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Register a new userRare Event Sampling Improves Mercury Instability Statistics
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Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercurys orbit will become unstable in the future. Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the future using a large number of direct numerical simulations with an N-body code, but were not able to obtain accurate estimates before 3 billion years in the future because Mercury instability events are too rare. In this paper we use a new rare event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to obtain accurate estimates of the probability of a Mercury instability event between 2 and 3 billion years in the future in the REBOUND N-body code. We show that QDMC provides unbiased probability estimates at a computational cost of up to 100 times less than direct numerical simulation. QDMC is easy to implement and could be applied to many problems in planetary dynamics in which it is necessary to estimate the probability of a rare event.
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We propose and analyze a generalized splitting method to sample approximately from a distribution conditional on the occurrence of a rare event. This has important applications in a variety of contexts in operations research, engineering, and computational statistics. The method uses independent trials starting from a single particle. We exploit this independence to obtain asymptotic and non-asymptotic bounds on the total variation error of the sampler. Our main finding is that the approximation error depends crucially on the relative variability of the number of points produced by the splitting algorithm in one run, and that this relative variability can be readily estimated via simulation. We illustrate the relevance of the proposed method on an application in which one needs to sample (approximately) from an intractable posterior density in Bayesian inference.
Boulders on the surfaces of planets, satellites and small bodies, as well as their geological associations, provide important information about surface processes. We analyzed all available images of the surface of Mercury that have sufficient resolution and quality to detect boulders, and we mapped all the boulders observed. The lower size limit of detectable boulders was ~5 m. All boulders found on Mercury are associated with fresh impact craters hundreds of meters in diameter or larger. We compared boulder population on Mercury with population of boulders of the same size on the Moon, and found that boulders on Mercury are ~30 times less abundant than in the lunar highlands. This exact quantitative estimate is inherently inaccurate due to the limitation in the source data; however, the significant relative rarity of boulders on Mercury can be firmly and reliably established. We discuss possible causes of the observed difference. Higher thermal stresses and more rapid material fatigue due to diurnal temperature cycling on Mercury may cause rapid disintegration of the upper decimeters of the boulder surface and thus contribute to more rapid boulder obliteration; however, these factors alone cannot account for the observed difference. A proposed thicker regolith on Mercury is likely to significantly reduce boulder production rate. A higher micrometeoritic flux on Mercury is likely to result in micrometeoritic abrasion being a dominant contributor to boulder degradation; this high abrasion rate likely shortens the boulder lifetime. A combination of these factors appears to be able to account for the relative rarity of boulders on Mercury.
The InSight mission has operated on the surface of Mars for nearly two Earth years, returning detections of the first Marsquakes. The lander also deployed a meteorological instrument package and cameras to monitor local surface activity. These instruments have detected boundary layer phenomena, including small-scale vortices. These vortices register as short-lived, negative pressure excursions and closely resemble those that could generate dust devils. Although our analysis shows InSight encountered more than 900 vortices and collected more than 1000 images of the martian surface, no active dust devils were imaged. In spite of the lack of dust devil detections, we can leverage the vortex detections and InSights daily wind speed measurements to learn about the boundary layer processes that create dust devils. We discuss our analysis of InSights meteorological data to assess the statistics of vortex and dust devil activity. We also infer encounter distances for the vortices and, therefrom, the maximum vortex wind speeds. Surveying the available imagery, we place upper limits on what fraction of vortices carry dust (i.e., how many are bonafide dust devils) and estimate threshold wind speeds for dust lifting. Comparing our results to detections of dust devil tracks seen in space-based observations of the InSight landing site, we can also infer thresholds and frequency of track formation by vortices. Comparing vortex encounters and parameters with advective wind speeds, we find evidence that high wind speeds at InSight may have suppressed the formation of dust devils, explaining the lack of imaged dust devils.
We develop a novel computational method for evaluating the extreme excursion probabilities arising from random initialization of nonlinear dynamical systems. The method uses excursion probability theory to formulate a sequence of Bayesian inverse problems that, when solved, yields the biasing distribution. Solving multiple Bayesian inverse problems can be expensive; more so in higher dimensions. To alleviate the computational cost, we build machine-learning-based surrogates to solve the Bayesian inverse problems that give rise to the biasing distribution. This biasing distribution can then be used in an importance sampling procedure to estimate the extreme excursion probabilities.
Since the discovery of the first exoplanet we have known that other planetary systems can look quite unlike our own. However, until recently we have only been able to probe the upper range of the planet size distribution. The high precision of the Kepler space telescope has allowed us to detect planets that are the size of Earth and somewhat smaller, but no previous planets have been found that are smaller than those we see in our own Solar System. Here we report the discovery of a planet significantly smaller than Mercury. This tiny planet is the innermost of three planets that orbit the Sun-like host star, which we have designated Kepler-37. Owing to its extremely small size, similar to that of Earths Moon, and highly irradiated surface, Kepler-37b is probably a rocky planet with no atmosphere or water, similar to Mercury.
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