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1. Three-dimensional General-relativistic Simulations of Neutrino-driven Winds from Rotating Proto-neutron Stars

   https://doi.org/10.3847/1538-4357/ac69da  

   Desai, Dhruv ; Siegel, Daniel M. ; Metzger, Brian D. ( May 2022 , The Astrophysical Journal)

   We explore the effects of rapid rotation on the properties of neutrino-heated winds from proto-neutron stars (PNS) formed in core-collapse supernovae or neutron-star mergers by means of three-dimensional general-relativistic hydrodynamical simulations with M0 neutrino transport. We focus on conditions characteristic of a few seconds into the PNS cooling evolution when the neutrino luminosities obey$L_{{\nu }_e}+L_{{\overline{\nu }}_e}\approx 7\times {10}^{51}$erg s⁻¹, and over which most of the wind mass loss will occur. After an initial transient phase, all of our models reach approximately steady-state outflow solutions with positive energies and sonic surfaces captured on the computational grid. Our nonrotating and slower rotating models (angular velocity relative to Keplerian Ω/Ω_K≲ 0.4; spin periodP≳ 2 ms) generate approximately spherically symmetric outflows with properties in good agreement with previous PNS wind studies. By contrast, our most rapidly spinning PNS solutions (Ω/Ω_K≳ 0.75;P≈ 1 ms) generate outflows focused in the rotational equatorial plane with much higher mass-loss rates (by over an order of magnitude), lower velocities, lower entropy, and lower asymptotic electron fractions, than otherwise similar nonrotating wind solutions. Although such rapidly spinning PNS are likely rare in nature, their atypical nucleosynthetic composition and outsized mass yields could render them important contributors of light neutron-rich nuclei compared to more common slowly rotating PNS birth. Our calculations pave the way to including the combined effects of rotation and a dynamically important large-scale magnetic field on the wind properties within a three-dimensional GRMHD framework.

    

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2. On the Local Existence of Solutions to the compressible Navier–Stokes-Wave System with a Free Interface

   https://doi.org/10.1007/s00021-024-00861-8  

   Kukavica, Igor ; Li, Linfeng ; Tuffaha, Amjad ( March 2024 , Journal of Mathematical Fluid Mechanics)

   We address a system of equations modeling a compressible fluid interacting with an elastic body in dimension three. We prove the local existence and uniqueness of a strong solution when the initial velocity belongs to the space$$H^{2+\epsilon }$$$H^{2+ϵ}$and the initial structure velocity is in$$H^{1.5+\epsilon }$$$H^{1.5+ϵ}$, where$$\epsilon \in (0,1/2)$$$ϵ\in (0,1/2)$.

    

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3. Probability flow solution of the Fokker–Planck equation

   https://doi.org/10.1088/2632-2153/ace2aa  

   Boffi, Nicholas M. ; Vanden-Eijnden, Eric ( July 2023 , Machine Learning: Science and Technology)

   The method of choice for integrating the time-dependent Fokker–Planck equation (FPE) in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation (SDE). Here, we study an alternative scheme based on integrating an ordinary differential equation that describes the flow of probability. Acting as a transport map, this equation deterministically pushes samples from the initial density onto samples from the solution at any later time. Unlike integration of the stochastic dynamics, the method has the advantage of giving direct access to quantities that are challenging to estimate from trajectories alone, such as the probability current, the density itself, and its entropy. The probability flow equation depends on the gradient of the logarithm of the solution (its ‘score’), and so isa-prioriunknown. To resolve this dependence, we model the score with a deep neural network that is learned on-the-fly by propagating a set of samples according to the instantaneous probability current. We show theoretically that the proposed approach controls the Kullback–Leibler (KL) divergence from the learned solution to the target, while learning on external samples from the SDE does not control either direction of the KL divergence. Empirically, we consider several high-dimensional FPEs from the physics of interacting particle systems. We find that the method accurately matches analytical solutions when they are available as well as moments computed via Monte-Carlo when they are not. Moreover, the method offers compelling predictions for the global entropy production rate that out-perform those obtained from learning on stochastic trajectories, and can effectively capture non-equilibrium steady-state probability currents over long time intervals.

    

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4. A Closer Look at the Evolution of Supercooled Cloud Droplet Temperature and Lifetime in Different Environmental Conditions with Implications for Ice Nucleation in the Evaporating Regions of Clouds

   https://doi.org/10.1175/JAS-D-22-0239.1  

   Roy, Puja ; Rauber, Robert M. ; Di Girolamo, Larry ( October 2023 , Journal of the Atmospheric Sciences)

   This study investigates the evolution of temperature and lifetime of evaporating, supercooled cloud droplets considering initial droplet radius (r₀) and temperature (), and environmental relative humidity (RH), temperature (T_∞), and pressure (P). The time (t_ss) required by droplets to reach a lower steady-state temperature (T_ss) after sudden introduction into a new subsaturated environment, the magnitude of ΔT=T_∞−T_ss, and droplet survival time (t_st) atT_ssare calculated. The temperature difference (ΔT) is found to increase withT_∞, and decrease with RH andP. ΔTwas typically 1–5 K lower thanT_∞, with highest values (∼10.3 K) for very low RH, lowP, andT_∞closer to 0°C. Results show thatt_ssis <0.5 s over the range of initial droplet and environmental conditions considered. Larger droplets (r₀= 30–50μm) can survive atT_ssfor about 5 s to over 10 min, depending on the subsaturation of the environment. For higher RH and larger droplets, droplet lifetimes can increase by more than 100 s compared to those with droplet cooling ignored.T_ssof the evaporating droplets can be approximated by the environmental thermodynamic wet-bulb temperature. Radiation was found to play a minor role in influencing droplet temperatures, except for larger droplets in environments close to saturation. The implications for ice nucleation in cloud-top generating cells and near cloud edges are discussed. UsingT_ssinstead ofT_∞in widely used parameterization schemes could lead to enhanced number concentrations of activated ice-nucleating particles (INPs), by a typical factor of 2–30, with the greatest increases (≥100) coincident with low RH, lowP, andT_∞closer to 0°C.

   Cloud droplet temperature plays an important role in fundamental cloud processes like droplet growth and decay, activation of ice-nucleating particles, and determination of radiative parameters like refractive indices of water droplets. Near cloud boundaries such as cloud tops, dry air mixes with cloudy air exposing droplets to environments with low relative humidities. This study examines how the temperature of a cloud droplet that is supercooled (i.e., has an initial temperature < 0°C) evolves in these subsaturated environments. Results show that when supercooled cloud droplets evaporate near cloud boundaries, their temperatures can be several degrees Celsius lower than the surrounding drier environment. The implications of this additional cooling of droplets near cloud edges on ice particle formation are discussed.

    

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5. Large-time behavior of solutions of parabolic equations on the real line with convergent initial data III: unstable limit at infinity

   Pauthier, Antoine ; Poláčik, Peter ( August 2022 , Partial Differential Equations and Applications)

   Abstract This is a continuation, and conclusion, of our study of bounded solutions u of the semilinear parabolic equation $$u_t=u_{xx}+f(u)$$ u t = u xx + f ( u ) on the real line whose initial data $$u_0=u(\cdot ,0)$$ u 0 = u ( · , 0 ) have finite limits $$\theta ^\pm $$ θ ± as $$x\rightarrow \pm \infty $$ x → ± ∞ . We assume that f is a locally Lipschitz function on $$\mathbb {R}$$ R satisfying minor nondegeneracy conditions. Our goal is to describe the asymptotic behavior of u ( x ,  t ) as $$t\rightarrow \infty $$ t → ∞ . In the first two parts of this series we mainly considered the cases where either $$\theta ^-\ne \theta ^+$$ θ - ≠ θ + ; or $$\theta ^\pm =\theta _0$$ θ ± = θ 0 and $$f(\theta _0)\ne 0$$ f ( θ 0 ) ≠ 0 ; or else $$\theta ^\pm =\theta _0$$ θ ± = θ 0 , $$f(\theta _0)=0$$ f ( θ 0 ) = 0 , and $$\theta _0$$ θ 0 is a stable equilibrium of the equation $${{\dot{\xi }}}=f(\xi )$$ ξ ˙ = f ( ξ ) . In all these cases we proved that the corresponding solution u is quasiconvergent—if bounded—which is to say that all limit profiles of $$u(\cdot ,t)$$ u ( · , t ) as $$t\rightarrow \infty $$ t → ∞ are steady states. The limit profiles, or accumulation points, are taken in $$L^\infty _{loc}(\mathbb {R})$$ L loc ∞ ( R ) . In the present paper, we take on the case that $$\theta ^\pm =\theta _0$$ θ ± = θ 0 , $$f(\theta _0)=0$$ f ( θ 0 ) = 0 , and $$\theta _0$$ θ 0 is an unstable equilibrium of the equation $${{\dot{\xi }}}=f(\xi )$$ ξ ˙ = f ( ξ ) . Our earlier quasiconvergence theorem in this case involved some restrictive technical conditions on the solution, which we now remove. Our sole condition on $$u(\cdot ,t)$$ u ( · , t ) is that it is nonoscillatory (has only finitely many critical points) at some $$t\ge 0$$ t ≥ 0 . Since it is known that oscillatory bounded solutions are not always quasiconvergent, our result is nearly optimal. 

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