Discrete linear stability and sensitivity analysis of fluid flows

Este trabajo presenta un método discreto para el cálculo de estabilidad hidrodinámica y análisis de sensibilidad a perturbaciones externas para ecuaciones diferenciales y en particular para las ecuaciones de Navier-Stokes compressible. Se utiliza una aproximación con variable compleja para obtener una precisión analítica en la evaluación de la matriz Jacobiana. Además, mapas de sensibilidad para la sensibilidad a las modificaciones del flujo de base y a una fuerza constante permiten identificar las regiones del campo fluido donde una modificacin (ej. fuerza puntual) tiene un efecto estabilizador del flujo. Se presentan cuatro casos de prueba: (1) un caso analítico para comprobar la derivación discreta, (2) una cavidad cerrada a bajo Reynolds para mostrar la mayor precisión en el cálculo de los valores propios con la aproximación de paso complejo, (3) flujo 2D en un cilindro circular para validar la metodología, y (4) flujo en un cavidad abierta, presentado para validar el método en casos de inestabilidades convectivamente inestables. Los tres últimos casos mencionados (2-4) se resolvieron con las ecuaciones de Navier-Stokes compresibles, utilizando un método Discontinuous Galerkin Spectral Element Method. Se obtuvo una buena concordancia para el caso de validación (3), cuando se comparó el nuevo método con resultados de la literatura. Además, este trabajo muestra que para el cálculo de los modos propios directos y adjuntos, así como para los mapas de sensibilidad, el uso de variables complejas es de suprema importancia para obtener una predicción precisa. El método descrito es aplicado al análisis para la estabilización de la estela generada por un disco actuador, que representa un modelo sencillo para hélices, rotores de helicópteros o turbinas eólicas. Se explora la primera bifurcación del flujo para un disco actuador, y se sugiere que está asociada a una inestabilidad de tipo Kelvin-Helmholtz, cuya estabilidad se controla con en el número de Reynolds y en la resistencia del disco actuador (o fuerza resistente). En primer lugar, se verifica que la disminución de la resistencia del disco tiene un efecto estabilizador parecido a una disminución del Reynolds. En segundo lugar, el análisis hidrodinmico discreto identifica dos regiones para la colocación de una fuerza puntual que controle las inestabilidades, una cerca del disco y otra en una zona aguas abajo. En tercer lugar, se muestra que la inclusión de un forzamiento localizado cerca del actuador produce una estabilización más eficiente que al forzar aguas abajo. El análisis de los campos de flujo controlados confirma que modificando el gradiente de velocidad cerca del actuador es más eficiente para estabilizar la estela. Estos resultados podrían proporcionar nuevas directrices para la estabilización de la estela de turbinas de viento o de marea cuando estén instaladas en un parque eólico y minimizar las interacciones no estacionarias entre turbinas. ABSTRACT A discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex-step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid-driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex-step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number is used to validate the methodology, and finally, (4) the flow past an open cavity is presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. An analysis for stabilising the wake past an actuator disc, which represents a simple model for propellers, helicopter rotors or wind turbines is also presented. We explore the first flow bifurcation for an actuator disc and it suggests that it is associated to a Kelvin- Helmholtz type instability whose stability relies on the Reynolds number and the flow resistance applied through the disc (or actuator forcing). First, we report that decreasing the disc resistance has a similar stabilising effect to an decrease in the Reynolds number. Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the disc and one far downstream where the instability originates. Third, we show that adding a localised forcing close to the actuator provides more stabilisation that forcing far downstream. The analysis of the controlled flow fields, confirms that modifying the velocity gradient close to the actuator is more efficient to stabilise the wake than controlling the sheared flow far downstream. An interesting application of these results is to provide guidelines for stabilising the wake of wind or tidal turbines when placed in an energy farm to minimise unsteady interactions.

Ice as a matrix for IR-matrix-assisted laser desorption/ionization: mass spectra from a protein single crystal.

Lasers emitting in the ultraviolet wavelength range of 260-360 nm are almost exclusively used for matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) of macromolecules. Reports about the use of lasers emitting in the infrared first appeared in 1990/1991. In contrast to MALDI in the ultraviolet, a very limited number of reports on IR-MALDI have since been published. Several matrices have been identified for infrared MALDI yielding spectra of a quality comparable to those obtained in the ultraviolet. Water (ice) was recognized early as a potential matrix because of its strong O-H stretching mode near 3 microm. Interest in water as matrix derives primarily from the fact that it is the major constituent of most biological tissues. If functional as matrix, it might allow the in situ analysis of macromolecular constituents in frozen cell sections without extraction or exchanging the water. We present results that show that IR-MALDI of lyophilized proteins, air dried protein solutions, or protein crystals up to a molecular mass of 30 kDa is possible without the addition of any separate matrix. Samples must be frozen to retain a sufficient fraction of the water of hydration in the vacuum. The limited current sensitivity, requiring at least 10 pmol of protein for a successful analysis needs to be further improved.

DNA sequencing by delayed extraction-matrix-assisted laser desorption/ionization time of flight mass spectrometry.

Matrix-assisted laser desorption/ionization (MALDI) time of flight mass spectrometry was used to detect and order DNA fragments generated by Sanger dideoxy cycle sequencing. This was accomplished by improving the sensitivity and resolution of the MALDI method using a delayed ion extraction technique (DE-MALDI). The cycle sequencing chemistry was optimized to produce as much as 100 fmol of each specific dideoxy terminated fragment, generated from extension of a 13-base primer annealed on 40- and 50-base templates. Analysis of the resultant sequencing mixture by DE-MALDI identified the appropriate termination products. The technique provides a new non-gel-based method to sequence DNA which may ultimately have considerable speed advantages over traditional methodologies.

Power system sensitivity analysis for probabilistic small signal stability assessment in a deregulated environment

Deregulations and market practices in power industry have brought great challenges to the system planning area. In particular, they introduce a variety of uncertainties to system planning. New techniques are required to cope with such uncertainties. As a promising approach, probabilistic methods are attracting more and more attentions by system planners. In small signal stability analysis, generation control parameters play an important role in determining the stability margin. The objective of this paper is to investigate power system state matrix sensitivity characteristics with respect to system parameter uncertainties with analytical and numerical approaches and to identify those parameters have great impact on system eigenvalues, therefore, the system stability properties. Those identified parameter variations need to be investigated with priority. The results can be used to help Regional Transmission Organizations (RTOs) and Independent System Operators (ISOs) perform planning studies under the open access environment.

Matrix effects: The Achilles heel of quantitative high-performance liquid chromatography-electrospray-tandem mass spectrometry

High-performance liquid chromatography coupled by an electrospray ion source to a tandem mass spectrometer (HPLC-EST-MS/ MS) is the current analytical method of choice for quantitation of analytes in biological matrices. With HPLC-ESI-MS/MS having the characteristics of high selectivity, sensitivity, and throughput, this technology is being increasingly used in the clinical laboratory. An important issue to be addressed in method development, validation, and routine use of HPLC-ESI-MS/MS is matrix effects. Matrix effects are the alteration of ionization efficiency by the presence of coeluting substances. These effects are unseen in the chromatograrn but have deleterious impact on methods accuracy and sensitivity. The two common ways to assess matrix effects are either by the postextraction addition method or the postcolumn infusion method. To remove or minimize matrix effects, modification to the sample extraction methodology and improved chromatographic separation must be performed. These two parameters are linked together and form the basis of developing a successful and robust quantitative HPLC-EST-MS/MS method. Due to the heterogenous nature of the population being studied, the variability of a method must be assessed in samples taken from a variety of subjects. In this paper, the major aspects of matrix effects are discussed with an approach to address matrix effects during method validation proposed. (c) 2004 The Canadian Society of Clinical Chemists. All rights reserved.

Eigenvalue sensitivity analysis for probabilistic small signal stability assessment

This paper presents a method to analyze the first order eigenvalue sensitivity with respect to the operating parameters of a power system. The method is based on explicitly expressing the system state matrix into sub-matrices. The eigenvalue sensitivity is calculated based on the explicitly formed system state matrix. The 4th order generator model and 4th order exciter system model are used to form the system state matrix. A case study using New England 10-machine 39-bus system is provided to demonstrate the effectiveness of the proposed method. This method can be applied into large scale power system eigenvalue sensitivity with respect to operating parameters.

Smart structure sensors based on embedded fibre Bragg grating arrays in aluminium alloy matrix by ultrasonic consolidation

Smart structure sensors based on embedded fibre Bragg grating (FBG) arrays in aluminium alloy matrix by ultrasonic consolidation (UC) technique have been proposed and demonstrated successfully. The temperature, loading and bending responses of the embedded FBG arrays have been systematically characterized. The embedded FBGs exhibit an average temperature sensitivity of ~36 pm °C-1, which is three times higher than that of normal FBGs, a bending sensitivity of 0.73 nm/m-1 and a loading responsivity of ~0.1 nm kg-1 within the dynamic range from 0 kg to 3 kg. These initial experimental results clearly demonstrate that the UC produced metal matrix structures can be embedded with FBG sensor arrays to become smart structures with capabilities to monitor the structure operation and health conditions in applications.

Effect of osmotic and matrix potential on Saprolegnia diclina and S. ferax

Growth of biomass and sporulation of pathogenic and non-pathogenic Saprolegnia species was markedly decreased at reduced water potentials. Oogonium and zoosporangium formation were more sensitive to reduced osmotic and matrix potentials than growth in biomass. Although little difference was observed between the effects of matrix and osmotic potentials, the Saprolegnia species investigated responded differently to those solutes utilized in control of osmotic potential. Biomas, oogonium and zoosporangium formation were greater in the presence of reduced osmotic potentials mediated by mannitol than equivalent potentials mediated by potassium chloride. Endogenous potassium levels varied little with reduced matrix or osmotic potentials. Conversly, mannitol content of colonies exposed to reduced osmotic potentials mediated by mannitol initailly increased while endogenous amino acid levels were observed to rise in response to moderately reduced water potentials. Sensitivity of Saprolegnia species to reduced potantials and effects on substrate colonization are discussed in the light of these observations.

Sensitivity of peptide conformational dynamics on clustering of a classical molecular dynamics trajectory

We investigate the sensitivity of a Markov model with states and transition probabilities obtained from clustering a molecular dynamics trajectory. We have examined a 500 ns molecular dynamics trajectory of the peptide valine-proline-alanine-leucine in explicit water. The sensitivity is quantified by varying the boundaries of the clusters and investigating the resulting variation in transition probabilities and the average transition time between states. In this way, we represent the effect of clustering using different clustering algorithms. It is found that in terms of the investigated quantities, the peptide dynamics described by the Markov model is sensitive to the clustering; in particular, the average transition times are found to vary up to 46%. Moreover, inclusion of nonphysical sparsely populated clusters can lead to serious errors of up to 814%. In the investigation, the time step used in the transition matrix is determined by the minimum time scale on which the system behaves approximately Markovian. This time step is found to be about 100 ps. It is concluded that the description of peptide dynamics with transition matrices should be performed with care, and that using standard clustering algorithms to obtain states and transition probabilities may not always produce reliable results.

Embedded fibre Bragg grating array sensors in aluminium alloy matrix by ultrasonic consolidation

Fibre Bragg Grating (FBG) array sensors have been successfully embedded in aluminium alloy matrix by ultrasonic consolidation (UC) technique. The temperature and loading responses of the embedded FBG arrays have been systematically characterised. The embedded grating sensors exhibit an average temperature sensitivity of ~36pm/°C, which is three times higher than that of normal FBGs, and a loading responsivity of ~0.1nm/kg within the dynamic range from 0kg to 3kg. This initial experiment clearly demonstrates that FBG array sensors can be embedded in metal matrix together with other passive and active fibres to fabricate smart materials to monitor the operation and health of engineering structures.

Integration of a 3D hydrogel matrix within a hollow core photonic crystal fibre for DNA probe immobilization

In this paper, we demonstrate the integration of a 3D hydrogel matrix within a hollow core photonic crystal fibre (HC-PCF). In addition, we also show the fluorescence of Cy5-labelled DNA molecules immobilized within the hydrogel formed in two different types of HC-PCF. The 3D hydrogel matrix is designed to bind with the amino groups of biomolecules using an appropriate cross-linker, providing higher sensitivity and selectivity than the standard 2D coverage, enabling a greater number of probe molecules to be available per unit area. The HC-PCFs, on the other hand, can be designed to maximize the capture of fluorescence to improve sensitivity and provide longer interaction lengths. This could enable the development of fibre-based point-of-care and remote systems, where the enhanced sensitivity would relax the constraints placed on sources and detectors. In this paper, we will discuss the formation of such polyethylene glycol diacrylate (PEGDA) hydrogels within a HC-PCF, including their optical properties such as light propagation and auto-fluorescence.

Effect of thermal and mechanical processing on tensile properties of powder formed 2124 aluminium and 2124 Al-SiC p metal matrix composite

The aging responses of 2124 Al-SiC p metal matrix composite (MMC) and unreinforced matrix alloy are studied and related to variations in tensile properties. The MMC is aged from Wo starting conditions: (i) stretched and naturally aged and (ii) re-solution treated. Accelerated aging occurs in both MMC conditions compared with unreinforced alloy. Tensile strengths and elastic moduli are improved in the MMC compared with the alloy, but ductility is reduced. Stretched MMC exhibits higher strength but lower ductility and modulus than re-solutioned MMC. The re-solutioned MMC fails by microvoid coalescence in low aging conditions, and by void nucleation and shear in high aging conditions. Failure of the stretched MMC initiates at the surface at specimen shoulders, illustrating the increased notch sensitivity of this condition, and propagates via a zigzag shear fracture mode. Zigzag facet size increases on gross aging. Particle fracture occurs during tensile failure, but also before testing as a result of the manufacturing process. © 1995 The Institute of Materials.

Embedded fibre Bragg grating array sensors in aluminium alloy matrix by ultrasonic consolidation

Fibre Bragg Grating (FBG) array sensors have been successfully embedded in aluminium alloy matrix by ultrasonic consolidation (UC) technique. The temperature and loading responses of the embedded FBG arrays have been systematically characterised. The embedded grating sensors exhibit an average temperature sensitivity of ~36pm/°C, which is three times higher than that of normal FBGs, and a loading responsivity of ~0.1nm/kg within the dynamic range from 0kg to 3kg. This initial experiment clearly demonstrates that FBG array sensors can be embedded in metal matrix together with other passive and active fibres to fabricate smart materials to monitor the operation and health of engineering structures.

Evaluating New Matrix Pooled Testing Methods for Detecting HIV Treatment Failure with and without Covariate Information

Thesis (Master's)--University of Washington, 2016-08

Aluminum and iron can be deposited in the calcified matrix of bone exostoses.

International audience