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We consider a model for the Antarctic Circumpolar Current in rotating spherical coordinates. After establishing global-in-time existence and uniqueness of classical solutions, we turn our attention to the issue of stability of a class of steady zonal solutions (i.e., time-independent solutions that vary only with latitude). By identifying suitable conserved quantities and combining them to construct a Lyapunov function, we prove a stability result.

We study two-dimensional stationary soliton gas in the framework of the time-independent reduction of the Kadomtsev-Petviashvili (KPII) equation, which coincides with the integrable two-way ``good'' Boussinesq equation in the xy-plane. This (2+0)D reduction enables the construction of the kinetic equation for the stationary gas of KP solitons by invoking recent results on (1+1)D bidirectional soliton gases and generalised hydrodynamics of the Boussinesq equation. We then use the kinetic theory to analytically describe two basic types of 2D soliton gas interactions: (i) refraction of a line soliton by a stationary soliton gas, and (ii) oblique interference of two soliton gases. We verify the analytical predictions by numerically implementing the corresponding KPII soliton gases via exact N-soliton solutions with N-large and appropriately chosen random distributions for the soliton parameters. We also explicitly evaluate the long-distance correlations for the two-component interference configurations. The results can be applied to a variety of physical systems, from shallow water waves to Bose-Einstein condensates., Comment: 11 pages, 4 figures

Well-posedness in time-weighted spaces for quasilinear (and semilinear) parabolic evolution equations $u'=A(u)u+f(u)$ is established in a certain critical case of strict inclusion $\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ for the domains of the (superlinear) function $u\mapsto f(u)$ and the quasilinear part $u\mapsto A(u)$. Based upon regularizing effects of parabolic equations, it is proven that the solution map generates a semiflow in a critical intermediate space. The applicability of the abstract results is demonstrated by several examples including a model for atmospheric flows and semilinear and quasilinear evolution equations with scaling invariance for which well-posedness in the critical scaling invariant intermediate spaces is shown., Comment: 25 pages

We present an experimental study on the perturbed evolution of Korteweg-deVries soliton gases in a weakly dissipative nonlinear electrical transmission line. The system's dynamics reveal that an initially dense, fully randomized, soliton gas evolves into a coherent macroscopic state identified as a soliton condensate through nonlinear spectral analysis. The emergence of the soliton condensate is driven by the spatial rearrangement of the systems's eigenmodes and by the proliferation of new solitonic states due to nonadiabatic effects, a phenomenon not accounted for by the existing hydrodynamic theories.

Asteroseismology gives us the opportunity to look inside stars and determine their internal properties. Based on these observations, estimations can be made for the amount of the convective boundary mixing and envelope mixing of such stars, and the shape of the mixing profile in the envelope. However, these results are not typically included in stellar evolution models. We aim to investigate the impact of varying convective boundary mixing and envelope mixing in a range based on asteroseismic modelling in stellar models, both for the stellar structure and for the nucleosynthetic yields. In this first study, we focus on the pre-explosive evolution of a 20Msun star and evolve the models to the final phases of carbon burning. We vary the convective boundary mixing, implemented as step-overshoot, with the overshoot parameter in the range 0.05-0.4 and the amount of envelope mixing in the range 1-10$^{6}$ with a mixing profile based on internal gravity waves. We use a large nuclear network of 212 isotopes to study the nucleosynthesis. We find that enhanced mixing according to asteroseismology of main-sequence stars, both at the convective core boundary and in the envelope, has significant effects on the nucleosynthetic wind yields. Our evolutionary models beyond the main sequence diverge in yields from models based on rotational mixing, having longer helium burning lifetimes and lighter helium-depleted cores. We find that the asteroseismic ranges of internal mixing calibrated from core hydrogen burning stars lead to similar wind yields as those resulting from the theory of rotational mixing. Adopting the seismic mixing levels beyond the main sequence, we find earlier transitions to radiative carbon burning compared to models based on rotational mixing. This influences the compactness and the occurrence of shell-mergers, which may affect the supernova properties and explosive nucleosynthesis., Comment: 18 pages, 14 figures, 2 tables

The $\gamma$-process in core-collapse supernovae (CCSNe) can produce a number of neutron-deficient stable isotopes heavier than iron (p-nuclei). However, current model predictions do to not fully reproduce the solar abundances. We investigate the impact of different explosion energies and parameters on the nucleosynthesis of p-nuclei, by studying stellar models with different initial masses and CCSN explosions. We find that the total p-nuclei yields are only marginally affected by the CCSN explosion prescriptions if the $\gamma$-process production is already efficient in the stellar progenitors due to a C-O shell merger. In most of CCSN explosions from progenitors without C-O shell merger, the $\gamma$-process yields increase with the explosion energy up to an order of magnitude, depending on the progenitor structure and the CCSN prescriptions. The trend of the p-nuclei production with the explosion energy is more complicated if we look at the production of single p-nuclei. The light p-nuclei tend to be the most enhanced with increasing the explosion energy. In particular, for the CCSN models where the $\alpha$-rich freeze-out component is ejected, the yields of the lightest p-nuclei increase by up to three orders of magnitude. We provide the first extensive study using different sets of massive stars of the impact of varying CCSN explosion prescriptions on the production of the p-nuclei. Unlike previous expectations and recent results in the literature, we find that the average production of p-nuclei tends to increase with the explosion energy. We also confirm that the pre-explosive production of p-nuclei in C-O shell mergers is a robust result, independently from the subsequent explosive nucleosynthesis. A realistic range of variations in the evolution of stellar progenitors and in the CCSN explosions might boost the CCSN contribution to the galactic chemical evolution of p-nuclei., Comment: 11 pages, 3 figures, 4 tables. Accepted for publication in A&A

We use Riemann problem for soliton gas as a benchmark for a detailed numerical validation of the spectral kinetic theory for the Korteweg-de Vries (KdV) and the focusing nonlinear Schr\"odinger (fNLS) equations. We construct weak solutions to the kinetic equation for soliton gas describing collision of two dense "polychromatic" soliton gases composed of a finite number of "monochromatic" components, each consisting of solitons with nearly identical spectral parameters of the scattering operator in the Lax pair. The interaction between the gas components plays the key role in the emergent, large-scale hydrodynamic evolution. We then use the solutions of the spectral kinetic equation to evaluate macroscopic physical observables in KdV and fNLS soliton gases and compare them with the respective ensemble averages extracted from the "exact" soliton gas numerical solutions of the KdV and fNLS equations. To numerically synthesise dense polychromatic soliton gases we develop a new method which combines recent advances in the spectral theory of the so-called soliton condensates and the effective algorithms for the numerical realisation of $n$-soliton solutions with large $n$., Comment: 43 pages, 18 figures

We present an extension of the set of models published in Limongi & Chieffi, 2018, ApJS, 237, 13, at metallicity two times solar, i.e. [Fe/H]=0.3. The key physical properties of these models at the onset of the core collapse are mainly due to the higher mass loss triggered by the higher metallicity: the super solar metallicity (SSM) models reach the core collapse with smaller He- and CO-core masses, while the amount of 12C left by the central He burning is higher. These results are valid for all the rotation velocities. The yields of the neutron capture nuclei expressed per unit mass of Oxygen (i.e. the X/O) are higher in the SSM models than in the SM ones in the non rotating case while the opposite occurs in the rotating models. The trend shown by the non rotating models is the expected one, given the secondary nature of the n-capture nucleosynthesis. Vice versa, the counter intuitive trend obtained in the rotating models is the consequence of the higher mass loss present in the SSM models that removes the H rich envelope faster than in the SM ones while the stars are still in central He burning, dumping out the entanglement (activated by the rotation instabilities) and therefore a conspicuous primary n-capture nucleosynthesis., Comment: 39 pages, 6 figures, 4 tables. Accepted for publication in ApJS

Recent developments in multi-dimensional simulations of core-collapse supernovae have considerably improved our understanding of this complex phenomenon. In addition to that, one-dimensional (1D) studies have been employed to study the explosion mechanism and its causal connection to the pre-collapse structure of the star, as well as to explore the vast parameter space of supernovae. Nonetheless, many uncertainties still affect the late stages of the evolution of massive stars, their collapse, and the subsequent shock propagation. In this review, we will briefly summarize the state-of-the-art of both 1D and 3D simulations and how they can be employed to study the evolution of massive stars, supernova explosions, and shock propagation, focusing on the uncertainties that affect each of these phases. Finally, we will illustrate the typical nucleosynthesis products that emerge from the explosion., Comment: 28 pages, 12 Figures

We present the evolution and the explosion of two massive stars, 15 and 25 M$_{\odot}$, spanning a wide range of initial rotation velocities (from 0 to 800 km/s) and three initial metallicities: Z=0 ([Fe/H]=$-\infty$), $3.236\times10^{-7}$ ([Fe/H]=-5), and $3.236\times10^{-6}$ ([Fe/H]=-4). A very large nuclear network of 524 nuclear species extending up to Bi has been adopted. Our main findings may be summarized as follows: a) rotating models above Z=0 are able to produce nuclei up to the neutron closure shell at N=50, and in a few cases up to N=82; b) rotation drastically inhibits the penetration of the He convective shell in the H rich mantle, phenomenon often found in zero metallicity non rotating massive stars; c) vice versa rotation favors the penetration of the O convective shell in the C rich layers with the consequence of altering significantly the yields of the products of the C, Ne, and O burning; d) none of the models that reach the critical velocity while in H burning, loses more the 1 M$_{\odot}$ in this phase; e) conversely, almost all models able to reach their Hayashi track exceed the Eddington luminosity and lose dynamically almost all their H rich mantle. These models suggest that rotating massive stars may have contributed significantly to the synthesis of the heavy nuclei in the first phase of enrichment of the interstellar medium, i.e., at early times., Comment: 91 pages, 37 figures, 13 tables. Accepted for publication in ApJS

According to a standard initial mass function, stars in the range 7-12 Msun constitute ~50% (by number) of the stars more massive than ~7 Msun, but, in spite of this, their evolutionary properties, and in particular their final fate, are still scarcely studied. In this paper we present a detailed study of the evolutionary properties of solar metallicity, non rotating stars in the range 7-15 Msun, from the pre main sequence phase up to the presupernova stage or up to an advanced stage of the thermally pulsing phase, depending on the initial mass. We find that (1) the 7.00 Msun develops a degenerate CO core and evolves as a classical AGB star in the sense that it does not ignite the C burning reactions; (2) stars with the initial mass M >= 9.22 Msun end their life as core collapse supernovae; (3) stars in the range 7.50 <= M/Msun <= 9.20 develop a degenerate ONeMg core and evolve through the thermally pulsing SAGB phase; 4) stars in the mass range 7.50 <= M/Msun <= 8.00 end their life as hybrid CO/ONeMg- or ONeMg- WD; (5) stars with the initial mass in the range 8.50 <= M/Msun <= 9.20 may potentially explode as electron capture supernovae., Comment: 79 pages, 40 figures, 13 tables. Accepted for publication on ApJS

Soliton gases represent large random soliton ensembles in physical systems that display integrable dynamics at the leading order. We report hydrodynamic experiments in which we investigate the interaction between two "beams" or "jets" of soliton gases having nearly identical amplitudes but opposite velocities of the same magnitude. The space-time evolution of the two interacting soliton gas jets is recorded in a 140-m long water tank where the dynamics is described at leading order by the focusing one-dimensional nonlinear Schrodinger equation. Varying the relative initial velocity of the two species of soliton gas, we change their interaction strength and we measure the macroscopic soliton gas density and velocity changes due to the interaction. Our experimental results are found to be in good quantitative agreement with predictions of the spectral kinetic theory of soliton gas despite the presence of perturbative higher-order effects that break the integrability of the wave dynamics.

We use the spectral kinetic theory of soliton gas to investigate the likelihood of extreme events in integrable turbulence described by the one-dimensional focusing nonlinear Schr\"odinger equation (fNLSE). This is done by invoking a stochastic interpretation of the inverse scattering transform for fNLSE and analytically evaluating the kurtosis of the emerging random nonlinear wave field in terms of the spectral density of states of the corresponding soliton gas. We then apply the general result to two fundamental scenarios of the generation of integrable turbulence: (i) the asymptotic development of the spontaneous (noise induced) modulational instability of a plane wave, and (ii) the long-time evolution of strongly nonlinear, partially coherent waves. In both cases, involving the bound state soliton gas dynamics, the analytically obtained values of the kurtosis are in perfect agreement with those inferred from direct numerical simulations of the the fNLSE, providing the long-awaited theoretical explanation of the respective rogue wave statistics. Additionally, the evolution of a particular non-bound state gas is considered providing important insights related to the validity of the so-called virial theorem., Comment: 13 pages, 5 figures

The $\gamma$-process nucleosynthesis in core-collapse supernovae is generally accepted as a feasible process for the synthesis of neutron-deficient isotopes beyond iron. However, crucial discrepancies between theory and observations still exist: the average production of $\gamma$-process yields from massive stars are too low to reproduce the solar distribution in galactic chemical evolution calculations, and the yields of the Mo and Ru isotopes are by a further factor of 10 lower than the yields of the other $\gamma$-process nuclei. We investigate the $\gamma$-process in 5 sets of core-collapse supernova models published in literature with initial masses 15, 20, and 25 M$_{\odot}$ at solar metallicity. We compared the $\gamma$-process overproduction factors from the different models. To highlight the possible effect of nuclear physics input, we also considered 23 ratios of two isotopes close to each other in mass, relative to their solar values. Further, we investigated the contribution of C-O shell mergers in the supernova progenitors as an additional site of the $\gamma$-process. Our analysis shows that a large scatter among the different models exists for both the $\gamma$-process integrated yields and the isotopic ratios. We found only 10 ratios that agree with their solar values, all the others differ by at least a factor of 3 from the solar values in all the considered sets of models. The $\gamma$-process within C-O shell mergers mostly influence the isotopic ratios that involve intermediate and heavy proton-rich isotopes with $\rm A>100$., Comment: Accepted for publication in A&A. 20 pages, 17 figures

Using a semi-analytical model of the evolution of the Milky Way, we show how secular evolution can create distinct overdensities in the phase space of various properties (e.g. age vs metallicity or abundance ratios vs age) corresponding to the thin and thick discs. In particular, we show how key properties of the Solar vicinity can be obtained by secular evolution, with no need for external or special events, like galaxy mergers or paucity in star formation. This concerns the long established double-branch behaviour of [alpha/Fe] vs metallicity and the recently found non-monotonic evolution of the stellar abundance gradient, evaluated at the birth radii of stars. We extend the discussion to other abundance ratios and we suggest a classification scheme, based on the nature of the corresponding yields (primary vs secondary or odd elements) and on the lifetimes of their sources (short-lived vs long-lived ones). The latter property is critical in determining the single- or double- branch behavior of an elementary abundance ratio in the Solar neighborhood. We underline the high diagnostic potential of this finding, which can help to separate clearly elements with sources evolving on different timescales and help determining the site of e.g. the r-process(es). We define the "abundance distance" between the thin and thick disc sequences as an important element for such a separation. We also show how the inside-out evolution of the Milky Way disc leads rather to a single-branch behavior in other disc regions., Comment: 20 pages, 16 figures, typos corrected, matches published version in MNRAS

In this paper we study a recently derived mathematical model for nonlinear propagation of waves in the atmosphere, for which we establish the local well-posedness in the setting of classical solutions. This is achieved by formulating the model as a quasilinear parabolic evolution problem in an appropriate functional analytic framework and by using abstract theory for such problems. Moreover, for $L_2$-initial data, we construct global weak solutions by employing a two-step approximation strategy based on a Galerkin scheme, where an equivalent formulation of the problem in terms of a new variable is used. Compared to the original model, the latter has the advantage that the $L_2$-norm is a Liapunov functional., Comment: 18 pages

We study the (1+1) focussing nonlinear Schr\"{o}dinger equation for an initial condition with compactly-supported parabolic profile and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural class of self-similar solutions, we provide a criterion for blow-up in finite time, generalising a result by Talanov et al. In the presence of dispersion, we numerically show that the same criterion determines, even beyond the semi-classical regime, whether the solution relaxes or develops a high-order rogue wave, whose onset time is predicted by the corresponding dispersionless catastrophe time. The sign of the chirp appears to determine the prevailing scenario among two competing mechanisms for rogue wave formation. For negative values, the numerical simulations are suggestive of the dispersive regularisation of a gradient catastrophe described by Bertola and Tovbis for a different class of smooth, bell-shaped initial data. As the chirp becomes positive, the rogue wave seems to result from the interaction of counter-propagating dispersive dam break flows, as in the box problem recently studied by El, Khamis and Tovbis. As the chirp and amplitude of the initial profile are relatively easy to manipulate in optical devices and water tank wave generators, we expect our observation to be relevant for experiments in nonlinear optics and fluid dynamics., Comment: 17 pages, 7 figures, 1 table, typos corrected, references added, figures improved

We report an optical fiber experiment in which we investigate the interaction between an individual soliton and a dense soliton gas. We evidence a refraction phenomenon where the tracer soliton experiences an effective velocity change due to its interaction with the optical soliton gas. This interaction results in a significant spatial shift that is measured and compared with theoretical predictions obtained via the inverse scattering transform (IST) theory. The effective velocity change associated with the refraction phenomenon is found to be in good quantitative agreement with the results of the spectral kinetic theory of soliton gas. Our results validate the collision rate ansatz that plays a fundamental role in the kinetic theory of soliton gas and also is at heart of generalized hydrodynamics of many-body integrable systems.