External Periodic Force Research Articles

Stochastic multiresonance in oscillators induced by bounded noise

Stochastic resonance (SR) in a harmonic oscillator with parametric bounded noise and external periodic force is investigated. By applying the property of bounded noise and using Cameron–Martin formula, infinite chains of linear differential equations are obtained for the spectral amplification, mean-square displacement, and variance. Multiple stochastic resonances are observed for these characteristics. Relationships with resonant tongues of the Mathieu equation are established. It is shown that similar effects can be observed in the case of harmonic noise external force. The case of two coupled oscillators is also studied. Analysis is based on a natural truncation of the infinite moment chains and using of the numerical matrix computations.

Dynamical behavior of micro-structured solids with conformable time fractional strain wave equation

The wave propagation in micro structured solids is described by conformable time fractional strain wave equation and should be able to account for several scales of micro-structure. (G′G2)-expansion method has been used to propagate the different types of solutions like hyperbolic functions, trigonometric functions and rational functional solutions. All the solutions are listed with their existence criterion on the parameters. A sufficient condition for the convergence of (G′G2)-expansion method is provided. Meantime, considered equation is transformed into planar dynamical system after using traveling wave transfiguration. Then quasiperiodic behavior is investigated for the discussed model for different values of the physical parameters (α,ϖ,ζ,V and β) after applying a periodic external force. Further, to strengthen the claimed results sensitive analysis is used for different initial value problems.

Electron-acoustic supernonlinear waves and their multistability in the framework of the nonlinear Schrödinger equation

Finite-amplitude supernonlinear electron-acoustic waves (EAWs) are investigated under the nonlinear Schrödinger (NLS) equation in a plasma system that is composed of cold electron fluid, immobile ions and q-nonextensive hot electrons. Using the wave transfiguration, the NLS equation is deduced in a dynamical system. The presence of finite-amplitude nonlinear and supernonlinear EAWs is shown by phase plane analysis. The effects of the nonextensive parameter (q) and the speed of waves (v) on different traveling wave solutions of EAWs are presented. Furthermore, by introducing a small external periodic force in the dynamical system, multistability behaviors of EAWs under the NLS equation are shown for the first time in classical plasmas.

Role of synaptic nonlinearity in persistent firing rate shifts caused by external periodic forcing

Information storage and processing in the brain largely relies on the neural population coding principle. In this framework, information is reflected in the population firing rate that reflects asynchronous irregular spiking of its constituent neurons. Periodic modulations of neural activity can lead to neural activity oscillations. Data indicate that such oscillations are ubiquitous in brain activity and are modulated, in frequency and amplitude, in a functionally meaningful manner. The relationship between oscillations and the population rate code remains an open issue. While ample works show how changes in the mean firing rate may alter neural oscillations, the reverse connection is unclear. One notable possibility is that oscillatory activity impinging on a neural population modulates its mean firing rate, thereby impacting information processing. We suggest that such modulation requires nonlinearities and propose nonlinear excitatory coupling via slow N-methyl-D-aspartate (NMDA) receptors as the prevalent mechanism. The aim of our paper is to theoretically explore to what extent the NMDA-related mechanism could account for oscillation-induced mean firing rate changes. We consider a mean-field model of a neural circuit containing an excitatory and an inhibitory population with linear transfer functions. Along with NMDA excitation, the model included fast recurrent excitatory and inhibitory connectivity. To explicitly study the effects of impinging oscillation on the rate dynamics, we subjected the circuit to a sinusoidal input signal imitating an input from distant brain regions or from a larger network into which the circuit is embedded. Using time-scale separation and time-averaging techniques, we developed a geometric method to determine the oscillation-induced mean firing rate shifts and validated it by numeric simulations of the model. Our results indicate that a large-amplitude stable firing rate shift requires nonlinear NMDA synapses on both the excitatory and the inhibitory populations. Our results delineate specific neural synaptic properties that enable neural oscillations to act as flexible modulators of the population rate code.

Spatiotemporal antiresonance in coupled reaction-diffusion systems.

We present a theoretical study of the spatiotemporal antiresonance in a system of two diffusively coupled chemical reactions, one of which is driven by an external periodic forcing. Although antiresonance is well known in various physical systems, the phenomenon in coupled chemical reactions has largely been overlooked. Based on the linearized dynamics around the steady state of the two-component coupled reaction-diffusion systems we have derived the general analytical expressions for the amplitude-frequency response functions of the driven and undriven components of the system. Our theoretical analysis is well corroborated by detailed numerical simulations on coupled Gray-Scott reaction-diffusion systems exhibiting antiresonance dip in the amplitude-frequency response curve as a result of destructive interference between the coupling and the periodic external forcing imparting differential stability of the two subsystems. This leads to the emergence of spatiotemporal patterns in an undriven subsystem, while the driven one settles down to a homogeneously stable steady state.

ДОСЛІДЖЕННЯ РЕЗОНАНСНИХ КОЛИВАНЬ СИСТЕМИ ТЕЛЕСКОПІЧНИЙ ГВИНТ – СИПКЕ СЕРЕДОВИЩЕ ЗУМОВЛЕНИХ ЗОВНІШНІМИ ПЕРІОДИЧНИМИ СИЛАМИ

The article presents the results of resonant oscillations theoretical research of the telescopic screw - granular material system caused by external periodic forces. In the theoretical part a mathematical model of bending vibrations of an elastic body is described, which rotates along a fixed axis with a constant angular velocity, provided that it moves with a constant relative linear velocity along the elastic body. In the experimental part, according to the obtained equations, it has been established for the various kinematic characteristics of the system, a telescopic screw-granular media of amplitude passing through resonance at the frequency of external periodic perturbation.The results of experimental research and recommendations for the selection of constructive kinematic for telescopic screw conveyor have been presented.

Frequency selection in a gravitationally stretched capillary jet in the jetting regime

A capillary jet falling under the effect of gravity continuously stretches while thinning downstream. We report here the effect of external periodic forcing on such a spatially varying jet in the jetting regime. Surprisingly, the optimal forcing frequency producing the most unstable jet is found to be highly dependent on the forcing amplitude. Taking benefit of the one-dimensional Eggers & Dupont (J. Fluid Mech., vol. 262, 1994, pp. 205–221) equations, we investigate the case through nonlinear simulations and linear stability analysis. In the local framework, the WKBJ (Wentzel–Kramers–Brillouin–Jeffreys) formalism, established for weakly non-parallel flows, fails to capture the nonlinear simulation results quantitatively. However, in the global framework, the resolvent analysis, supplemented by a simple approximation of the required response norm inducing breakup, is shown to correctly predict the optimal forcing frequency at a given forcing amplitude and the resulting jet breakup length. The results of the resolvent analysis are found to be in good agreement with those of the nonlinear simulations.

Time-periodic solution to a two-phase model with magnetic field in a periodic domain

In the paper, we consider a two-phase model with magnetic field and a time periodic external force in a periodic domain in RN. The existence of the time-periodic solutions to the model is obtained by the topological degree theory and parabolic regularization method.

Propagation of Ion-Acoustic Solitary Waves for Damped Forced Zakharov Kuznetsov Equation in a Relativistic Rotating Magnetized Electron-Positron-Ion Plasma

The purpose of this paper is to determine the nonlinear properties of the ion-acoustic solitary waves (IASW) propagating obliquely, under the influence of external periodic force combining with a damping term in a rotating, weakly relativistic and magnetized electron-positron-ion plasma. Reductive perturbation technique is employed to derive the damped forced Zakharov Kuznetsov (DFZK) equation. Using the momentum conservation law, ion acoustic solitary wave solution is obtained for DFZK equation. Considerable effects are found in the structures of IASW with the variation of the ratio of temperature of electron and positron, concentration of positron, obliqueness, relativity, ion temperature, magnetic field and due to the presence of external forces. Numerical simulations are depicted for clear vision of the propagating properties of IASW.

ON TIME PERIODIC SOLUTIONS TO THE GENERALIZED BBM-BURGERS EQUATION WITH TIME-DEPENDENT PERIODIC EXTERNAL FORCE

In this paper, we consider the generalized BBM-Burgers equation with periodic external force in Rn. Existence and uniqueness of time periodic solutions that have the same period as the external force are established in some suitable function space for the space dimension n≥ 3. Moreover, we also discuss the time asymptotic stability of the time periodic solution. The proof is mainly based on the contraction mapping theorem and continuous argument.

Time-Periodic Solution to the Compressible Navier-Stokes/Allen-Cahn System

In this paper, we investigate the time-periodic solution to a coupled compressible Navier- Stokes/Allen-Cahn system which describes the motion of a mixture of two viscous compressible fluids with a time periodic external force in a periodic domain in ℝN. The existence of the time-periodic solution to the system is established by using an approach of parabolic regularization and combining with the topology degree theory, and then the uniqueness of the period solution is obtained under some smallness and symmetry assumptions on the external force.

Global existence of solution for Monge–Ampére equation with an external periodic force on 3-dimensional torus

This paper is devoted to construction of a non-convex global solution for Monge–Ampére equation with an external periodic force on 3-dimensional torus. More precisely, we show that this non-convex solution is a periodic solution, which is unique in a ball with radius 1.

Resonant drift of synchronized spiral waves in excitable media.

Many methods have been employed to investigate the drift behavior of spiral waves in an effort to understand and control their dynamics. Here, we propose a joint method to control the dynamics of spiral waves by applying both a rotating external field and periodic forcing. First, spirals in different regimes (including rigidly rotating, meandering, and drifting spirals) are synchronized by suitable rotating external fields. Then, under weak periodic forcing at frequencies equal to those of the external fields, the synchronized spirals undergo a directional and simple drift. Dependence of the drift velocity of the synchronized spiral on the initial rotational phase of the rotating external field and on the initial phase of the periodic forcing is studied in detail. We hope that our theoretical results can be observed in experiments, such as in the Belousov-Zhabotinsky reaction.

Control of thermal current in the Brownian heat pump

Here heat conduction in the Brownian heat pump (BHP) driven by external periodic forces is investigated. By means of numerical simulation, we found that thermal current of the BHP can be controlled by means of the external periodic forces. As phase shift ϕ of the BHP takes smaller values, if one end of the BHP is regulated only by one periodic force, the thermal current can go from the end to the other end of the BHP. Whereas for the greater values of ϕ , the thermal current can go from the other end to the end adjusted by the periodic force. With the increment of amplitude of the periodic force, a thermal current reversal phenomenon takes places in the BHP. In the system, there also exists a critical phenomenon about ϕ , at whose critical point its thermal current is almost equal to zero no matter how the amplitude of the periodic force is changed. If the two ends of the BHP are adjusted simultaneously by their own periodic forces, its thermal current takes both positive and negative values, and oscillates periodically with the phase difference between the two periodic forces. The results will possess a crucial significance in understanding performance mechanisms of nano-machines and organisms.

Co-solvent induced piezoelectric γ-phase nylon-11 separator for sodium metal battery

Nylon-11, the most studied member of the odd-numbered nylon family, is a promising functional material for future electronic devices or energy storage systems. To utilize nylon-11 in those applications, it is necessary to control the formation of the applicable metastable crystal phases such as the piezoelectric γ-phase or ferroelectric δ′-phase. Herein, we describe a facile method of fabricating metastable γ-phase nylon-11 fibers via electrospinning with a tailored solvent system. By using a solvent mixture of 1,1,1,3,3,3-hexafluoro-2-propanol and trifluoroacetic acid [HFIP:TFA (75:25 mol%)], we could fully eliminate the formation of the most stable α-phase and create metastable γ-phase nylon-11 fibers. The electrospun γ-phase nylon-11 fibrous membrane displayed a typical piezoelectric response when it experienced a periodic external force. Furthermore, the γ-phase nylon-11 fibrous membrane exhibited higher thermal stability, electrolyte wettability, and ionic conductivity than the conventional Celgard separator. Consequently, it achieved decent performance when applied as a separator in a sodium metal half-cell. This study indicates that piezoelectric γ-phase nylon-11 fibrous membranes have great potential for further development in energy harvesting and storage, especially as piezo-separators in self-charging power cells.

Motion of a Smooth Foil in a Fluid under the Action of External Periodic Forces. II

Motion of a Smooth Foil in a Fluid under the Action of External Periodic Forces. II

Effect of the fractional oscillator noise in the overdamped linear oscillator with the presence of a periodic force

The overdamped linear oscillator with periodic external force driven by the fractional oscillator (FO) noise is considered and investigated. The correlation function of the FO noise presents power-law-like function, exponential-like function and oscillatory decays similar to those of the harmonic noise. The amplitude of the stationary state of the first moment is obtained and analyzed in relation to the parameters of the system; it presents non-monotonic behaviors which are related to the resonance phenomenon.

The resonance behavior in the fractional harmonic oscillator with time delay and fluctuating mass

We study stochastic resonance (SR) in a fractional harmonic oscillator with time delay and mass fluctuation. Using a moment equation, we derive the exact analytical expression of the output amplitude and find that fluctuations in the output amplitude are nonmonotonic. Using numerical simulations we verify the accuracy of the analytical result. We find (i) that the evolution of output amplitude versus the frequency of the external periodic force exhibits One-Peak SR and Two-Peaks SR, resonance region and resonance form largely depend on the noise correlation rate and noise intensity, (ii) that the evolution of output amplitude versus the noise intensity exhibits One-Peak SR and the increasing time delay lower the critical driving frequency, and (iii) that the evolution of output amplitude versus feedback gain performs diverse resonance forms, the increasing time delay widens the region for occurrence of SR and diversifies the resonance form.

Analytical solitary wave solution of the dust ion acoustic waves for the damped forced modified Korteweg-de Vries equation in q-nonextensive plasmas

Analytical solitary wave solution of the dust ion acoustic waves is studied due to the damped forced modified Korteweg-de Vries equation in an unmagnetized collisional dusty plasma consisting of negatively charged dust grain, positively charged ions, q-nonextensive electrons, and neutral particles in the presence of external periodic force. Using reductive perturbation technique, the damped forced modified Korteweg-de Vries equation is obtained for the dust ion acoustic waves. Momentum consevation law is used to obtain the dust ion acoustic solitary wave solutions in the framework of the damped forced modified Korteweg-de Vries equation. The effects of different physical parameters such as entropic index, dust ion collisional frequency, strength and frequency of the external periodic force, speed of the traveling wave and the parameter which is the ratio between the unperturbed densities of the dust ions and electrons are investigated on the analytical solution of the dust ion acoustic waves. It is observed that those parameters have significant effects on the structures of the damped forced dust ion acoustic solitary waves. The results of the present paper may have applications in laboratory and space plasma environments.

Vibration suppression for post-capture spacecraft via a novel bio-inspired Stewart isolation system

In the process of on-orbit capture mission, some undesirable vibrations arising from the relative motions between the servicing spacecraft and the target are inevitable, which can make the post-capture combined spacecraft unstable or even tumbling. Therefore, suppressing post-capture vibrations is critical to mission success. In this work, a novel bio-inspired X-shape structure-based Stewart isolation platform (XSSIP) system is first proposed to install between the satellite platform and the capture mechanism. It can suppress the post-capture vibrations of a free-floating spacecraft subjected to the impulsive or periodic external forces. Beneficial nonlinear stiffness and nonlinear damping characteristics with the existence of X-shape structure can be acquired, which is helpful to achieve much better vibration isolation performance in multiple directions. Different from the traditional ground vibration isolation system, the dynamic equations of the 6-DOF under-constrained system in the weightless environment of space are established by Lagrange's principle. Influences on vibration isolation performance of the XSSIP system incurred by different structural parameters are systematically studied under either periodic or impulsive excitations. In addition, ADAMS simulation is conducted to verify the accuracy and feasibility of the theoretical model. Compared with the traditional spring-mass-damper (SMD)-based Stewart isolation platform system, the XSSIP system possesses an obvious advantage and offers a highly efficient passive way for suppressing post-capture vibrations of the floating spacecraft.