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For linear elastic problems, it is well-known that mesh generation dominates the total analysis time. Different types of methods have been proposed to directly or indirectly alleviate this burden associated with mesh generation. We review in this paper a subset of such methods centred on tighter coupling between computer aided design (CAD) and analysis (finite element or boundary element methods). We focus specifically on frameworks which rely on constructing a discretisation directly from the functions used to describe the geometry of the object in CAD. Examples include B-spline subdivision surfaces, isogeometric analysis, NURBS-enhanced FEM and parametric-based implicit boundary definitions. We review recent advances in these methods and compare them to other paradigms which also aim at alleviating the burden of mesh generation in computational mechanics.
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In this review an overview on some recent developments in deformation quantization is given. After a general historical overview we motivate the basic definitions of star products and their equivalences both from a mathematical and a physical point of view. Then we focus on two topics: the Morita classification of star product algebras and convergence issues which lead to the nuclear Weyl algebra.
This is a survey on recent developments in Ricci flows.
This paper will appear in the Proceedings of the 1995 Santa Cruz Summer Institute. The paper is a survey of recent developments in the theory of toric varieties, including new constructions of toric varieties and relations to symplectic geometry, combinatorics and mirror symmetry.
Recent developments concerning oscillatory spacelike singularities in general relativity are taking place on two fronts. The first treats generic singularities in spatially homogeneous cosmology, most notably Bianchi types VIII and IX. The second deals with generic oscillatory singularities in inhomogeneous cosmologies, especially those with two commuting spacelike Killing vectors. This paper describes recent progress in these two areas: in the spatially homogeneous case focus is on mathematically rigorous results, while analytical and numerical results concerning generic behavior and so-called recurring spike formation are the main topic in the inhomogeneous case. Unifying themes are connections between asymptotic behavior, hierarchical structures, and solution generating techniques, which provide hints for a link between the nature of generic singularities and a hierarchy of hidden asymptotic symmetries.
Radiogenic heating is a key component of the energy balance and thermal evolution of the Earth. It contributes to mantle convection, plate tectonics, volcanoes, and mountain building. Geo-neutrino observations estimate the present radiogenic power of our planet. This estimate depends on the quantity and distribution of heat-producing elements in various Earth reservoirs. Of particular geological importance is radiogenic heating in the mantle. This quantity informs the origin and thermal evolution of our planet. Here we present: currently reported geo-neutrino observations; estimates of the mantle geo-neutrino signal, mantle radiogenic heating, and mantle cooling; a comparison of chemical Earth model predictions of the mantle geo-neutrino signal and mantle radiogenic heating; a brief discussion of radiogenic heating in the core, including calculations of geo-neutrino signals per pW/kg; and finally a discussion of observational strategy.
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