Nonlinear phenomena in thermoacoustics: A comparison between single-mode and multi-mode methods

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies and amplitudes of limit cycles. In frequency domain analyses, a quasi-linear transfer function between acoustic velocity and heat release rate perturbations, called the flame describing function (FDF), is obtained from a flame model or experiments. The FDF is a function of the frequency and amplitude of velocity perturbations but only contains the heat release response at the forcing frequency. While the gain and phase of the FDF provide insight into the nonlinear dynamics of the system, the accuracy of its predictions remains to be verified for different types of nonlinearity. In time domain analyses, the governing equations of the fully coupled problem are solved to find the time evolution of the system. One method is to discretize the governing equations using a suitable basis, such as the natural acoustic modes of the system. The number of modes used in the discretization alters the accuracy of the solution. In our previous work we have shown that predictions using the FDF are almost exactly the same as those obtained from the time-domain using only one mode for the discretization. We call this the single-mode method. In this paper we compare results from the single-mode and multi-mode methods, applied to a thermoacoustic system of a premixed flame in a tube. For some cases, the results differ greatly in both amplitude as well as frequency content. This study shows that the contribution from higher and subharmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Hence multi-mode simulations are necessary, and the single-mode method or the FDF may be insufficient to capture some of the complex nonlinear behaviour in fhermoacoustics.

When will a flame describing function approach to thermoacoustics work well?

In any thermoacoustic analysis, it is important not only to predict linear frequencies and growth rates, but also the amplitude and frequencies of any limit cycles. The Flame Describing Function (FDF) approach is a quasi-linear analysis which allows the prediction of both the linear and nonlinear behaviour of a thermoacoustic system. This means that one can predict linear growth rates and frequencies, and also the amplitudes and frequencies of any limit cycles. The FDF achieves this by assuming that the acoustics are linear and that the flame, which is the only nonlinear element in the thermoacoustic system, can be adequately described by considering only its response at the frequency at which it is forced. Therefore any harmonics generated by the flame's nonlinear response are not considered. This implies that these nonlinear harmonics are small or that they are sufficiently filtered out by the linear dynamics of the system (the low-pass filter assumption). In this paper, a flame model with a simple saturation nonlinearity is coupled to simple duct acoustics, and the success of the FDF in predicting limit cycles is studied over a range of flame positions and acoustic damping parameters. Although these two parameters affect only the linear acoustics and not the nonlinear flame dynamics, they determine the validity of the low-pass filter assumption made in applying the flame describing function approach. Their importance is highlighted by studying the level of success of an FDF-based analysis as they are varied. This is achieved by comparing the FDF's prediction of limit-cycle amplitudes to the amplitudes seen in time domain simulations.

A species conserving genetic algorithm for multimodal function optimization

This paper introduces a new technique called species conservation for evolving parallel subpopulations. The technique is based on the concept of dividing the population into several species according to their similarity. Each of these species is built around a dominating individual called the species seed. Species seeds found in the current generation are saved (conserved) by moving them into the next generation. Our technique has proved to be very effective in finding multiple solutions of multimodal optimization problems. We demonstrate this by applying it to a set of test problems, including some problems known to be deceptive to genetic algorithms.

Material parameter extraction in THz-TDS using a converging beam transfer function

We demonstrate a parameter extraction algorithm based on a theoretical transfer function, which takes into account a converging THz beam. Using this, we successfully extract material parameters from data obtained for a quartz sample with a THz time domain spectrometer. © 2010 IEEE.

Anaesthetic impairment of immune function is mediated via GABA(A) receptors.

BACKGROUND: GABA(A) receptors are members of the Cys-loop family of neurotransmitter receptors, proteins which are responsible for fast synaptic transmission, and are the site of action of wide range of drugs. Recent work has shown that Cys-loop receptors are present on immune cells, but their physiological roles and the effects of drugs that modify their function in the innate immune system are currently unclear. We are interested in how and why anaesthetics increase infections in intensive care patients; a serious problem as more than 50% of patients with severe sepsis will die. As many anaesthetics act via GABA(A) receptors, the aim of this study was to determine if these receptors are present on immune cells, and could play a role in immunocompromising patients. PRINCIPAL FINDINGS: We demonstrate, using RT-PCR, that monocytes express GABA(A) receptors constructed of α1, α4, β2, γ1 and/or δ subunits. Whole cell patch clamp electrophysiological studies show that GABA can activate these receptors, resulting in the opening of a chloride-selective channel; activation is inhibited by the GABA(A) receptor antagonists bicuculline and picrotoxin, but not enhanced by the positive modulator diazepam. The anaesthetic drugs propofol and thiopental, which can act via GABA(A) receptors, impaired monocyte function in classic immunological chemotaxis and phagocytosis assays, an effect reversed by bicuculline and picrotoxin. SIGNIFICANCE: Our results show that functional GABA(A) receptors are present on monocytes with properties similar to CNS GABA(A) receptors. The functional data provide a possible explanation as to why chronic propofol and thiopental administration can increase the risk of infection in critically ill patients: their action on GABA(A) receptors inhibits normal monocyte behaviour. The data also suggest a potential solution: monocyte GABA(A) receptors are insensitive to diazepam, thus the use of benzodiazepines as an alternative anesthetising agent may be advantageous where infection is a life threatening problem.

Quasi-static three-point bending of carbon fiber sandwich beams with square honeycomb cores

Sandwich beams comprising identical face sheets and a square honeycomb core were manufactured from carbon fiber composite sheets. Analytical expressions were derived for four competing collapse mechanisms of simply supported and clamped sandwich beams in three-point bending: core shear, face microbuckling, face wrinkling, and indentation. Selected geometries of sandwich beams were tested to illustrate these collapse modes, with good agreement between analytic predictions and measurements of the failure load. Finite element (FE) simulations of the three-point bending responses of these beams were also conducted by constructing a FE model by laying up unidirectional plies in appropriate orientations. The initiation and growth of damage in the laminates were included in the FE calculations. With this embellishment, the FE model was able to predict the measured load versus displacement response and the failure sequence in each of the composite beams. © 2011 American Society of Mechanical Engineers.

Performance of low density parity check codes as a function of actual and assumed noise levels

We investigate how sensitive Gallager's codes are, when decoded by the sum-product algorithm, to the assumed noise level. We have found a remarkably simple function that fits the empirical results as a function of the actual noise level at both high and low noise levels. © 2004 Elsevier B.V.

Performance of low density parity check codes as a function of actual and assumed noise levels

We investigate how sensitive Gallager's codes are, when decoded by the sum-product algorithm, to the assumed noise level. We have found a remarkably simple function that fits the empirical results as a function of the actual noise level at both high and low noise levels. ©2003 Published by Elsevier Science B. V.

Damage development in an armor ceramic under quasi-static indentation

The objective of the present study is to assess the capabilities of a recently developed mechanism-based model for inelastic deformation and damage in structural ceramics. In addition to conventional lattice plasticity, the model accounts for microcrack growth and coalescence as well as granular flow following comminution. The assessment is made through a coupled experimental/computational study of the indentation response of a commercial armor ceramic. The experiments include examinations of subsurface damage zones along with measurements of residual surface profiles and residual near-surface stresses. Extensive finite element computations are conducted in parallel. Comparisons between experiment and simulation indicate that the most discriminating metric in the assessment is the spatial extent of subsurface damage following indentation. Residual stresses provide additional validation. In contrast, surface profiles of indents are dictated largely by lattice plasticity and thus provide minimal additional insight into the inelastic deformation resulting from microcracking or granular flow. A satisfactory level of correlation is obtained using property values that are either measured directly or estimated from physically based arguments, without undue reliance on adjustable (nonphysical) parameters. © 2011 The American Ceramic Society.

A Salmonella Typhimurium-Typhi genomic chimera: a model to study Vi polysaccharide capsule function in vivo.

The Vi capsular polysaccharide is a virulence-associated factor expressed by Salmonella enterica serotype Typhi but absent from virtually all other Salmonella serotypes. In order to study this determinant in vivo, we characterised a Vi-positive S. Typhimurium (C5.507 Vi(+)), harbouring the Salmonella pathogenicity island (SPI)-7, which encodes the Vi locus. S. Typhimurium C5.507 Vi(+) colonised and persisted in mice at similar levels compared to the parent strain, S. Typhimurium C5. However, the innate immune response to infection with C5.507 Vi(+) and SGB1, an isogenic derivative not expressing Vi, differed markedly. Infection with C5.507 Vi(+) resulted in a significant reduction in cellular trafficking of innate immune cells, including PMN and NK cells, compared to SGB1 Vi(-) infected animals. C5.507 Vi(+) infection stimulated reduced numbers of TNF-α, MIP-2 and perforin producing cells compared to SGB1 Vi(-). The modulating effect associated with Vi was not observed in MyD88(-/-) and was reduced in TLR4(-/-) mice. The presence of the Vi capsule also correlated with induction of the anti-inflammatory cytokine IL-10 in vivo, a factor that impacted on chemotaxis and the activation of immune cells in vitro.