External Periodic Perturbations Research Articles

Higher-order dust kinetic Alfvén wave solitons and quasi-periodic waves in a polarized dusty plasma

This investigation presents the study of dust kinetic Alfvén wave solitons (DKAWSs) and quasi-periodic waves in a polarized dusty plasma comprising inertial dust, Cairns–Tsallis (CT) distributed ions and electrons. Using the reductive perturbation method, the KdV equation is derived and the Tanh-method is employed to derive its solution to study the dust kinetic Alfvén solitary structures. Furthermore, by considering the contribution of higher-order effects, the KdV-type inhomogeneous equation is derived and its solution results in the formation of dressed DKAWSs. The combined effects of polarization force and other plasma parameters on the characteristics of different kinds of DKAWSs are analyzed. Most importantly, from the conservation of KdV equations in the presence of external periodic perturbations, the study of quasi-periodic wave has also been illustrated. The analysis shows that the periodic solitonic behavior is transformed to quasi-periodic and also approaches chaotic oscillations. By changing different physical parameters, the numerical analysis of nonlinear DKAWs from periodic to quasi-periodic and to chaotic behavior has also been presented with external perturbation. The findings of this investigation are useful to understand the insight into physics of nonlinear phenomena for studying the dynamics of DKAWSs in space and astrophysical plasma environments.

An alternate approach to simulate the dynamics of perturbed liquid drops.

Liquid drops when subjected to external periodic perturbations can execute polygonal oscillations. In this work, a simple model is presented that demonstrates these oscillations and their characteristic properties. The model consists of a spring-mass network such that masses are analogous to liquid molecules and the springs correspond to intermolecular links. Neo-Hookean springs are considered to represent these intermolecular links. The restoring force of a neo-Hookean spring depends nonlinearly on its length such that the force of a compressed spring is much higher than the force of the spring elongated by the same amount. This is analogous to the incompressibility of liquids, making these springs suitable to simulate the polygonal oscillations. It is shown that this spring-mass network can imitate most of the characteristic features of experimentally reported polygonal oscillations. Additionally, it is shown that the network can execute certain dynamics, which so far have not been observed in a perturbed liquid drop. The characteristics of dynamics that are observed in the perturbed network are polygonal oscillations, rotation of network, numerical relations (rational and irrational) between the frequencies of polygonal oscillations and the forcing signal, and that the shape of the polygons depends on the parameters of perturbation.

Nonlinear excitations of magnetosonic solitary waves and their chaotic behavior in spin-polarized degenerate quantum magnetoplasma.

The quantum hydrodynamic model is used to study the nonlinear propagation of small amplitude magnetosonic solitons and their chaotic motions in quantum plasma with degenerate inertialess spin-up electrons, spin-down electrons, and classical inertial ions. Spin effects are considered via spin pressure and macroscopic spin magnetization current, whereas the exchange effects are considered via adiabatic local density approximation. By applying the reductive perturbation method, the Korteweg-de Vries type equation is derived for small amplitude magnetosonic solitary waves. We present the numerical predictions about the conservative system's total energy in spin-polarized and usual electron-ion plasma and observed low energy in spin-polarized plasma. We also observe numerically that the soliton characteristics are significantly affected by different plasma parameters such as soliton phase velocity increases by increasing quantum statistics, magnetization energy, exchange effects, and spin polarization density ratio. Moreover, it is independent of the quantum diffraction effects. We have analyzed the dynamic system numerically and found that the magnetosonic solitary wave amplitude and width are getting larger as the quantum statistics and spin magnetization energy increase, whereas their amplitude and width decrease with increasing spin concentration. The wave width increases for high values of quantum statistic and exchange effects, while their amplitude remains constant. Most importantly, in the presence of external periodic perturbations, the periodic solitonic behavior is transformed to quasiperiodic and chaotic oscillations. It is found that a weakly chaotic system is transformed to heavy chaos by a small variation in plasma parameters of the perturbed spin magnetosonic solitary waves. The work presented is related to studying collective phenomena related to magnetosonic solitary waves, vital in dense astrophysical environments such as pulsar magnetosphere and neutron stars.

Chimera states in networks under external periodic perturbations

Chimera states in networks under external periodic perturbations

Active change in the state of self-oscillations in machines and mechanisms in a system with various types of nonlinearities of an arbitrary structure under the action of a impulse or harmonic disturbing force

The method of actively changing the state of self-oscillations in machines and mechanisms in a system with various types of nonlinearities of an arbitrary structure under the action of external periodic perturbations was proposed. The differential equations of the method take into account two types of external force periodic disturbances: impulse and harmonic.

Suppression of chaos in a generalized Duffing oscillator with fractional-order deflection

A generalized Duffing oscillator with fractional-order deflection can be used to model the oscillatory motion of a buckled beam with simply supported or hinged ends. In this work, the problem of suppression of chaos in such a Duffing oscillator is considered. We show the appropriate range of parameters for the control of horseshoe chaos by introducing external periodic resonant excitation and parametric excitation as chaos-suppressing perturbation. Through the Melnikov technique, we obtain that in addition to the frequency, the phase difference between the chaos-inducing excitation and the chaos-suppressing excitation of systems plays a key role in chaos suppression. Given the optimum phase that satisfies the inhibition theorems, we compare the chaos-suppressing efficiency of external and parametric periodic perturbations for the principal resonance case. Compared with parametric (external) excitation, external (parametric) excitation with a frequency above (below) a critical value is more effective in suppressing homoclinic chaos because it provides a wider amplitude range. The results hold for an arbitrary deflection order as either an integer or a fraction, which depends on the material and bending properties of the beam, as long as its value is larger than 1. Moreover, the critical value of the frequency will shift to a larger value as the deflection order increases.

Study of the effect of external periodic flow perturbations on heat transfer intensity in the impact jet

The aim of this work is to experimentally study unsteady heat transfer in an impact jet flowing onto a heated surface with the presence of large-scale structures and separated flows, as well as to search for possible mechanisms for controlling heat transfer by introducing external disturbances into the flow. In the work, a series of experiments was carried out to study an axisymmetric jet flowing normally onto a heated surface. The jet was both under natural conditions with different flow regimes and under external excitation at various frequencies and amplitudes. The instantaneous and average velocity and temperature fields in the near-wall part of the jet are measured using the PIV and PLIF methods. The correlations of velocity fluctuations and temperature fluctuations, which characterize the intensity of turbulent heat transfer, are calculated. It is shown that at different frequencies of external excitation of the jet, the intensity of turbulent transfer in the region of jet impingement on the wall changes. In the region of jet impingement on the wall, flow separation was recorded. It is shown that the interaction of the coherent structure with the wall leads to a local increase in the outflow of heat from the heated surface. The distributions of the heat transfer coefficient along the heated surface were also measured using a thermal imaging camera for various flow regimes, distances from the nozzle exit to the barrier, frequencies and amplitudes of the external flow disturbance. It is shown that when the jet is excited at different frequencies of the jet excitation, the heat transfer increases or decreases.

Combustion instability control in the model of combustion chamber

An experimental study of the influence of external periodic perturbations on the instability of the combustion chamber in a pulsating combustion. As an external periodic disturbances were used sound waves emitted by the electrodynamics. The purpose of the study was to determine the possibility of using the method of external periodic perturbation to control the combustion instability. The study was conducted on a specially created model of the combustion chamber with a swirl burner in the frequency range from 100 to 1400 Hz. The study found that the method of external periodic perturbations may be used to control combustion instability. Depending on the frequency of the external periodic perturbation is observed as an increase and decrease in the amplitude of the oscillations in the combustion chamber. These effects are due to the mechanisms of synchronous and asynchronous action. External periodic disturbance generated in the path feeding the gaseous fuel, showing the high efficiency of the method of management in terms of energy costs. Power required to initiate periodic disturbances (50 W) is significantly smaller than the thermal capacity of the combustion chamber (100 kW).

Control of disturbances of a hypersonic viscous shock layer on a flat plate

Receptivity of a viscous shock layer on a flat plate aligned at an angle of attack to external multiwave acoustic perturbations is studied. It is shown that external acoustic waves and periodic controlled perturbations introduced from the surface of the plate mounted at an angle of attack smaller than 20° generate entropy-vortex disturbances with a similar spatial distribution in the viscous shock layer. This result allows numerical implementation of the interference method of controlling disturbances generated in the viscous shock layer on the plate by external acoustic waves at one frequency and at a spectrum of frequencies by introducing blowing-suction perturbations on the plate surface with appropriate amplitudes and phases.

Multistablity, bistability and bubbles phenomena in a periodically forced ethanol fermentor

The numerical investigation results of the dynamic behavior of an ethanol fermentor excited by external sinusoidal periodic perturbations are reported. The characteristics of the discriminant of the cubic polynomial of the steady state autonomous model of the unforced fermentor were used to divide the parameter space into regions with different number of steady state solutions. The bioethanol fermentor exhibits interesting complicated dynamic behavior when the center of forcing is close to a static limit point (SLP) i.e. the discriminant=0. Numerical simulations have presented evidence for the existence of multistability, bistability and bubbles phenomena in the forced bioethanol fermentor. This is – to the best of our knowledge – the first study that shows these phenomena in the forced bioethanol fermentor. Multistablity is characterized by the coexistence of several attractors. It has been shown that, the multistability exhibits the coexistence of three attractors, two of them are chaotic and one quasi-periodic, and the bistability exhibits the coexistence of two attractors, one of them is periodic and the other is either periodic, quasi-periodic or chaotic attractor. In the multistabiliy region, we have observed that changing the forcing amplitude with the sequence of events there is an appearance of the bistability and then a transition to multistabilty. It has been shown that, the bubble region acts as a period doubling killer, which has a lethal effect in killing the universal period doubling scenario to chaos by reversing the sequence to period halving. It is also shown that, the unforced (14.55% increase in ethanol average concentration relative to the steady state operation) or forced (8.87% increase in ethanol average concentration relative to the steady state operation) unsteady state operations give better fermentor performance than the steady state operations with respect to the average ethanol concentration and yield. The investigation shows that the nature and the position of the center of forcing have significant effect on the dynamic response of the periodically forced fermentors. It has been found that, the forcing could be beneficial or harmful to the fermentor performance depending on the position of center of forcing. The system shows interesting phase planes at certain forcing amplitudes.

ChemInform Abstract: Measurements and Calculations of Oscillations and Phase Relations in the Driven Gas-Phase Combustion of Acetaldehyde

Oscillations in light emission and species concentrations, are measured as periodic perturbations are simultaneously applied to the input rates of acetaldehyde and oxygen in the gas‐phase combustion of acetaldehyde in a continuous‐flow stirred tank reactor for conditions where the autonomous reaction itself is oscillatory. The experimental results are compared with the predictions of a five‐variable thermokinetic model. We measure periodic responses in the fundamental entrainment band (ratio of frequency of perturbation to frequency of response equal to unity) for four different values of phase shift between the acetaldehyde and oxygen perturbation wave forms as we vary the frequency and amplitude of the external periodic perturbations. Outside of the entrainment bands we find quasiperiodic response. We determine the phases of the light emission and six species concentrations, as measured with a mass spectrometer, with respect to the periodic perturbation, the variation of these phases across the fundamental entrainment band for different values of reactant phase shift and for different amplitudes of perturbation, and the effects of the phase shift between the two input perturbations on the light emission response of the system for different frequencies of perturbation. Both the experiments and calculations predict a widening of the entrainment band with an increase in perturbation amplitude, and the same variation in bandwidths for the four values of reactant phase shift studied. The experiments and calculations also predict the same general trends in light phase and species phases (difference between the light emission and species concentrations with respect to the perturbing wave form) as the band is traversed for different amplitudes of perturbation and for different values of reactant phase shift. Some discrepancies in the species phases exist; however, the similarities which exist between the experiments and the calculations provide further substantiation for the model. We find that changing the phase shift between reactant inflows from 0° to 360° produces a sharp change in light phase near 180°, in both the experiments and calculations. In general, we also find that the light emission remains entrained near the total flux minimum of the perturbing wave form, and we attribute this correlation to the net heat loss which arises from the reactant flux through the reactor.

Postural Responses Evoked by Platform Pertubations Are Dominated by Continuous Feedback

Is human balance control dominated by time invariant continuous feedback mechanisms or do noncontinuous mechanisms play a significant role like intermittent control? The goal of this paper is to quantify how much of the postural responses evoked by pseudorandom external periodic perturbations can be explained by continuous time invariant feedback control. Nine healthy subjects participated in this study. Center of mass and ankle torque responses were elicited by periodic platform perturbations in forward-backward directions containing energy in the 0.06- to 4.5-Hz frequency band. Subjects had their eyes open (EO) or eyes closed (EC). Responses were decomposed into a periodic component and a remnant (stochastic) component using spectral analysis. It is concluded that periodic responses can explain most of the evoked responses, although the remnant power spectral densities (PSDs) were significant especially for slow responses (<0.2 Hz) and largest for EC. The found remnant PSD did depend on the sensory condition but not on the platform perturbation amplitude. The ratio of the body sway and ankle torque remnant PSD reflects the body dynamics. Both findings are consistent with the idea that estimation of body orientation is part of a continuous feedback loop and that (stochastic) estimation errors increase when one source of sensory information is removed. The findings are not consistent with the idea that discrete or discontinuous intermittent feedback mechanisms significantly shape postural responses.

Resonance-induced oscillons in a reaction-diffusion system

A new type of oscillon that arises from interaction between subcritical Turing and wave instabilities is found in a system of reaction-diffusion equations. These oscillons can be induced resonantly by localized external periodic perturbations. This phenomenon may be useful for frequency selection and/or information processing.

Parametric perturbations and non-feedback controlling chaotic motion

In this paper we generalize analytic studies the problems related tosuppression of chaos and non--feedback controlling chaotic motion.We develop an analytic method of the investigation of qualitativechanges in chaotic dynamical systems under certain external periodicperturbations. It is proven that for polymodal maps one canstabilize chosen in advance periodic orbits. As an example, thequadratic family of maps is considered. Also we demonstrate that for a piecewise linearfamily of maps and for a two-dimensional map having a hyperbolicattractor there are feedback-free perturbations which lead to thesuppression of chaos and stabilization of certain periodic orbits.

Forced excitations and excitable chaos in the photosensitive Oregonator under periodic sinusoidal perturbations

The responses of an excitable system to external periodic perturbations are studied by using the photosensitive Oregonator that is a three variable model of the photosensitive Belousov–Zhabotinsky reaction. The system is set at the vicinity of the subcritical Hopf bifurcation point, and sinusoidal perturbation is given by light: ϕ ( α , ν ) = ϕ 0 − α A 0 sin ⁡ ( 2 π ν τ ) . The dynamic threshold for firing appears as a U-shaped line in ν – α plane. Under high-frequency perturbations, the system shows a subthreshold period-doubling cascade, subthreshold chaotic responses (excitable chaos) and reaches firing chaos as a result of expansion of orbits around the fixed point.

Periodic precursors of nonlinear dynamical transitions.

We study the resonant response of a nonlinear system to external periodic perturbations. We show by numerical simulation that the periodic resonance curve may anticipate the dynamical instability of the unperturbed nonlinear periodic system, at parameter values far away from the bifurcation points. In the presence of noise, the buried intrinsic periodic dynamics can be picked out by analyzing the system's response to periodic modulation of appropriate intensity.

Chaos to periodicity and periodicity to chaos by periodic perturbations in the Belousov–Zhabotinsky reaction

A three-variable model of the Belousov–Zhabotinsky reaction system subject to external sinusoidal perturbations is investigated by means of frequency spectrum analysis. In the period-1 window of the model, the transitions from periodicity to chaos are observed; in the chaotic window, the transitions from chaos to periodicity are found. The former might be understood by the circle map of two coupled oscillators, and the latter is partly explained by the resonance between the main frequency of the chaos and the frequency of the external periodic perturbations.

Fingerprints of determinism in an apparently stochastic corrosion process.

We detect hints of determinism in an apparently stochastic corrosion problem. This experimental system has industrial relevance as it mimics the corrosion processes of pipelines transporting water, hydrocarbons, or other fuels to remote destinations. We subject this autonomous system to external periodic perturbations. Keeping the amplitude of the superimposed perturbations constant and varying the frequency, the system's response is analyzed. It reveals the presence of an optimal forcing frequency for which maximal response is achieved. These results are consistent with those for a deterministic system and indicate a classical resonance between the forcing signal and the autonomous dynamics. Numerical studies using a generic corrosion model are carried out to complement the experimental findings.

Effects of external periodic perturbations on short-term heart rate variability in healthy subjects and ischemic heart disease patients

Aims: To characterise the frequency response of short-term heart rate variability to external periodic perturbations in healthy and ischemic heart disease subjects. Methods: Eleven healthy men and 11 ischemic heart disease patients were enrolled in this study. The frequency response of heart rate variability was assessed during periodic eyes opening test and controlled breathing at frequencies ranging from 0.08 to 0.25 Hz using autoregressive spectral analysis. Results: In subjects of both groups the mean heart rate and blood pressure were unchanged across experimental sessions. In healthy subjects eyes opening at rate of 8 and 6 times/min (0.12 and 0.10 Hz) evoked high-power peaks ( P<0.05) at the same frequencies in the R–R power spectrum. The largest frequency response of heart rate variability was seen during eyes opening at 0.1 Hz ( P<0.05). Ischemic heart disease patients failed to respond to periodic eyes opening with any changes in heart rate variability. During controlled breathing healthy subjects showed the highest heart rate variability frequency responses when breath frequency was 0.1 Hz ( P<0.05). Comparatively, patients with ischemic heart disease had reduced frequency responses of heart rate variability at all breath rates and its magnitude did not depend on the perturbation frequency. Conclusions: Our results demonstrate that the frequency response of short-term heart rate variability to external periodic perturbations is dependent on the perturbation frequency and the presence disease processes in the cardiovascular system.

Resonant forcing of a silent Hodgkin-Huxley neuron.

Dynamical behavior of a silent Hodgkin-Huxley neuron subjected to external periodic perturbations is investigated. Induced dynamics for this forced system, exhibit nonlinear resonance with respect to the forcing frequency. Within the U-shaped resonance curve, both regular (phase locked) and irregular spike sequences are invoked. For appropriate tuning frequencies, this simple system generates spike trains recordings similar to ones observed in actual experiments.