Pulsed Perturbation Research Articles

Rocking block stability under periodic and random perturbations

We analyze the dynamics of a rigid block subject to ground acceleration, simulating the effects of both an earthquake and the emergence of an eventual earthquake replica. For a single pulse, we find that the escape time τ (elapsed time for the block overturning) shows a periodic dependence with the pulsed duration time. This behavior reveals an asymmetric pattern in the parameter space for the direction of the block overturning. Fixing τ to its maximum value, a second pulsed perturbation (replica) is simulated via two protocols: one describing a kick of fixed amplitude and another described by a perturbation of variable amplitude chosen from a random distribution, which can be considered first with only positive values, and second with positive and negative values. The first protocol does not enhance τ unless the kick is applied immediately after turning off the first pulse. However, using the variable amplitude perturbation, a remarkable enhancement of the duration of the sustained vibrations of the block is observed. More interestingly, we show the emergence of revivals of the rocking motion after the system has initially ceased to vibrate. A frequency–amplitude phase diagram indicates that the system possesses a preferred operational range of parameters from which valuable information could be extracted. This could improve our understanding of the rocking performance of the system.

Runaway electron mitigation with pulsed localized vertical magnetic field perturbation in ADITYA tokamak

To reduce the risk of severe damage to the vessel and inner peripherals of any tokamak and its safe operation, a robust technique for the mitigation of runaway electrons (REs) is required. The REs in ADITYA tokamak are effectively mitigated by an application of local vertical magnetic field (LVF) perturbation. The LVF perturbation is applied using a pair of electromagnetic coils placed at the top and bottom of the ADITYA vacuum vessel in a Helmholtz configuration at one toroidal location. Powered by a capacitor bank power supply, these coils can produce a localized vertical magnetic field at the plasma center in the range of ∼150 G–260 G for a variable duration of 5–20 ms. The LVF pulse is first applied at the breakdown/current-ramp phase, where the REs are generated in the discharges initiated by the conventional ohmic breakdown in ADITYA. With the application of LVF pulse the REs are significantly reduced as indicated by the reduction in the REs generated hard x-ray flux. It has been observed that to extract the REs efficiently, an LVF pulse of magnitude at least ∼1% of the toroidal magnetic field with a minimum duration of ∼5 ms should be applied. The LVF perturbation is applied at different times into the discharge, i.e. during the breakdown/current ramp-up phase and current flat-top phase. The REs are significantly reduced in all the phases and improved discharge consistency. The LVF acts as an error field and a short-pulse of the LVF influences the REs more in comparison to the thermal electrons due to the faster velocities of the REs.

Optimal control of a Wilson-Cowan model of neural population dynamics.

Nonlinear dynamical systems describe neural activity at various scales and are frequently used to study brain functions and the impact of external perturbations. Here, we explore methods from optimal control theory (OCT) to study efficient, stimulating "control" signals designed to make the neural activity match desired targets. Efficiency is quantified by a cost functional, which trades control strength against closeness to the target activity. Pontryagin's principle then enables to compute the cost-minimizing control signal. We then apply OCT to a Wilson-Cowan model of coupled excitatory and inhibitory neural populations. The model exhibits an oscillatory regime, low- and high-activity fixed points, and a bistable regime where low- and high-activity states coexist. We compute an optimal control for a state-switching (bistable regime) and a phase-shifting task (oscillatory regime) and allow for a finite transition period before penalizing the deviation from the target state. For the state-switching task, pulses of limited input strength push the activity minimally into the target basin of attraction. Pulse shapes do not change qualitatively when varying the duration of the transition period. For the phase-shifting task, periodic control signals cover the whole transition period. Amplitudes decrease when transition periods are extended, and their shapes are related to the phase sensitivity profile of the model to pulsed perturbations. Penalizing control strength via the integrated 1-norm yields control inputs targeting only one population for both tasks. Whether control inputs drive the excitatory or inhibitory population depends on the state-space location.

Attracting sets for one class of asymptotically compact systems with pulsed perturbation

The authors consider the pulsed dynamical systems generated by evolutionary processes. The trajectories of these processes undergo the pulsed perturbation when the energy functional reaches some fixed limit value. The generalization of the classical theory of global attractors of infinite dimensional dynamical systems in case of systems with impulse actions is carried out. It is established that for the dissipative pulsed dynamical system generated by the asymptotically compact semigroup, there exists a uniform attractor, i.e., a compact uniformly attracting set, minimal among all such sets in the phase space of the system. The result is applied to the weakly nonlinear wave equation with dissipation, the trajectories of which are subjected to impulsive perturbations upon attainment of a certain fixed subset in the phase space, so called the impulse set.

Influence of Impulse Disturbances on Oscillations of Nonlinearly Elastic Bodies

A method for studying the effect of impulse perturbation on the longitudinal oscillations of a homogeneous constant cross-section of the body and the elastic properties of a material which satisfies the essentially nonlinear law of elasticity has been developed. A mathematical model of the process is presented, which is an equation of hyperbolic type with a small parameter at the discrete right-hand side. The latter expresses the effect of impulse perturbation on the oscillatory process. As for the boundary conditions considered in the work, they are classic of the first, second and third genera. The methodology is based on: the principle of oscillation frequency in nonlinear systems with many degrees of freedom and distributed parameters; basic provisions of asymptotic methods of nonlinear mechanics; the idea of using special periodic Ateb-functions to construct solutions of some classes of nonlinear differential equations; properties of completeness and orthonormality of functions that describe the forms of oscillations of undisturbed motion. In general, the above allowed to obtain relations that describe for the first approximation the defining parameters of the oscillations of an elastic body. Their peculiarity is that even for undisturbed motion, the natural frequency of oscillations depends on the amplitude, and therefore, under the action of a periodic (over time) pulse force on the elastic body, both resonant and nonresonant processes are possible in the latter. It, in contrast to an elastic body with linear or quasilinear elastic properties of the body is determined not only by its basic physical and mechanical properties, but also by the amplitude of oscillations. As a special case, the oscillations of the body under the action of a constant periodic momentum perturbation are considered. It is shown that for the nonresonant case for the first approximation it does not affect the laws of change of amplitude and frequency of the process. As for the resonant is the amplitude of origin through the main resonance significantly depends not only on the speed but also on the points of action of the pulsed perturbation. Moreover, the closer the point of application of the pulsed force to the middle of the elastic body under boundary conditions of the first kind is greater (for boundary conditions of the second kind closer to the end).

Success rate analysis of the response of an excitable laser to periodic perturbations.

We use statistical tools to characterize the response of an excitable system to periodic perturbations. The system is an optically injected semiconductor laser under pulsed perturbations of the phase of the injected field. We characterize the laser response by counting the number of pulses emitted by the laser, within a time interval, ΔT, that starts when a perturbation is applied. The success rate, SR(ΔT), is then defined as the number of pulses emitted in the interval ΔT, relative to the number of perturbations. The analysis of the variation of SR with ΔT allows separating a constant lag of technical origin and a frequency-dependent lag of physical and dynamical origin. Once the lag is accounted for, the success rate clearly captures locked and unlocked regimes and the transitions between them. We anticipate that the success rate will be a practical tool for analyzing the output of periodically forced systems, particularly when very regular oscillations need to be generated via small periodic perturbations.

Evolution of the Global Carbon Cycle and Climate Regulation on Earth

AbstractThe existence of stabilizing feedbacks within Earth's climate system is generally thought to be necessary for the persistence of liquid water and life. Over the course of Earth's history, Earth's atmospheric composition appears to have adjusted to the gradual increase in solar luminosity, resulting in persistently habitable surface temperatures. With limited exceptions, the Earth system has been observed to recover rapidly from pulsed climatic perturbations. Carbon dioxide (CO2) regulation via negative feedbacks within the coupled global carbon‐silica cycles are classically viewed as the main processes giving rise to climate stability on Earth. Here we review the long‐term global carbon cycle budget, and how the processes modulating Earth's climate system have evolved over time. Specifically, we focus on the relative roles that shifts in carbon sources and sinks have played in driving long‐term changes in atmospheric pCO2. We make the case that marine processes are an important component of the canonical silicate weathering feedback, and have played a much more important role in pCO2 regulation than traditionally imagined. Notably, geochemical evidence indicate that the weathering of marine sediments and off‐axis basalt alteration act as major carbon sinks. However, this sink was potentially dampened during Earth's early history when oceans had higher levels of dissolved silicon (Si), iron (Fe), and magnesium (Mg), and instead likely fostered more extensive carbon recycling within the ocean‐atmosphere system via reverse weathering—that in turn acted to elevate ocean‐atmosphere CO2 levels.

Stationary and Self-Similar Waves in a Rod with Bimodular Nonlinearity, Dissipation, and Dispersion

Propagation of longitudinal elastic waves in a rod with bimodular nonlinearity, linear dissipation, and geometrical dispersion of phase velocity is analyzed. Analytical and numerical solutions are obtained for stationary and self-similar waveforms and pulsed perturbations that propagate in the rod without shape changes, and a corresponding graphical analysis is presented.

Propagation acoustic signal in the multifractional gas suspension

The dispersion and dissipation of the acoustic signal in a multifraction gas suspension is investigated. A closed linearized system of differential equations of the perturbed motion of a multifraction gas suspension and the analytical dependence of the complex wave number on the perturbation frequency are presented. Using the fast Fourier transform method, calculations were performed on the propagation of pulsed perturbations in the considered media. The influence of the parameters of the dispersed phase on the dispersion and dissipation of the acoustic signal is analyzed.

Experimental Investigation of the Dynamical Modes of Four Pulse‐Coupled Chemical Micro‐Oscillators

We present an experimental system of four identical microreactors (MRs) in which the photosensitive oscillatory Belousov-Zhabotinsky (BZ) reaction occurs. The inhibitory coupling of these BZ MRs is organized via pulses of light coming to each MR from a computer projector. These pulses are induced by spike(s) in other MR(s) of the same network. Time delay between the spike in one BZ MR and the pulsed perturbation of the other BZ MR(s), the amplitude of light pulses, their duration, and the connectivity of the MRs are controlled by the LabVIEW software. Recording the dynamics of the BZ reaction in the MRs via a microscope equipped with a CCD camera, we observe all the main dynamical modes of our network of MRs, which are the IP (in-phase), AP (anti-phase), W (walk), and WR (walk reverse) for the unidirectional coupling, and the IP, two-cluster, three-cluster, and splay modes for the all-to-all coupling. Our software detects all the modes of the network automatically and makes it possible to switch between them on demand using a few special "switching" pulses. As the result of the present work, the experimental implementation of the adaptive behaviour of the pulse-coupled chemical micro-oscillator networks becomes available.

A freely yawing axisymmetric bluff body controlled by near-wake flow coupling

Flow-induced oscillations of a wire-mounted, freely yawing axisymmetric round bluff body and the induced loads are regulated in wind tunnel experiments (Reynolds number $60\,000<Re_{D}<200\,000$) by altering the reciprocal coupling between the body and its near wake. This coupling is controlled by exploiting the receptivity of the azimuthal separating shear layer at the body’s aft end to controlled pulsed perturbations effected by two diametrically opposed and independently controlled aft-facing rectangular synthetic jets. The model is supported by a thin vertical wire upstream of its centre of pressure, and prescribed modification of the time-dependent flow-induced loads enables active control of its yaw attitude. The dynamics of the interactions and coupling between the actuation and the cross-flow are investigated using simultaneous, time-resolved measurements of the body’s position and phase-locked particle image velocimetry measurements in the yawing plane. It is shown that the interactions between trains of small-scale actuation vortices and the local segment of the aft-separating azimuthal shear layer lead to partial attachment, and the ensuing asymmetric modifications of the near-wake vorticity field occur within 15 actuation cycles (approximately three convective time scales), which is in agreement with measurements of the flow loads in an earlier study. Open- and closed-loop actuation can be coupled to the natural, unstable motion of the body and thereby affect desired attitude control within 100 convective time scales, as is demonstrated by suppression or enhancement of the lateral motion.

Nonadiabatic transition probabilities in a time-dependent Gaussian pulse or plateau pulse: Toward experimental tests of the differences from Dirac's transition probabilities.

For a quantum system subject to a time-dependent perturbing field, Dirac's analysis gives the probability of transition to an excited state |k⟩ in terms of the norm square of the entire excited-state coefficient ck(t) in the wave function. By integrating by parts in Dirac's equation for ck(t) at first order, Landau and Lifshitz separated ck (1)(t) into an adiabatic term ak (1)(t) that characterizes the gradual adjustment of the ground state to the perturbation without transitions and a nonadiabatic term bk (1)(t) that depends explicitly on the time derivative of the perturbation at times t' ≤ t. Landau and Lifshitz stated that the probability of transition in a pulsed perturbation is given by |bk(t)|2, rather than by |ck(t)|2. We use the term "transition probability" to refer to the probability that a true excited-state component is present in the time-evolved wave function, as opposed to a smooth modification of the initial state. In recent work, we have examined the differences between |bk(t)|2 and |ck(t)|2 when a system is perturbed by a harmonic wave in a Gaussian envelope. We showed that significant differences exist when the frequency of the harmonic wave is off-resonance with the transition frequency. In this paper, we consider Gaussian perturbations and pulses that rise via a half Gaussian shoulder to a level plateau and later return to zero via a down-going half Gaussian. While the perturbation is constant, the transition probability |bk(t)|2 does not change. By contrast, |ck(t)|2 continues to oscillate while the perturbation is constant, and its time averaged value differs from |bk(t)|2. We suggest a general type of experiment to prove that the transition probability is given by |bk(t)|2, not |ck(t)|2. We propose a ratio test that does not require accurate knowledge of transition matrix elements or absolute field intensities.

Time-resolved Hall conductivity of pulse-driven topological quantum systems

We address the question of how the time-resolved bulk Hall response of a two dimensional honeycomb lattice develops when driving the system with a pulsed perturbation. A simple toy model that switches a valley Hall signal by breaking inversion symmetry is studied in detail for slow quasi-adiabatic ramps and sudden quenches, obtaining an oscillating dynamical response that depends strongly on doping and time-averaged values that are determined both by the out of equilibrium occupations and the Berry curvature of the final states. On the other hand, the effect of irradiating the sample with a circularly-polarized infrared pump pulse that breaks time reversal symmetry and thus ramps the system into a non-trivial topological regime is probed. Even though there is a non quantized average signal due to the break down of the Floquet adiabatical picture, some features of the photon-dressed topological bands are revealed to be present even in a few femtosecond timescale. Small frequency oscillations during the transient response evidence the emergence of dynamical Floquet gaps which are consistent with the instantaneous amplitude of the pump envelope. On the other hand, a characteristic heterodyining effect is manifested in the model. The presence of a remnant Hall response for ultra-short pulses that contain only a few cycles of the radiation field is briefly discussed.

Heterogeneous microstructure evolution in Ti-6Al-4V alloy thin-wall components deposited by plasma arc additive manufacturing

Microstructural heterogeneity was observed in titanium alloys deposited by high-energy density beam additive manufacturing (AM) technologies in the as-built condition; these heterogeneities included the presence of coarse prior-β columnar grains, non-equilibrium layer bands(LBs), and mixed microstructures. This is particulary prominent with plasma arc AM (PAM), which has a higher heat input when compared to laser beam and electron beam AM technologies. In this study, several Ti-6Al-4V layers were deposited by PAM to investigate the characteristics of the generated microstructural heterogeneity. The results show that epitaxial growth of prior β columnar grains in the same direction is inhibited by pulsed perturbation, which results in formation of columnar grains with near-equiaxed grains. Horizontal LBs could be observed after depositing six layers. The phase transformation (β → α) followed the Burgers orientation relationship, resulting in triangular stars or rhombic patterns. Precipitation of secondary α nano dispersoids occurred along{10-10} orientation. The LB region of heterogeneity was affected by thermal cycles in the β-transus and the recrystallisation temperature ranges, which leads to α lamellae of the same orientation finally forming coarse α colonies, and dispersion strengthening of the α lamellae with α nano depersoids contributes to the microhardness.

Dynamic modes in a network of five oscillators with inhibitory all-to-all pulse coupling.

The dynamic modes of five almost identical oscillators with pulsatile inhibitory coupling with time delay have been studied theoretically. The models of the Belousov-Zhabotinsky reaction and phase oscillators with all-to-all coupling have been considered. In the parametric plane Cinh-τ, where Cinh is the coupling strength and τ is the time delay between a spike in one oscillator and pulsed perturbations of all other oscillators, three main regimes have been found: regular modes, when each oscillator gives only one spike during the global period T, C (complex) modes, when the number of pulses of different oscillators is different, and OS (oscillations-suppression) modes, when at least one oscillator is suppressed. The regular modes consist of several cluster modes and are found at relatively small Cinh. The C and OS modes observed at larger Cinh intertwine in the Cinh-τ plane. In a relatively narrow range of Cinh, the dynamics of the C modes are very sensitive to small changes in Cinh and τ, as well as to the initial conditions, which are the characteristic features of the chaos. On the other hand, the dynamics of the C modes are periodic (but with different periods) and well reproducible. The number of different C modes is enormously large. At still larger Cinh, the C modes lose sensitivity to small changes in the parameters and finally vanish, while the OS modes survive.

Exploring phase control with square pulsed perturbations

We discuss the phase control technique consisting of an applied square pulsed periodic perturbation. We explore the effect of such perturbations to the different terms of the Duffing oscillator. We find that the effect depends sensitively on how the perturbation is applied, indeed, it is specially effective when it modulates the cubic and the linear term and uneffective when applied to the driving term. Our results highlight the highly nontrivial role of the phase when applying a second periodic perturbation to a chaotic system.

System Theoretic Analysis of Battery Charging Optimization

Lithium-ion batteries have attractive features for many applications, and are widely used as high-energy density storage devices. The internal electrochemical and chemical reactions occurring during charge/discharge make Li-ion batteries sensitive to demand sequences and operating conditions. Battery management systems are necessary to keep cells within acceptable operating ranges to prolong life, reduce charging losses, and mitigate failure. One particular area of recent investigation is incorporating pulsed perturbations in charging protocols. Typical arguments for pulsed perturbations involve reduced chemical impedance and reduced electrode/electrolyte polarization which decrease losses, and electrode diffusion capabilities which can reduce losses and mitigate plating. However, published experimental and simulation evidence is contradictory, with some either arguing in favor pulsed charging and some indicating no effect or worse performance. While experimental results are useful, the measurable results are subtle enough that experimental conditions and uncertainty can be a plausible argument against both positive and negative results. In this work, we ask the following question: What are the features of a battery as a dynamic system that must appear in order for optimal charging sequences to include a periodic component? The answer to this question is then used to illuminate whether some of the physical, mechanistic explanations for the positive effects of perturbations are valid. The analysis considers two cases: finding the current trajectory to minimize the energy required to supply a fixed amount of charge to a battery, and finding the current trajectory to maximize the charge supplied to the battery while meeting constraints on internal variables related to the deposition of lithium on the anode electrode. Under the assumption that the trajectories for the relevant battery parameters can be predicted using a linear time-invariant dynamic system, analytic solutions are obtained. Using these analytic solutions, we extract conditions on the battery model that must be satisfied in order for the solutions to contain a periodic component. In the case of energy minimization, it can be shown that the the electrochemical impedance must approach the imaginary axis, while in the case of meeting constraints, a necessary condition is developed involving the response of the internal variables to an impulse in charging current. By examining the impedance spectra and impulse responses of typical Li-ion batteries, these results indicate that that pulsed or sinusoidal perturbations do not appear in the optimal charging sequence. It should be emphasized that this analysis does not provide definitive arguments for or against pulse charging or any evidence against any particular experimental results. However, this study provides important guidance when considering a physical explanation for the benefits of pulsed or sinusoidal ripple charging. Figure 1

Sound waves in multifractional liquids with bubbles

The propagation of sound waves in multifractional mixtures of liquid with vapor–gas and gas bubbles of different sizes and different compositions with phase transitions is studied. The dispersed phase consists of N+M fractions having various gases in bubbles and different in the bubbles radii. Phase transitions accounted for N fractions. The total bubble volume concentration is small (less than 1%). The dispersion relation is derived and dispersion curves is built. The evolution of the weak pulsed perturbations of the pressure in this mixture was calculated numerically.

Degradation of the current-carrying capacity of low-temperature superconducting composites under the action of thermal perturbations

The stability of transport current introduced into a niobium titanium superconducting composite subjected to an external pulsed thermal perturbation has been studied. Stable states have been theoretically analyzed by solving Fourier and Maxwell equations that describe the thermoelectrodynamic states of lowtemperature superconductors with flux creep. It has been shown that, if the transport current is permanently introduced, subcritical thermal perturbations, i.e., perturbations that do not take the composite to a normal state provided that the current does not exceed the quench current, may result in the appearance of unstable current states. The higher the energy of the external thermal perturbation, the lower the instability onset current. It has been found that the degradation of the current-carrying capacity of the superconducting composite is due to intense heat release inside the superconductor, which is initiated by the thermal perturbations, and depends on the current input rate, the instant of time the current input is terminated, and cooling conditions.

Energy constraints in pulsed phase control of chaos

Phase control of chaos is a powerful technique but little is known about its physical constraints, relevant for real systems. As a fact, it has not been explored whether this technique can also be applied when the controlling perturbation is not harmonic. Here we apply phase control on a driven double well Duffing oscillator using periodic rectangular pulsed perturbations instead of the classical sinusoidal perturbations. Experimental measurements and numerical simulations show that this kind of perturbation is also able to stabilize the chaotic orbits for an adequate selection of the phase. Furthermore, as the duty cycle of the perturbation (that is, the fraction of the time that the periodically pulsed control is active) is increased, two separate regimes occur. In the first one, the perturbations leading to stabilization of periodic solutions are of constant energy (taken as the product of the duty cycle and the amplitude) and in the second one, a saturation phenomenon occurs, implying that increasing energy values of the perturbations are wasted. Our results unveil the versatility of the pulsed phase control scheme and the importance of energy constraints.