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This article presents the application of continuous Floquet theory in solid-state nuclear magnetic resonance (NMR). Continuous Floquet theory extends the traditional Floquet theory to non-continuous Hamiltonians, enabling the description of observable effects not fully captured by the traditional Floquet theory due to its requirement for a periodic Hamiltonian. We present closed-form expressions for computing first- and second-order effective Hamiltonians, streamlining integration with the traditional Floquet theory and facilitating application in NMR experiments featuring multiple modulation frequencies. Subsequently, we show examples of the practical application of continuous Floquet theory by investigating several solid-state NMR experiments. These examples illustrate the importance of the duration of the pulse scheme regarding the width of the resonance conditions and the near-resonance behavior. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of quantum scrambling, characterized by the out-of-time ordered correlators (OTOCs), in a non-Hermitian quantum kicked rotor subjected to quasi-periodical modulation in kicking potential. Quasi-periodic modulation with incommensurate frequencies creates a high-dimensional synthetic space, where two different phases of quantum scrambling emerge: the freezing phase characterized by the rapid increase of OTOCs towards saturation, and the chaotic scrambling phase featured by the linear growth of OTOCs with time. We find the dynamical transition from the freezing phase to the chaotic scrambling phase, which is assisted by increasing the real part of the kicking potential along with a zero value of its imaginary part. The opposite transition occurs with the increase in the imaginary part of the kicking potential, demonstrating the suppression of quantum scrambling by non-Hermiticity. The underlying mechanism is uncovered by the extension of the Floquet theory. Possible applications in the field of quantum information are discussed. [ABSTRACT FROM AUTHOR]

In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allows us to revisit a recent result of admissibility, obtaining an alternative formulation with a particular simplicity. [ABSTRACT FROM AUTHOR]

The spinning circular solar sail is a promising spacecraft for long-duration missions. This work reveals its structural dynamic and stability behavior under the periodically time-varying solar radiation pressure and gravitational force. The geometric stiffness generated by the centrifugal force due to spinning and the coupling effect between the deformation and solar radiation pressure are taken into account. The von Kármán plate theory is adopted by neglecting the high-frequency in-plane vibrations and considering the effect of the in-plane internal force on the transverse vibration. The partial differential equation of the spinning solar sail is derived and further spatially discretized into periodically time-varying equations of motion. Effects of Poisson ratio and radius ratio on natural frequencies and mode shapes are analyzed, and curve veering phenomena are then observed. Steady-state periodic responses of the solar sail under the solar radiation pressure with different orbit distances, incident angles, and spinning angular velocities are analyzed. The stability analysis is rigorously performed by the Floquet theory rather than the commonly used approach of conducting the eigenvalue analysis at a series of specific discrete time nodes. Moreover, the stability boundary associated with transverse vibrations is determined, which contributes to the parameter design of the spinning solar sail. [ABSTRACT FROM AUTHOR]

In this article, we investigate the spectral stability of periodic traveling waves for a cubic-quintic and double dispersion equation. Using the quadrature method, we find explict periodic waves and we also present a characterization for all positive and periodic solutions for the model using the monotonicity of the period map in terms of the energy levels. The monotonicity of the period map is also useful to obtain the quantity and multiplicity of non-positive eigenvalues for the associated linearized operator and to do so, we use tools of the Floquet theory. Finally, we prove the spectral stability by analyzing the difference between the number of negative eigenvalues of a convenient linear operator restricted to the space constituted by zero-mean periodic functions and the number of negative eigenvalues of the matrix formed by the tangent space associated to the low order conserved quantities of the evolution model. [ABSTRACT FROM AUTHOR]

Light-matter interactions have emerged as a new research focus recently offering promises of unveiling novel physics and leading to applications under nonequilibrium conditions. The quantized Hall conductivities predicted by Floquet theory assuming a Fermi-Dirac distribution however deviate from experimental observations. To resolve these puzzles, we consider the effect of nonequilibrium electron occupation to study the anomalous, valley, and spin Hall effects of a prototype monolayer transition metal dichalcogenide MoS2. We find that spin Hall conductivity can be effectively suppressed approaching zero value by linearly polarized light under near resonant excitations. In contrast, it is substantially enhanced by circularly polarized light, originating from optical selection rules and topological phase transitions. Besides, the quantized anomalous Hall conductivity is much reduced if nonequilibrium occupations of Floquet bands are considered. Our study provides a novel avenue for engineering various Hall effects in two-dimensional materials using light, holding great promises for future device applications. [ABSTRACT FROM AUTHOR]

In many industries’ applications, one deals with pipes conveying fluid. Besides, the implementation of advanced materials in manufacturing of new-brand structures is developing. Consequently, in this paper, one of the most important dynamics analyzes that an advanced pipe conveying fluid may meet it is addressed. For the first time, linear and nonlinear dynamics of a pipe reinforced with graphene nanoplatelets (GPL pipe) that conveys pulsating flow is presented. The Euler–Bernoulli beam model follows the plug flow model in order to formulate the problem. The method of multiple scales (MMS) applied to the discretized couple nonlinear gyroscopic governing equations with the aim of specifying the instability region and the steady-state response of the GPL pipe subjected to the principal parametric resonance of one of its modes, as a consequence of pulsating flow. Respectively, the Floquet theory and the Runge–Kutta fourth-order (RK4) method are applied to the linear governing equations and nonlinear governing equations for the sake of confirming the current MMS results. It is deduced that a small amount usage of GPL reinforcement phase improves substantially the resistance against static instability, and the critical fluid excitation amplitude fraction, meanwhile declines the instability region bandwidth, and the steady-state response of the pipe. In contrary, it is confirmed that a heavier fluid makes reverse the preceding statements with respect to a lighter fluid. The aforementioned findings shed light on the essential design keys that outstandingly affect the mechanics of the GPL pipe conveying pulsating fluid that lead and conduct forthcoming studies and open new horizons for designers in industry implementations. [ABSTRACT FROM AUTHOR]

Understanding the ecological and evolutionary dynamics of populations is critical for both basic and applied purposes in a variety of biological contexts. Although several modeling frameworks have been developed to simulate eco-evolutionary dynamics, many fewer address how to model structured populations. In a prior paper, we put forth the first modeling approach to simulate eco-evolutionary dynamics in structured populations under the G function modeling framework. However, this approach does not allow for accurate simulation under fluctuating environmental conditions. To address this limitation, we draw on the study of periodic differential equations to propose a modified approach that uses a different definition of fitness more suitable for fluctuating environments. We illustrate this method with a simple toy model of life history trade-offs. The generality of this approach allows it to be used in a variety of biological contexts. [ABSTRACT FROM AUTHOR]

The paper proposes algorithm for angular motion control of a dynamically elongated spacecraft. The algorithm is based on the direct Lyapunov method using matrix control coefficients. The calculated mechanical torque is implemented using magnetorquers. Control parameters are selected using Floquet theory to ensure convergence to the required motion. • An algorithm for attitude control of a dynamically elongated spacecraft is proposed. • The algorithm is based on the direct Lyapunov method using matrix control gains. • A methodology for matrix gain selection is based on Floquet theory. • The algorithm performance for 3U CubeSat three-axis stabilization is demonstrated. [ABSTRACT FROM AUTHOR]

Phonon polaritons are hybrid states of light and matter that are typically realised when optically active phonons couple strongly to photons. We suggest a new approach to realising phonon polaritons, by employing a transverse-pumping Raman scheme, as used in experiments on cold atoms in optical cavities. This approach allows hybridisation between an optical cavity mode and any Raman-active phonon mode. Moreover, this approach enables one to tune the effective phonon–photon coupling by changing the strength of the transverse pumping light. We show that such a system may realise a phonon-polariton condensate. To do this, we find the stationary states and use Floquet theory to determine their stability. We thus identify distinct superradiant and lasing states in which the polariton modes are macroscopically populated. We map out the phase diagram of these states as a function of pump frequencies and strengths. Using parameters for transition metal dichalcogenides, we show that realisation of these phases may be practicably obtainable. The ability to manipulate phonon mode frequencies and attain steady-state populations of selected phonon modes provides a new tool for engineering correlated states of electrons. [ABSTRACT FROM AUTHOR]

AbstractIn several industries, the handling of fluid-filled micropipes is common. New-brand structures are increasingly being manufactured using advanced materials. This article tackles one of the crucial dynamic analyses that an advanced fluid-filled micropipe encounters. The dynamics of a graphene nanoplatelets-reinforced micropipe (GPL micropipe) under pulsating laminar flow for the first time is examined. The Euler-Bernoulli beam model follows the modified couple stress theory (MCST) and von-Karman’s nonlinear strain to formulate the problem. The impression of the flow profile exerted by a real flow as a consequence of fluid viscosity, is taken into account. The plug flow model results are compared to those regarding real flow consideration. Using the method of multiple scales (MMS), we determine the instability area and the steady state response of the GPL micropipe subjected to the principal parametric resonance of one of its modes due to pulsating laminar flow by applying this method to the discretized couple nonlinear gyroscopic governing equations. The Floquet theory treats the linear equations and fourth-order Runge–Kutta (RK4) method attacks nonlinear ones to validate MMS findings. It is confirmed that the 0.3% addition of the GPL to matrix phase significantly enhances its advanced attributes, making it a highly effective material. The GPL reinforcement phase in the FGO pattern increases the critical flow velocity that exhibits the micropipe to static instability by 37.98%, and critical flow stimulation amplitude fraction by 152.19%, while declines instability area bandwidth by 36.95%, and steady state response by 67.17% relative to a non-reinforced micropipe. A denser flow degrades the corresponding values by 18.40%, 42.59%, 41.67%, and 227.28% in comparison to a lighter fluid. The declared findings provide crucial insights into the key design elements affecting significantly the functioning of fluid-filled GPL micropipes system, and regulate future research and expand openings for industry applications. [ABSTRACT FROM AUTHOR]

We investigate solutions of the classical Mathieu–Hill (MH) equation that characterizes the dynamics of trapped ions. The analytical model we introduce demonstrates the equations of motion are equivalent to those of a harmonic oscillator (HO). Two independent approaches are used, based on two classes of complex solutions of the MH equation. This paper addresses both a damped HO and parametric oscillator (PO) for an ion confined in an electrodynamic (Paul) trap, along with stability and instability regions for the associated periodic orbits. [ABSTRACT FROM AUTHOR]

A version of the Floquet theory for first order delay differential equations is proposed. Formula of solutions representation is obtained. On this basis, the stability of first order delay differential equations is studied. An analogue of the classical integral Lyapunov–Zhukovskii test of stability is proved. New, in comparison with all known, tests of the exponential stability are obtained on the basis of the Floquet theory. A possibility to achieve the exponential stability is connected with oscillation of solutions. [ABSTRACT FROM AUTHOR]

We consider the problem of tracking arbitrary free nutating trajectories of the Lagrange top using linear feedback. The equations of motion of the top are linearised about the desired trajectories. Due to the inherent symmetries, this yields a system of linear equations with periodically varying coefficients governing the error dynamics. It is shown that the higher-order dynamics of the Lagrange top leads to nuances in the implementation of the control. Two different control strategies are implemented in the present work. These are applicable for impulsive and short-duration disturbances, respectively. The control effort is in the form of a body-fixed torque input about the symmetry axis and a vertical space-fixed force input. In both the proposed control strategies, the iterative application of the control effort over multiple periods is shown to stabilise the error. These strategies are shown to work for significantly large errors. [ABSTRACT FROM AUTHOR]

This contribution highlights that a linear periodic Hamiltonian system preserves a symplectic structure if a particular dissipation is present. This specific structure is defined by the algebraic properties of μ -symplectic matrices and symmetry of its eigenvalues. A method is established for the stability analysis of this class of systems consisting of damped and coupled Mathieu equations. It enables an efficient computation of the corresponding stability chart. One main strength of the method is the calculation of the stability chart even for large parameter values, especially for the amplitude of the parametric excitation and the system response itself. The proposed stability analysis is applied in detail on two examples consisting of two coupled equations. [ABSTRACT FROM AUTHOR]

In this study, a bifurcation analysis of the piezoelectric neuron system (PNS) is conducted utilizing the time-domain minimum residual method (TMRM). From a biophysical standpoint, integrating piezoelectric devices into a nonlinear neuron circuit enables the conversion of external pressure or sound wave signals into electrical signals. The primary content of this research are as follows: initially, the piezoelectric neuron system is analytically solved by employing the TMRM, yielding high-precision periodic solutions. Subsequently, a detailed bifurcation analysis is performed leveraging these high-precision solutions. The findings demonstrate that the neuronal system experiences a periodic-doubling bifurcation when the amplitude of external stimuli surpasses a specific threshold. With further increases in the stimulus, this periodic-doubling response evolves into a periodic response. Moreover, changes in cell membrane resistance will lead to complex nonlinear behaviors such as stable or unstable period-1 solutions and stable or unstable and critically stable period-3 solutions in the system. These findings offer a theoretical foundation for the advanced design of intelligent functional neuron arrays and sensors. [ABSTRACT FROM AUTHOR]

Dynamical symmetries of laser-dressed matter determine the selection rules that influence its absorption spectrum. We explore selection rules for polarization-sensitive absorption in Floquet matter, using Floquet group theory in synthetic dimensions. We present comprehensive tables of selection rules that polarization-structured light impose on Floquet dark states and Floquet dark bands. Notably, our tables encompass nonlinear absorption for all nonlinear orders, revealing that different nonlinear orders follow distinct polarization selection rules, potentially leading to polarization-tunable optical filters. [ABSTRACT FROM AUTHOR]

The control of electron spin, crucial to the stability of matter, offers new possibilities for manipulating the properties of molecules and materials with potential applications in spintronics and chemical reactions. Recent experiments have demonstrated that electron transmission through chiral molecules depends on the electron spin orientation, a phenomenon known as chiral-induced spin selectivity (CISS). In this study, we show that CISS can be observed in achiral systems driven by an external circularly polarized laser field in the framework of Floquet engineering. By using the Floquet theory for a time-periodically driven system to investigate spin-dependent electron transport in a two-terminal setup, we demonstrate that the spin polarization can approach unity if the light intensity is sufficiently strong, the rate of dephasing is sufficiently low, and the average chemical potential of the two leads is within an appropriate range of values, which is narrow because of the high frequency of the laser field. To obtain a broader range of energies for large spin polarization, a combination of chiral molecules and light–matter interactions is considered, and the spin polarization of electrons transported through a helical molecule driven by a laser field is evaluated. [ABSTRACT FROM AUTHOR]

Low-dimensional materials with topologically protected edge states have wide applications in spintronic, valleytronic, and optoelectronic nanodevices. Different from the valley-resolved quantum anomalous Hall (VQAH) state and spin-polarized quantum anomalous Hall (VSQAH), the photon-induced topological states in kagome-lattice nanoribbons (KLNR) can generate both valley and spin-polarized edge states without magnetic substrate or Rashba spin-orbit coupling (SOC). Via the Floquet theory, we also propose a 0-photon-extraction scheme to obtain the effective Hamiltonian under low-frequency light for the first time, and we analyze the topological properties and phase transition of the irradiated kagome system, similar with those in the high-frequency case. We then design an all-optically controlled valley-resolved spin filter based on KLNR. Transmissions and local current distributions of the proposed nanodevice confirm this spin-filter effect, which can indeed be switched by left- or right-circularly-polarized (LCP/RCP) light. We believe these optically controlled models can be extended to the design of magnetism-free spin-valley filter or switcher in the future. [ABSTRACT FROM AUTHOR]

The parameterization method has demonstrated remarkable efficacy in the construction of reduced order models for nonlinear dynamical systems, which are mostly applied to depict the dynamics near a fixed point or a forced periodic solution perturbed from it. In this paper, we develop a method based on direct linear algebra to construct reduced order models around the limit cycles of high dimensional autonomous self-excited nonlinear systems. In particular, Taylor–Fourier series is adopted to parameterize the invariant manifold around a periodic solution of the self-excited systems. The basic theory and derivation of equations are presented in terms of matrices and Kronecker product, which benefits computer implementation and enhances computational efficiency. Two approaches to solve co-homological equations based on Floquet normal form and direct linear algebra are introduced and compared. The method based on Floquet normal form proves to be impossible to be applied in the high dimensional cases due to the extensive computing consumption. To facilitating the implementation, an iterative formula for the series expansion of generic nonlinear functions by composition of elementary function is also proposed. The reduced order models of a self-excited wing model, a rotor-stator rubbing model and a FEM rotor model are constructed. It is shown that the proposed approaches are valuable in predicting responses of high-dimensional self-excited nonlinear systems and can greatly reduce the computational costs. [ABSTRACT FROM AUTHOR]

When dielectric-elastomer (DE) resonators are operated under large alternating voltage excitations, strong geometric and material nonlinearities can significantly affect the dynamic performance. Based on the virtual work principle, a dynamic model of a circular DE resonator is established in this work. Static analysis is conducted to study the impacts of the control voltage on the strain and natural frequency of the DE resonator at equilibrium. A modified Incremental Harmonic Balance and arc-length methods are used to obtain dynamic responses of the system excited by alternating voltages, and stability analysis is conducted using the Floquet theory. The effects of the mechanical parameters are studied, and period-doubling bifurcations are observed, which are produced by the parametric excitation of the voltage. The bifurcation phenomenon is comprehensively investigated through analysis of the voltage, stress, and damping coefficient, which provides design guidance for DE resonators. [ABSTRACT FROM AUTHOR]

A new heteronuclear decoupling sequence for solid-state NMR and magic angle spinning faster than 60 kHz was recently introduced [Simion et al., J. Chem. Phys. 157, 014202 (2022)]. It was dubbed ROtor-Synchronized Phase-Alternated Cycles (ROSPAC), and it offers robustness for a large range of chemical shifts and low radio-frequency (RF) powers and is almost independent of the radio-frequency power. Here, we theoretically explore the robustness of the ROSPAC sequence toward 1H offset and RF field inhomogeneities, as well as the spacing effect of the π pulses on the decoupling efficiency. We use a generalized theoretical framework based on the Floquet theory to assess these parameters. The optimum decoupling conditions, where the magnitude of the second-order cross-terms and first-order resonance conditions are small, were identified. [ABSTRACT FROM AUTHOR]

The intricate relationship between topology and disorder in non-equilibrium quantum systems presents a captivating avenue for exploring localization phenomenon. Here, we look for a suitable platform that enables an in-depth investigation of the topic. To this end, we delve into the nuanced analysis of the topological and localization characteristics exhibited by a one-dimensional dimerized Kitaev chain under periodic driving and perform detailed analyses of the Floquet Majorana modes. Such a non-equilibrium scenario is made further interesting by including a spatially varying quasiperiodic potential with a temporally modulated amplitude. Apriori, the motivation is to explore an interplay between dimerization and a quasiperiodic disorder in a topological setting which is also known to demonstrate unique (re-entrant) localization properties. While the topological properties of the driven system confirm the presence of zero and π Majorana modes, the phase diagram obtained by constructing a pair of topological invariants ( Z × Z ), also referred to as the real space winding numbers, at different driving frequencies reveal intriguing features that are distinct from the static scenario. In particular, at either low or intermediate frequency regimes, the phase diagram concerning the zero mode involves two distinct phase transitions, one from a topologically trivial to a non-trivial phase, and another from a topological phase to an Anderson localized phase. On the other hand, the study of the Majorana π mode unveils the emergence of a unique topological phase, characterized by complete localization of both the bulk and the edge modes, which may be called as the Floquet topological Anderson phase. Moreover, different frequency regimes showcase distinct localization features which can be examined via the localization toolbox, namely, the inverse and the normalized participation ratios. Specifically, the low and high-frequency regimes demonstrate the existence of completely extended and localized phases, respectively. While at intermediate frequencies, we observe the critical (multifractal) phase of the model which is further investigated via a finite-size scaling analysis of the fractal dimension. Finally, to add depth into our study, we have performed a mean level spacing analyses and computed the Hausdorff dimension which yields specific characteristics inherent to the critical phase, offering profound insights into its underlying properties. [ABSTRACT FROM AUTHOR]

Faraday instability of viscous liquid films with Maxwell–Cattaneo (MC) heat flux on an infinite, heated horizontal substrate subject to vertical time-varying periodic vibration is investigated theoretically. The MC effect means that the response of the heat flux to a temperature gradient obeys a relaxation time law rather than a classical Fourier time law. Applying the classic Floquet theory to linear analysis, a recursive relation is obtained. When considering the MC effect, a new phenomenon appears at a large wave number k. The neutral stability curves branch new tongues that turn left rather than right as before, but the tongues still move up and right as the wave number increases. Furthermore, typical harmonic (H) and subharmonic (SH) alternation behavior continues to exist. Interestingly, the first tongue of a branch is H or SH, implying that there is a transition following the branches. However, near the critical wave number kc of a branch, the SH and H almost overlap. As Cattaneo number C increases, the tongue-like unstable zones of branches become wider, and the critical wave number kc of the appeared branch becomes small. As the driving frequency ω decreases, the branch tongues become elongated and the critical wave number kc of the appeared branch becomes small. [ABSTRACT FROM AUTHOR]

Cavity electromagnonic system, which simultaneously consists of cavities for photons, magnons (quanta of spin waves), and acoustic phonons, provides an exciting platform to achieve coherent energy transduction among different physical systems down to single quantum level. Here we report a dynamical phase-field model that allows simulating the coupled dynamics of the electromagnetic waves, magnetization, and strain in 3D multiphase systems. As examples of application, we computationally demonstrate the excitation of hybrid magnon-photon modes (magnon polaritons), Floquet-induced magnonic Aulter-Townes splitting, dynamical energy exchange (Rabi oscillation) and relative phase control (Ramsey interference) between the two magnon polariton modes. The simulation results are consistent with analytical calculations based on Floquet Hamiltonian theory. Simulations are also performed to design a cavity electro-magno-mechanical system that enables the triple phonon-magnon-photon resonance, where the resonant excitation of a chiral, fundamental (n = 1) transverse acoustic phonon mode by magnon polaritons is demonstrated. With the capability to predict coupling strength, dissipation rates, and temporal evolution of photon/magnon/phonon mode profiles using fundamental materials parameters as the inputs, the present dynamical phase-field model represents a valuable computational tool to guide the fabrication of the cavity electromagnonic system and the design of operating conditions for applications in quantum sensing, transduction, and communication. [ABSTRACT FROM AUTHOR]

This paper is devoted to a charge transfer model with cross-diffusion under Neumann boundary conditions. We investigate how the cross-diffusion could destabilize the stable periodic solutions bifurcating from the unique positive equilibrium point. By the implicit function theorem and Floquet theory, we obtain some conditions on the self-diffusion and cross-diffusion coefficients under which the stable periodic solutions can become unstable. New irregular Turing patterns then generate by the destabilization of stable spatially homogeneous periodic solutions. We also present some numerical simulations to further support the results of theoretical analysis. [ABSTRACT FROM AUTHOR]

In this article, we study a predator–prey system, which includes impulsive stocking prey and a nonlinear harvesting predator at different moments. Firstly, we derive a sufficient condition of the global asymptotical stability of the predator–extinction periodic solution utilizing the comparison theorem of the impulsive differential equations and the Floquet theory. Secondly, the condition, which is to maintain the permanence of the system, is derived. Finally, some numerical simulations are displayed to examine our theoretical results and research the effect of several important parameters for the investigated system, which shows that the period of the impulse control and impulsive perturbations of the stocking prey and nonlinear harvesting predator have a significant impact on the behavioral dynamics of the system. The results of this paper give a reliable tactical basis for actual biological resource management. [ABSTRACT FROM AUTHOR]

Piston–cylinder pairs are very common in industrial mechanisms. While a piston is primarily designed for axial reciprocating motion, the occurrence of secondary motions—lateral and rotational—due to the small clearance between the piston and the cylinder may lead to frictional contact, energy loss, wear and an increase in unwanted leakage. This study focuses on mitigating the secondary motion of a ringless piston. The influence of a Rayleigh step bearing and partial surface texturing with numerous micro-dimples on the dynamic stability of the secondary motion is studied. A linear model was used to obtain the trajectory of the secondary motion and Floquet theory was applied to analyze the stability and draw stability maps. The influence of various texturing and step parameters, including the dimple area density and aspect ratio for partial texturing, as well as the length and depth of treatment for both partial texturing and step profiles, on the stability of the secondary motion was examined. The normalization method is presented, enabling the expansion of the results for various operating conditions and geometries. Conclusions and guidelines regarding the optimal parameters, in terms of a wider stability range and higher decay rate, are formulated. [ABSTRACT FROM AUTHOR]

A comparative analysis is presented of bandgap formation mechanism in homogeneous prestressed beams with periodic external supports, hinges and attached local masses. Based on the Floquet theory the analytical expressions are derived for deviation functions defining bandgap structure. Several periodic topological structures are considered: meta beams with intermediate external supports and attached masses, internal hinges paired with masses. For periodic structures the band gap dispersion equations are derived, dispersion curves are plotted and analyzed. The innovation in this paper is the results concerning widening of the resonant bandwidth of a meta beam phononic bandgaps by merging of multiple separated bandgaps generated by the internal hinges or external intermediate supports with attached masses. [ABSTRACT FROM AUTHOR]

The present study introduces an improved discretization method for predicting milling stability based on the the semi-discretization method (SDM) proposed and updated by Insperger [1, 2] and the full-discretization method (FDM) presented by Ding [3]. Compared to the SDM and FDM, the enhanced discretization method incorporates a suitable state-space representation of the milling process. The time delay and state components are discretized using a straightforward linear interpolation technique, while the time-periodic component is estimated through numerical integration. The proposed method, which is ultimately validated in terms of computational efficiency and numerical accuracy, demonstrates superior computational efficiency in comparison to the SDM and FDM methods. Furthermore, it exhibits no loss of numerical precision in traditional cutting conditions and shows higher numerical accuracy compared to the SDM and FDM methods during highly interrupted milling operations. The algorithm codes are additionally provided in the supplementary file. [ABSTRACT FROM AUTHOR]

This short review explores the physics journey of Professor Amit Dutta, illuminating his collaborative contributions with students and peers. We mainly focus on standard approaches to understanding non-equilibrium quantum dynamics and ground-state criticality using quantum informatic measures like ground-state fidelity, the Loschmidt echo and/or the decoherence factor. Using Floquet theory as a tool, we also discuss the dynamics of hard-core bosonic chain, shedding light on the phenomenon of dynamical localization and different analytically approachable limits of Floquet theory. The review further extends to probe the physics of topological phase transitions in driven/quenched systems, where we mainly focus on the non-equilibrium response of topological systems and topological state preparation. Finally, we also discuss late-time quantum dynamics leading to the thermalization of open and closed systems, where we review contemporary approaches to the applicability of thermodynamic principles in microscopic quantum systems and the macroscopic emergence of statistical mechanics in driven/quenched ergodic systems. Throughout this memoir, Professor Amit Dutta's important scientific contributions are mentioned for their impact on advancing our understanding of quantum dynamics and statistical mechanics. [ABSTRACT FROM AUTHOR]

The goal of this study was to develop a linear feedback control method to increase the energy produced for a parametrically excited energy-harvesting system. The chosen control design uses state feedback based on the Lyapunov–Floquet transformation to direct the system dynamics toward a previously chosen trajectory. The methodology of this work was based on the studies of Sinha and Butcher. They developed stability and control analysis techniques based on Floquet theory and the approximation of the state transition matrix of systems that have periodic coefficients in time. It was observed that the stability and instability conditions of the system were obtained from the choice of physical parameters related to the parametric excitation force. When the control technique was applied to the system, it was found that the suggested control effectively directed the system's trajectory in the direction of the predetermined trajectory. The application of control significantly increased the energy generation compared with the uncontrolled system, which was seen when comparing the energy generated by the uncontrolled system and the net energy generated by the controlled system. [ABSTRACT FROM AUTHOR]

Small-signal stability analysis is essential for the safe operation and parameter design of power electronic-dominated grids. Unbalanced conditions introduce more frequency-coupling terms, which are unneglectable in the stability assessment. This paper proposes a novel Linear Time-Periodic (LTP) theory-based stability analysis method and focuses on grid-connected voltage-source converters (VSCs) without improved unbalancing controls. Firstly, the analysis of fundamental solutions of the LTP system reveals that each LTP mode is characterized by a unique damping factor and multiple oscillation frequencies, defined by LTP eigenvalues and related transformation vectors, i.e., (λi,Vi(t)). Then, a method for calculating (λi,Vi(t)) is proposed using the characteristic matrix of the Harmonic State-Space (HSS) model. An iterative sorting method based on the time-domain interpretation of HSS eigenvalues/eigenvectors is proposed to determine accurate (λi,Vi(t)) in the case of the minimum truncation order. Finally, generalized definitions and calculation methods of the widely used indicators for modal analysis are presented to assess system stability and guide the parameter design. Numerical and simulation results verify the proposed stability analysis method and indicate its advantages compared to the existing Floquet and HSS methods.

We present a framework that uses a continuous frequency space to describe and design solid-state nuclear magnetic resonance (NMR) experiments. The approach is similar to the well-established Floquet treatment for NMR, but it is not restricted to periodic Hamiltonians and allows the design of experiments in a reverse fashion. The framework is based on perturbation theory on a continuous Fourier space, which leads to effective, i.e., time-independent, Hamiltonians. It allows the back-calculation of the pulse scheme from the desired effective Hamiltonian as a function of spin-system parameters. We show as an example how to back-calculate the rf irradiation in the MIRROR experiment from the desired chemical-shift offset behavior of the sequence. [ABSTRACT FROM AUTHOR]

AbstractControlling thermal loads in heat transfer systems that produce high heat flux is a real mechanical challenge. Various cooling/heating techniques are available to achieve the reliability requirements of electronic devices. Among them, the use of nanofluids is one of the important techniques that provide long term stability, higher cooling rates, decreased pumping power needs, and cost-effectiveness. Instability in fluids typically occurs when a disturbance affects the equilibrium of forces of external, inertial, or viscous origin acting on a system. The disturbances may arise from the surroundings due to small changes in the boundary conditions, surface roughness, free stream turbulence, noise, etc. In several circumstances, these disturbances are very small and hence cannot be measured with the available instruments but can be observed after the instability sets in. In this study, we focus on examining the effect of time-periodic vertical gravity modulation on the initiation of natural convection in a porous medium saturated with a nanofluid. The porous medium is characterized by being heated at the bottom and possessing anisotropic properties in terms of permeability and thermal diffusivity. Specifically, we investigate the onset of convection in water-based nanofluids that contain metallic (Cu) and metal oxide (Al2O3) particles. The Khanafer-Vafai-Lightstone (KVL) nanofluid model is employed to describe the behavior of the nanofluids, and the thresholds for convective instability are determined using the Mathieu functions. In addition, we study the instabilities of synchronous and subharmonic modes and explore their transitions along with practical applications. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic behavior of a tethered satellite system in an elliptical orbit as the tethered subsatellite is deployed from a mother satellite at an out-of-plane angle while maintaining the tether at a constant in-plane pitch angle by a predefined control force acting on the subsatellite. A variable-length pendulum model is employed to describe the purely out-of-plane tether deployment dynamics, from which an analytical tether deployment control law is derived. The stability condition of the analytical control law is examined by Floquet theory. The corresponding analytical deployment law is asymptotically stable, and the requirement for a positive tension control input is guaranteed to ensure the controllability of the tether system. Following deployment, the critical conditions for the out-of-plane libration of the tethered subsatellite to become chaotic during the station-keeping phase are examined. Finally, simulation results reveal that the proposed approach can effectively and rapidly identify periodic, quasiperiodic, and chaotic motions using bifurcation diagrams, which provides valuable insights for enhancing the stability and reliability of such tethered satellite systems. • Proposed an analytical deployment law for a purely out-of-plane tethered satellite. • Revealed nonlinear phenomena of the system during the station-keeping phase. • Explored bifurcation characteristic and chaotic windows of the system. [ABSTRACT FROM AUTHOR]

A good pulse control strategy should depend on the numbers of pests and natural enemies as determined via an integrated pest control strategy. Taking this into consideration, here, a nonlinear impulsive predator-prey model with improved Leslie-Gower and Beddington-DeAngelis functional response terms is qualitatively analyzed. The existence of a periodic solution for pest eradication has been obtained and the critical condition of global asymptotic stability has been established by using the impulsive differential equation Floquet theory. Furthermore, the conditions for the lasting survival of the system has been proved by applying a comparison theorem for differential equations. Additionally, a stable positive periodic solution has been obtained by applying bifurcation theory. To understand how nonlinear pulses affect the dynamic behavior of a system, MATLAB was used to conduct numerical simulations to show that the model has very complex dynamical behavior. [ABSTRACT FROM AUTHOR]

Natural rubber is a critical material that is essential to industry and transportation. In order to reduce the cost of rubber tapping and improve the efficiency and profitability of rubber production, the 4GXJ-2 portable electric rubber cutter and automatic rubber tapping robot have been developed. In their vibration tool holder, the planetary rotor with variable speed self rotation and uniform eccentric revolution is the most important transmission component, and its instability will cause irregular vibration of the tapping tool, thereby reducing the accuracy of vibration cutting and increasing noise. Base on the ANCF (Absolute Nodal Coordinate Formulation) 3D-beam element and 3D REF (3D Ring on Elastic Foundation), a novel eccentric 3D REF model of a planetary rotor is proposed. By introducing multiple coordinate systems, the coupled motion of uniform eccentric revolution, variable speed self rotation and flexible deformation is decomposed and the influences of these motions on the centrifugal force and Coriolis force are more clearly derived. The model is degraded and validated by comparing with other examples of a rotating circular ring model and uniformly eccentrically revolving annular plate. According to the Floquet theory and Runge−Kutta method, the unstable region of revolution speed of a planetary rotor in rubber tapping machinery is predicted as [817 rad/s, 909 rad/s], [1017 rad/s, 1095 rad/s] and [1263 rad/s,1312 rad/s]. Compared with the rubber-tapping experiment of rubber tapping machinery, the validity of the proposed model is further verified. This model provides important design references for the speed settings of those rubber tapping machines. [ABSTRACT FROM AUTHOR]

The stability properties of the Hill equation are discussed, especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu-Hill equation for a trapped ion are characterized by employing the Floquet theory and Hill's method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters a and q that are real. Characteristic curves are introduced naturally by the Sturm–Liouville problem for the well-known even and odd Mathieu equations c e m (z , q) and s e m (z , q) . In the case of a Paul trap, the stable solution corresponds to a superposition of harmonic motions. The maximum amplitude of stable oscillations for ideal conditions (taken into consideration) is derived. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for both axial and radial motion, where the former is described by the canonical Mathieu equation. Anharmonic corrections for nonlinear Paul traps are discussed within the frame of perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter and we demonstrate they are shifted towards negative values of the a parameter. The applications of the results include but are not restricted to 2D and 3D ion traps used for different applications such as mass spectrometry (including nanoparticles), high resolution atomic spectroscopy and quantum engineering applications, among which we mention optical atomic clocks and quantum frequency metrology. [ABSTRACT FROM AUTHOR]

This article investigates the security ensured state estimation problem for cyber‐physical system via a data‐driven method. First, based on the fact that different packets possess varying a degree of significance, that is, some packets play more important roles in the state estimation than others, a novel stochastic important‐data‐based (IDB) attack mechanism is constructed from the attacker's perspective, which can focus on attacking the important packets thus is expected to achieve more destructiveness. Second, as a countermeasure to the proposed IDB attack, a new data‐driven compensation method is proposed, for the first attempt, to compensate for the attack effect and enhance the estimation quality. The designed defense strategy has the following two advantages: (1) only system input and output data are utilized to establish the novel estimator, without knowing the actual system model knowledge, and (2) by constructing a data‐driven output predictor to compensate for the data loss, the accuracy of the state estimation can be efficiently improved. With the aid of the least squares technique and completing square technique, a minimum upper bound matrix for the estimation error covariance is obtained by properly designing the estimator gain. Finally, an illustrative example is given to highlight the destructiveness of the designed stochastic IDB attack and the effectiveness of the proposed novel data‐based compensation method. [ABSTRACT FROM AUTHOR]

The long- and finite-wavelength instabilities of weakly viscoelastic film on an oscillating inclined plane are investigated. By using the Chebyshev series solution with the Floquet theory, the combined effects of viscoelasticity and forcing amplitude on instability are described when the inclined plane oscillates in streamwise and wall-normal directions. For long-wavelength instability, the solution to the eigenvalue problem is obtained analytically by the asymptotic expansion method. Results show that the Floquet exponent is independent of the wall-normal oscillation amplitude. The effects of inclined angle, gravity and surface tension on the stability of viscoelastic liquid film are also discussed. For finite-wavelength instability, numerical results corresponding to the wall-normal oscillation disclose that with the increase of viscoelasticity, the unstable gravitational boundary moves to a higher wavenumber, and the critical amplitudes of subharmonic and harmonic instabilities are reduced. The neutral curve of gravity instability for streamwise oscillatory flow is divided into two parts, and a stable bandwidth is formed for a large value of the viscoelastic parameter. Besides, a new oscillatory mode is identified at small angles of inclination, which will be enhanced if the effect of viscoelasticity is incorporated. [ABSTRACT FROM AUTHOR]

Acoustic black holes (ABHs) are known as efficient structural dampers. Periodic lattices are identified as an efficient way to forbidden wave propagation in targeted frequency bandgaps (BGs). The paper demonstrates the possibility to merge the ABH effect with Bragg BGs. The geometrical layout leading to this double effect consists of a plate of periodically modulated thickness by a combination of cosine functions of the spatial coordinates constituting an ABH-like cell, coated with a thin damping layer. The resulting metamaterial allows the realization of solid, stiff, and nonresonant panels over a wide frequency range, including low frequencies, without increasing the mass. First, the band structure is analyzed in the conservative case (without damping layer) using a plane wave expansion model following Kirchhoff's assumptions. The results show the existence of low-frequency BGs that can be controlled by only three geometric parameters, which are defined on the type of lattice chosen (square or hexagonal). Next, a finite size panel is designed for the hexagonal lattice. Experimental characterization of the demonstrator with and without viscoelastic coating shows very attractive broadband vibration mitigation performances due to the fact that the dissipation produced by the ABH effect does not deter filtering effects produced in the BG. [ABSTRACT FROM AUTHOR]

In this paper, we establish the monotonicity of the period map in terms of the energy levels for certain periodic solutions of the equation - φ ′ ′ + φ - φ k = 0 , where k > 1 is a real number. We present a new approach to demonstrate this property, utilizing spectral information of the corresponding linearized operator around the periodic solution and tools related to Floquet theory. [ABSTRACT FROM AUTHOR]

Introducing a time-periodicity into a system parameter leads to parametric excitation, which in general, may cause a parametric resonance with exponentially increased vibration. Applying a parametric excitation but carefully tuning its frequencies to multiple parametric anti-resonance frequencies is investigated here. The parametric excitation here is realized by an open-loop control at the system boundary that allows for an energy flow into or from the system. A parametric anti-resonance successfully triggers an energy transfer between specific vibration modes of the system and occurs in systems with at least two degrees of freedom. Such an energy transfer increases the overall dissipation of kinetic energy of a lightly damped system. This contribution presents an approach to accelerate the mitigation of transient vibrations by applying a multi-frequency parametric excitation with two or more parametric anti-resonance frequencies. The potential application in a MEMS sensor arrangement consisting of two and more coupled flexible beams exemplifies the method. Starting from the minimum system with two degrees of freedom, the averaging method is applied to analyze the transient slow flow, leading to an analytical approximation of the transition time response of a pulsed multi-frequency parametric excitation system. For a specific example, a reduction of 96.7% of the transient vibrations is achievable. [ABSTRACT FROM AUTHOR]

Several investigators have taken advantage of electromagnetic shunt-tuned mass dampers to achieve concurrent vibration mitigation and energy harvesting. For nonlinear structures such as the Duffing oscillator, it has been shown that the novel nonlinear electromagnetic resonant shunt-tuned mass damper inerter (NERS-TMDI) can mitigate vibration and extract energy for a wider range of frequencies and forcing amplitudes when compared to competing technologies. However, nonlinear systems such as the NERS-TMDI are known to exhibit complex stability behavior, which can strongly influence their performance in simultaneous vibration control and energy harvesting. To address this problem, this paper conducts a global stability analysis of the novel NERS-TMDI using three approaches: the multi-parametric recursive continuationWe emphasize that these assume method, Floquet theory, and Lyapunov exponents. A comprehensive parametric analysis is also performed to evaluate the impact of key design parameters on the global stability of the system. The outcome indicates the existence of complex nonlinear behavior, such as detached resonance curves, and the transition of periodic stable solutions to chaotic solutions. Additionally, a parametric study demonstrates that the nonlinear stiffness has a minimal impact on the linear stability of the system but can significantly impact the nonlinear stability performance, while the transducer coefficient has an impact on the linear and nonlinear stability NERS-TMDI. Finally, the global sensitivity analysis is performed relative to system parameters to quantify the impact of uncertainty in system parameters on the dynamics. Overall, our findings show that simultaneous vibration control and energy harvesting come with a considerable instability trade-off that limits the range of operation of the NERS-TMDI. [ABSTRACT FROM AUTHOR]

The accurate simulation of complex dynamics in fluid flows demands a substantial number of degrees of freedom, i.e. a high-dimensional state space. Nevertheless, the swift attenuation of small-scale perturbations due to viscous diffusion permits in principle the representation of these flows using a significantly reduced dimensionality. Over time, the dynamics of such flows evolves towards a finite-dimensional invariant manifold. Using only data from direct numerical simulations, in the present work we identify the manifold and determine evolution equations for the dynamics on it. We use an advanced autoencoder framework to automatically estimate the intrinsic dimension of the manifold and provide an orthogonal coordinate system. Then, we learn the dynamics by determining an equation on the manifold by using both a function-space approach (approximating the Koopman operator) and a state-space approach (approximating the vector field on the manifold). We apply this method to exact coherent states for Kolmogorov flow and minimal flow unit pipe flow. Fully resolved simulations for these cases require $O(10^3)$ and $O(10^5)$ degrees of freedom, respectively, and we build models with two or three degrees of freedom that faithfully capture the dynamics of these flows. For these examples, both the state-space and function-space time evaluations provide highly accurate predictions of the long-time dynamics in manifold coordinates. [ABSTRACT FROM AUTHOR]

A state–space integer–order approximation of commensurate–order systems is obtained using a data–driven interpolation approach based on Loewner matrices. Precisely, given the values of the original fractional–order transfer function at a number of generalised frequencies, a descriptor–form state–space model matching these frequency response values is constructed from a suitable Loewner matrix pencil, as already suggested for the reduction of high–dimensional integer–order systems. Even if the stability of the resulting integer–order system cannot be guaranteed, such an approach is particularly suitable for approximating (infinite–dimensional) fractional–order systems because: (i) the order of the approximation is bounded by half the number of interpolation points, (ii) the procedure is more robust and simple than alternative approximation methods, and (iii) the procedure is fairly flexible and often leads to satisfactory results, as shown by some examples discussed at the end of the article. Clearly, the approximation depends on the location, spacing and number of the generalised interpolation frequencies but there is no particular reason to choose the interpolation frequencies on the imaginary axis, which is a natural choice in integer–order model reduction, since this axis does not correspond to the stability boundary of the original fractional–order system. [ABSTRACT FROM AUTHOR]

Chatter causes great damage to the machining process, and the selection of appropriate process parameters through chatter stability analysis is of great significance for achieving chatter-free machining. This article proposes a milling stability analysis method based on the barycentric rational interpolation differential quadrature method (DQM). The dynamics of the milling process considering the regeneration effect is first modelled as a time-delay differential equation (DDE). When adjacent pitch angles of the milling cutter are symmetric, the milling dynamic equation contains a single time delay. Otherwise, when adjacent pitch angles are asymmetric, the dynamic equation contains multiple time delays. The barycentric rational interpolation DQM is then used to approximate the differential and delay terms of the milling dynamics equation, and to construct a state transition matrix between adjacent milling periods. Finally, the chatter stability lobe diagram (SLD) is obtained based on the Floquet theory. According to the SLD, the appropriate spindle speed can be selected to obtain the maximum stable axial depth of cutting, thereby effectively improving the material removal rate. The accuracy and efficiency of the proposed method have been validated by two widely used milling models, and the results show that the proposed method has good accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]