Generating analysis topology using virtual topology operators

AbstractVirtual topology operations have been utilized to generate an analysis topology definition suitable for downstream mesh generation. Detailed descriptions are provided for virtual topology merge and split operations for all topological entities, where virtual decompositions are robustly linked to the underlying geometry. Current virtual topology technology is extended to allow the virtual partitioning of volume cells. A valid description of the topology, including relative orientations, is maintained which enables downstream interrogations to be performed on the analysis topology description, such as determining if a specific meshing strategy can be applied to the virtual volume cells. As the virtual representation is a true non-manifold description of the sub-divided domain the interfaces between cells are recorded automatically. Therefore, the advantages of non-manifold modelling are exploited within the manifold modelling environment of a major commercial CAD system without any adaptation of the underlying CAD model. A hierarchical virtual structure is maintained where virtual entities are merged or partitioned. This has a major benefit over existing solutions as the virtual dependencies here are stored in an open and accessible manner, providing the analyst with the freedom to create, modify and edit the analysis topology in any preferred sequence

Parametric design velocity computation for CAD-based design optimization using adjoint methods

This paper presents an efficient optimization process, where the parameters defining the features in a feature-based CAD model are used as design variables. The process exploits adjoint methods for the computation of gradients, and as such the computational cost is essentially independent of the number of design variables, making it ideal for optimization in large design spaces. The novelty of this paper lies in linking the adjoint surface sensitivity information with geometric sensitivity values, referred to as design velocities, computed for CAD models created in commercial CAD systems (e.g. CATIA V5 or Siemens NX)

Provenance of Eocene river sediments from the central northern Sierra Nevada and implications for paleotopography

Geochronology of fluvial deposits can be used to characterize provenance, the paleotopography of sediment source regions, and the development of regional drainage systems. We present U-Pb and (U-Th)/He ages of detrital zircon grains from Eocene gravels preserved in several paleoriver systems along the western flank of the central and northern Sierra Nevada. These ages allow us to trace the sourcing of detritus in paleorivers and to constrain the evolution of the Sierra Nevada range front. U-Pb zircon age distributions are bimodal, with a dominant peak between 110 and 95 Ma and smaller but significant peaks in the Middle to Late Jurassic, matching the predominant ages of the Sierra Nevada batholith. A small fraction (<6%) of grains has pre-Mesozoic ages, which consistently match ages from prebatholithic assemblages within the northern part of the range. (U-Th)/He ages of a subset of double-dated zircons cluster between 114 and 74 Ma and are consistent with batholithic (U-Th)/He cooling ages in the northern Sierra. Our results indicate that the Eocene river systems in the central northern Sierra Nevada likely had proximal headwaters and had relatively steep axial gradients, draining smaller areas than was commonly thought. This also suggests that the northern Sierra Nevada would have had an established drainage divide and would have acted as a major topographic barrier during the early to mid-Cenozoic. The data presented here support a model of the Eocene northern Sierra Nevada characterized by a western slope with a gradient broadly similar to that of today

16 Multiple Linear Regression Viewpoints

This paper analyzes two methods for testing moderation effects in regression models that contain a continuous dependent variable, a continuous independent variable, and a dichotomized grouped moderator; a test of the interaction term in the full regression model and a test of the difference between the simple slopes. Typically, researchers test the significance of the interaction term. Based on mathematical equations and empirical examples, we argue that the test for the difference between the simple slopes should be utilized when researchers are interested in testing for moderation effects. By decomposing the test statistics for these two methods, we demonstrate that the test for the difference between the simple slopes has increased power and less Type II error, while retaining equivalent Type I error rates. oderated relationships in social science research exist when the relationship between two variables, X and Y, varies depending on the value of a third variable Z. This study examines a specific type of moderated relationship with a continuous dependent variable (Y), a continuous independent variable (X), and an independent dichotomous categorical variable (Z). Given these variables, a moderated relationship exists if the relationship between X and Y is different for both levels of Z. This can be estimated with an interaction term using the following regression equatio

A reduced-order model for gradient-based aerodynamic shape optimisation

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This work presents a reduced order model for gradient based aerodynamic shape optimization. The solution of the fluid Euler equations is converted to reduced Newton iterations by using the Least Squares Petrov-Galerkin projection. The reduced order basis is extracted by Proper Orthogonal Decomposition from snapshots based on the fluid state. The formulation distinguishes itself by obtaining the snapshots for all design parameters by solving a linear system of equations. Similarly, the reduced gradient formulation is derived by projecting the full-order model state onto the subspace spanned by the reduced basis. Auto-differentiation is used to evaluate the reduced Jacobian without forming the full fluid Jacobian explicitly during the reduced Newton iterations. Throughout the optimisation trajectory, the residual of the reduced Newton iterations is used as an indicator to update the snapshots and enrich the reduced order basis. The resulting multi-fidelity optimisation problem is managed by a trust-region algorithm. The ROM is demonstrated for a subsonic inverse design problem and for an aerofoil drag minimization problem in the transonic regime. The results suggest that the proposed algorithm is capable of aerodynamic shape optimization while reducing the number of full-order model queries and time to solution with respect to an adjoint gradient based optimisation framework

Bis(4-amino­pyridinium) tetra­chlorido­cobaltate(II)

In the title compound, (C5H7N2)2[CoCl4], the cobalt(II) ion is coordinated by four chloride ions in a slightly distorted tetra­hedral geometry. The crystal packing is stabilized by inter­molecular N—H⋯Cl hydrogen bonding, forming a three-dimensional network. The crystal was a non-merohedral twin emulating tetra­gonal symmetry, but being in fact ortho­rhom­bic