A bodner-partom visco-plastic dynamic sphere benchmark problem

Developing benchmark analytic solutions for problems in solid and fluid mechanics is very important for the purpose of testing and verifying computational physics codes. Our primary objective in this research is to obtain a benchmark analytic solution to the equation of motion in radially symmetric spherical coordinates. An analytic solution for the dynamic response of a sphere composed of an isotropic visco-plastic material and subjected to spherically symmetric boundary conditions is developed and implemented. The radial displacement u is computed by solving the equation of motion, a linear second-order hyperbolic PDE. The plastic strains εp and εp are computed by solving two non-linear first-order ODEs in time. We obtain a solution for u in terms of the plastic strain components and boundary conditions in the form of an infinite series. Computationally, at each time step, we set up an iteration scheme to solve the PDE-ODE system. The linear momentum equation is solved using the plastic strains from the previous iteration, then the plastic strain equations are solved numerically using the new displacement. We demonstrate the accuracy and convergence of our benchmark solution under spatial mesh, time step, and eigenmode refinement

Explanatory pluralism in the medical sciences: theory and practice

Explanatory pluralism is the view that the best form and level of explanation depends on the kind of question one seeks to answer by the explanation, and that in order to answer all questions in the best way possible, we need more than one form and level of explanation. In the first part of this article, we argue that explanatory pluralism holds for the medical sciences, at least in theory. However, in the second part of the article we show that medical research and practice is actually not fully and truly explanatory pluralist yet. Although the literature demonstrates a slowly growing interest in non-reductive explanations in medicine, the dominant approach in medicine is still methodologically reductionist. This implies that non-reductive explanations often do not get the attention they deserve. We argue that the field of medicine could benefit greatly by reconsidering its reductive tendencies and becoming fully and truly explanatory pluralist. Nonetheless, trying to achieve the right balance in the search for and application of reductive and non-reductive explanations will in any case be a difficult exercise

Differential diagnosis of perinatal hypophosphatasia: radiologic perspectives

Perinatal hypophosphatasia (HPP) is a rare, potentially life-threatening, inherited, systemic metabolic bone disease that can be difficult to recognize in utero and postnatally. Diagnosis is challenging because of the large number of skeletal dysplasias with overlapping clinical features. This review focuses on the role of fetal and neonatal imaging modalities in the differential diagnosis of perinatal HPP from other skeletal dysplasias (e.g., osteogenesis imperfecta, campomelic dysplasia, achondrogenesis subtypes, hypochondrogenesis, cleidocranial dysplasia). Perinatal HPP is associated with a broad spectrum of imaging findings that are characteristic of but do not occur in all cases of HPP and are not unique to HPP, such as shortening, bowing and angulation of the long bones, and slender, poorly ossified ribs and metaphyseal lucencies. Conversely, absent ossification of whole bones is characteristic of severe lethal HPP and is associated with very few other conditions. Certain features may help distinguish HPP from other skeletal dysplasias, such as sites of angulation of long bones, patterns of hypomineralization, and metaphyseal characteristics. In utero recognition of HPP allows for the assembly and preparation of a multidisciplinary care team before delivery and provides additional time to devise treatment strategies

INTEGRATING A BILINEAR INTERPOLATION FUNCTION ACROSS QUADRILATERAL CELL BOUNDARIES Integrating a Bilinear Interpolation Function Across Quadrilateral Cell Boundaries Integrating a Bilinear Interpolation Function Across Quadrilateral Cell Boundaries

Abstract Computational models of particle dynamics often exchange solution data with discretized continuum-fields using interpolation functions. These particle methods require a series expansion of the interpolation function for two purposes: numerical analyses used to establish the models consistency and accuracy, and logical-coordinate evaluation used to locate particles within a grid. This report presents a new method of developing discrete-expansions for interpolation; they are similar to multi-variable expansions but, unlike a Taylor's series, discrete-expansions are valid throughout a discretized domain. Discrete-expansions are developed herein by parametrically integrating the interpolation function's total-differential between two particles located within separate, non-contiguous cells. Discrete-expansions are valid for numerical analyses since they acknowledge the functional dependence of interpolation and account for mapping discontinuities across cell boundaries. The use of discrete-expansions for logical-coordinate evaluation provides an algorithmically robust and computationally efficient particle localization method. Verification of this new method is demonstrated herein on a simple test problem

A bodner-partom visco-plastic dynamic sphere benchmark problem

Developing benchmark analytic solutions for problems in solid and fluid mechanics is very important for the purpose of testing and verifying computational physics codes. Our primary objective in this research is to obtain a benchmark analytic solution to the equation of motion in radially symmetric spherical coordinates. An analytic solution for the dynamic response of a sphere composed of an isotropic visco-plastic material and subjected to spherically symmetric boundary conditions is developed and implemented. The radial displacement u is computed by solving the equation of motion, a linear second-order hyperbolic PDE. The plastic strains εp and εp are computed by solving two non-linear first-order ODEs in time. We obtain a solution for u in terms of the plastic strain components and boundary conditions in the form of an infinite series. Computationally, at each time step, we set up an iteration scheme to solve the PDE-ODE system. The linear momentum equation is solved using the plastic strains from the previous iteration, then the plastic strain equations are solved numerically using the new displacement. We demonstrate the accuracy and convergence of our benchmark solution under spatial mesh, time step, and eigenmode refinement