Investigating the effectiveness of Padé-type approximations

Both algebraic and numerical Padé-type approximants represent improvements on more common approaches as far as accuracy is concerned. However, the derivation of an algebraic Padé approximation first requires the computation of a power series approximation to the target function, and Padé-type stencils typically involve more operations than other schemes. We attempt to quantify the improvement in accuracy expected alongside the associated increase in computational expense. We do so for a set of problems chosen to depict differing behaviours in a range of target functions. We apply the compact schemes introduced by Lele (which have since been used in problems requiring their “spectral-like” resolution) to various PDEs intended to represent a range of phenomena in fluid dynamics (e.g. the 2D Helmholtz equation, as found in fluid potential fields; the 1D, linear heat equation; and, the conservative form of the Burgers’equation). Of particular interest is the Van der Pol oscillator model which serves as an analogy for the near-wake flow oscillations observed in the von Karman vortex street of a slender bluff body in cross-flow. Measuring the accuracy and computational run-time of each method, we found that, for example, for the heat equation, we found a 1.8% average error reduction with a51% increase in run-time for the 4th-order accurate Classical Padé-type stencil in comparison to the standard central difference stencil. Similar comparisons can be made for the algebraic approximation, although the run-time is reduced while the error improvement is enhanced (by comparison with a corresponding Taylor series approximation)

Short Story: “Villain’s Suicide”

As B.R. Ambedkar stated in Annihilation of Caste, day laborers only suffer grueling labor on subsistence wages owing to their terror of punishment given to those who question it. This story reminds readers that so-called ritual impurity or untouchability has never stopped non-privileged caste people from being violated through touch and sexual abuse. The agitation over the 2012 Delhi gang rape and the more recent revelations of #MeToo occur amidst a long history of low-income Dalit women and girls routinely facing rape and other forms of repeated sexual assault from powerful landowners whose word can stop or start their wages. This story allows us to listen to the conversations and internal monologue of two-day laborers, both of whom struggle on a non-living wage. Devamani waits for her abuse to end, hoping the next generation will not be treated as a spittoon for men’s bodily fluids. Meanwhile, her friend Suguna finds the only way possible to feed her extended family

Separation of Am(III) from Cm(III) and Eu(III) by electro-spun polystyrene- immobilized CyMe4-BTPhen

The synthesis of a novel 5-(4-vinylphenyl)-CyMe4-BTPhen actinide selective ligand using selenium free synthetic procedures is reported. For the first time, we report the electrospinning of this actinide selective ligand into a polystyrene fiber and investigate its selective removal of Am(III) from Eu(III) and Am(III) from Cm(III). The functionalized fibres demonstrated a separation factor of SFAm/Eu ∼ 57 and a small, but significant separation of SFAm/Cm ∼ 2.9 at 4 M HNO3

Rapid distortion theory on transversely sheared mean flows of arbitrary cross section

This paper is concerned with Rapid Distortion Theory on transversely sheared mean flows that (among other things) can be used to analyze the unsteady motion resulting from the interaction of a turbulent shear flow with a solid surface. It expands on a previous analysis of Goldstein, Leib and Afsar (J. Fluid Mech. Vol. 824, pp. 477-51) that uses a pair of conservation laws to derive upstream boundary conditions for planar mean flows and extends these findings to transversely sheared flows of arbitrary cross section. The results, which turn out to be quite general, are applied to the specific case of a round jet interacting with the trailing edge of a flat plate and used to calculate the radiated sound field, which is then compared with experimental data taken at the NASA Glenn Research Center

Improved jet noise predictions in subsonic flows using an approximate composite asymptotic expansion of the adjoint Green's function in Goldstein's analogy

Our recent work on jet noise modeling (Afsar et al. 2019, PhilTrans. A., vol. 377) has confirmed that non-parallel flow effects are needed to determine the wave propagation aspect of the jet noise problem. The acoustic spectrum calculated using an asymptotic representation of non-parallel flow effects produces the correct spectral shape of the small angle radiation beyond that which can be predicted using a parallel (i.e. non-spreading) mean flow approximation to determine the wave propagation tensor in Goldstein’s generalized acoustic analogy formulation. While the peak noise predicted using this approach works remarkably well at low frequencies (up to and slightly beyond the peak Strouhal number), the high frequency prediction in Afsar et al. (2019) relied upon an ad-hoc composite asymptotic formula for the propagator that was also restricted to the small angle spectra. In this paper we therefore attempt to remedy this defect by using the O(1) frequency locally parallel flow Green’s function as a kind-of outer solution to the propagator tensor in which the non-parallel flow theory used in the latter reference acts as the ’inner’ solution that is valid at low frequencies and is transcendentally small beyond the peak frequency. The hope is that this approach will allow more robust high frequency predictions with a single set of turbulence parameters for the acoustic spectrum at any given acoustic Mach number. In other words, both non-parallel and locally parallel regions of the propagator tensor solution are multiplied by the same turbulence source structure in the acoustic spectrum integral. The paper highlights the basic formalism of the low frequency jet noise theory and sum- marises the technical problems and strategy we use to extend this approach to higher frequen- cies