The structure of the asteroid 4 Vesta as revealed by models of planet-scale collisions

Asteroid 4Vesta seems to be a major intact protoplanet, with a surface composition similar to that of the HED (howardite-eucrite-diogenite) meteorites. The southern hemisphere is dominated by a giant impact scar, but previous impact models have failed to reproduce the observed topography. The recent discovery that Vesta's southern hemisphere is dominated by two overlapping basins provides an opportunity to model Vesta's topography more accurately. Here we report three-dimensional simulations of Vesta's global evolution under two overlapping planet-scale collisions. We closely reproduce its observed shape, and provide maps of impact excavation and ejecta deposition. Spiral patterns observed in the younger basin Rheasilvia, about one billion years old, are attributed to Coriolis forces during crater collapse. Surface materials exposed in the north come from a depth of about 20kilometres, according to our models, whereas materials exposed inside the southern double-excavation come from depths of about 60-100kilometres. If Vesta began as a layered, completely differentiated protoplanet, then our model predicts large areas of pure diogenites and olivine-rich rocks. These are not seen, possibly implying that the outer 100kilometres or so of Vesta is composed mainly of a basaltic crust (eucrites) with ultramafic intrusions (diogenites).

Family models of independence/interdependence and their intergenerational similarity in Germany, Turkey, and India

Family change theory suggests three ideal-typical family models characterized by different combinations of emotional and material interdependencies in the family. Its major proposition is that in economically developing countries with a collectivistic background a family model of emotional interdependence emerges from a family model of complete interdependence. The current study aims to identify and compare patterns of family-related value orientations related to family change theory across three cultures and two generations. Overall, N = 919 dyads of mothers and their adolescent children from Germany, Turkey, and India participated in the study. Three clusters were identified representing the family models of independence, interdependence, and emotional interdependence, respectively. Especially the identification of an emotionally interdependent value pattern using a person-oriented approach is an important step in the empirical validation of family change theory. The preference for the three family models differed across as well as within cultures and generations according to theoretical predictions. Dyadic analyses pointed to substantial intergenerational similarities and also to differences in family models, reflecting both cultural continuity as well as change in family-related value orientations.

Values of children and family models of adolescents: An eleven-culture study

Starting from Kagitcibasi's (2007) conceptualization of family models, this study compared N = 2961 adolescents' values across eleven cultures and explored whether patterns of values were related to the three proposed family models through cluster analyses. Three clusters with value profiles corresponding to the family models of interdependence, emotional interdependence, and independence were identified on the cultural as well as on the individual level. Furthermore, individual-level clusters corresponded to culture-level clusters in terms of individual cluster membership. The results largely support Kagitcibasi's proposition of changing family models and demonstrate their representation as individual-level value profiles across cultures.

Representation via Probabilities: Models of Probabilistic Modeling

How do probabilistic models represent their targets and how do they allow us to learn about them? The answer to this question depends on a number of details, in particular on the meaning of the probabilities involved. To classify the options, a minimalist conception of representation (Su\'arez 2004) is adopted: Modelers devise substitutes (``sources'') of their targets and investigate them to infer something about the target. Probabilistic models allow us to infer probabilities about the target from probabilities about the source. This leads to a framework in which we can systematically distinguish between different models of probabilistic modeling. I develop a fully Bayesian view of probabilistic modeling, but I argue that, as an alternative, Bayesian degrees of belief about the target may be derived from ontic probabilities about the source. Remarkably, some accounts of ontic probabilities can avoid problems if they are supposed to apply to sources only.

ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. I. ATMOSPHERIC DYNAMICS VIA THE SHALLOW WATER SYSTEM

Within the context of exoplanetary atmospheres, we present a comprehensive linear analysis of forced, damped, magnetized shallow water systems, exploring the effects of dimensionality, geometry (Cartesian, pseudo-spherical, and spherical), rotation, magnetic tension, and hydrodynamic and magnetic sources of friction. Across a broad range of conditions, we find that the key governing equation for atmospheres and quantum harmonic oscillators are identical, even when forcing (stellar irradiation), sources of friction (molecular viscosity, Rayleigh drag, and magnetic drag), and magnetic tension are included. The global atmospheric structure is largely controlled by a single key parameter that involves the Rossby and Prandtl numbers. This near-universality breaks down when either molecular viscosity or magnetic drag acts non-uniformly across latitude or a poloidal magnetic field is present, suggesting that these effects will introduce qualitative changes to the familiar chevron-shaped feature witnessed in simulations of atmospheric circulation. We also find that hydrodynamic and magnetic sources of friction have dissimilar phase signatures and affect the flow in fundamentally different ways, implying that using Rayleigh drag to mimic magnetic drag is inaccurate. We exhaustively lay down the theoretical formalism (dispersion relations, governing equations, and time-dependent wave solutions) for a broad suite of models. In all situations, we derive the steady state of an atmosphere, which is relevant to interpreting infrared phase and eclipse maps of exoplanetary atmospheres. We elucidate a pinching effect that confines the atmospheric structure to be near the equator. Our suite of analytical models may be used to develop decisively physical intuition and as a reference point for three-dimensional magnetohydrodynamic simulations of atmospheric circulation.

Analytical Models of Exoplanetary Atmospheres. II. Radiative Transfer via the Two-Stream Approximation

We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior) and solutions for the temperature-pressure profiles. Generally, the problem is mathematically under-determined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat and the properties of scattering both in optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing and incoming fluxes in the convective regime.

Discontinuity in the responses of ecosystem processes and multifunctionality to altered soil community composition

Ecosystem management policies increasingly emphasize provision of multiple, as opposed to single, ecosystem services. Management for such "multifunctionality" has stimulated research into the role that biodiversity plays in providing desired rates of multiple ecosystem processes. Positive effects of biodiversity on indices of multifunctionality are consistently found, primarily because species that are redundant for one ecosystem process under a given set of environmental conditions play a distinct role under different conditions or in the provision of another ecosystem process. Here we show that the positive effects of diversity (specifically community composition) on multifunctionality indices can also arise from a statistical fallacy analogous to Simpson's paradox (where aggregating data obscures causal relationships). We manipulated soil faunal community composition in combination with nitrogen fertilization of model grassland ecosystems and repeatedly measured five ecosystem processes related to plant productivity, carbon storage, and nutrient turnover. We calculated three common multifunctionality indices based on these processes and found that the functional complexity of the soil communities had a consistent positive effect on the indices. However, only two of the five ecosystem processes also responded positively to increasing complexity, whereas the other three responded neutrally or negatively. Furthermore, none of the individual processes responded to both the complexity and the nitrogen manipulations in a manner consistent with the indices. Our data show that multifunctionality indices can obscure relationships that exist between communities and key ecosystem processes, leading us to question their use in advancing theoretical understanding-and in management decisions-about how biodiversity is related to the provision of multiple ecosystem services.