Periodic Forcing Research Articles

Flow structure of radiatively driven convection in inertial and rotating frames under steady and periodic radiative forcing

Flow structure of radiatively driven convection in inertial and rotating frames under steady and periodic radiative forcing

Synchronization by an External Periodic Force in Ensembles of Globally Coupled Phase Oscillators

Synchronization by an External Periodic Force in Ensembles of Globally Coupled Phase Oscillators

Novel category of environmental effects on gravitational waves from binaries perturbed by periodic forces

Novel category of environmental effects on gravitational waves from binaries perturbed by periodic forces

Education and women in high-skill occupations in India

Purpose This paper aims to examine women’s likelihood of being employed in a high-skill occupation compared to men in India. It also analyses the impact of education on women’s likelihood of entering a high-skill occupation. Design/methodology/approach This study uses data from Periodic Labour Force Survey 2018–19. National Classification of Occupations 2004 is used to classify the occupations in three categories, i.e. high-skill, medium-skill and low-skill. The paper uses ordered probit with Heckman’s sample selection method to estimate the impact of gender identity and education on women’s likelihood of entering high-skill occupations. Findings The results show that female workers are more likely to be employed in high-skill occupations than male workers. Formal years of schooling and technical education further improve women’s probability of working in high-skill occupations compared to men. However, an increase in monthly per capita expenditure of the households improves men’s chances of being employed in high-skill occupations in comparison to women. It suggests that gender norms are still relevant. Originality/value Studies have found occupational segregation in India with a large share of women being employed in low-wage work. This study examines the issue by focusing on the skill level of occupations. It found that women have a higher likelihood of entering high-skill occupations in India and education is playing an important role in it.

Wave fields under the influence of a random-driven force: The Burgers equation

In this work, we examine the classical Burgers equation and investigate the effects of a random force on the wave field. Two scenarios are considered: the impact of a random force on different wave fields within the viscous Burgers equation and the effect of a periodic random force in the inviscid Burgers equation. For the first case, we demonstrate that the random force primarily causes wave fronts to increase or decrease depending on the dispersion parameter. For an initially deformed sinusoidal wave, the external force causes the mean wave field to spread out and dampen over time. The Cole-Hopf transformation is also used to obtain asymptotically the averaged wave field in certain regimes. For the inviscid problem, we assume the random force to be periodic with random phase to show that the mean wave field corresponds to the solution of the classical inviscid Burgers equation without external forces.

Time-delay feedback control on vertical vibration of maglev train under unsteady aerodynamic force

The stability and safety of maglev trains are significantly affected by unsteady aerodynamic forces during high-speed operation. In this paper, we employ a time-delay feedback control strategy to suppress the nonlinear vertical vibrations of maglev train under periodic unsteady aerodynamic force. Firstly, the amplitude-frequency response equation of the maglev vehicle is derived using the multiple scales method, and the stability of the steady-state solutions is determined. Then, the influences of velocity feedback gain coefficient and velocity time delay on the nonlinear vibrations of the maglev vehicle are investigated. The optimal value range of the time delay is identified. The results demonstrate that the time delay feedback control can effectively suppress the nonlinear vibration of maglev vehicles and enhance their operational stability under the premise of reasonable selection of time delay parameters. The theoretical research presented in this paper can serve as a theoretical reference for the design, improvement, and optimization of control systems for high-speed maglev trains.

Periodic forces combined with feedback induce quenching in a bistable oscillator.

The coexistence of an abnormal rhythm and a normal steady state is often observed in nature (e.g., epilepsy). Such a system is modeled as a bistable oscillator that possesses both a limit cycle and a fixed point. Although bistable oscillators under several perturbations have been addressed in the literature, the mechanism of oscillation quenching, a transition from a limit cycle to a fixed point, has not been fully understood. In this study, we analyze quenching using the extended Stuart-Landau oscillator driven by periodic forces. Numerical simulations suggest that the entrainment to the periodic force induces the amplitude change of a limit cycle. By reducing the system with an averaging method, we investigate the bifurcation structures of the periodically driven oscillator. We find that oscillation quenching occurs by the homoclinic bifurcation when we use a periodic force combined with quadratic feedback. In conclusion, we develop a state-transition method in a bistable oscillator using periodic forces, which would have the potential for practical applications in controlling and annihilating abnormal oscillations. Moreover, we clarify the rich and diverse bifurcation structures behind periodically driven bistable oscillators, which we believe would contribute to further understanding the complex behaviors in non-autonomous systems.

Uniform measure attractors for nonautonomous stochastic tamed 3D Navier–Stokes equations with almost periodic forcing

This article provides a characterization of uniform measure attractors for non-autonomous stochastic tamed 3D Navier–Stokes equations, specifically with a almost-periodic external force term. The existing literature has primarily focused on measure attractors within an autonomous framework; however, when the forcing function is almost periodic, the solution process generated by the corresponding equations behaves as a non-autonomous Markov process, rendering the existing framework inapplicable. Therefore, it is crucial to investigate this within a new framework, which is the motivation behind the study of uniform measure attractors in this paper.

Analysis of the influence of nonlinear energy sink parameters applicable to helicopter main reduction systems

Abstract In response to the vibration problem of helicopter fuselage caused by continuous rotor periodic excitation force, a nonlinear energy sink is considered to be installed on the main reduction transmission channel to reduce the vibration level of the fuselage. This article conducts an analysis of the influence of nonlinear energy sink structure parameters under harmonic excitation force, establishes a coupled dynamic model of helicopter main reduction/absorber/fuselage, and uses harmonic balance method and stability analysis theory to analyze the periodic solution and stability of the system. Using the vibration amplitude of the system as the evaluation criterion, the influence of damping, stiffness, and mass ratio on the vibration suppression effect of the nonlinear energy sink was explored. The results showed that as the damping of the nonlinear energy sink increased, the resonance frequency of the coupled system shifted to the left, and the vibration amplitude of the main reduction system increased; As the stiffness of the nonlinear energy sink increases, the vibration amplitude of the coupled system will first decrease and then increase, gradually approaching the vibration amplitude of the system without coupled dampers; The influence of mass ratio on system amplitude follows the same trend as the influence of stiffness. By optimizing, the structural parameters of the nonlinear absorber with good vibration suppression effect are ultimately obtained.

On the analytical soliton approximations to damping forced Zakharov-Kuznetsov equation arising in dissipative nonthermal magnetized plasma

Abstract This paper aims to analyse the nonlinear characteristics of ion-acoustic solitary waves (IASWs) in a plasma system that is collisional and homogeneous in nature. The system under consideration comprises positive ions, negative ions, and nonthermal electrons and is influenced by an ambient magnetic field. To analyse the system, we utilize the reductive perturbation technique (RPT) and obtain the damped forced Zakharov-Kuznetsov (DFZK) equation. The DFZK equation provides a solitary wave solution when an external periodic force is present. Through numerical analysis of DFZK, we have observed that different parameters, e.g., the nonthermal parameters (r,q), the direction cosine, the temperature ratio of a positive ion to an electron, the temperature ratio of a negative ion to an electron, the density ratio of a negative ion to a positive ion source strength, and the source frequency, affect the phase velocity and the structures of IASWs significantly. This finding could help clarify the plasmas observed in the D- and F-regions of Earth's ionosphere, as well as in laboratory experiments where pair ions and nonthermal electrons are key characteristics.

Increasing Horizontal Controlled Force Delivery Capabilities of Aerial Manipulators by Leveraging the Environment

Delivering large horizontal controlled forces for long periods with aerial manipulators is not an easy task to accomplish; several factors including disturbances, reaction forces from the on-board arm or actuator’s limitations might diminish their horizontal force delivery capabilities. Aiming to mitigate these drawbacks, this paper presents a comprehensive study of the force delivery capabilities of aerial manipulators leveraging the environment. The methodology to evaluate the aforementioned capabilities is the Generalized-Jacobian-based force ellipsoid, which was applied to different types of both free-flying and attached-to-the-environment aerial manipulators. In addition, large controlled force delivery experiments with the mentioned manipulators were conducted on physics-engine-based robotics simulation software. The obtained results categorically demonstrate that aerial manipulators leveraging the environment are capable of delivering larger forces than their free-flying counterparts, which has not been proved in the literature so far in the field of aerial robotics.

Nonlinear resonance in an overdamped Duffing oscillator as a model of paleoclimate oscillations.

The cause of the dominant 100-kyr cycles in Earth's paleoclimate in the last 800 000 years has since long been debated. We analyze geological temperature proxy data and retrieve an anharmonic potential from time series data. The obtained potential has bistable features but has significant differences compared to the quartic potentials derived from theoretical energy-based models. Subsequently, we demonstrate the existence of vibrational resonance (VR) and nonlinear resonance phenomena at the combination tones of the driving frequencies in a simple bistable potential without self-sustained oscillations. We find that periodic forcing by the obliquity and frequencies similar tothose of the precession cycle can generate output dominated by 100-kyr cycles, thereby offering a mechanism for explaining the observations in geological data. While previous studies of VR have assumed one periodic driver to have a frequency much higher than the other, we show that for a range of amplitudes, both phenomena can occur at the orbital cycle frequencies. We find that the nonlinear resonance phenomenon is more robust to noise than VR between eccentricity and obliquity and emerges within a much larger range of amplitudes of forcing. Finally, we conclude that it is conceivable that nonlinear resonance between obliquity and precession might explain the spectral frequencies observed in the late Pleistocene.

Supertransient Chaos in a Single and Coupled Liénard Systems.

We report the appearance of supertransient chaos in a single and two-coupled Liénard system with the influence of external periodic force. The existence of transient dynamics in a model is significantly long before it settles into the asymptotic steady state of periodic dynamics understood as supertransient chaos. The two diffusively coupled forced Liénard systems exhibit extremely long transient dynamics when their frequencies of the external forcing are slightly mismatched. Additionally, the coupled system signifies supertransient hyperchaotic dynamics for a specific set of system parameters. This study involves different numerical characterizations, statistical analysis, and hardware implementation using an analog electronic circuit.

Green’s Tensor of BIOT’s Equations by Stationary Oscillations

Various mathematical models of deformable solids mechanics are used in the study of seismic processes in the earth's crust. The processes of waves propagation are most studied in elastic media. But these models do not take into account many real properties of the ambient array. These are, for example, the presence of groundwater, which complicates the construction and operation of surface and underground structures, affect the magnitude and distribution of stresses. Models, which take into account the water saturation form the earth's crust structures, the presence of gas bubbles, etc., are multi-component medium. A variety of multicomponent media, the complexity of the processes associated with their deformation, lead to a large difference in the methods of analysis and modelling used in the solution of wave problems. In this paper the processes of wave propagation in a two-component Biot medium under the action of periodic forces of various forms are considered. Using the Fourier transform of generalized functions, fundamental solutions are constructed - the Green's tensor of the Biot equations and its properties are studied. This tensor describes the process of propagation of harmonic waves of a fixed frequency in spaces of dimension N = 1,2,3 under the action of power sources concentrated at the origin of coordinates, described by a singular delta function. On its basis, generalized solutions of these equations are constructed under the action of various sources of periodic disturbances, which are described by both regular and singular generalized functions. For regularly acting forces, integral representations of solutions are given, which can be used to calculate the stress-strain state of a porous water-saturated medium

Kinetics in the Two-Level System with Strong Time-De-pendent Coupling of Its States to the Phonon Bath: Spin-Boson Description

Using the methods of nonequilibrium statistical mechanics, the master equation for the density matrix of an open dissipative quantum system is obtained under conditions, when the coupling between the electronic states of the system and the nuclear displacements in it is controlled by the alternating field. A time-dependent polaron transformation is proposed, which made it possible to solve kinetic equations using an expansion in a parameter characterizing transitions between “phonon-dressed” electronic states of the system. As an example, a mechanism is shown that can control the kinetics in a two-level system by applying a periodic force field to electron-phonon coupling.

Investigating multi-soliton patterns and dynamical characteristics of the (3+1)-dimensional equation via phase portraits

In this study, we investigate the deeper characteristics of the modified Ito equation, which can be applied across various scientific domains to represent systems influenced by noise and randomness. Multi-solitons, including 1-wave, 2-wave, and 3-wave solitons, have been successfully generated using a multiple exponential-function approach. For visual representation, the outcomes are displayed through 3D, 2D, density, and contour plots. The wave transformation is then applied to convert the studied model into an ordinary differential equation. Following this, the dynamic nature of the model is examined from various viewpoints, including bifurcation, chaotic phenomena, multistability, and sensitivity analysis. Bifurcation shows how the solution of a planar system depends on equilibrium points, and when an outward periodic force is implemented to the unperturbed planar system, it reveals chaotic characteristics. These are analyzed using tools such as 3-dimensional and 2-dimensional plots, time scale plots, and Poincaré maps. Additionally, the model’s sensitivity is assessed with varying initial values. The results underscore the effectiveness and relevance of the proposed approaches for examining solitons within a broad spectrum of nonlinear systems.

Adjustability and Stability of Flow Control by Periodic Forcing: A Numerical Investigation

Adjustability and Stability of Flow Control by Periodic Forcing: A Numerical Investigation

Caste affiliation and access to high-authority jobs in the Indian service sector

Restricting high authority jobs to a specific section of society leads to market inefficiencies, resulting in higher costs and lower quality of goods and services due to suboptimal management. Moreover, such favouritism exacerbates social inequalities across occupational hierarchies. Given India’s caste-based societal structure, it is crucial to investigate whether all social groups have equal access to top management and leadership positions. Using the 2019–2020 Periodic Labour Force Survey and binary logit models, this study reveals significant disparities in securing high-authority roles between lower and upper castes. The results show an average marginal effect of −7.3% for lower castes relative to upper castes. These disparities are further amplified if the lower caste individual is female, resides in a urban area, or holds a graduate-level education.

Jointly stationary solutions of periodic Burgers flow

For the one dimensional Burgers equation with a random and periodic forcing, it is well-known that there exists a family of invariant measures, each corresponding to a different average velocity. In this paper, we consider the coupled invariant measures and study how they change as the velocity parameter varies. We show that the derivative of the invariant measure with respect to the velocity parameter exists, and it can be interpreted as the steady state of a diffusion advected by the Burgers flow.

On the boundedness of solutions of a forced discontinuous oscillator

We study the global boundedness of the solutions of a non-smooth forced oscillator with a periodic and real analytic forcing. We show that the impact map associated with this discontinuous equation becomes a real analytic and exact symplectic map when written in suitable canonical coordinates. By an accurate study of the behaviour of the map for large amplitudes and by employing a parametrization KAM theorem, we show that the periodic solutions of the unperturbed oscillator persist as two-dimensional tori under conditions that depend on the Diophantine conditions of the frequency, but are independent on both the amplitude of the orbit and of the specific value of the frequency. This allows the construction of a sequence of nested invariant tori of increasing amplitude that confine the solutions within them, ensuring their boundedness. The same construction may be useful to address such persistence problem for a larger class of non-smooth forced oscillators.