Interface topology and evolution of particle patterns on deformable drops in turbulence

The capture of neutrally buoyant, sub-Kolmogorov particles at the interface of deformable drops in turbulent flow and the subsequent evolution of particle surface distribution are investigated. Direct numerical simulation of turbulence, phase-field modelling of the drop interface dynamics and Lagrangian particle tracking are used. Particle distribution is obtained considering excluded-volume interactions, i.e. by enforcing particle collisions. Particles are initially dispersed in the carrier flow and are driven in time towards the surface of the drops by jet-like turbulent fluid motions. Once captured by the interfacial forces, particles disperse on the surface. Excluded-volume interactions bring particles into long-term trapping regions where the average surface velocity divergence sampled by the particles is zero. These regions correlate well with portions of the interface characterized by higher-than-mean curvature, indicating that modifications of the surface tension induced by the presence of very small particles will be stronger in the highly convex regions of the interface.

Neutrino trapping in extremely compact Tolman VII spacetimes

Extremely compact objects trap gravitational waves or neutrinos, assumed to move along null geodesics in the trapping regions. The trapping of neutrinos was extensively studied for spherically symmetric extremely compact objects constructed under the simplest approximation of the uniform energy density distribution, with radius located under the photosphere of the external spacetime; in addition, uniform emissivity distribution of neutrinos was assumed in these studies. Here we extend the studies of the neutrino trapping for the case of the extremely compact Tolman VII objects representing the simplest generalization of the internal Schwarzschild solution with uniform distribution of the energy density, and the correspondingly related distribution of the neutrino emissivity that is thus again proportional to the energy density; radius of such extremely compact objects can overcome the photosphere of the external Schwarzschild spacetime. In dependence on the parameters of the Tolman VII spacetimes, we determine the “local” and “global” coefficients of efficiency of the trapping and demonstrate that the role of the trapping is significantly stronger than in the internal Schwarzschild spacetimes. Our results indicate possible influence of the neutrino trapping in cooling of neutron stars.

Normal forms for strong magnetic systems on surfaces: trapping regions and rigidity of Zoll systems

We prove a normal form for strong magnetic fields on a closed, oriented surface and use it to derive two dynamical results for the associated flow. First, we show the existence of invariant tori and trapping regions provided a natural non-resonance condition holds. Second, we prove that the flow cannot be Zoll unless (i) the Riemannian metric has constant curvature and the magnetic function is constant, or (ii) the magnetic function vanishes and the metric is Zoll. We complement the second result by exhibiting an exotic magnetic field on a flat two-torus yielding a Zoll flow for arbitrarily weak rescalings.

Spontaneous transition rates near the focus of a parabolic mirror with identification of the vectorial modes involved

Each natural mode of the electromagnetic field within a parabolic mirror exhibits spatial localization and polarization properties that can be exploited for the quantum control of its interaction with atomic systems. The region of localization is not restricted to the focus of the mirror leading to a selective response of atomic systems trapped on its vicinity. We report calculations of the spontaneous emission rates for an atom trapped inside the mirror accounting for all atomic polarizations and diverse trapping regions. It is shown that electric dipole transitions can be enhanced near the focus of a deep parabolic mirror with a clear identification of the few vectorial modes involved. Out of the focus the enhancement vanishes gradually, but the number of relevant modes remains small. Ultimately this represents a quantum electrodynamic system where internal and external degrees of freedom cooperate to maximize a selective exchange and detection of single excitations.

Solution Bounds, Stability, and Estimation of Trapping/Stability Regions of Some Nonlinear Time-Varying Systems

Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science, and control problems. Yet, practically valuable results are rare in this area. This paper develops a novel approach, which bounds the solution norms, derives the corresponding stability criteria, and estimates the trapping/stability regions for some nonautonomous and nonlinear systems, which arise in various application domains. Our inferences rest on deriving a scalar differential inequality for the norms of solutions to the initial systems. Utility of the Lipschitz inequality linearizes the associated auxiliary differential equation and yields both the upper bounds for the norms of solutions and the relevant stability criteria. To refine these inferences, we introduce a nonlinear extension of the Lipschitz inequality, which improves the developed bounds and allows estimation of the stability/trapping regions for the corresponding systems. Finally, we confirm the theoretical results in representative simulations.

The mass flux of volatiles from volcanic eruptions on Mercury

<p>Mercury has been extensively resurfaced by large, effusive lava plains [1–2]. Similar lava plains on the Moon, the maria, are known to contain volatiles [3–4] and are estimated to have outgassed ~10<sup>16</sup> kg of CO and S and ~10<sup>14</sup> kg of H<sub>2</sub>O, with the bulk of volatiles being released during peak mare emplacement ~3.5 Ga ago [5]. If volcanic activity released substantial volatiles on the Moon [6–7], then it is possible that substantial volatiles were also volcanically released on Mercury, albeit with different chemical species [6–9]. Here we seek to understand the potential contribution of outgassing to volatile deposits, specifically for Mercury’s volatile species (S, CH<sub>4</sub>, Cl, and N-H).</p><p>We analyze the production function of volcanic plains deposits on Mercury and find that the volume of outgassed basalts on Mercury is 2 to 3 orders of magnitude larger than that predicted for the Moon [8]. We use a variety of experimental petrology studies [10–12] to predict the dominant species and their abundances associated with these eruptions on Mercury, providing estimates for both low-gas and high-gas scenarios for different oxygen fugacities (IW-3 and IW-7). The most prevalent volatile species predicted for Mercury (S, CH<sub>4</sub>, and Cl) are 1 to 4 orders of magnitude more abundant than what is predicted for the most abundant volatiles outgassed on the Moon (CO, S, and H<sub>2</sub>O) [5].</p><p>On the Moon, it has been predicted that volatiles outgassed from the formation of the maria may have been present in sufficient volumes to produce a transient atmosphere capable of aiding in the transport of H<sub>2</sub>O to cold-trapping regions [5]. At mantle pressures and Mercury’s extremely reducing conditions, H<sub>2</sub>O is not predicted to be present in the magma [e.g., 6–12]. Therefore, Mercury’s outgassed volatiles are of a different composition from the H<sub>2</sub>O ice observed at Mercury’s poles today [e.g., 13], and the polar H<sub>2</sub>O-ice deposits are better explained by some external delivery mechanism (likely cometary impacts). But the fate of large volumes of volatiles other than H<sub>2</sub>O is an important unanswered question for Mercury.</p><p>The large volumes of outgassed volatiles calculated here suggest that volcanism on Mercury may have resulted in the transient production of anomalously high atmospheric pressures of short lifetime due to solar proximity. If Mercury’s atmospheric loss rate was insufficient to lose all of the erupted gases, then it is possible that ancient, outgassed volatiles remain trapped in the planet’s subsurface today. The fate of Mercury’s outgassed volatiles is an important open question that we discuss in this work.</p><p>References: [1] Head et al. (2011). [2] Denevi et al. (2013). [3] Boyce et al. (2010). [4] McCubbin et al. (2010). [5] Needham and Kring (2017). [6] Nittler et al. (2011). [7] Zolotov et al. (2013). [8] Peplowski et al. (2016). [9] Greenwood et al. (2018). [10] Anzures et al. (2017). [11] Armstrong et al. (2015). [12] Libourel et al. (2003). [13] Lawrence et al. (2013).</p>

Influence of the Earth's ring current strength on Størmer's allowed and forbidden regions of charged particle motion

Størmer's particles' trapping regions for a planet with an intrinsic dipolar magnetic field are considered, taking into account the ring current which arises due to the trapped particles' drift for the case of the Earth. The influence of the ring current on the particle trapping regions' topology is investigated. It is shown that a critical strength of the ring current exists under which further expansion of the trapping region is no longer possible. Before reaching this limit, the dipole field, although deformed, retains two separated Størmer regions. After transition of critical magnitude, the trapping region opens up, and charged particles, which form the ring current, get the opportunity to leave it, thus decreasing the ring current strength. Numerical calculations have been performed for protons with typical energies of the Earth's radiation belt and ring current. For the Earth's case, the Dst index for the critical ring current strength is calculated.

3D simulations of planet trapping at disc–cavity boundaries

Inward migration of low-mass planets and embryos of giant planets can be stopped at the disc–cavity boundaries due to co-orbital corotation torque. We performed the first global three-dimensional (3D) simulations of planet migration at the disc–cavity boundary, and have shown that the boundary is a robust trap for low-mass planets and embryos. A protoplanetary disc may have several such trapping regions at various distances from the star, such as at the edge of the stellar magnetosphere, the inner edge of the dead zone, the dust-sublimation radius and the snow lines. Corotation traps located at different distances from a star, and moving outward during the disc dispersal phase, may possibly explain the observed homogeneous distribution of low-mass planets with distance from their host stars.

Influence of the Earth's ring current strength on the Størmer's allowed and forbidden regions of charged particles motion

Størmer's particles' trapping regions for a planet with an intrinsic dipolar magnetic field are considered, taking into account the ring current which arises due to the trapped particles drift for the case of Earth. The influence of the ring current on the particles' trapping regions topology is investigated. It is shown that a critical strength of the ring current exists, under which further expansion of the trapping region is no longer possible. Before reaching this limit, the dipole field, although deformed, retains two separated Størmer regions. After transition of critical magnitude, the trapping region opens up and charged particles, which form the ring current, get the opportunity to leave it (go to infinity or come to the trapping region from infinity), thus decreasing the ring current strength. Numerical calculations have been performed for protons with typical energies of Earth's radiation belt and ring current. For the Earth case, the Dst index for the critical ring current strength is calculated.

Numerical Study of Multiple Attractors in the Parallel Inductor–Capacitor–Memristor Circuit

Dynamical phenomena in the parallel inductor–capacitor–memristor circuit are studied numerically. A systematic search for coexisting attractors is carried out. The existence of multiple attractors is observed and bifurcation diagrams are constructed. Basins of attraction are computed. The coexistence of attractors is proved using interval analysis tools. The existence of periodic attractors is confirmed by applying the interval Newton method to prove the existence of stable periodic orbits of an associated return map. For numerically observed chaotic attractors the existence of attractors is proved by constructing trapping regions enclosing chaotic trajectories of the return map. The existence of topological chaos is proved using the method of covering relations.