A NASTRAN primer for the analysis of rotating flexible blades

This primer provides documentation for using MSC NASTRAN in analyzing rotating flexible blades. The analysis of these blades includes geometrically nonlinear (large displacement) analysis under centrifugal loading, and frequency and mode shape (normal modes) determination. The geometrically nonlinear analysis using NASTRAN Solution sequence 64 is discussed along with the determination of frequencies and mode shapes using Solution Sequence 63. A sample problem with the complete NASTRAN input data is included. Items unique to rotating blade analyses, such as setting angle and centrifugal softening effects are emphasized

Efficient Iterative Solvers for Stochastic Galerkin Discretizations of Log-Transformed Random Diffusion Problems

We consider the numerical solution of a steady-state diffusion problem where the diffusion coefficient is the exponent of a random field. The standard stochastic Galerkin formulation of this problem is computationally demanding because of the nonlinear structure of the uncertain component of it. We consider a reformulated version of this problem as a stochastic convection-diffusion problem with random convective velocity that depends linearly on a fixed number of independent truncated Gaussian random variables. The associated Galerkin matrix is nonsymmetric but sparse and allows for fast matrix-vector multiplications with optimal complexity. We construct and analyze two block-diagonal preconditioners for this Galerkin matrix for use with Krylov subspace methods such as the generalized minimal residual method. We test the efficiency of the proposed preconditioning approaches and compare the iterative solver performance for a model problem posed in both diffusion and convection-diffusion formulations

Efficient Iterative Algorithms for the Stochastic Finite Element Method with Application to Acoustic Scattering

In this study, we describe the algebraic computations required to implement the stochastic finite element method for solving problems in which uncertainty is restricted to right hand side data coming from forcing functions or boundary conditions. We show that the solution can be represented in a compact outer product form which leads to efficiencies in both work and storage, and we demonstrate that block iterative methods for algebraic systems with multiple right hand sides can be used to advantage to compute this solution. We also show how to generate a variety of statistical quantities from the computed solution. Finally, we examine the behavior of these statistical quantities in one setting derived from a model of acoustic scattering. UMIACS-TR-2002-10

Application of Proper Orthogonal Decomposition Methods in Reactive Pore Diffusion Simulations

Reactive pore diffusion is an important process in automotive exhaust-gas aftertreatment modelling the overall conversion of pollutants. It features highly nonlinear source terms from chemical reactions coupled with transport processes. This work examines the application of model reduction by proper orthogonal decomposition. It is shown that this technique can be successfully applied to the system using separate bases for each species. Using a basis obtained for baseline conditions, predictions can be made for species profiles within a pore system for different conditions, potentially leading to significantly reduced computational requirements

Ageing-associated DNA methylation dynamics are a molecular readout of lifespan variation among mammalian species.

BACKGROUND: Mammalian species exhibit a wide range of lifespans. To date, a robust and dynamic molecular readout of these lifespan differences has not yet been identified. Recent studies have established the existence of ageing-associated differentially methylated positions (aDMPs) in human and mouse. These are CpG sites at which DNA methylation dynamics show significant correlations with age. We hypothesise that aDMPs are pan-mammalian and are a dynamic molecular readout of lifespan variation among different mammalian species. RESULTS: A large-scale integrated analysis of aDMPs in six different mammals reveals a strong negative relationship between rate of change of methylation levels at aDMPs and lifespan. This relationship also holds when comparing two different dog breeds with known differences in lifespans. In an ageing cohort of aneuploid mice carrying a complete copy of human chromosome 21, aDMPs accumulate far more rapidly than is seen in human tissues, revealing that DNA methylation at aDMP sites is largely shaped by the nuclear trans-environment and represents a robust molecular readout of the ageing cellular milieu. CONCLUSIONS: Overall, we define the first dynamic molecular readout of lifespan differences among mammalian species and propose that aDMPs will be an invaluable molecular tool for future evolutionary and mechanistic studies aimed at understanding the biological factors that determine lifespan in mammals