The 41 0-kilometer seismic discontinuity is generally considered to be caused by a phase transformation of the main constituent of the upper mantle, olivine, ot-(Mg,Fe)2SiO4, to P-(Mg,Fe)2SiO4. Recent data show that H20 dissolves in olivine and other nominally anhydrous mantle minerals and that the partitioning of H20 between olivine and P-(Mg,Fe)2Si04 is about 1:10. Such behavior strongly affe...

We present a new algorithm to solve the problem of rock deformation. The method is based on a ‘classical’ Lagrangian finite element solver in which the connectivity between the nodes of the numerical mesh is updated at the end of each time (or deformation) step. The method, which we term Dynamic Lagrangian Remeshing (DLR), relies on the theory of Delaunay triangulation and produces optimal fini...

We present a finite element method with a finite thickness embedded weak discontinuity to analyze ductile fracture problems. The formulation is restricted to small geometry changes. The material response is characterized by a constitutive relation for a progressively cavitating elastic–plastic solid. As voids nucleate, grow and coalesce, the stiffness of the material degrades. An embedded weak ...

Introduction. When a fiber-reinforced viscoelastic material is cooled from cure temperature to room temperature the different coefficients of thermal expansion of the matrix and fibers lead to residual stresses. To study this phenomenon in detail, we consider a thin, isotropic, thermorheologically simple, linearly viscoelastic plate reinforced by a random system of fibers lying in the plane of ...

Elasticity theory is an important component of continuum mechanics and has had widely spread applications in science and engineering. Material interfaces are ubiquity in nature and man-made devices, and often give rise to discontinuous coefficients in the governing elasticity equations. In this work, the matched interface and boundary (MIB) method is developed to address elasticity interface pr...

The regression discontinuity (RD) design is one of the most widely used nonexperimental methods for causal inference and program evaluation. Over last two decades, statistical econometric RD analysis have expanded matured, there now a large number methodological results identification, estimation, inference, validation. We offer curated review this literature organized around popular frameworks...

We define and study a calculus of discontinuity, a version of displacement calculus, which is a logic of segmented strings in exactly the same sense that the Lambek calculus is a logic of strings. Like the Lambek calculus, the displacement calculus is a sequence logic free of structural rules, and enjoys Cut-elimination and its corollaries: the subformula property, decidability, and the finite ...

This paper makes two generalisations of categorial calculus of discontinuity. In the rst we introduce unary modalities which mediate between continuous and discontinuous strings. In the second each of the modes of adjunction of the proposal to date, concatenation, juxtaposition and interpolation, are augmented with variants. Linguistic illustration and motivation is provided, and we show how ad...