of GN20. We detect spatially resolved \paa, out to a radius of 6 kpc, distributed in a clumpy morphology. The star formation rate derived from \paa\ (144 $\pm$ 9 \msunperyear) is only 7.7 $\pm 0.5 $\% of the infrared star formation rate (1860 $\pm$ 90 \msunperyear). We attribute this to very high extinction (A$_V$ = 17.2 $\pm$ 0.4 mag, or A$_{V,mixed}$ = 44 $\pm$ 3 mag), especially in the nucleus of GN20, where only faint \paa\ is detected, suggesting a deeply buried starburst. We identify four, spatially unresolved, clumps in the \paa\ emission. Based on the double peaked \paa\ profile we find that each clump consist of at least two sub-clumps. We find mass upper limits consistent with them being formed in a gravitationally unstable gaseous disk. The UV bright region of GN20 does not have any detected \paa\ emission, suggesting an age of more than 10 Myrs for this region of the galaxy. From the rotation profile of \paa\ we conclude that the gas kinematics are rotationally dominated and the $v_{rot}/\sigma_{m} = 3.8 \pm 1.4$ is similar to low-redshift LIRGs. We speculate that the clumps seen in GN20 could contribute to building up the inner disk and bulge of GN20., Comment: 13 pages, 7 figures, accepted for publication in A&A

The SPT0311-58 system resides in a massive dark matter halo at z ~ 6.9. It hosts two dusty galaxies (E and W) with a combined star formation rate of ~3500 Msun/yr. Its surrounding field exhibits an overdensity of sub-mm sources, making it a candidate proto-cluster. We use spatially-resolved spectroscopy provided by the JWST/NIRSpec Integral Field Unit (IFU) to probe a field of view (FoV) ~ 17 x 17 kpc^2 around this object. These observations have revealed ten new galaxies at z ~ 6.9, characterised by dynamical masses spanning from ~10^9 to 10^10 Msun and a range in radial velocities of ~ 1500 km/s, in addition to the already known E and W galaxies. The implied large number density, and the wide spread in velocities, indicate that SPT0311-58 is at the core of a proto-cluster, immersed in a very massive dark matter halo of ~ 5 x 10^12 Msun. Hence, it represents the most massive proto-cluster ever found at the EoR. We also study the dynamical stage of the system and find that it likely is not fully virialised. The galaxies exhibit a great diversity of properties showing a range of evolutionary stages. We derive their ongoing Ha-based unobscured SFR, and find that its contribution to the total SF varies significantly across the galaxies in the system. Their ionization conditions range from those typical of field galaxies at similar redshift recently studied with JWST to those found in more evolved objects at lower z. The metallicity spans more than 0.8 dex across the FoV, reaching nearly solar values in some cases. The detailed IFU spectroscopy of the E galaxy reveals that it is actively assembling its stellar mass, showing sub-kpc inhomogeneities, and a metallicity gradient that can be explained by accretion of low metallicity gas from the IGM. The kinematic maps indicate departures from regular rotation, high turbulence, and a possible pre-collision minor merger. (Abridged), Comment: Revised version: minor changes, improved figures, updated references

In 2004, Rosas and Sagan developed the theory of symmetric functions in noncommuting variables, achieving results analogous to classical symmetric functions. On the other hand, in 2004, Desrosiers, Lapointe and Mathieu introduced the theory of symmetric functions in superspace, which involve both commuting and anticommuting variables, extending the classic theory. Here, we introduce symmetric functions in noncommuting variables in superspace. We define the classical symmetric functions in noncommuting variables to superspace: monomials, power sums, elementaries and complete homogeneous, which generalize both the ones studied by Rosas and Sagan and the ones studied by Desrosiers, Lapointe and Mathieu. We also define Schur--type functions in noncommuting variables in superspace., Comment: 9 figures