Linear Stability

The stability of an immiscible layer of fluid bounded by two other fluids of different viscosities and migrating through a porous medium is analysed, both theoretically and experimentally. Linear stability analyses for both one-dimensional and radial flows are presented, with particular emphasis upon the behaviour when one of the interfaces is highly stable and the other is unstable. For one-dimensional motion, it is found that owing to the unstable interface, the intermediate layer of fluid eventually breaks up into drops.However, in the case of radial flow, both surface tension and the continuous thinning of the intermediate layer as it moves outward may stabilize the system. We investigate both of these stabilization mechanisms and quantify their effects in the relevant parameter space. When the outer interface is strongly unstable, there is a window of instability for an intermediate range of radial positions of the annulus. In this region, as the basic state evolves to larger r...

We present some examples of detailed analysis of intrinsic localized modes in lattices, using the accurate numerical methods derived from the proof of existence of MacKay-Aubry. We report on some improvements on the methods, which are then used to the fullest to obtain the Floquet analysis of the breather solutions. Such calculations are possible taking into account the whole lattice,

We analyze a second-order, nonlinear delay-differential equation with negative feedback. The characteristic equation for the linear stability of the equilibrium is completely solved, as a function of two parameters describing the strength of the feedback and the damping in the autonomous system. The bifurcations occurring as the linear stability is lost are investigated by the construction of a center manifold:

Light-emitting diode (LED) nonlinear differential gain (DG) and differential phase (DP) were measured, since they are important performance factors in video signal transmission. Typical, experimentally measured temperature dependence of DG and DP is also presented. A linearizing method for minimizing LED DG and DP distortions, using predistortion, is proposed and experimentally examined. With this technique, and with precise adjustment of the predistortion circuits, the DG of a typical LED was improved from 12.5 percent to less than 1 percent, and the DP from 2.8° to 1°. This corresponds to an improvement in second and third-order harmonic distortions of 19 dB and 21 dB, respectively. DG and DP were measured with respect to the 3.58-MHz color subcarrier frequency superimposed on the 15.75-kHz horizontal scanning sawtooth wave. The linearization stability with regard to temperature variation was lowered to be less than 1-percent DG and 1° DP in the temperature range from 15 to 45°C.

The linear stability theory is used to investigate analytically the effects of gravity modulation on convection in a homogenous porous layer heated from below. The gravitational field consists of a constant part and a sinusoidally varying part, which is tantamount to a vertically oscillating porous layer subjected to constant gravity. The linear stability results are presented for the specific case of low amplitude vibration for which it is shown that increasing the frequency of vibration stabilises the convection.

Numerical orbit integrations have been conducted to characterize the types of tra-jectories in the one-dimensional Newtonian three-body problem with equal masses and negative energy. Essentially three different types of motions were found to exist. They may be ...

This work concentrates on the lateral oscillations in vehicles, also called shimmy, with a particular empha- sis on aircraft. A mathematical model of a nose landing gear is discussed with geometric detail that has been mostly neglected in the past research. Stability criteria for the shimmy-free operation of the landing gear are derived using linear stability analysis. Nonlinear analy- sis is used not only to study the qualitative behaviour of the Hopf bifurcation but also to analyze the system be- yond the Hopf bifurcation. The manuscript concludes with suggestions for future research.

This work aimed to evaluate trunk muscle forces, internal loads and stability margin under some simulated standing postures, with and without external loads, using a nonlinear finite element model of the T1–S1 spine with realistic nonlinear load-displacement properties. A novel kinematics-based algorithm was applied that exploited a set of spinal sagittal rotations, initially calculated to minimize balancing moments, to solve

In this paper we have examined the linear stability of triangular equilibrium points in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. We have found the position of triangular equilibrium points of our problem. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. The equations of motion are affected by radiation pressure force, oblateness and P-R drag. All classical results involving photogravitational and oblateness in restricted three body problem may be verified from this result. With the help of characteristic equation, we discussed the stability. Finally we conclude that triangular equilibrium points are unstable.