Tidal disruptions: A continuum theory for solid bodies

Although the theory of Roche 1847 for the tidal disruption limits of orbiting satellites assumes a fluid body, a length to diameter of exactly 2.07:1, and a particular body orientation, the theory is commonly applied to the satellites of the Solar System and to small asteroids and comets passing nearby a planet. Clearly these bodies are neither fluid nor generally are that elongated, so a more appropriate theory is needed. Here we present exact analytical results for the distortion and disruption limits of solid spinning ellipsoidal bodies subjected to tidal forces, using the Drucker-Prager strength model with zero cohesion. It is the appropriate model for dry granular materials such as sands and rocks, for rubble-pile asteroids and comets, and for larger satellites, asteroids and comets where the cohesion can be ignored. This study uses the same approach as the studies of spin limits for solid ellipsoidal bodies given in [Holsapple, K.A., 2001. Icarus 154, 432-448; Holsapple, K.A., 2004. Icarus 172, 272-303]. It is a static theory that predicts conditions for breakup and predicts the nature of the deformations at the limit state, but does not track the dynamics of the body as it comes apart. The strength is characterized by a single material parameter associated with an angle of friction, which can range from zero to 90°. The case with zero friction angle has no shear strength whatsoever, so it is then the model of a fluid or gas. The case of 90° represents a material that cannot fail in shear, but still has zero tensile strength. Typical dry soils have angles of friction of 30°-40°. Since the static fluid case is included in the theory as a special case, the classical results of Roche [Roche, E.A., 1847. Acad. Sci. Lett. Montpelier. Mem. Section Sci. 1, 243-262] and Jeans [Jeans, J.H., 1917. Mem. R. Astron. Soc. London 62, 1-48] are included and re-derived in their entirety; but the general solid case has much more variety and applicability. We consider both the spin-locked case, appropriate for most satellites of the Solar System; and the zero spin case, a possible case for a passing stray body. Detailed plots of many special cases are presented, in terms of shape, orientation and mass densities. A very typical result gives a closest approach d=1.5(ρ/ρP)^1/3R in terms of the planet radius R, and the satellite and planet mass densities ρ and ρP. We also use the theory to distinguish between conditions allowing global shape changes leading to new equilibrium states, or those leading to complete disruption. We apply the theory to the potentially hazardous Asteroid 99942 Apophis due to pass very near the Earth in 2029, and conclude it is extremely unlikely to experience any tidal readjustments during its passage. The states of many of the satellites of the Solar System are compared to the theory, and we find that all are well within their tidal disruption limits for expected values of the internal friction.     

Catastrophic disruption of asteroids and family formation: a review of numerical simulations including both fragmentation and gravitational reaccumulations

In the last few years, thanks to the development of sophisticated numerical codes, a major breakthrough has been achieved in our understanding of the processes involved in small body collisions. In this review, we summarize the most recent results provided by numerical simulations, accounting for both the fragmentation of an asteroid and the gravitational interactions of the generated fragments. These studies have greatly improved our knowledge of the mechanisms that are at the origin of some observed features in the asteroid belt. In particular, the simulations have demonstrated that, for bodies larger than several kilometers, the collisional process not only involves the fragmentation of the asteroid but also the gravitational interactions between the ejected fragments. This latter mechanism can lead to the formation of large aggregates by gravitational reaccumulation of smaller fragments, and helps explain the presence of large members within asteroid families. Numerical simulations of the complete process have thus reproduced successfully for the first time the main properties of asteroid families, each formed by the disruption of a large parent body, and provided information on the possible internal structure of the parent bodies. A large amount of work remains necessary, however, to understand in deeper detail the physical process as a function of material properties and internal structures that are relevant to asteroids, and to determine in a more quantitative way the outcome properties such as fragment shapes and rotational states.     

Inference of herder presence from GPS collar data of semi-free range cattle

Although global positioning system (GPS) location data have been used to derive animal movement parameters including step length, rarely have these parameters been used to predict animal responses to human interventions. In this study, we tested whether GPS-derived step length of semi-free range cattle is a function of herder presence. The derived step-length model was used to predict herder presence on independent cattle GPS collar data. We also tested whether cattle foraging behaviour is explained by herder activity and vegetation greenness. We used logistic regression to model herder presence as a function of step length and relate cattle behaviour with herder activity and vegetation greenness. The field-based step length model successfully predicted herder presence on GPS collar data. The average predicted frequency of herder presence for the GPS-collared herds was 31%, whilst the field-based GPS frequency was 27%. Herding activities and vegetation greenness also explained different cattle foraging behaviour.     

华南板块早中生代陆内造山过程——以雪峰山-九岭为例

雪峰山-九岭造山带位于华南板块的中心区域,是一条典型的陆内造山带。通过详细的野外地质观察,雪峰山在早中生代经历了3期构造变形:D1为上部指向NW的韧性剪切,D2代表了一期反向褶皱-逆冲构造事件,以及D3期的水平挤压形成的直立的褶皱、劈理和线理。而在九岭,早中生代大规模脆-韧性域构造变形叠加在早古生代韧性变形之上,形成了一系列极性NW逆冲断层和不对称褶皱。雪峰山-九岭陆内造山带形成于早中生代,造山作用可以分为两个阶段,即245~225Ma的挤压变形阶段和225~215Ma的垮塌-岩浆侵位阶段。雪峰山-九岭造山带的构造特点表明,华南板块东南缘古太平洋板块向北西方向的俯冲可能引发了早中生代的陆内造山过程。     

Climatic oscillations in central Italy during the Last Glacial–Holocene transition: the record from Lake Accesa

This paper presents an event stratigraphy based on data documenting the history of vegetation cover, lake‐level changes and fire frequency, as well as volcanic eruptions, over the Last Glacial–early Holocene transition from a terrestrial sediment sequence recovered at Lake Accesa in Tuscany (north‐central Italy). On the basis of an age–depth model inferred from 13 radiocarbon dates and six tephra horizons, the Oldest Dryas–Bølling warming event was dated to ca. 14 560 cal. yr BP and the Younger Dryas event to ca. 12 700–11 650 cal. yr BP. Four sub‐millennial scale cooling phases were recognised from pollen data at ca. 14 300–14 200, 13 900–13 700, 13 400–13 100 and 11 350–11 150 cal. yr BP. The last three may be Mediterranean equivalents to the Older Dryas (GI‐1d), Intra‐Allerød (GI‐1b) and Preboreal Oscillation (PBO) cooling events defined from the GRIP ice‐core and indicate strong climatic linkages between the North Atlantic and Mediterranean areas during the last Termination. The first may correspond to Intra‐Bølling cold oscillations registered by various palaeoclimatic records in the North Atlantic region. The lake‐level record shows that the sub‐millennial scale climatic oscillations which punctuated the last deglaciation were associated in central Italy with different successive patterns of hydrological changes from the Bølling warming to the 8.2 ka cold reversal. Copyright © 2006 John Wiley & Sons, Ltd.     

Mountain building and exhumation processes through time: inferences from nature and models

Orogenic belts involving initially hot lithospheres, as exemplified by accretionary-type orogens, commonly show distributed deformation and retrograde PT paths with a concomitant decrease in pressure and temperature. Paths may track geotherms, indicating thermal equilibrium, consistent with slow strain and exhumation rates, limited strain localization, and consequently limited topographical gradients and distributed erosion. Such patterns are more common in Precambrian times than in younger periods of the Earth history. In contrast, orogens involving initially stiff lithospheres show exhumation PT paths that track isothermal decompression reflecting high strain rates along major shear zones, a feature typical of Phanerozoic collision belts. Field evidence, analogue and numerical models emphasize that strain localization has first-order consequences for the tectonic evolution of orogenic zones including structure, metamorphism, exhumation processes, topography, erosion and sedimentation modes.