A possible mechanism for the capture of microparticles by the earth and other planets of the solar system

By application of Lyttleton's theory for the formation of comets, it is shown that a possible mechanism for the origin and formation of a concentration of cosmic particles around the earth and the other planets of the solar system exists. In the vicinity of the neutral point, where the velocity of colliding particles is not greater than 6 km/s, it is found that if the solid particles after collision must remain in a solid state, there can be no possibility of accretion for Mercury, Mars, and the Moon, where the maximum value of the distance of the center of the planet to the asymptotic trajectory is less than the radius of the planet. On the other hand, the capture radii of microparticles in solid form varies from a minimum of 2.95 planetary radii for Venus and 3.47 for the Earth, to about 986 for Jupiter

Non-breaking wave effects on buoyant particle distributions

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in DiBenedetto, M. H. Non-breaking wave effects on buoyant particle distributions. Frontiers in Marine Science, 7, (2020): 148, doi:10.3389/fmars.2020.00148.The dispersal of buoyant particles in the ocean mixed layer is influenced by a variety of physical factors including wind, waves, and turbulence. Microplastics observations are often made at the free surface, which is strongly forced by surface gravity waves. Many studies have used numerical simulations to examine how turbulence and wave effects (e.g., breaking waves, Langmuir circulation) control buoyant particle dispersal at the ocean surface. However these simulations are not wave phase-resolving. Therefore, the effects of an unsteady free surface due to surface gravity waves remain unknown in this context. To address this, we develop an analytical model for the distribution of buoyant particles as a function of wave-phase under wind-wave conditions in deep-water. Using this analytical model and complementary numerical simulations, we quantify the effects of a nonbreaking, monochromatic, progressive wave train on the equilibrium vertical and horizontal distributions of buoyant particles. We find that waves result in non-uniform horizontal distributions of particles with more particles under the wave crests than the troughs. We also find that the waves can stretch or compress the equilibrium vertical distribution. Finally, we consider the effects of waves on the sampling of microplastics with a towed net, and we show that waves have the ability to lower the measured concentrations relative to nets sampling without the influence of waves.This work was supported by the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, and by the US National Science Foundation under grant no. CBET-1706586

Parallel Exhaustive Search without Coordination

We analyze parallel algorithms in the context of exhaustive search over totally ordered sets. Imagine an infinite list of "boxes", with a "treasure" hidden in one of them, where the boxes' order reflects the importance of finding the treasure in a given box. At each time step, a search protocol executed by a searcher has the ability to peek into one box, and see whether the treasure is present or not. By equally dividing the workload between them, $k$ searchers can find the treasure $k$ times faster than one searcher. However, this straightforward strategy is very sensitive to failures (e.g., crashes of processors), and overcoming this issue seems to require a large amount of communication. We therefore address the question of designing parallel search algorithms maximizing their speed-up and maintaining high levels of robustness, while minimizing the amount of resources for coordination. Based on the observation that algorithms that avoid communication are inherently robust, we analyze the best running time performance of non-coordinating algorithms. Specifically, we devise non-coordinating algorithms that achieve a speed-up of $9/8$ for two searchers, a speed-up of $4/3$ for three searchers, and in general, a speed-up of $\frac{k}{4}(1+1/k)^2$ for any $k\geq 1$ searchers. Thus, asymptotically, the speed-up is only four times worse compared to the case of full-coordination, and our algorithms are surprisingly simple and hence applicable. Moreover, these bounds are tight in a strong sense as no non-coordinating search algorithm can achieve better speed-ups. Overall, we highlight that, in faulty contexts in which coordination between the searchers is technically difficult to implement, intrusive with respect to privacy, and/or costly in term of resources, it might well be worth giving up on coordination, and simply run our non-coordinating exhaustive search algorithms

Local regularity for parabolic nonlocal operators

Weak solutions to parabolic integro-differential operators of order $\alpha \in (\alpha_0, 2)$ are studied. Local a priori estimates of H\"older norms and a weak Harnack inequality are proved. These results are robust with respect to $\alpha \nearrow 2$. In this sense, the presentation is an extension of Moser's result in 1971.Comment: 31 pages, 3 figure

Local Lipschitz regularity for degenerate elliptic systems

We start presenting an $L^{\infty}$-gradient bound for solutions to non-homogeneous $p$-Laplacean type systems and equations, via suitable non-linear potentials of the right hand side. Such a bound implies a Lorentz space characterization of Lipschitz regularity of solutions which surprisingly turns out to be independent of $p$, and that reveals to be the same classical one for the standard Laplacean operator. In turn, the a priori estimates derived imply the existence of locally Lipschitz regular solutions to certain degenerate systems with critical growth of the type arising when considering geometric analysis problems, as recently emphasized by Rivi\`er

Geomorphic evolution of a storm-dominated carbonate ramp (c. 549 Ma), Nama Group, Namibia

The well-exposed Hoogland Member (c. 549 Ma) of the northern Nama Group (Kuibis Subgroup), Namibia, represents a storm-dominated carbonate ramp developed in a foreland basin of terminal Proterozoic age. The ramp displays facies gradients involving updip grainstones which pass downdip into broad, spatially extensive tracts of microbial laminites and finely laminated mudstones deposited above and below storm wave base. Trough cross-bedded, coarse grainstones are shown to transit downdip into finer-grained calcarenites, irregular microbial laminites and mottled laminites. Siliciclastic siltstones and shales were deposited further downdip. Platform growth was terminated through smothering by orogen-derived siliciclastic deposits. Ramp morphology was controlled by several different processes which acted across many orders of magnitude (millimetres to kilometres), including in situ growth of mats and reefs, scouring by wave-produced currents, and transport and infilling of coarse-grained carbonates and fine-grained carbonates and clastics. At the smallest scale, ‘roughening’ of the sea-floor through heterogeneous trapping and binding by microbial mats was balanced by smoothing of the sea-floor through accumulation of loose sediment to fill the topographic lows within the upward-propagating mat. At the next scale up, parasequence development involved roughening of the sea-floor through shoal growth and grainstone progradation, balanced by sea-floor smoothing through shale infilling of resulting downdip accommodation, as well as the metre-scale topographic depressions within the mosaic of shoal-water facies. At even larger (sequence/platform) scales, roughening of the sea-floor occurred through aggradation and progradation of thick carbonates, balanced by infilling of the foreland basin with orogen-derived siliciclastic sediments. At all scales a net balance was achieved between sea-floor roughening and sea-floor smoothing to maintain a more or less constant ramp profile

Generation of interface for an Allen-Cahn equation with nonlinear diffusion

In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property