Autooscillatory System Research Articles

Lip-valve interactions with the resonant bore of a trombone

Players of brass instruments usually play at a pitch close to one of the strong resonances of the instrument bore, but can easily play either above or below a resonance. Simple one-degree-of freedom models having aperture in phase with longitudinal lip displacement do not readily explain auto-oscillationwith realistic values of lip losses and cannot explain oscillation at frequencies below resonance. Experimental measurements of lip motion, pressures and flows show that the lips’ longitudinal motion leads the transverse: the lips move downstream closed, then open, then retract while open. Because of the forward sweeping motion, flow starts before the lips open. The sweeping motion has two important effects: first, it allows a range of phases between pressure and flow. Second, it means that the DC pressure acts on a larger area in the forward motion than during retraction. Both have consequences for oscillation energetics. A simple calculation of the PdV work done on the longitudinal component of motion, using measured quantities, indicates that it could provide a substantial fraction of the energy necessary for auto-oscillation with lossy lips. These mechanisms might have implications for other auto-oscillatory systems such as the vocal folds.

Self-oscillations that cause the destruction of intermolecular bonds in the water coolant of a nuclear power plant

The digital acoustic model of a nuclear reactor (DAMNR) is presented as an auto-oscillatory system belonging to a special class of nonlinear dissipative systems capable of generating undamped oscillations. It is established that a water-water power reactor with a turbulent flow of a coolant is an open system of high complexity with a large number of elements, the connections between which are not predetermined, but probabilistic. Elements of the coolant circuit with negative dissipation (negative friction) are identified. It is shown that they self-organize chaotic turbulent pulsations and vortices into ordered wave oscillations, the frequency of which is determined by the Thomson (Kelvin) formula. In radio engineering circuits, an electronic self-oscillating generator with transformer feedback has similar properties. The presence of negative resistance in nonlinear dynamical systems leads to self-organization of chaotic turbulent perturbations and generation of self-oscillations in the form of acoustic standing waves (ASW). On the basis of theoretical and experimental data, the reliability of a previously unknown property of a reactor with connected pipelines - the ability to generate several ASW simultaneously-was confirmed. The use of DAMNR in the design and operation of nuclear power plants allows to identify the sources of ASW occurring in the coolant, the conditions for their occurrence and frequency.

Synthesis of an analytical solution of an auto-oscillatory system with chaotic behavior

Synthesis of an analytical solution of an auto-oscillatory system with chaotic behavior

Vapor Cartesian diver

The article proposes a new research object for a general physics course—the vapour Cartesian diver, designed to study the properties of saturated water vapour. Physics education puts great importance on the study of the saturated vapour state, as it is related to many fundamental laws and theories. For example, the temperature dependence of the saturated water vapour pressure allows the teacher to demonstrate the Le Chatelier’s principle: increasing the temperature of a system in a dynamic equilibrium favours the endothermic change. That means that increasing the temperature increases the amount of vapour present, and so increases the saturated vapour pressure. The experimental setup proposed in this paper can be used as an example of an auto-oscillatory system, based on the properties of saturated vapour. The article describes a mathematical model of physical processes that occur in the experiment, and proposes a numerical solution method for the acquired system of equations. It shows that the results of numerical simulation coincide with the self-oscillation parameters from the real experiment. The proposed installation can also be considered as a model of a thermal engine.

Whispering gallery mode resonators in microwave physics and technologies

We review the main results of the development of whispering gallery mode (WGM) resonators and their unique applications due to their quasi-optical functionality. Several types of advanced WGM resonators are proposed by the authors. The theoretical results are described for the resonators with an analytical solution of the electromagnetic problems. Special emphasis is given to the interaction of moving charged particles and waves of cylindrical resonators. Important aspects are described concerning the developed sapphire resonators, for which an exact solution can only be found by using specially designed computer program products. A separate section of the paper is devoted to application aspects of the WGM resonators. In particular, it describes advanced solutions for overcoming the problems of measuring the small microwave (MW) surface impedance of unconventional superconductors in the form of large-area thin films and small samples under study. In addition, a demonstration of accurate complex permittivity measurements of small volumes of lossy liquids is provided. Special emphasis is given to highly stable MW signal sources, namely Ka-band transistor-based feedback oscillator and solid-state maser WGM oscillators. Recently obtained results are presented of experimental studies of the auto-oscillatory system developed on the basis of the WGM resonator with relativistic electron beam.

Generator of chaotic microwave oscillations based on a high-power bipolar transistor

A chaotic microwave autooscillatory system has been designed, implemented on a high-power bipolar transistor (2T 982 A-2), and studied. The experiments showed stable generation of chaotic oscillations in a 5.26–5.44 GHz range with a spectral power density of 1.3 × 10−3 W/MHz.

Auto-oscillatory system based on dielectric resonator with whispering-gallery modes

The generation mechanism of microwave radiation in the system with azimuthally-periodical current of an electron beam that excites a high-Q quasi-optical dielectric resonator was developed. Eigen parameters of a cylindrical Teflon resonator were determined. Radiation was locked in the investigated system by a detector of 8-mm wave band. Design philosophy of microwave oscillators with high-Q resonators, in which electromagnetic “whispering gallery” modes are excited by electron beam, was developed.

Controlled oscillations in chain of unidirectionally coupled bistable oscillators with chaotic dynamics

Equations of a chain of n (n = 1, 2, ...) unidirectionally coupled bistable oscillators possessing chaotic dynamics are presented. Numerical analysis has been performed for a system of three identical autooscillatory systems with nonlinear elements admitting cubic approximation. It is shown that, as the degree of coupling between units in the chain increases, their motions in the phase space become more complicated and even chaotization of oscillations may take place at the parameters with which separate oscillators exhibit regular motions in the autonomous regimes. The features of the influence of a driving oscillator on the motions of a driven bistable subsystem are related to filtration of the driving signal in the circuit of the driven subsystem.

Chaotic dynamics of oscillator based on lossless circuit

Equations that describe a new autooscillatory system with chaotic dynamics based on a lossless oscillatory circuit are presented. This system is capable of generating chaotic oscillations with irregular variations in the amplitude (amplitude chaos) at a small change in frequency. Bifurcation diagrams (one- and two-parametric), time series of the oscillatory process, and power spectra of the proposed system are presented.

Lagrangian formulation of the linear autonomous magnetization dynamics in spin-torque auto-oscillators

A Lagrangian formalism is used to find steady-state solution of the Landau–Lifshitz–Gilbert–Slonczewski equation corresponding to the linear autonomous dynamics of a magnetic auto-oscillatory system subject to the action of a spin-polarized electric current. In such a system, two concurrent dissipative mechanisms, arising from the positive intrinsic dissipation and the negative current-induced one, take place simultaneously and make the excitation of a steady precessional motion of the magnetization vector conceivable. The proposed formulation leads to the definition of a complex generalized non-Hermitian Eigenvalue problem, both in the case of a macrospin model and in the more general case of an ensemble of magnetic particles interacting each other through magnetostatic and exchange interactions. This method allows to identify the spin-wave normal modes which become unstable in the presence of the two competing dissipative contributions and provides an accurate estimation of the value of the excitation threshold current.

10.1007/s11455-008-2002-x

A chaotic autooscillatory system described by an equation with delayed argument is proposed, in which the oscillations are controlled by means of a chaotizing feedback algorithm. The results of numerical analysis of the proposed system are presented.

Controlled stochastization of oscillations in a chaotic delayed-feedback system

A mathematical model of the ring autooscillatory system, which possesses chaotic dynamics and comprises a nonlinear amplifier with a differentiating element in the feedback chain, a nonlinear oscillatory circuit, and a delay line, is considered. Numerical analysis has been performed for irregularly varying initial conditions. These conditions were set by the solutions of equations describing chaos that simulated intrinsic noises of a real autooscillatory system. It is shown that the irregularly varying conditions of excitation can lead to stochastization of the chaotic oscillations, in which case the oscillatory process becomes irreproducible.

Chaos in a bistable chain of two unidirectionally coupled autooscillatory systems with time delay

We have studied the dynamics of a chain of two unidirectionally coupled delay-feedback autooscillatory systems possessing smooth asymmetric amplitude characteristics and the initial conditions of opposite signs, which result in the formation of two basins of attraction in the chain. The results of numerical simulations of the process of chaotization in a driven autooscillatory system and the transition of its oscillations to a state of forced synchronization with a change in the basin of attraction are presented. The mechanism of chaotization is considered.

F1-ATPase as an auto-oscillatory system

In a relatively simple mathematical model we analyze the possibility of auto-oscillatory modes of F 1 -ATPase during ATP hydrolysis.

On the possibility for an autooscillatory system under external periodic drive action to exhibit universal behavior characteristic of the transition to chaos via period-doubling bifurcations in conservative systems

We propose a model of an autooscillatory system that admits the physical realization of the universal Hamiltonian-type critical behavior at a threshold of the transition to chaos that is characteristic of conservative systems. For this model, an approximate discrete map is obtained and the coordinates of the corresponding critical point are evaluated.

Noise-induced synchronization of spatiotemporal chaos in the Ginzburg-Landau equation

We have studied noise-induced synchronization in a distributed autooscillatory system described by the Ginzburg-Landau equations, which occur in a regime of chaotic spatiotemporal oscillations. A new regime of synchronous behavior, called incomplete noise-induced synchronization (INIS), is revealed, which can arise only in spatially distributed systems. The mechanism leading to the development of INIS in a distributed medium under the action of a distributed source of noise is analytically described. Good coincidence of analytical and numerical results is demonstrated.

Controlled chaotic system with time delay

A chaotic autooscillatory system described by an equation with delayed argument is proposed, in which the oscillations are controlled by means of a chaotizing feedback algorithm. The results of numerical analysis of the proposed system are presented.

Transition to phase synchronization in a system with periodic dynamics under the action of a chaotic signal

Intermittent behavior has been studied near the boundary of phase synchronization in an autooscillatory system with periodic dynamics under the action of an external chaotic signal. It is shown that the intermittency obeys the same scenario as that observed in the case of interaction between two coupled chaotic oscillators.

Intermittent generalized synchronization in distributed autooscillatory media described by complex Ginzburg-Landau equations

The appearance of an intermittent regime at the boundary of the generalized chaotic synchronization region has been found for distributed autooscillatory systems described by the complex Ginzburg-Landau equations, which occur in the regime of spatiotemporal chaos. The type of the observed intermittent generalized synchronization behavior is established.

Analysis of a controlled chaotic autooscillatory system based on an anharmonic oscillator model

The mathematical model of a new autooscillatory system with chaotic dynamics based on self-excitation of an anharmonic oscillator is considered. The results of numerical analysis show the possibility of generating chaotic oscillations with linear gain in the delayed feedback and controlling chaos by means of parametric self-action.