Periodic Perturbations Research Articles

Perturbation context in paced finger tapping tunes the error-correction mechanism

Sensorimotor synchronization (SMS) is the mainly specifically human ability to move in sync with a periodic external stimulus, as in keeping pace with music. The most common experimental paradigm to study its largely unknown underlying mechanism is the paced finger-tapping task, where a participant taps to a periodic sequence of brief stimuli. Contrary to reaction time, this task involves temporal prediction because the participant needs to trigger the motor action in advance for the tap and the stimulus to occur simultaneously, then an error-correction mechanism takes past performance as input to adjust the following prediction. In a different, simpler task, it has been shown that exposure to a distribution of individual temporal intervals creates a “temporal context” that can bias the estimation/production of a single target interval. As temporal estimation and production are also involved in SMS, we asked whether a paced finger-tapping task with period perturbations would show any time-related context effect. In this work we show that a perturbation context can indeed be generated by exposure to period perturbations during paced finger tapping, affecting the shape and size of the resynchronization curve. Response asymmetry is also affected, thus evidencing an interplay between context and intrinsic nonlinearities of the correction mechanism. We conclude that perturbation context calibrates the underlying error-correction mechanism in SMS.

Universal density shift coefficients for the thermal conductivity and shear viscosity of a unitary Fermi gas

We measure universal temperature-independent density shifts for the thermal conductivity κT and shear viscosity η, relative to the high temperature limits, for a normal phase unitary Fermi gas confined in a box potential. We show that a time-dependent kinetic theory model enables extraction of the hydrodynamic transport times τη and τκ from the time-dependent free decay of a spatially periodic density perturbation, yielding the static transport properties and density shifts, corrected for finite relaxation times. Published by the American Physical Society 2024

A Novel Method for Analyzing Global Bifurcation and Global Hysteresis of FGM Truncated Conical Shell Structure

In the dynamic bifurcation and dynamic hysteresis of a system, our first consideration is the tiny changes in time that can lead to variations in the vector field, potentially causing the occurrence of system dynamic bifurcation and dynamic hysteresis. This paper presents a novel method for analyzing the global bifurcation and hysteresis of Functionally Graded Material (FGM) truncated conical shell structure under aerodynamics and in-plane force along meridian near internal resonances. This method involves introducing the ratio of vector fields as a periodic perturbation parameter in the system’s nonlinear second-order ordinary differential governing equations. This allows for the analysis of the nonlinear ordinary differential equations as algebraic equations, yielding algebraic expressions that only involve parameters and do not contain state variables. Subsequently, the global bifurcation set and global hysteresis set of FGM truncated conical shell structure are obtained, providing the parameters interval ranges for the stability and instability of FGM truncated conical shell structure. By utilizing MAPLE software for numerical simulation, the images of the global bifurcation set and global hysteresis set about the amplitude of in-plane load are first simulated numerically. Subsequently, the amplitude graphs of the equilibrium points are numerically simulated for validation. The results demonstrate a perfect alignment between the images of the global bifurcation set and global hysteresis set and the data from the amplitude graphs of the equilibrium point. Due to the periodicity of the periodic perturbation parameter, it shuttles between different persistent regions as other parameters change, leading to the generation of chaotic solutions in the governing equations. The validity of the obtained results is confirmed through comparisons with existing literature.

Emergence of extreme events from randomly chirped condensate

We explore rogue wave emergence in generic wave systems governed by the nonlinear Schrödinger equation. We highlight the interplay between the stochastic focusing induced by a random chirp of a continuous wave condensate and modulation instability of the condensate to periodic and/or random perturbations. We show that regardless of its statistical properties, the random chirp of the condensate leads to a non-Gaussian, heavy-tailed probability density distribution of peak powers of the waves excited atop of the condensate, which is a statistical signature of rogue waves, or more broadly, extreme events in physics.

Perturbation-response dynamics of coupled nonlinear systems.

How nonlinear systems dynamically respond to external perturbations essentially determines their function. Weak perturbations induce response dynamics near a stable operating point, often approximately characterized by linear response theory. However, stronger driving signals may induce genuinely nonlinear responses, including tipping transitions to qualitatively different dynamical states. Here, we analyze how inter-unit coupling impacts responses to periodic perturbations. We find that already in minimal systems of two identical and linearly coupled units, coupling impacts the dynamical responses in a distinct way. Any non-zero coupling strength extends the regime of non-tipping local responses relative to uncoupled units. Intriguingly, finite coupling may be more effective than infinitely strong coupling in keeping responses from tipping. Interestingly, already weak coupling may create novel response modes in strongly driven systems, implying the existence of multiple tipping points instead of only one. These results persist for systems of non-identical units, systems with nonlinear coupling, and larger networks of coupled units.

The bifurcation, chaotic behavior and exact solutions of the fractional stochastic Jimbo–Miwa equations

The Jimbo–Miwa equation is the second equation in the KP hierarchy of integrable systems. In this paper, this equation is extended and introduced with the stochastic process and fractional derivatives. Firstly, the phase portrait of the Hamiltonian system generated by it is studied to understand its bifurcation behavior. Additionally, non-periodic and periodic perturbation terms are added to this system. Different values are assigned to the parameters in the perturbation terms to analyze its sensitivity and the resulting chaos is obtained. Finally, through integration techniques, the expression of the solution of this equation is obtained. These solutions are related to rational functions, trigonometric functions, exponential functions and Jacobi elliptic functions. To observe the form of the solutions more intuitively, 3D and 2D numerical simulations are conducted on the solutions and the solution images of the stochastic fractional differential equation are given by Matlab software. Compared with the existing literature, the research on the stochastic fractional equation of this equation is relatively rare and the analysis of the phase portrait is even scarcer. Our solution method is quite different from that in the previous literature. Therefore, this paper is novel. The conclusion of this paper will be of great help for the practical application of this equation.

Periodic and Axial Perturbations of Chaotic Solitons in the Realm of Complex Structured Quintic Swift-Hohenberg Equation

This research work employs a powerful analytical method known as the Riccati Modified Extended Simple Equation Method (RMESEM) to investigate and analyse chaotic soliton solutions of the (1 + 1)-dimensional Complex Quintic Swift–Hohenberg Equation (CQSHE). This model serves to describe complex dissipative systems that produce patterns. We have found that there exist numerous chaotic soliton solutions with periodic and axial perturbations to the intended CQSHE, provided that the coefficients are constrained by certain conditions. Furthermore, by applying a sophisticated transformation, the provided transformative approach RMESEM transforms CQSHE into a set of Nonlinear Ordinary Differential Equations (NODEs). The resulting set of NODEs is then transformed into an algebraic system of equations by incorporating the extended Riccati NODE to assume a series form solution. The soliton solutions to this system of equations can be found as periodic, hyperbolic, exponential, rational-hyperbolic, and rational families of functions. A variety of 3D and contour visuals are also provided to graphically illustrate the axially and periodically perturbed dynamics of these chaotic soliton solutions and the formation of fractals. Our findings are noteworthy because they shed light on the chaotic nature of the framework we are examining, enabling us to better understand the dynamics that underlie it.

Complementary extended state observer‐based model‐free sliding mode control for a PMSM in cathode copper production

AbstractThis study introduces a model‐free sliding mode control scheme based on a complementary extended state observer (CESO) for a permanent magnet synchronous motor (PMSM) in cathode copper production. First, an ultra‐local model of the PMSM is proposed. Compared with the existing ultra‐local model, the ultra‐local model proposed in this study divides the disturbances into periodic and aperiodic perturbations. Furthermore, based on the proposed ultra‐local model, a CESO is proposed. Compared to the linear extended state observer (LESO) and the non‐linear extended state observer (NLESO), the proposed CESO combines the advantages of the LESO and the NLESO. The proposed CESO exhibits reduced disturbance estimation errors and greater resilience to significant periodic and minor aperiodic disturbances. By leveraging the ultra‐local model, a novel combined control strategy is devised, utilizing the CESO and a model‐free sliding mode control. The stability of the proposed control scheme has been verified through the Lyapunov stability theorem and the Hurwitz stability criterion. Subsequently, comparative simulations on disturbance rejection are conducted under periodic and aperiodic disturbances, illustrating the efficacy of the proposed control approach.

A Hinge Moment Alleviation Control Strategy for Morphing Tail Aircraft Based on a Data-Driven Method

Morphing airplane technology is currently a focal point of research. For morphing airplanes, besides effective morphing strategies and control schemes, the hinge moment at the root of the vertical tail during morphing is a critical factor influencing flight safety. To prevent failure in tail morphing due to excessive hinge moments, this paper analyzes the hinge moment characteristics of the variable vertical tail structure in high-speed flight, based on a flying wing model from the China Aerodynamics Research and Development Center. The proposed adaptive morphing tail hinge moment reduction (AMTHR) method is model-free, utilizing real-time data to dynamically adjust the rudder and reduce hinge moments without requiring prior knowledge of system dynamics. This method utilizes the concept of extremum-seeking control by introducing periodic perturbations to the system and adjusting the control input based on their impact on the output. This approach drives the output toward an extremum point, enabling real-time reduction of the vertical tail hinge moment. Finally, the simulation analysis is carried out under the conditions of no wind and gust disturbance, and the effect of this method on the load reduction of the tail hinge moment is verified.

Tidal triggering of seismic swarm associated with hydrothermal circulation at Blanco ridge transform fault zone, Northeast Pacific

Seismicity associated with hydrothermal systems (e.g., submarine volcanoes, mid-oceanic ridges, oceanic transform faults, etc.) share a complex relationship with the tidal forcing and induced fluid flow process under different tectonic settings. The hydrothermal circulation drives the deformation at the brittle-ductile transition zone within a permeable brittle crust. Although the tidal loading amplitudes are too small to generate a brittle deformation, the incremental pressure exerted by the tidal loading can modulate the flow of hydrothermal fluid circulation and trigger the critically stressed faults or fracture zones. We present a compelling case of tidal modulation in seismicity along the Blanco Ridge Transform Fault Zone (BRTFZ), in the northeast Pacific. The strong diurnal and fortnightly periodicity has been observed in the deeper seismic swarm (7–15 km), whereas the shallow seismic swarm (0–7 km) does not exhibit any such tidal periodicity. The dominance of diurnal and fortnightly periodicity in the deeper seismic swarm is explained by the high amplitude tidal cycles providing additional stress on the fluid circulation at the crust-mantle boundary. Moreover, our robust statistical correlation of seismicity with tidal stress and resonance destabilization model under rate-and-state friction formalism suggests that the fault segments are conditionally unstable and more sensitive to periodic tidal stress perturbation.

Thermal convection subjected to perturbations from the bottom of a top open cavity

Perturbations are very common in the transition and heat transfer of thermal convection in nature and industry. Accordingly, thermal convection on a top-open cavity subjected to periodic and random perturbations is investigated using three-dimensional numerical simulation. A great number of numerical experiments are performed at various Rayleigh numbers and a fixed Prandtl number of 0.71 by introducing periodic and random numerical perturbations. Numerical results demonstrate that there exists the effect of periodic perturbations on the transition route over 3.5 × 103 ≤ Ra ≤ 8.5 × 104. That is, the transition route to chaos is sensitive to the amplitude of random perturbations for, e.g., 0.01 ≤ Ar ≤ 0.05, which is also characterized. Furthermore, heat transfer enhancement under periodic and random perturbations is quantified with the scaling law. This study sheds new light on the influence of periodic and random perturbations on thermal convection on the top-open cavity below heating. The possibility to control heat transfer is revealed by introducing random perturbations on the bottom of the top-open cavity.

Hybrid intelligent framework for designing band gap-rich 2D metamaterials

An artificial intelligence machine learning-based design framework is proposed to design lattice-based metamaterials with hexagonal symmetry that deliver wide band gaps at user-desired frequency ranges between 0 and 1000 kHz. The design approach starts by selecting a traditional, easy-to-manufacture parent lattice-based material that does not necessarily exhibit wide or functional band gaps. Subsequently, the parent lattice is transformed into a band-gap-rich lattice by superposing periodic triangular-shaped perturbations (i.e., zigzag-sine-based curvatures) with controllable frequencies and magnitudes on its ligaments. Finally, the frequency and magnitude parameters needed to deliver a specific band gap between 0 and 1000 kHz are determined using a hybrid intelligent framework, developed based on an Adaptive Neuro-Fuzzy Inference Systems (ANFIS). The ANFIS network integrates fuzzy logic expert models and artificial neural networks’ machine learning capabilities. Such a hybrid network is known for its ability to model strongly nonlinear and complex data. The data used in training the ANFIS models is generated using parametric finite element-based simulations where band gaps corresponding to a wide range of perturbation frequencies and magnitudes are computationally determined. The parametric study showed a nonlinear and complex topology-band gap characteristic relation; however, the Adaptive Neuro-Fuzzy Inference System (ANFIS) proved capable of modeling the observed complex topology-band gap behavior efficiently. The accuracy of the ANFIS models exceeded 99 % in several design ranges (i.e., perturbation parameters ranges). These were designated as high-accuracy design regions and were highlighted in the proposed design approach. Using multiple case studies with different band gap requirements, the ANFIS-based design framework proved effective in delivering customized lattice-based metamaterials with user-defined band gap frequencies.

Modified honeycomb cores for enhancing the durability of sandwich structures under low-velocity impact

Honeycomb cores are essential components of composite sandwich structures, and enhancing their ability to withstand out-of-plane loads can improve the resilience of sandwich structures under low-velocity transverse impacts. Therefore, this study computationally investigates the potential for improving the out-of-plane strength of honeycomb cores by superposing periodic sinusoidal perturbations to their cell walls. Such perturbations have been used to enhance the acoustic properties of honeycomb cores. Results demonstrated that introducing these perturbations can improve the strength of honeycomb cores under localized out-of-plane loadings resembling colliding with small objects at low impact speeds. Superposed perturbations increased the out-of-plane strength by a maximum of 28.5 % and eliminated the post-buckling softening behavior. Moreover, they increased the toughness, represented by the area under the force-displacement curve, under localized out-of-plane loads by a maximum of 56.7%. The perturbed honeycomb cores showed more sensitivity to the frequency of the superposed perturbations than their magnitude.

Investigating the invariant solutions of (1+1)-dimensional Sawada–Kotera model using Lie symmetries analysis

Here attention is focused on the (1+1)-dimensional Sawada–Kotera (SK) model that is prominent in mathematical physics and engineering to analyze plasmas and coherent systems for communication. Our techniques offer fresh perspectives on the model’s attributes and structure, deepening our comprehension of the underlying dynamics. First, the SK model is reduced to ordinary differential equations by constructing the Lie symmetries and using the associated transformation. Graphs are used to build and display invariant solutions. This strategy has caused the revelation of novel constant solutions that have not been found in the previous works. We offer new understandings of nature and changes observed during the SK derivation by taking advantage of the Lie symmetries powerful tools. Next, the fluctuating layout of proposed framework is examined from several perspectives such as sensitivity and bifurcation analysis. We examined the bifurcation analysis of planar dynamical system by using bifurcation theory. We also include an external periodic perturbation term that breaks regular patterns in the perturbed dynamical system. Graphical structures are provided to display the invariant solutions. The sensitivity of the SK model is determined to be strong after sensitivity analysis under different initial conditions. These results are fascinating, fresh, and conceptually useful for understanding the suggested framework. In mathematics and the applied sciences, forecasting and learning about new technologies are greatly aided by the dynamic aspect of system processing.

Restructuring dynamics of surface species in bimetallic nanoparticles probed by modulation excitation spectroscopy

Restructuring of metal components on bimetallic nanoparticle surfaces in response to the changes in reactive environment is a ubiquitous phenomenon whose potential for the design of tunable catalysts is underexplored. The main challenge is the lack of knowledge of the structure, composition, and evolution of species on the nanoparticle surfaces during reaction. We apply a modulation excitation approach to the X-ray absorption spectroscopy of the 30 atomic % Pd in Au supported nanocatalysts via the gas (H2 and O2) concentration modulation. For interpreting restructuring kinetics, we correlate the phase-sensitive detection with the time-domain analysis aided by a denoising algorithm. Here we show that the surface and near-surface species such as Pd oxides and atomically dispersed Pd restructured periodically, featuring different time delays. We propose a model that Pd oxide formation is preceded by the build-up of Pd regions caused by oxygen-driven segregation of Pd atoms towards the surface. During the H2 pulse, rapid reduction and dissolution of Pd follows an induction period which we attribute to H2 dissociation. Periodic perturbations of nanocatalysts by gases can, therefore, enable variations in the stoichiometry of the surface and near-surface oxides and dynamically tune the degree of oxidation/reduction of metals at/near the catalyst surface.

Two-Dimensional Surface Periodic Flows of an Incompressible Fluid in Various Models of the Medium

A comparative analysis of the properties of two-dimensional infinitesimal periodic perturbations propagating over the incompressible fluid surface in various representations of the medium density profiles is carried out. Stratified and homogeneous in density viscous or ideal liquids are considered. Calculations are carried out by methods of the theory of singular perturbations. Dispersion relations and dependences of phase and group velocities for surface waves in physically observed variables are given. The change in the meaning of dispersion relations during the transition from ideal liquids to viscous and from homogeneous to stratified is shown. Taking into account the influence of electric charge does not qualitatively change the nature of two-dimensional dispersion relations. An increase in the surface density of the electric charge leads to a decrease in the wavelength at a fixed frequency and has no noticeable effect on the fine structure of the periodic flow.

Exploring chaos and ergodic behavior of an inductorless circuit driven by stochastic parameters

There exist extensive studies on periodic and random perturbations of various smooth maps investigating their dynamics. Unlike smooth maps, non-smooth maps are yet to be studied extensively under a stochastic regime. This paper presents a stochastic piecewise-smooth map derived from a simple inductorless switching circuit. The stochasticity is introduced in parameter values. The distribution of the parameter values is bounded and randomly selected from uniform and triangular distributions and ranges between high and low bifurcation parameter values of the deterministic map. Due to this inherent stochasticity in parameter values, the time evolution of the state variable cannot be predicted at a specific time instant. We observe that the state variable exhibits completely ergodic behavior when the minimum value of the parameter is the same as the minimum bifurcation parameter of the deterministic system. However, the ensemble average of the state variable converges to a fixed value. The system demonstrates nonchaotic behavior for a particular range of parameter values but the deterministic map in that bifurcation range shows interplay between chaos and periodic orbits. The values of Lyapunov exponents decrease monotonically with increased asymmetry of the distribution from which the bifurcation parameter values are chosen. We determine the probability density function of the stochastic map and verify its invariance under initial conditions. The most noteworthy result is the disappearance of chaotic behavior when the lower range of the distribution is varied while maintaining a fixed upper threshold for a particular distribution, even though the deterministic map exhibits an array of periodic and chaotic behaviors within the range. As the period-incrementing cascade with chaotic inclusion only occurs in nonsmooth maps, this paper numerically shows the stochasticity of a piecewise-smooth map obtained from a practical system for the first time where randomness is introduced in the parameter space.

Synchronization of Canards in Coupled Canard-Generating Bonhoeffer-Van Der Pol Oscillators Subject to Weak Periodic Perturbations

Synchronization of Canards in Coupled Canard-Generating Bonhoeffer-Van Der Pol Oscillators Subject to Weak Periodic Perturbations

Quasi-CJ rotating detonation with partially premixed methane-oxygen injection: Numerical simulation and experimental validation

The efficiency gain of rotating detonation depends on several loss factors related to the chamber geometry, the injection principle, the propellants and their mass flow rates, and the equivalence ratio. Numerical simulation can help quantify these losses, and this work presents a Large Eddy Simulation (LES) of rotating detonation in an annular chamber and its validation against experiments. The simulation captured the mixing processes, the overall dynamics of the detonation, the deflagration, and the burnt gas expansion. The injection device was numerically designed to ensure partial premixing of the propellants before injection into the chamber. The chamber had a length of 110 mm, an outer diameter of 80 mm, and a radial width of 10 mm. The mixture consisted of gaseous CH4 and O2 with an equivalence ratio of 1.2 and a mass flow rate of 160 g/s. Combustion kinetics was modeled using a skeletal mechanism with 62 reactions and 16 species. The boundary conditions were adiabatic slip walls. The results reproduce well the detonation velocity (within 1% deviation) and the pressure variation behind the wave. The simulated OH* chemiluminescence compares well with experimental high-speed imaging of the outlet and side of the chamber. The simulation results indicate that 65% of the propellant mass is well mixed in front of the wave whereas 15% of the mixture is burned by deflagration. They show that CH4 and O2 do not axially stratify because they have similar injection dynamics between periodic perturbations induced by the rotating detonation. Good propellant mixing and low deflagration losses explain the high experimental detonation velocity, about 90% of DCJ, and a high combustion efficiency of 98%. These agreements between the computational and experimental results indicate that the simulation is capable of capturing the physical scales relevant to RDC operation and producing reliable results for RDC design.

Dynamics around the Earth–Moon triangular points in the Hill restricted 4-body problem

This paper investigates the motion of a small particle moving near the triangular points of the Earth–Moon system. The dynamics are modeled in the Hill restricted 4-body problem (HR4BP), which includes the effect of the Earth and Moon as in the circular restricted 3-body problem (CR3BP), as well as the direct and indirect effect of the Sun as a periodic time-dependent perturbation of the CR3BP. Due to the periodic perturbation, the triangular points of the CR3BP are no longer equilibrium solutions; rather, the triangular points are replaced by periodic orbits with the same period as the perturbation. Additionally, there is a 2:1 resonant periodic orbit that persists from the CR3BP into the HR4BP. In this work, we investigate the dynamics around these invariant objects by performing a center manifold reduction and computing families of 2-dimensional invariant tori and their linear normal behavior. We identify bifurcations and relationships between families. Mechanisms for transport between the Earth, L4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_4$$\\end{document}, and the Moon are discussed. Comparisons are made between the results presented here and in the bicircular problem (BCP).