Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment-magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures-models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The SGS energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pressure (β = 0.25, 1, 2.5, 5, 25 p ) and sonic Mach numbers ( = M 2, 2.5, 4 s ). Furthermore, we make a comparison to traditional, phenomenological eddy-viscosity and α β γ − − closures. We find only mediocre performance of the kinetic eddy-viscosity and α β γ − − closures, and that the magnetic eddy-viscosity closure is poorly correlated with the simulation data. Moreover, three of five coefficients of the traditional closures exhibit a significant spread in values. In contrast, our new closures demonstrate consistently high correlations and constant coefficient values over time and over the wide range of parameters tested. Important aspects in compressible MHD turbulence such as the bi-directional energy cascade, turbulent magnetic pressure and proper alignment of the EMF are well described by our new closures.

We derive oscillatory signals in correlation functions in two-field open inflation by means of the in-in formalism; such signatures are caused by resonances between oscillations in the tunnelling field and fluctuations in the inflaton during the curvature dominated, intermediate and subsequent inflationary regime. While amplitudes are model-dependent, we find distinct oscillations in the power and bi-spectrum that can act as a direct probe of the curvature dominated phase and thus, indirectly, strengthen the claim of the string landscape if they were observed. We comment on the prospects of detecting these tell-tale signs in current experiments, which is challenging, but not impossible.At the technical level, we pay special attention to the applicability conditions for truncation fluctuations to the light (inflaton) field and derive upper limits on the oscillation amplitude of the heavy field. A violation of these bounds requires a multi-field analysis at the perturbed level.1 In the original treatment by Coleman and De Luccia (CdL), the bubble expands almost at the speed of light after it has nucleated; the inner edge of its wall traces out hyperbolic surfaces in the surrounding Minkowski space (in the bubble interior) which are asymptotic to the light cone at the origin of the bubble. These surfaces of constant (negative) spatial curvature are precisely where the field is constant. They subsequently correspond to surfaces of constant CMB temperature, which is our definition of constant cosmic time. Thus, the whole of the observable (infinite) universe today fits in the space-time interior of the finite bubble. In the two-field model that we consider the universe inside the bubble is actually finite [6], which is sometimes referred to as quasi-open inflation.2 This line of reasoning is hampered by the measure problem [44,45] (see [46] for a review or proposed measures). The earliest attempt at making quantitative predictions for Ω k in open inflation can be found in [47], and for quasi-open inflation [6] in [48].

We performed two-dimensional, fully compressible, time-implicit simulations of convection in a solar-like model with the MUSIC code. Our main motivation is to explore the impact of a common tactic adopted in numerical simulations of convection that use realistic stellar conditions. This tactic is to artificially increase the luminosity and to modify the thermal diffusivity of the reference stellar model. This work focuses on the impact of these modifications on convective penetration (or overshooting) at the base of the convective envelope of a solar-like model. We explore a range of enhancement factors for the energy input (or stellar luminosity) and confirm the increase in the characteristic overshooting depth with the increase in the energy input, as suggested by analytical models and by previous numerical simulations. We performed high-order moments analysis of the temperature fluctuations for moderate enhancement factors and find similar flow structure in the convective envelope and the penetration region, independently of the enhancement factor. As a major finding, our results highlight the importance of the impact of penetrative downflows on the thermal background below the convective boundary. This is a result of compression and shear which induce local heating and thermal mixing. The artificial increase in the energy flux intensifies the heating process by increasing the velocities in the convective zone and at the convective boundary, revealing a subtle connection between the local heating of the thermal background and the plume dynamics. This heating also increases the efficiency of heat transport by radiation which may counterbalance further heating and helps to establish a steady state. We suggest that the modification of the thermal background by penetrative plumes impacts the width of the overshooting layer. Additionally, our results suggest that an artificial modification of the radiative diffusivity in the overshooting layer, rather than only accelerating the thermal relaxation, could also alter the dynamics of the penetrating plumes and thus the width of the overshooting layer. Results from simulations with an artificial modification of the energy flux and of the thermal diffusivity should thus be regarded with caution if used to determine an overshooting distance.

Even though compressible plasma turbulence is encountered in many astrophysical phenomena, its effect is often not well understood. Furthermore, direct numerical simulations are typically not able to reach the extreme parameters of these processes. For this reason, large-eddy simulations (LES), which only simulate large and intermediate scales directly, are employed. The smallest, unresolved scales and the interactions between small and large scales are introduced by means of a subgrid-scale (SGS) model. We propose and verify a new set of nonlinear SGS closures for future application as an SGS model in LES of compressible magnetohydrodynamics (MHD). We use 15 simulations (without explicit SGS model) of forced, isotropic, homogeneous turbulence with varying sonic Mach number M s = 0.2 to 20 as reference data for the most extensive a priori tests performed so far in literature. In these tests we explicitly filter the reference data and compare the performance of the new closures against the most widely tested closures. These include eddy-viscosity and scale-similarity type closures with different normalizations. Performance indicators are correlations with the turbulent energy and cross-helicty flux, the average SGS dissipation, the topological structure and the ability to reproduce the correct magnitude and direction of the SGS vectors. We find that only the new nonlinear closures exhibit consistently high correlations (median value >0.8) with the data over the entire parameter space and outperform the other closures in all tests. Moreover, we show that these results are independent of resolution and chosen filter scale. Additionally, the new closures are effectively coefficient-free with a deviation of less than 20%.