An example of applications of the elementary catastrophe theory in Hamiltonian systems

The convection in atmosphere discussed in ref. [1] is rigorously treated by considering the variation of environmental temperature with the height. This represents an example of applications of the elementary catastrophe theory in Hamiltonian systems.     

The Study on the Thermal Stability of CLA in Egg Yolk

Conjugated linoleic acids (CLA) have been a subject of extensive investigation for their anticarcinogenic, hypolipidemic, antiatherosclerotic and immune-enhancing activities. Stability of CLA in foods has not received much attention by both academics and industry. Although CLA has shown many beneficial effects, its decomposition must be prevented when CLA in foods is processed, stored and transported. However, no study to date has addressed the stability of CLA in foods. The present study was carried out further to examine the stability of CLA in egg yolk during the storage and frying, using gas liquid chromatography (GLC) and silver ion high-performance liquid chromatography (Agt-HPLC). The eggs, containing 4.0% CLA per gramme of egg yolk, were 40s. Either storage for 6 months or frying for 40 s did not significantly change the composition of CLA in egg yolk. However, the degradation of CLA was statistically significant when the CLA components of egg yolk protected CLA from degradation. It is concluded that CLA is well preserved in egg before it is consumed.     

A family of multiderivative methods for the numerical solution of the Schrödinger equation

A family of multiderivative methods with minimal phase-lag are introduced in this paper, for the numerical solution of the Schrödinger equation. The methods are called multiderivative since uses derivatives of order two, four or six. Numerical application of the new obtained methods to the Schrödinger equation shows their efficiency compared with other similar well known methods of the literature.Active Member of the European Academy of Sciences and Arts     

Network theory of the nonlinear behaviour of polymer melts. Simple shear flow

Summary The network model developed in a previous paper is applied to the simple shear flow of polymer melts. The constitutive equation obtained consists of two terms. One of them describes the stress due to the network strands which exist at the onset of the deformation, dissociate during the deformation and result in a single integral constitutive equation with a strain dependent damping function. The formulation of the damping function in invariant form seems to be almost impossible.The second normal stress differenceN ₂ of the model is not zero,but has negative values. According to our model this is a consequence of the deformation dependence of the disentanglement process. The theory is compared with experimental data for a LDPE melt. It is found that the model explains the main features of the shear flow behaviour of the LDPE melt investigated preciously.

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Zusammenfassung Das Netzwerk-Modell, das in einer vorangegangenen Arbeit entwickelt wurde, wird für die einfache Scherströmung von Polymerschelzen angewendet. Die abgeleitete rheologische Zustandsgleichung besteht aus zwei Gliedern. Das erste beschreibt die Spannung-Dehnung-Beziehung der Kettensegmente, die zu Beginn der Deformation existieren und während der Deformation aufgelöst werden. Es hat die Form der einfachen Integralbeziehung mit einer Gedächtnisfunktion. Es ist kaum möglich, die dabei erhaltene Gedächtnisfunktion als Funktion der Invarianten der der Tensoren darzustellen. Die zweite Normal-SpannungsdifferenzN ₂ des Modells ist nicht Null und hat einen negativen Wert. Dies ist nach unserem Modell eine Folge der Deformationsabhängigkeit des Entschlaufungsprozesses. Die Theorie wird mit dem experimentellen Daten für eine LDPE-Schmelze verglichen, wobei sich zeigt, daß das Modell die wesentlichen Merkmale des Scherverhaltens der LDPE-Schmelze gut erklärt.

     

A review of the role of DSC analysis in the design of fluorozirconate glasses for fibre optic applications

The relatively poor thermal stability of fluorozirconate glasses is a major factor preventing the realisation of their true potential for fibre optic applications. A range of methods based on both isothermal and non-isothermal DSC techniques, which can be employed to evaluate the thermal stability of fluorozirconate glasses, are described. The relevance of these thermal stability criteria to the design of fluorozirconate compositions capable of yielding high quality optical fibres is discussed.     

Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

Operation of the quasi-optical gyrotron at harmonics of the gyrofrequency

This paper investigates the performance of a quasioptical gyrotron, when the electron beam interacts with the radiation fields at harmonics of the gyrofrequency. The nonlinear equations of motion are obtained in the slow-timescale. The expression for the linear gain is derived and the conditions for excitation are given (frequency threshold, optimal operating point, bean current and resonator quality thresholds). In the nonlinear regime, it is shown that maximum efficiencies comparable to those at the fundemental (50%) are possible, albeit at a prohitively high radiation field amplitude, while realistically feasible field amplitudes can give somewhat smaller, but nevertheless still high efficiencies (15%). Finally, the results are suplemented by empirical scaling laws, useful for experimental designs.     

Effect of substituents (NH_2,OH,F) on structures and stability of lithofluorosilylenoids

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Surfactant in the gaseous phase II. Influence on stability of foams and thin liquid films

The influence of the vapors ofn-amyl orn-decyl alcohol on the stability of single thin liquid films, single bubbles, and foam columns was determined. It was found that the presence of surfactant vapors lowered the stability of foams and single foam films. The mechanism of the destabilizing action of the surfactant vapors on wet, dynamic foams under dynamic conditions is discussed. It is shown that the destabilizing action of the surfactant vapors is a further indication that surface elasticity forces are the main factor determining stability of wet, dynamic foams.     

FRICTIONAL DISSIPATION AND NONLINEAR BAROTROPIC INSTABILITY

Based on the nonlinear quasi-geostrophic barotropic vorticity equation with Ekman friction, the criteria for nonlinear barotropic stability of the zonal basic flows are derived using Serrin-Joseph energy approach and through total energy, total enstrophy and their linear combination, separately, in terms of variational principle. Since the new transformation for Euler equation is utilized, the estimation of eigenvalue is more accurate, and the previous results of the author are improved very well.