On the signal degradation induced by the interpolation and the sampling rate reduction in aeroacoustics hybrid methods

Taking place within more extensive work that focuses on hybrid methods in aeroacoustics, the present study is devoted to the data transfer operations that are to be performed between two stages of a hybrid calculation. More precisely, the article focuses on two typical operations that usually accompany such data transfer, which are (i) the sampling rate reduction and (ii) the interpolation of the unsteady perturbations to be transmitted from one stage to the other. First part of the paper analyzes the two main issues of such operations, which are the spuriousing and the aliasing phenomena. For doing so, the usual notions of the interpolation theory are revisited before they are synthesized within an original approach. The here proposed formalism allows to understand better both the spuriousing and the aliasing phenomena, as well as to accurately predict the impact of the latter on the data to be transmitted in terms of signal degradation. Second part of the paper provides an illustration and a validation of these theoretical developments via a direct application to a typical aerodynamic noise problem (aeroacoustic emission by a 2D cylinder cross flow). There, it is further shown how the here proposed formalism can help in improving aeroacoustics hybrid calculations by predicting (and thus possibly minimizing) the bias to be induced on the acoustic extrapolation stage because of the aliasing and/or spuriousing effects inherited from the sampling rate reduction and/or interpolation of CFD data—which is likely to occur in any hybrid scenario. Copyright © 2012 John Wiley & Sons, Ltd.     

Reaching multi‐nanosecond timescales in combined QM/MM molecular dynamics simulations through parallel horsetail sampling

We report an enhanced sampling technique that allows to reach the multi‐nanosecond timescale in quantum mechanics/molecular mechanics molecular dynamics simulations. The proposed technique, called horsetail sampling, is a specific type of multiple molecular dynamics approach exhibiting high parallel efficiency. It couples a main simulation with a large number of shorter trajectories launched on independent processors at periodic time intervals. The technique is applied to study hydrogen peroxide at the water liquid–vapor interface, a system of considerable atmospheric relevance. A total simulation time of a little more than 6 ns has been attained for a total CPU time of 5.1 years representing only about 20 days of wall‐clock time. The discussion of the results highlights the strong influence of the solvation effects at the interface on the structure and the electronic properties of the solute. © 2017 Wiley Periodicals, Inc.     

An improved Sampling Strategy for the Measurement of VOCs in Air,Based on Cooled Sampling and Analysis by Thermodesorption-GC-MS/FID

Abstract

Reliable and comprehensive sampling methods are required to obtain accurate data for VOC concentrations in air samples. The major drawback of the adsorption tube sampling method, widely employed in environmental studies, is the fact that C₂ compounds are usually not trapped quantitatively.

The focus of this work was thus to improve sampling based on adsorption tubes packed with Molsieve and Carbosieve. To improve the sampling efficiency for the C₂ compounds, a cooling device, based on Peltier cooling was constructed, which could be operated at a temperature down to ?30°C.

Experiments under laboratory and field conditions were carried out to study the influence of the sampling temperatuie on the recovery of ethane and ethene as the most volatile VOCs. The results clearly demonstrate the need for a cooled sampling device for the analysis of C₂ compounds in air. Under the investigated conditions, the recoveries with ambient temperature sampling were only in the range of 38–46% for ethane and 33–59% for ethene respectively, in comparison to the cooled sampling device. These findings are only valid for the described conditions and can change significantly with temperature and concentration. A generalisation of the recovery is thus very difficult to give.

The use of the sampling device for a field study is reported, where samples were collected simultaneously at three different altitudes in a diurnal profile on the slope of the Schulterberg mountain in Tyrol (Austria).     

On reconstruction of objects from measurements of the diffracted field (*)

The aim of this paper is the shape restoration of a plane object from measurements of its diffracted field at a discrete and finite set of points. The plane sampling lattice is supposed: i) rectangular; ii)periodic.

The problem is approached as an interpolation one. A numerical algorithm for practical reconstructions is presented. A-priori limitations on the perimeter of the object and conditions on the samples lead to a-priori bounds able to estimate the precision of the reconstruction.     

Erratum: The average degree of an edge-chromatic critical graph II

In the article “The average degree of an edge-chromatic critical graph II” by Douglas R. Woodall (J. Graph Theory 56 (2007), 194-218), it was claimed that the average degree of an edge-chromatic critical graph with maximum degree $\mathrm{\Delta }$ is at least $\text{◂⋅▸}\frac{2}{3}\left(\mathrm{\Delta }+1\right)$ if $\mathrm{\Delta }⩾2$, at least $\text{◂+▸}\frac{2}{3}\mathrm{\Delta }+1$ if $\mathrm{\Delta }⩾8$, and at least $\text{◂⋅▸}\frac{2}{3}\left(\mathrm{\Delta }+2\right)$ if $\mathrm{\Delta }⩾15$. Unfortunately there were mistakes in the proof of the last two of these results, which are now proved only if $\mathrm{\Delta }⩾18$ and $\mathrm{\Delta }⩾30$, respectively.     

The Bertini irreducibility theorem for higher codimensional slices

In [3], Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their work by proving an analogous bound for the dimension of the exceptional locus in the setting of linear subspaces of higher codimensions.