Academic literature on the topic 'Functional Hopf Formulation'

Conjugated linoleic acid (CLA), one of the polyunsaturated conjugated fatty acids, has garnered increased attention in recent years due to its potential health advantages. Antioxidant, anti-inflammatory, anti-atherosclerotic, antimutagenic, and anticarcinogenic properties of CLA are widely acknowledged. Lean body mass, immune-induced muscle wasting prevention, and fat reduction are among the additional health advantages of CLA that have been shown in animal and cell-line research. Owing to studies of their positive effects on several models of chronic inflammatory illnesses and metabolic disorders, conjugated fatty acids have garnered a lot of attention lately. The geometrical and positional isomers of octadecadienoic acid that have double bonds in conjugated positions are referred to together as conjugated linoleic acid. The usual range of CLA concentration in meat and dairy products is 0.3–0.8% CLA per g of fat, with the cis-9, trans-11 isomer accounting for 73–93% of the total CLA. Consequently, the synthesis of CLA has garnered more attention in studies in recent years. Future use of CLA as a lipid will be highly beneficial. Because of its many health benefits, CLA has been gaining more and more attention every day. We hope that CLA will be utilized in functional foods in the future. It is currently utilized as a medication in the form of capsules for a variety of uses. This chapter covers the composition, metabolism, biological effects, biochemical effects, current research, and applications of CLA.

Abstract Every historian of archaic Greece has to come to terms with the First Sacred War. Located with welcome precision in time by the source material in the 5 90s and 5 Sos, involving many of the major Greek cities and powers of the period, and significantly affecting the life and functions of one of the major sanctuaries and oracles of Greece, the war has to be incorporated into any narrative or analysis. Yet for the modern historiography of archaic Greece it presents acute dilemmas of method and credibility. The problems are not those presented by Athenian history, where it is the historicity or otherwise of a growing list of documents (or of ‘documents’) which poses the major challenge, compounded by growing awareness of the rolling nature of oral tradition and its impact on ‘history’.1 Rather, with the First Sacred War we have to deal with a tradition which suddenly appears in crystallized written form long after the event, so that modern scholarship has an unwelcome choice between cautious acceptance en bloc and a quasi-archaeological disinterment of the various layers which inevitably deconstructs the whole. The exposition which follows here will therefore have to oscillate between the registers of modern and ancient historiography, I hope without loss of clarity, in an effort to reach a formulation which stands some chance of conveying the truth.

We discussed some aspects of the responses of chemical systems, linear or nonlinear, to perturbations on several earlier occasions. The first was the responses of the chemical species in a reaction mechanism (a network) in a nonequilibrium stable stationary state to a pulse in concentration of one species. We referred to this approach as the “pulse method” (see chapter 5 for theory and chapter 6 for experiments). Second, we studied the time series of the responses of concentrations to repeated random perturbations, the formulation of correlation functions from such measurements, and the construction of the correlation metric (see chapter 7 for theory and chapter 8 for experiments). Third, in the investigation of oscillatory chemical reactions we showed that the responses of a chemical system in a stable stationary state close to a Hopf bifurcation are related to the category of the oscillatory reaction and to the role of the essential species in the system (see chapter 11 for theory and experiments). In each of these cases the responses yield important information about the reaction pathway and the reaction mechanism. In this chapter we focus on the design of simple types of response experiments that make it possible to extract mechanistic and kinetic information from complex nonlinear reaction systems. The main idea is to use “neutral” labeled compounds (tracers), which have the same kinetic and transport properties as the unlabeled compounds. In our previous work we have shown that by using neutral tracers a class of response experiments can be described by linear response laws, even though the underlying kinetic equations are highly nonlinear. The linear response is not the result of a linearization procedure, but it is due to the use of neutral tracers. As a result the response is linear even for large perturbations, making it possible to investigate global nonlinear kinetics by making use of linear mathematical techniques. Moreover, the susceptibility functions from the response law are related to the probability densities of the lifetimes and transit times of the various chemical species, making it easy to establish a connection between the response data and the mechanism and kinetics of the process.

Quality characteristics of bakery products rely partially on the amount and type of fats in their formulation. This study focused on producing emulsified shortenings with high oleic palm oil fractions to be thermo-mechanically characterized and used in the baking of high-fat cookies. Palm oil and hydrogenated fats were commonly used in bakery shortenings to achieve texture and flavor. However, saturated and trans-fats have been shown to cause detrimental health effects, motivating their reduction and replacement by unsaturated fats. Blending of fats and the use of emulsifiers are low-cost techniques to produce pumpable shortenings; alternative fats that comply with functional and sensory requirements of current baking fats. High oleic palm oil (HOPO) is a novel oil with a lower content of saturated fat and higher content of oleic acid compared to traditional palm oil (TPO). High oleic red olein (HORO) is a carotene-rich fraction of HOPO. In this study, emulsified shortenings containing HOPO, HORO, and TPO were produced under identical conditions to reach 30% saturated fat. DSC peaks of mid-melting triglycerides in TPO were not present in HOPO or HORO, reflected in lower SFC and hardness of HOPO and HORO shortenings vs. TPO shortening. However, all formulations resulted in similar onset temperatures of crystallization and melting points. Despite thermal and physical differences between shortenings, physical properties of shortening-containing cookies were not statistically different. It was demonstrated how HOPO and HORO can be used as alternative fats to TPO in the making of shortenings to be used in baking applications.

The operation envelope of modern gas turbines is affected by thermoacoustically induced combustion oscillations. The understanding and development of active and passive means for their suppression is crucial for the design process and field introduction of new gas turbine combustion systems. Whereas the propagation of acoustic sound waves in gas turbine combustion systems has been well understood, the flame induced acoustic source terms are still a major topic of investigation. The dynamics of combustion processes can be analyzed by means of flame transfer functions which relate heat release fluctuations to velocity fluctuations caused by a flame. The purpose of this paper is to introduce and to validate a novel computational approach to reconstruct flame transfer functions based on unsteady excited RANS simulations and system identification. Resulting time series of velocity and heat release are then used to reconstruct the flame transfer function by application of a system identification method based on Wiener-Hopf formulation. CFD/SI approach has been applied to a typical gas turbine burner. 3D unsteady simulations have been performed and the flame transfer results have been validated by comparison to experimental data. In addition the method has been benchmarked to results obtained from sinusoidal excitations.

In order to achieve low levels of pollutants modern gas turbine combustion systems operate in lean and premixed modes. However, under these conditions self-excited combustion oscillations due to a complex feedback mechanism between pressure and heat release fluctuations can be found. These instabilities may lead to uncontrolled high pressure amplitude oscillations which can damage the whole combustor. The flame induced acoustic source terms are still analytically not well described and are a major topic of thermo-acoustic investigations. For the analysis of thermo-acoustic phenomena in gas turbine combustion systems flame transfer functions can be utilized. The purpose of this paper is to introduce and to investigate modeling parameters, which could influence a novel computational approach to reconstruct flame transfer functions known as the CFD/SI method. The flame transfer function estimation is made by application of a system identification method based on Wiener-Hopf formulation. Varying acoustic boundary conditions, combustion models and time resolutions may strongly affect the reconstructed flame response characterizing overall system dynamics. The CFD/SI approach has been applied to a generic gas turbine burner to derive a flame response. 3D unsteady simulations excited with white noise have been performed and the reconstructed flame transfer functions have been validated with experimental data. Moreover, the impact on the reconstructed flame transfer functions because of different boundary condition configurations has been examined.

This paper presents a set of methodologies for the extraction of linear growth and damping rates associated with transversal eigenmodes at screech level frequencies in thermoacoustically non-compact gas turbine combustion systems from time domain data. Knowledge of these quantities is of high technical relevance as an required input for the design of damping devices for high frequency oscillations. In addition, validation of prediction tools and flame models as well as the thermoacoustic characterization of a given unstable/stable operation point in terms of their distance from the Hopf bifurcation point occurs via the system growth/damping rates. The methodologies solely rely on dynamic measurement data (i.e. unsteady heat release and/or pressure recordings) while avoiding the need of any external excitation (e.g. via sirens), and are thus in principle suitable for the employment on operational engine data. Specifically, the following methodologies are presented: 1) The extraction of pure acoustic damping rates (i.e. without any flame contribution) from oscillatory chemiluminescence and pressure recordings. 2) The obtainment of net growth rates of linearly stable operation points from oscillatory pressure signals. 3) The identification of net growth rates of linearly unstable operation points from noisy pressure envelope data. The fundamental basis of these procedures is the derivation of appropriate stochastic differential equations, which admit analytical solutions that depend on the global system parameters. These analytical expressions serve as objective functions against which measured data are fitted to yield the desired growth or damping rates. Bayesian methods are employed to optimize precision and confidence of the fitting results. Numerical test cases given by time domain formulations of the acoustic conservation equations including high-frequency flame models as well as acoustic damping terms are set up and solved. The resulting unsteady pressure and heat release data are then subjected to the proposed identification methodologies to present corresponding proof of principles and grant suitability for employment on real systems.