Search

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Periodically driven systems provide a novel route to control the topology of quantum materials. In particular, Floquet theory allows an effective band description of periodically-driven systems through the Floquet Hamiltonian. Here, we study the time evolution of d-wave superconductors irradiated with intense circularly-polarized laser light. We consider the Floquet t–J model with time-periodic interactions, and investigate its mean-field dynamics by formulating the time-dependent Gutzwiller approximation. We observe the development of the idxy-wave pairing amplitude along with the original d x 2 − y 2 -wave order upon gradual increasing of the field amplitude. We further numerically construct the Floquet Hamiltonian for the steady state, with which we identify the system as the fully-gapped d + id superconducting phase with a nonzero Chern number. We explore the low-frequency regime where the perturbative approaches in the previous studies break down, and find that the topological gap of an experimentally-accessible size can be achieved at much lower laser intensities. Light-matter interaction provides advanced solutions to engineer quantum phases of matter. The authors unveil the emergence of a topological gap in superconductors when circularly polarized light impinges on the material, thereby disclosing accessible strategies to implement novel quantum technologies. [ABSTRACT FROM AUTHOR]

For periodic linear control systems with bounded control range, an autonomized system is introduced by adding the phase to the state of the system. Here, a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists. It is determined by the spectral subspaces of the homogeneous part which is a periodic linear differential equation. Using the Poincaré sphere, one obtains a compactification of the state space allowing us to describe the behavior "near infinity" of the original control system. Furthermore, an application to quasi-affine systems yields a unique control set with nonvoid interior. [ABSTRACT FROM AUTHOR]

Purpose: This paper is aimed at a three-segment micro-beam of micro-electro-mechanical system (MEMS). The influences of parametric vibration and the presence of size effect on the nonlinear response and stability of multi-segment micro-beam (MSMB) are investigated. Methods: The governing equations of MSMB are derived by Hamilton's principle. Continuous model is transformed into discrete model by Galerkin method. The approximate analytical solution is solved by method of multi-scale (MMS). The stability of the system is analyzed by Floquet theory. Further considering the size effect of MSMB, the modified couple stress theory is used to derive the strain energy of MSMB. Results: The presence of parametric excitation enhances the nonlinear behavior of the system, the amplitude peak is significantly improved and the bifurcation occurs at smaller excitation amplitudes. The existence of damping promotes the stability of the system, while increasing the fold angle expands the instability region of system. The modified coupled stress theory predicts a system with decreased the amplitude of frequency response and weakened nonlinearity. Meanwhile, the bifurcation of system starts to appear at higher excitation amplitude. However, influence of the size effect on the system weakens with increase of the excitation amplitude. Conclusions: The combined parametric excitation and direct excitation can be generated by utilizing the particularity of the own structure of MSMB, which can significantly amplify the vibration amplitude of the system and obtain the wide nonlinear response platform. It provides a theoretical basis for applying MSMB to improve the sensitivity and bandwidth performance of micro-gyroscopes. [ABSTRACT FROM AUTHOR]

This study investigates the dynamic flow of a Newtonian fluid through two coaxial cylinders, each rotating at speeds Ω 1 (t) (inner cylinder) and Ω 2 (t) (outer cylinder). We derive equations of motion for disturbances in balance, yielding a controlled system characterized by parameters such as Taylor number, wave number, frequency ratio, and interior cylinder frequency. We introduce numerical techniques for solving this system, employing spectral Chebychev collocation for spatial resolution and a combined approach of Floquet theory and Runge–Kutta method for temporal resolution. Our refined approach enables comprehensive analysis of fluid dynamics within the rotating coaxial cylinders, showcasing the interplay of various control parameters. [ABSTRACT FROM AUTHOR]

Vibration mitigation has been an important research interest in the past decades. In this paper, the enhancement of vibration suppression of thick beams is investigated. The Timoshenko beam is considered, and finite element method is used to discretize governing equations for the beam consisting of axial load. The stability of the system is studied both numerically by using Floquet theory, and analytically by employing averaging perturbation method. Effects of the thickness change, also boundary conditions are provided. The results demonstrate that, by adding extra boundary condition, the stability of the beam increases under the same circumstances. It means that, boundary condition can play important role in mitigating the vibration. Moreover, considering the thick beam reveals that the equivalent damping of the beam enhances. In this case, the excitation amplitude as well as the excitation frequency will increase. Therefore, under the same condition, the thicker the beam is, the more stable it will be. [ABSTRACT FROM AUTHOR]

One of the main challenges in the industry is having trained and efficient operators in manufacturing lines. Smart adaptive guidance systems are developed that offer assistance to the operator during assembly. Depending on the operator's level of execution, the system should be able to serve a different guidance response. This paper investigates the assessment and classification of the operator's functional state using observed task execution times. Five different classifiers are studied for operator functional state classification on task execution time series. The experiments are based on an industry case and the ground truth is provided by an expert rule-based system. Three classification scenarios are defined that segment the problem on the level of the task, the individual, or the team. Furthermore, the investigation includes the evaluation of four distinct window-size configurations. The examination of how these scenarios and window-sizes influence the studied dataset across diverse classifiers reveals that achieving enhanced accuracy necessitates a larger input dimension. In this context, Convolutional Neural Networks predominantly exhibit superior performance compared to alternative classifiers. Careful attention needs to be paid to performance over classes and skills, but results confirm the validity of the approach for data-driven operator functional state classification. [ABSTRACT FROM AUTHOR]

Biomimetic underwater robots use lateral periodic oscillatory motion to propel forward, which is seen in most fishes known as body-caudal fin (BCF) propulsion. The lateral oscillatory motion makes slender-bodied fish-like robots roll unstable. Unlike the case of human-engineered aquatic robots, many species of fish can stabilize their roll motion to perturbations arising from the periodic motions of propulsors. To first understand the origin of the roll instability, the objective of this paper was to analyze the parameters affecting the roll-angle stability of an autonomous fish-like underwater swimmer. Eschewing complex models of fluid–structure interaction, we instead consider the roll motion of a nonholonomic system inspired by the Chaplygin sleigh, whose center of mass is above the ground. In past work, the dynamics of a fish-like periodic swimmer have been shown to be similar to that of a Chaplygin sleigh. The Chaplygin sleigh is propelled by periodic torque in the yaw direction. The roll dynamics of the Chaplygin sleigh are linearized and around a nominal limit cycle solution of the planar hydrodynamic Chaplygin sleigh in the reduced velocity space. It is shown that the roll dynamics are then described as a non-homogeneous Mathieu equation where the periodic yaw motion provides the parametric excitation. We study the added mass effects on the sleigh's linear dynamics and use the Floquet theory to investigate the roll stability due to parametric excitation. We show that fast motions of the model for swimming are frequently associated with roll instability. The paper thus sheds light on the fundamental mechanics that present trade-offs between speed, efficiency and stability of motion of fish-like robots. [ABSTRACT FROM AUTHOR]

To study the attitude dynamics of a magnetically driven dual-spin spherical capsule robot (DSCR), a fourth-order periodic time-varying nonlinear dynamic equation for the DSCR under the action of complex external torque was established based on Euler dynamics. The nonlinear dynamic characteristic of the DSCR was studied by using the incremental harmonic balance (IHB) method and the Runge–Kutta (RK) method. A semi-analytical periodic solution of the attitude dynamics equation was obtained, and the stability of periodic solutions was analyzed based on Floquet theory. By using the bifurcation diagram, time domain diagram, phase diagram, Poincare map and Lyapunov exponent diagram as analysis methods, the global nonlinear dynamic response of the DSCR was studied. The change rule of the global topological structure of the system and the path of the system to chaos were obtained when the magnetic flux density and the magnetic field frequency changed in a large range. The spatial universal uniform rotating magnetic field (SURMF) experimental platform and the axis orientation measurement device were built to verify the dynamic characteristics of the DSCR. The experimental analysis results were in good agreement with the theoretical calculation data. [ABSTRACT FROM AUTHOR]

This work deals with the stability problem of elastic composite cantilever beams subjected to a delayed, periodically changing follower force. The equation of motion of the periodic system with time delay is deduced based on some previous works. Composite beams with and without delamination are considered, and the finite element method is applied to carry out the spatial discretization of the structures. Besides, for the delaminated case further two cases are involved. The first case is when the delamination is in the midplane of the beam, while the second case involves an asymmetrically placed delamination, respectively. The Floquet theory is applied to derive the transition matrix of the periodic system. An important aspect is that the time delay and the principal period of the dynamic force are equal to each other. The discretization over the time domain is performed by using the Chebyshev polynomials of the first kind. Basically, there are five parameters governing the dynamic problem including among others the time delay and the static and dynamic forces. The stability behavior is shown for the intact and delaminated beams on the parameter planes for large number of cases by using the unit circle criteria. The presence and absence of structural damping is also analyzed in each case. The results indicate that some planes are sensitive to the mesh resolution, others are not. Moreover, on some planes significant differences may take place between the intact and delaminated beams from the standpoint of stable zones. [ABSTRACT FROM AUTHOR]

Backgrounds: The axially moving structures are commonly seen in the transporting belt, the tracks of heavy engineering vehicles and the manufacturing process. In many practical engineering fields, the material properties of the axially moving structures are not uniform. Purposes: The aim of the present paper is to provide some basic movement rules and stability evidence for the axially moving structures with non-uniformly distributed materials. The present paper investigates the dynamics of an axially moving plate with periodical distributed material properties. Methods: The equation of motion of the material periodically distributed axially moving plate is established based on the Poisson–Kirchhoff plate theory. The assumed mode method is applied to discretize the equation of motion of the axially moving plate into ordinary differential equations. The Floquet theory is adopted to analyze the stability of the parametric excitation system. Results: The effects of the mass density and the elastic modulus of the material on the stability of the system are researched. The effectiveness of the Floquet theory is proved by numerical simulations. Conclusions: From the results, the divergence and flutter types of instability of the plate can be observed in a vibration period. The plate is more stable when the material properties are approaching. [ABSTRACT FROM AUTHOR]

Objective: Periodic configuration of mechanical and civil structures has shown great potential for noise and vibration reduction. However, the use of Cartesian coordinates in studying periodicity effects in elastic structures overlooks the benefits of radially periodic configurations when dealing with wave propagation in large flexible plates disturbed by a small source area. This paper presents an easy-to-use numerical approach to predicting bandgap characteristics in polar coordinates. Methodology: To demonstrate the vibration-attenuation effect, we consider a circular radially periodic plate model. We use an adapted Wave Finite-Element method in numerical experiments to demonstrate the existence of the attenuation effect. To verify the numerical results, we apply an adapted Floquet theory to polar coordinates. Results and Conclusions: Our findings indicate that theoretical and numerical results are in excellent agreement considering a new parameter that introduces the distance from the origin. The adapted Wave Finite-Element approach and Floquet theory presented here demonstrate their potential to model more complex structures in polar coordinates. [ABSTRACT FROM AUTHOR]

Dynamics, control, and stability of roll oscillations of a biased ship in regular sea waves are investigated. The ship under roll oscillation is modelled as the classical Helmholtz–Duffing oscillator with strongly nonlinear asymmetric restoring moment characteristics. The incremental harmonic balance method, amended with a pseudo-arc-length continuation approach, is employed to obtain the uncontrolled and controlled frequency responses. The primary and subharmonic responses of the uncontrolled system are examined through the period-doubling route to chaos path. The same ship roll model is then investigated under state feedback control with time delay. In the control scheme, a moving weight is actuated by the delay controller to generate the anti-rolling moment. The stability of periodic responses is studied using the semi-discretization method with extended Floquet theory. Bifurcation points on periodic response branches are identified from the eigenvalue study. The effect of gains and time delay in the feedback loop in controlling the primary and subharmonic responses is investigated. Several chaotic responses obtained through period-doubling route to chaos paths are successfully controlled. Stable, periodic, and steady-state solutions obtained from the IHB method are verified by numerical integration of the equation of motion as and when applicable. Solutions are aided with phase portrait, Poincaré map, time history, and Fourier spectrum for better clarity. It is shown that appropriate selections of control parameters can effectively reduce the roll amplitude to a great extent with the improved measure of stability. [ABSTRACT FROM AUTHOR]

Dynamical stabilization is the ability of a statically diverging stationary state to gain stability by periodically modulating its physical properties in time. This phenomenon is getting recent interest because it is one of the exploited feature of Floquet engineering that develops new exotic states of matter in the quantum realm. Nowadays, dynamical stabilization is done by applying periodic modulations much faster than the natural diverging time of the Floquet systems, allowing for some effective stationary equations to be used instead of the original dynamical system to rationalize the phenomenon. In this work, by combining theoretical models and precision desktop experiments, we show that it is possible to dynamically stabilize a system, in a "synchronized" fashion, by periodically injecting the right amount of external action in a pulse wave manner. Interestingly, the Initial Value Problem underlying this fundamental stability problem is related to the Boundary Value Problem underlying the determination of bound states and discrete energy levels of a particle in a finite potential well, a well-known problem in quantum mechanics. This analogy offers a universal semi-analytical design tool to dynamically stabilize a mass in a potential energy varying in a square-wave fashion. [ABSTRACT FROM AUTHOR]

Motivated by recent experimental demonstrations of Floquet topological insulators, there have been several theoretical proposals for using structured light, either spatial or spectral, to create other properties such as flat bands and vortex states. In particular, the generation of vortex states in a massive Dirac fermion insulator irradiated by light carrying nonzero orbital angular momentum (OAM) has been proposed. Here, we evaluate the orbital magnetization and optical conductivity as physical observables for such a system. We show that the OAM of light induces nonzero orbital magnetization and current density. The orbital magnetization density increases linearly as a function of the OAM degree. In certain regimes, we find that orbital magnetization density is independent of the system size, width, and Rabi frequency of light. It is shown that the orbital magnetization arising from our Floquet theory is large and can be probed by magnetometry measurements. Furthermore, we study the optical conductivity for various types of electron transitions between different states such as vortex, edge, and bulk that are present in the system. Based on the peaks in conductance, a scheme for the detection of vortex states is proposed. Recent experimental demonstrations of Floquet topological insulators have sparked theoretical proposals to utilize structured light, either spatially or spectrally, to generate additional properties like flat bands and vortex states. Here, the authors examine the effects of light's orbital angular momentum, revealing non-zero orbital magnetization and current density, and investigate the optical conductivity for diverse electron transitions within the system, including vortex, edge, and bulk states. [ABSTRACT FROM AUTHOR]

In this paper, a new method named constrained parameter-splitting perturbation method for improving the solutions obtained from the parameter-splitting perturbation method is proposed for solving the problems in some extremal cases, such as the strongly nonlinear vibration of an Euler–Bernoulli cantilever. The proposed method takes the advantages of both the perturbation method and the harmonic balance method. The idea is that the solution obtained by the parameter-splitting perturbation method is substituted into the equation of motion and then the accumulative error of the equation is minimized for determining the unknown splitting parameters under the constraints constructed under the frame of harmonic balance method. The forced vibration of an oscillator with cubic geometric nonlinearity and inertia nonlinearity and the forced vibration of a planar microcantilever beam with a lumped tip mass are studied as examples to reveal the efficacy of the proposed method. The inspection of the steady-state response including its stability is conducted by means of comparing the frequency-response curves obtained by the proposed method with those obtained by the numerical continuation method and harmonic balance method, respectively, to show the efficacy and the advantages of the proposed method. Meanwhile, the nonlinear ordering effect on the solutions of the proposed method is also studied by comparing the results obtained by using different nonlinear orderings in the systems. In the last, we found through convergence examinations that it is necessary to have corrections to the erroneous solution which are obtained by harmonic balance method and Floquet theory in stability analysis. [ABSTRACT FROM AUTHOR]

A novel high-order discretization method for the prediction of milling stability is proposed in this paper to increase the accuracy and efficiency considering the differential of directional cutting coefficient and vibration velocities. Same to the existing full-discretization method (FDM) and semi-discretization method (SDM), the milling system is expressed as a linear time-periodic equation and the time period is discretized into discrete time intervals to approximate the solution. In this algorithm, the cutting force coefficient matrix of the whole integrand is reconstructed to lay the foundation for the fast and accurate approximation. Then, the monodromy matrix (or the Floquet matrix) is calculated by the method used in the temporal finite element analysis (TFEA) instead of the multiple recursive algorithms which can improve the computational time. Finally, the computational efficiency is defined in a new way which gives quantitative comparisons for different discretization methods. It is shown that the proposed method can reduce the computational cost by 91–95% when the same errors are required. [ABSTRACT FROM AUTHOR]

Nonequilibrium quantum states can be controlled via the driving field in periodically driven systems. Such control, which is called Floquet engineering, has opened various phenomena, such as the light-induced anomalous Hall effect. There are expected to be some essential differences between the anomalous Hall and spin Hall effects of periodically driven systems because of the difference in time-reversal symmetry. However, these differences remain unclear due to the lack of Floquet engineering of the spin Hall effect. Here we show that when the helicity of circularly polarized light is changed in a periodically driven t2g-orbital metal, the spin current generated by the spin Hall effect remains unchanged, whereas the charge current generated by the anomalous Hall effect is reversed. This difference is protected by the symmetry of a time reversal operation. Our results offer a way to distinguish the spin current and charge current via light and could be experimentally observed in pump-probe measurements of periodically driven Sr2RuO4. Non-equilibrium states can be induced in a given system using periodic driving and the underlying physics understood using Floquet theory. Here, the authors model a periodically driven t2g-orbital metal and demonstrate how the spin Hall and anomalous Hall effects are realized and can be distinguished by their response to circularly polarized light with different helicities. [ABSTRACT FROM AUTHOR]

Lattice sandwich structures are broadly used in aerospace, navigation, and high-speed rail engineering. In engineering practice, the airflow outside the vehicle or aircraft always exhibits the pulsatile property, which makes the elastic structural components and the external airflow a parametric excitation system. In this paper, the parametric vibration stability analysis and dynamic characteristics of a lattice sandwich plate interacting with the pulsatile external airflow are studied. The equation of motion is derived using Hamilton's principle and discretized using the assumed mode method. The linear potential flow theory is applied to derive the perturbation aerodynamic pressure. The stability of the system is analyzed using the Floquet theory and validated by numerical simulations. The effects of design parameters of the lattice sandwich plate on the stability of the system are discussed. From the simulations and discussions, some practical principles for the optimal design of lattice sandwich structures in the aerodynamic environment are proposed. [ABSTRACT FROM AUTHOR]

In this paper we develop two new approaches for directly assessing stability of nonlinear wave-based solutions, with application to jointed elastic bars. In the first stability approach, we strain a stiffness parameter and construct analytical stability boundaries using a wave-based method. Not only does this accurately determine stability of the periodic solutions found in the example case of two bars connected by a nonlinear joint, but it directly governs the response and stability of parametrically forced continuous systems without resorting to discretization, a new development in of itself. In the second stability approach, we pose a perturbation eigenproblem residue (PER) and show that changes in the sign of the PER locate critical points where stability changes from stable to unstable, and vice-versa. Lastly, we discuss follow-on research using the developed stability approaches. In particular, we identify an opportunity to study stability around internal resonance, and then identify a need to further develop and interpret the PER approach to directly predict stability. [ABSTRACT FROM AUTHOR]

When an intense light field strongly interacts with the band structure of a solid, the formation of hybrid light-matter quantum states becomes possible. Examples of such Floquet-Bloch states have been reported, but engineering of the band structure using Floquet states can suffer from dissipation and decoherence. Sustaining the necessary quantum coherence of the light-matter interactions requires robust electronic states in combination with strong fields of suitable polarization and frequency. Here, we explore the quantum coherent coupling of nano-focused surface plasmon polaritons (SPP) to distinct electronic states in the band structure of a solid. We observe above-threshold electron emission from the Au(111) Shockley surface state by the absorption of up to seven SPP quanta. Using time-resolved photoelectron spectroscopy the coherence of the interaction of the SPPs with the surface state during electron emission is investigated and the process is shown to be similar to light-driven above threshold electron emission. Ultimately, our work could render SPP-based Floquet engineering in nano-optical systems feasible. Floquet theory describes transient states driven by a light-matter interaction and could potentially be used to engineer the band structure and the topology of solid-state systems. Here, the authors investigate coherent photoemission from a gold surface caused by a strong surface plasmon polariton excitation, which could be used to realize surface plasmon polariton driven Floquet effects in nanostructures. [ABSTRACT FROM AUTHOR]

Purpose: As per the dynamical system theory, a Lyapunov–Perron (L–P) transformation can transform a linear quasi-periodic system to a time-invariant form under certain conditions. However, to the best of author's knowledge, a systematic approach to analytically compute such a transformation is not available in the literature. In this work, a simple yet practical method to compute the L–P transformation matrix is discussed comprehensively. Methods: In this work, the authors demonstrate the conversion of a commutative linear quasi-periodic system into a time-invariant system using Floquet type theory. Moreover, for a linear non-commutative parametrically excited quasi-periodic system satisfying diophantine condition, the authors employ an intuitive state augmentation and the time independent normal forms (TINF) technique to transform it into a time-invariant form. Results: The temporal and phase space variations computed from the proposed approach are compared with the numerical techniques for both commutative and non-commutative quasi-periodic systems. Additionally, the element-wise variation of L–P transformation matrix is computed and compared with numerical solution. Conclusion: The proposed approach is validated and proven to be applicable to both commutative and non-commutative linear quasi-periodic systems satisfying diophantine condition. Moreover, the closed form analytical expression for the L–P transformation matrix for parametrically excited linear quasi-periodic system can be obtained with this approach. [ABSTRACT FROM AUTHOR]

In this work the problem of a delaminated composite cantilever beam subjected to a retarded periodically changing follower axial force is taken into consideration. The equation of motion is deduced based on a previous work including finite element discretization in space. On the other hand the delayed system is captured by the Chebyshev polynomials of the first kind in the time domain. The most important aspect of the model is that multiple time delay is considered, i.e., the principal period of the parametric excitation is not equal to the delay. Under these conditions the stability of the system is investigated using the Floquet theory and the unit circle criterion. The stability diagrams are determined for large number of cases focusing essentially on the effect of delamination on the stable domains. The main conclusion is that although the delamination length and thicknesswise position does not have an essential effect on the stability domains, the definite offset of the limit curves may be observed. In contrast, the relation of time delay and principal period influences substantially the shape and nature of limit curves on certain parameter planes. [ABSTRACT FROM AUTHOR]

Migratory birds travel over impressively long distances. Consequently, they have to adopt flight regimes being both efficient—in order to spare their metabolic resources—and robust to perturbations. This paper investigates the relationship between both aspects, i.e., energetic performance and stability, in flapping flight of migratory birds. Relying on a poly-articulated wing morphing model and a tail-like surface, several families of steady flight regime have been identified and analysed. These families differ by their wing kinematics and tail opening. A systematic parametric search analysis has been carried out, in order to evaluate power consumption and cost of transport. A framework tailored for assessing limit cycles, namely Floquet theory, is used to numerically study flight stability. Our results show that under certain conditions, an inherent passive stability of steady and level flight can be achieved. In particular, we find that progressively opening the tail leads to passively stable flight regimes. Within these passively stable regimes, the tail can produce either upward or downward lift. However, these configurations entail an increase of cost of transport at high velocities penalizing fast forward flight regimes. Our model-based predictions suggest that long range flights require a furled tail configuration, as confirmed by field observations, and consequently need to rely on alternative mechanisms to stabilize the flight. [ABSTRACT FROM AUTHOR]

The stability prediction is an effective approach to suppress the unstable milling process caused by the regenerative chatter. Through updating a numerical solution scheme (NSS), a fast prediction method is proposed in this paper. Firstly, a NSS is constructed by combining the Lagrange polynomial and Euler's method. Then, the solution of the differential equations described the milling process is transformed into the initial-value problem of the equation which is expressed by the built NSS over each small discrete time interval. Subsequently, the state transition matrix over one tooth passing period is established to predict the stability lobe diagram (SLD) via the Floquet theory. Finally, the computational performances of the proposed method are verified by the single and two DOF dynamic models. Compared with the complete discretization scheme, the computational accuracy and efficiency of the proposed method are increased by 2.69 times and 2.01 times, respectively. The proposed method reduces the computational accuracy by 2.16 times in comparison to the first-order full-discretization method, but it increases the computational efficiency by 2.2 times. [ABSTRACT FROM AUTHOR]

The advent of ultrafast laser science offers the unique opportunity to combine Floquet engineering with extreme time resolution, further pushing the optical control of matter into the petahertz domain. However, what is the shortest driving pulse for which Floquet states can be realised remains an unsolved matter, thus limiting the application of Floquet theory to pulses composed by many optical cycles. Here we ionized Ne atoms with few-femtosecond pulses of selected time duration and show that a Floquet state can be observed already with a driving field that lasts for only 10 cycles. For shorter pulses, down to 2 cycles, the finite lifetime of the driven state can still be explained using an analytical model based on Floquet theory. By demonstrating that the amplitude and number of Floquet-like sidebands in the photoelectron spectrum can be controlled not only with the driving laser pulse intensity and frequency, but also by its duration, our results add a new lever to the toolbox of Floquet engineering. Floquet engineering aims at inducing new properties in materials with light. Here the authors have used pulses of variable durations, to investigate its applicability in the femtosecond domain. Surprisingly, they found that it holds to the few-cycle limit. [ABSTRACT FROM AUTHOR]

Two major concerns with the nonlinear energy sink (NES) when used as a passive vibration absorber are the mass of the NES and the threshold of external excitation to initiate the targeted energy transfer (TET). This work proposes an inertial NES with nonlinear damping to address the aforementioned concerns. An inerter replaces the conventional NES's mass to reduce the absorber system's effective mass. The addition of nonlinear damping created instability and therefore initiated the strongly modulated response (SMR) even for lower excitation amplitude which is the most favorable condition for TET. A base excited linear primary system appended with the proposed NES is used to demonstrate the claims. Multi-harmonic balance method (MHBM) combined with arc-length continuation and Floquet theory generates the frequency response plots and identifies the stable and unstable periodic solution branches. Numerical studies at the unstable periodic solution obtained by MHBM revealed the existence of SMR. The slow flow dynamics and the slow invariant manifold (SIM) associated with the SMR are derived using the complexification averaging (CX-A) method combined with the singular perturbation theory. The SIM topology is investigated for variations in the strength of nonlinearity, nonlinear damping factor, and mass ratio. The performance of the proposed inertial NES with nonlinear damping is compared with that of a conventional NES with viscous damping, and the merits are highlighted. It is observed that with the addition of nonlinear damping in the inertial NES, the SMR is initiated even at low excitation amplitude, and efficient energy transfer takes place from the linear oscillator to NES. The combined approach using MHBM and CX-A provided better insight into the analysis of NES-based vibration absorber systems. [ABSTRACT FROM AUTHOR]

A number of experiments have evidenced signatures of enhanced superconducting correlations after photoexcitation. Initially, these experiments were interpreted as resulting from quasi-static changes in the Hamiltonian parameters, for example, due to lattice deformations or melting of competing phases. Yet, several recent observations indicate that these conjectures are either incorrect or do not capture all the observed phenomena, which include reflectivity exceeding unity, large shifts of Josephson plasmon edges, and appearance of new peaks in terahertz reflectivity. These observations can be explained from the perspective of a Floquet theory involving a periodic drive of system parameters, but the origin of the underlying oscillations remains unclear. In this paper, we demonstrate that following incoherent photoexcitation, long-lived oscillations are generally expected in superconductors with low-energy Josephson plasmons, such as in cuprates or fullerene superconductor K3C60. These oscillations arise from the parametric generation of plasmon pairs due to pump-induced perturbation of the superconducting order parameter. We show that this bi-plasmon response can persist even above the transition temperature as long as strong superconducting fluctuations are present. Our analysis offers a robust framework to understand light-induced superconducting behavior, and the predicted bi-plasmon oscillations can be directly detected using available experimental techniques. Light-induced superconductivity is a recent phenomenon where many aspects of the underlying physics are still to be fully understood. Here, the authors analyse coupled Ginzburg-Landau and Maxwell equations to investigate the dynamics of the quantum states when a superconductor is irradiated by a laser pulse. [ABSTRACT FROM AUTHOR]

Regenerative chatter is the most important factor affecting the stability of the milling process. It is core for suppressing chatter and improving production efficiency to accurately and efficiently identify the stable region of milling chatter. Therefore, according to the theory of predictor-corrector, three predictor–corrector methods (PCM) are, respectively, proposed for the milling stability region by applying the fourth-order Adams-Bashforth-Moulton formula, Simpson formula, and Hamming formula. Firstly, the regenerative chatter milling process is described as a second-order time-delay differential equation (DDE) with periodic coefficients. Thus, the forced vibration time can uniformly be discretized as a time node set. Secondly, the fourth-order Adams-Bashforth formula is used to predict the displacement at every time node, whereas the fourth-order Adams-Moulton formula can be employed to correct this predicted value. In addition, the fourth-order Simpson formula and Hamming formula can also correct the predicted value. Thus, a higher precision discrete prediction-correction expansion is constructed for the transformation of DDE into the state transition express. The Floquet theory can be depended on to present the judgment criterion of milling stability. Moreover, finally, under the same milling process parameters, comparisons of both the stability lobe curve and the local discrete error curve show that the PCM has a faster convergence rate than the 1st-SDM (first-order semi-discretization method) and 2nd-FDM (second-order full-discretization method). This shows that the PCM can obtain better computational accuracy under the same discrete number, whereas the PCM is significantly higher computational efficiency over 1st-SDM and 2nd-FDM. Meanwhile, considering the actual machining environment, helix angle effect and multiple modes effect of the tool are analyzed; experimental verification considering multiple modes with helix angle further indicates the applicability of the PCM. [ABSTRACT FROM AUTHOR]

We consider the Dirac operators with singular potentials 1 D A , Φ , m , Γ δ Σ = D A , Φ , m + Γ δ Σ where 2 D A , Φ , m = ∑ j = 1 n α j - i ∂ x j + A j + α n + 1 m + Φ I N is a Dirac operator on R n with variable magnetic and electrostatic potentials A = (A 1 ,... , A n) , Φ , and the variable mass m. In formula (2), α j are the N × N Dirac matrices, that is α j α k + α k α j = 2 δ jk I N , I N is the unit N × N matrix, N = 2 n + 1 / 2 , Γ δ Σ is a singular delta-potential supported on C 2 - hypersurface Σ ⊂ R n periodic with respect to the action of a lattice G on R n. We consider the self-adjointnes and discretness of the spectrum of unbounded in L 2 (T , C N) operators associated with the formal Dirac operator (1) on the torus T = R N ∕ G . We study the band-gap structure of the spectrum of self-adjoint operators D in L 2 (R n , C N) associated with the formal Dirac operator (1) on R n with G -periodic regular and singular potentials. We also consider the Fredholm property and the essential spectrum of unbounded operators associated with non-periodic regular and singular potentials supported on G -periodic smooth hypersurfaces in R n. [ABSTRACT FROM AUTHOR]

We study stability of so-called synchronous slowly oscillating periodic solutions (SOPSs) for a system of identical delay differential equations (DDEs) with linear decay and nonlinear delayed negative feedback that are coupled through their nonlinear term. Under a row sum condition on the coupling matrix, existence of a unique SOPS for the corresponding scalar DDE implies existence of a unique synchronous SOPS for the coupled DDEs. However, stability of the SOPS for the scalar DDE does not generally imply stability of the synchronous SOPS for the coupled DDEs. We obtain an explicit formula, depending only on the spectrum of the coupling matrix, the strength of the linear decay and the values of the nonlinear negative feedback function near plus/minus infinity, that determines the stability of the synchronous SOPS in the asymptotic regime where the nonlinear term is heavily weighted. We also treat the special cases of so-called weakly coupled systems, near uniformly coupled systems, and doubly nonnegative coupled systems, in the aforementioned asymptotic regime. Our approach is to estimate the characteristic (Floquet) multipliers for the synchronous SOPS. We first reduce the analysis of the multidimensional variational equation to the analysis of a family of scalar variational-type equations, and then establish limits for an associated family of monodromy-type operators. We illustrate our results with examples of systems of DDEs with mean-field coupling and systems of DDEs arranged in a ring. [ABSTRACT FROM AUTHOR]

Dispersal-induced growth (DIG) occurs when several populations with time-varying growth rates, each of which, when isolated, would become extinct, are able to persist and grow exponentially when dispersal among the populations is present. This work provides a mathematical exploration of this surprising phenomenon, in the context of a deterministic model with periodic variation of growth rates, and characterizes the factors which are important in generating the DIG effect, and the corresponding conditions on the parameters involved. [ABSTRACT FROM AUTHOR]

The problem of the linear stability of the stratified Kolmogorov flow driven by a sinusoidal in space force in a viscous and diffusive Boussinesq fluid is re-visited using the Floquet theory, Galerkin approximations and the method of (generalized) continued fractions. Numerical and analytical arguments are provided in favor of a conjecture that an ideal stratified Kolmogorov flow is prone to short-wave instability for Richardson numbers markedly greater than the critical Richardson number Ri = ¼ that appears in the Miles–Howard theorem. The short-wave instability of the stratified Kolmogorov flow is conjectured to be due to a resonance amplification of the Doppler-shifted internal gravity wave modes, in the presence of critical levels of the main flow that are ignored in the proof of the Miles–Howard theorem, but it is emphasized that the complete resolution of the above paradox is a task for future research. [ABSTRACT FROM AUTHOR]

In this paper, an n-star general dynamic model of tethered satellite system with closed-loop configuration is provided. An analytical method for periodic solution stability of the general dynamic model is proposed based on Floquet theory, which proved that the periodic solution stability of the system depends on the maximum modulus for the eigenvalue of a matrix related to the Jacobian matrix. The periodic solution stability of a 3-star system with equilateral triangle as the initial configuration is analyzed as an example based upon the analytical method, and the results are verified by numerical simulation. The critical spin angular velocity caused by the tether mass and the parameter variation of the 3-star system is analyzed. The results show that the analytical method of periodic solution stability can solve the critical stable spin angular velocity of the tethered satellite system accurately, and the 3-star system can guarantee stable spin in the case of the spin angular velocity is higher than the critical spin angular velocity. [ABSTRACT FROM AUTHOR]

In previous studies of linear rotary systems with active magnetic bearings, parametric excitation was introduced as an open-loop control strategy. The parametric excitation was realized by a periodic, in-phase variation of the bearing stiffness. At the difference between two of the eigenfrequencies of the system, a stabilizing effect, called anti-resonance, was found numerically and validated in experiments. In this work, preliminary results of further exploration of the parametric excitation are shared. A Jeffcott rotor with two active magnetic bearings and a disk is investigated. Using Floquet theory, a deeper insight into the dynamic behavior of the system is obtained. Aiming at a further increase of stability, a phase difference between excitation terms is introduced. [ABSTRACT FROM AUTHOR]