Growth Of Oscillation Amplitude Research Articles

Formulation of electron motion in a storage ring with a betatron tune varying with time and a dipole shaker working at a constant frequency

In order to reduce the beam density efficiently for a safe beam abort, we analytically studied the motion of an aborted electron beam undergoing a sinusoidal kick by a beam shaker working at a constant frequency. Since the rf power is switched off, the betatron tune changes gradually with time due to chromatic effects. Chromatic aberration, together with a finite energy spread, enhances the dilution effect of the beam density, while the change in betatron tune with time causes a phase slippage that suppresses the growth of oscillation amplitude by the beam shaker. In order to treat such a situation properly, we formulated the motion of an aborted electron beam, taking into account nonlinear chromatic effects, under the adiabatic condition that the change in betatron tune is much slower than the betatron oscillation. In addition, by considering the case of a linearly varying betatron tune, it is shown that the response of an aborted electron beam can be interpreted as a superposition of waves, i.e., diffraction of waves. Our investigation not only provides a criteria for the determination of shaker's frequency for a safe beam abort but also has applications to resonance crossing phenomena.

Semi-inverse method in nonlinear mechanics: application to couple shell- and beam-type oscillations of single-walled carbon nanotubes

We demonstrate the application of the efficient semi-inverse asymptotic method to resonant interaction of the nonlinear normal modes belonging to different branches of the CNT vibration spectrum. Under condition of the 1:1 resonance of the beam and circumferential flexure modes we obtain the dynamical equations, the solutions of which describe the coupled stationary states. The latter are characterized by the non-uniform distribution of the energy along the circumferential coordinate. The non-stationary solutions for obtained equations correspond to the slow change of the energy distribution. It is shown that adequate description of considered resonance processes can be achieved in the domain variables. They are the linear combinations of the shell- and beam-type normal modes. Using such variables we have analyzed not only nonlinear normal modes but also the limiting phase trajectories describing the strongly non-stationary dynamics. The evolution of the considered resonance processes with the oscillation amplitude growth is analyzed by the phase portrait method and verified by the numerical integration of the respective dynamical equations.

Gas Resonant Oscillations Considering Gas Relaxation Properties

The model of gas oscillations under external harmonic load considering the gas relaxation properties and environment resistance force has been developed. The studies carried out using numerical analysis show that coincidence of the environment oscillation frequency with the external load oscillation frequency results in resonance, followed by the environment unlimited oscillation amplitude growth without considering its internal resistance. Resonant oscillations occurring under the environment resistance forces demonstrate the results as follows: May be the either damped oscillations in case of large resistance factor values, undamped oscillation in the process of stabilized amplitude and by the bifurcation amplitude change in the process of damped or undamped oscillation. The type of the oscillation process depends on the relation between the relaxation factor and the environment resistance factor.

Sexually transmitted infections and mate-finding Allee effects

Infectious diseases can seriously impact dynamics of their host species. In this study, we model and analyze an interaction between a sexually transmitted infection and its animal host population affected by a mate-finding Allee effect. Since mating drives both host reproduction and infection transmission, the Allee effect shapes the transmission rate of the infection which we show takes a saturating form. Our model combining sexually transmitted infections with the mate-finding Allee effect in the host produces quite rich dynamics, including oscillations, several multistability regimes, and infection-induced host extinction. However, many of these complex patterns are restricted to a relatively narrow parameter range. We find that the host extinction occurs at intermediate levels of infection virulence, as well as for Allee effect strengths much lower than when the infection is absent. In both cases, a sequence of events comprising destabilization of an endemic equilibrium, growth of oscillation amplitude, and a heteroclinic bifurcation forms an underlying mechanism. We apply our model to the feline immunodeficiency virus (FIV) in domestic cats.

A study on the effect of synchronization by an angle modulated signal in a single loop optoelectronic oscillator

The present paper, aside considering the influence of a forcing signal, discusses the effect of frequency modulated synchronizing signal on optoelectronic oscillator and the corresponding FM–AM conversion for the injection synchronized optoelectronic oscillator is studied. A method to calculate the locking range of a synchronized angle modulated OEO is presented. The amplitude and phase equations are derived using the cyclic passage theory utilizing Barkhausen's criteria. The variation of modulation index and locking range with fiber delay has been presented. Finally, the growth of oscillation amplitude and the phase-plane plot of the system are studied. It is to be noted that nothing has been reported on the synchronizing capability of the angle modulated OEO as far as the knowledge of the authors goes.

A low‐dimensional spectral approach for the nonlinear overstability of purely elastic fluids

AbstractThe conditions for the emergence and stability of finite amplitude purely elastic (non‐inertial) overstability are examined for axisymmetric Taylor–Couette flow of an Oldroyd‐B fluid in the narrow‐gap limit. The study is a detailed account of the formulation and results published previously [Khayat, Phys. Rev. Lett. 1997; 78: 4918]. The flow field is obtained as a truncated Fourier representation for velocity, pressure and stress in the axial direction, and in terms of symmetric and antisymmetric Chandrasekhar functions along the radial direction. The Galerkin projection of the various modes onto the conservation and constitutive equations leads to a closed low‐dimensional nonlinear dynamical system with 20o of freedom. In contrast to our previous model that was based on the simplifying rigid‐free boundary conditions [Khayat, Phys. Fluids A 1995; 7: 2191], the present formulation incorporates the more realistic rigid–rigid boundary conditions, and is capable of capturing quantitatively the flow sequence observed in the experiment of Muller et al. [J. Non‐Newtonian Fluid Mech. 1993; 46: 315] for a highly elastic (Boger) fluid under conditions of negligible inertia. Existing linear analysis results are first recovered by the present formulation, which predict the exchange of stability between the circular Couette flow and oscillatory Taylor vortex flow via a postcritical Hopf bifurcation as the Deborah number exceeds a critical value. The stability conditions of the limit cycle are determined using the method of multiple scales. The present nonlinear theory predicts, as experiment suggests, the growth of oscillation amplitude of the velocity and the emergence of higher harmonics in the power spectrum as the Deborah number increases. Good agreement is obtained between theory and experiment. Copyright © 2002 John Wiley & Sons, Ltd.