Resonance Region Research Articles

Nonlinear wave propagation in a two-dimensional lattice model of textile metamaterials

Abstract An original parametric lattice model is formulated to describe the propagation of harmonic elastic waves in two-dimensional textile metamaterials. Within a weak nonlinear regime, the free undamped motion of the textile metamaterial, starting from a spatially periodic pretensioned configuration, is governed by nonlinear differential difference equations. Quadratic and cubic nonlinearities arise from the elastic contact between plain woven yarns. By applying the asymptotic method of multiple scales, the nonlinear dynamics of the periodic cell are governed by an ordered hierarchy of linear perturbation equations. Therefore, by virtue of the linearity and spatial periodicity, the Floquet-Bloch theory is recursively applied at each order of the perturbation equations to study the linear and nonlinear dispersion properties. Specifically, the lowest order solutions return the linear dispersion diagram characterizing the free undamped propagation of small-amplitude harmonic waves. Within the technical range of the parameters, the dispersion diagram shows the coexistence of two passbands, separated by a large mid-frequency stopband. By virtue of an energy-based classification criterion, the different polarizations of the waves propagating in the low-frequency and high-frequency bands are disclosed. The higher orders allow to determine analytically the combined effects of the nonlinearities on the dispersion properties, in the absence of internal resonances. In particular, the wavefrequencies exhibit a quadratic dependence on the wave oscillation amplitude, characterized by a systematic softening behavior. Moreover, the amplitudes of the damped nonlinear response induced by the external excitation due to a harmonically oscillating pretension are analyzed in the frequency domain and the instability regions of the primary resonance are obtained in the whole range of feasible mechanical parameters. Finally, analytical results are successfully validated by numerical simulations in the time domain.

CP asymmetry from the effect of the isospin symmetry breaking during B-meson decay

Abstract The direct CP asymmetry in quasi-two-body decays of $B \rightarrow (V\rightarrow \pi^{+}\pi^{-})P $ is investigated in the perturbative QCD method, where P represents a pseudoscalar meson and V refers to $\rho$, $\omega$ and $\phi$ mesons, respectively. We present the amplitude of the quasi-two-body decay process and investigate the effects of mixed resonances involving $\rho^{0}-\omega$, $\rho^{0}-\phi$ and $\omega-\phi$, while considering the impact of isospin symmetry breaking. We observe a significant CP asymmetry when the invariant mass of the $\pi^{+}\pi^{-}$ pair within the resonance ranges of $\rho$, $\omega$ and $\phi$ mesons. Consequently, we proceed to quantify the regional CP asymmetry in these resonance regions. A significant difference is observed when comparing results obtained with and without the interference of the three vector mesons and isospin conservation. The CP asymmetry results obtained from the three-body decay process, without interference due to isospin conservation by the perturbative QCD method, are in agreement with the newly updated data acquired by the LHCb experiment. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Subtraction of the tt¯ contribution in tWb¯ production at the one-loop level

The tWb¯ production contributes to the real corrections to the tW cross section. It would interfere with the top quark pair production, causing difficulties in a clear definition of the tWb¯ events. The subtraction of the tt¯ contributions has been performed in the diagram removal or diagram subtraction schemes for the tree-level processes. However, these schemes rely on the ability to identify the double resonant diagrams and thus can not be extended to loop diagrams. We propose a new scheme to subtract the tt¯ contributions by power expansion of the squared amplitude in the resonant region. In order to cancel the infra-red divergences of the loop amplitudes, a widely used method is to introduce the dipole counter-terms, an ingredient in calculations of the full next-to-leading order QCD corrections. In our scheme, these counter-terms are also power-expanded. As a proof of principle, we calculate the one-loop correction to the dd¯ → b¯Wt process, and present the invariant mass distribution of the Wb¯ system.

Automated Resonance Fitting for Nuclear Data Evaluation

Global and national efforts to deliver high-quality nuclear data to users have a wide-ranging impact, affecting applications in national security, reactor operations, basic science, medicine, and more. Cross-section evaluation is a major part of this effort, combining theory and experimentation to produce recommended values and uncertainties for reaction probabilities. Resonance region evaluation is a specialized type of nuclear data evaluation that can require significant manual effort and months of time from expert scientists. In this article, nonconvex, nonlinear optimization methods are combined with concepts of inferential statistics to infer a resonance model from experimental data in an automated manner that is not dependent on prior evaluation(s). This methodology aims to enhance the workflow of a resonance evaluator by minimizing time, effort, and the potential for bias from prior assumptions, while enhancing reproducibility and documentation, thereby addressing well-known challenges in the field.

Frequency Response of a Nonlinear Vibration Isolator Containing a Viscoelastic End-Stop Buffer

Considering that a mechanical spring can be compressed or stretched only, a protected object is prone to detach from the support spring when the system falls into the resonant region. To avoid this phenomenon, a nonlinear vibration isolator containing a viscoelastic end-stop buffer is developed, which can exhibit stiffness–hardening or stiffness–softening characteristics. Because the restoring force is asymmetrical and piecewise linear, a modified averaging method is applied to obtain steady-state solutions, which contain a bias term. A numerical method is then used to verify the analytical solutions, and their stability is determined. Finally, the effects of the structural parameters on the frequency response and force transmissibility are investigated. The jump avoidance condition is subsequently given. The results show that the modified averaging method is more accurate than the classical method. Decreasing the stiffness ratio can reduce the transmissibility peak and resonance frequency. Applying heavy damping in the end-stop buffer is beneficial for reducing transmissibility in the resonant region, whereas the isolation performance at high frequencies remains unchanged. The developed vibration system exhibits better isolation performance than the linear system when stiffness–softening characteristics are considered.

On estimations of Dawn spacecraft’s capture probability into 1:1 ground-track resonance around Vesta

Abstract This paper develops semi-analytical and analytical methodologies to estimate the probability of the Dawn spacecraft being captured into a 1:1 ground-track resonance around Vesta. The spacecraft, using low-thrust propulsion, approached the asteroid Vesta, and one significant challenge during this phase is crossing ground-track resonances with the asteroid. As the capture phenomenon is dependent on the initial condition of the trajectory, it is necessary to accurately estimate the probability of such a capture. Firstly, the system dynamics are described by a model incorporating Hamiltonian perturbations from the irregular gravitational field up to the second degree and order, and continuous low-thrust that is constant in magnitude and directed in the opposite direction of the spacecraft’s velocity. The resonance region is enclosed by separatrices which are approximated with a fourth-order polynomial for quantitative analysis. The Hamiltonian, serving as a proxy for the system’s energy, changes when the spacecraft crosses the separatrices, and these changes are quantified using a global adaptive quadrature method. Finally, the probability of capture into ground-track resonance is estimated based on the energy change across the separatrices, and the accuracy and efficiency of the developed semi-analytical and analytical methodologies are investigated by comparing them to numerical simulations based on the perturbed Hamilton’s equations of motion. This research makes a significant contribution to the field of astrodynamics by providing a systematic and efficient approach to estimating the probability of resonance capture.

Polarization Scattering Regions: A Useful Tool for Polarization Characteristic Description

Polarimetric radar systems play a crucial role in enhancing microwave remote sensing and target identification by providing a refined understanding of electromagnetic scattering mechanisms. This study introduces the concept of polarization scattering regions as a novel tool for describing the polarization characteristics across three spectral regions: the polarization Rayleigh region, the polarization resonance region, and the polarization optical region. By using ellipsoidal models, we simulate and analyze scattering across varying electrical sizes, demonstrating how these sizes influence polarization characteristics. The research leverages Cameron decomposition to reveal the distinctive scattering behaviors within each region, illustrating that at higher-frequency bands, scattering approximates spherical symmetry, with minimal impact from the target shape. This classification provides a comprehensive view of polarization-based radar cross-section regions, expanding upon traditional single-polarization radar cross-section regions. The results show that polarization scattering regions are practical tools for interpreting polarimetric radar data across diverse frequency bands. The applications of this research in radar target recognition, weather radar calibration, and radar polarimetry are discussed, highlighting the importance of frequency selection for accurately capturing polarization scattering features. These findings have significant implications for advancing weather radar technology and target recognition techniques, particularly as radar systems move towards higher frequency bands.

Mechanisms of mass transfer effect for the vapor-gas bubble under acoustic excitation

This paper theoretically explores the mechanisms of the mass transfer effect for the vapor-gas bubble under acoustic excitation. The mathematical model for the mixture bubble mass transfer is established based on the perturbation method. The threshold of the mixture bubble under different vapor mass fractions is compared with those of the gas bubble. The threshold represents the amplitude condition at which the molar quantity of gas within the bubble achieves the dynamic equilibrium state, which dictates whether the bubble expands or contracts. The main conclusions are summarized as follows: (1) The vapor mass fraction inside the mixture bubble has a significant effect on the mass transfer processes, including bubble growth, gas diffusion, and convection. (2) As the initial valor mass fraction increases, the resonance region moves in the direction of a decreasing equilibrium radius. In the region far above resonance, threshold curves of the mixture bubble show either an upward trend or a downward trend. (3) The bubble radius, vapor mass fraction, and threshold value all undergo variations during the mixture bubble's growth or shrinkage processes.

Stress tunable spin dynamics of a magnetic vortex under resonant magnetic fields

In this study, we investigated the stress-controlled magnetization processes and dynamic susceptibility of a magnetic vortex in FeGa disk under an external magnetic field. Our primary objectives were to elucidate the nucleation process of a magnetic vortex and explore the modulatory effects of mechanical stress on its behavior. Our findings reveal that the applied stress can regulate the spin arrangement, leading to different hysteresis loops with kinks of different switching processes in the magnetization. Specifically, tensile stress induces a buckling state, facilitating the transition from the parallel spin to the vortex state in smaller disks and introducing a distinct kink in the hysteresis loop. Conversely, compressive stress causes the disappearance of the original intermediate state in larger disks, leading to a smoother hysteresis loop. Notably, the stress-introduced magnetic anisotropy altered the resonance region of the system. These findings offer valuable insights into the design and optimization of magnetic storage devices and magnetic field sensors, highlighting the potential of harnessing mechanical stress as a tuning parameter for enhancing their performance.

On the motion of a dynamically symmetric satellite in one case of multiple parametric resonance

The paper studies the motions of a dynamically symmetric satellite (rigid body) relative to the center of mass in the central Newtonian gravitational field on a weakly elliptical orbit in the neighborhood of its stationary rotation (cylindrical precession). We consider the values of the parameters for which, in the limiting case of a circular orbit, one of the frequencies of small linear oscillations is equal to unity and the other is equal to zero, and the rank of the coefficient matrix of the linearized equations of the perturbed motion is equal to two, as well as a small neighborhood of this resonant point in the three-dimensional space of parameters. The resonant periodic motions of the satellite, analytical in fractional powers of a small parameter (the eccentricity of the orbit of the satellite's center of mass), are constructed. A rigorous nonlinear analysis of their stability is carried out. The methods of KAM theory are used to describe two- and three-frequency conditionally periodic motions of a satellite, with frequencies of different orders in a small parameter. A number of general theoretical issues concerning the considered multiple parametric resonance in Hamiltonian systems with two degrees of freedom that are close to autonomous and periodic in time are discussed. Several qualitatively different variants of parametric resonance regions are constructed. It is shown that in the general case the nature of nonlinear resonant oscillations of the system is determined by the first approximation system in a small parameter.

Toward a unified description of hadron scattering at all energies

The construction of general amplitudes satisfying symmetries and S-matrix constraints has been the primary tool in studying the spectrum of hadrons for over half a century. In this work, we present a new parametrization, which can fulfill many expectations of S-matrix and Regge theory and connects the essential physics of hadron scattering in the resonance region and in asymptotic limits. In this construction, dynamical information is entirely contained in Regge trajectories that generalize resonance poles in the complex energy plane to moving poles in the angular momentum plane. We highlight the salient features of the model, compare with existing literature on dispersive and dual amplitudes, and benchmark the formalism with an initial numerical application to the ρ and σ/f0(500) mesons in ππ scattering. Published by the American Physical Society 2024

Dynamic response of SDOF systems with inerter or clutching inerter damper under harmonic excitations

In this study, the dynamic response of single degree-of-freedom (SDOF) systems equipped with an inerter or a clutching inerter damper (CID) under harmonic force or base excitation is investigated. Under harmonic force excitation, an inerter must work with an appropriate damping element to prevent the kinetic energy it absorbs from being returned to the primary system. However, the addition of the damping element introduces extra damping force, which can deteriorate the force transmissibility within certain frequency ranges. In comparison, the piecewise nature of the CID effectively overcomes this limitation. Since this piecewiseness is a typical nonlinear feature, the averaging method is employed to solve the system response. The obtained approximate analytical solution is compared with the solution derived from the equivalent linearization method (ELM). It is found that the resonant frequency calculated by the ELM is significantly higher than the numerical solution for inertance [Formula: see text]. In contrast, the results indicate that the averaging method provides higher accuracy and avoids overestimating the resonant frequency. Under harmonic base excitation, an increase in the inertance of the inerter reduces both the system damping ratio and the excitation amplitude. The reduction in the damping ratio theoretically increases response sensitivity, leading to higher resonance amplitudes. However, this potential increase in resonance amplitude is outweighed by the substantial decrease in excitation amplitude. As a result, the dominant effect of reduced excitation amplitude leads to an overall decrease in the resonance amplitude. In addition, due to the low-pass filtering characteristic of the inerter, its vibration suppression effectiveness rapidly deteriorates in the high-frequency range. Similarly, the CID experiences a decline in vibration suppression at high frequencies for the same reason. Nevertheless, it outperforms the inerter in the resonant region, owing to its distinctive energy-dissipating properties.

Investigation of Single Proton Dissociation

We consider the single proton diffraction dissociation at low missing masses focusing on the interplay between diffractive processes and resonance production. The model incorporates the concept of duality, where the observed cross sections are explained by both smooth background processes and discrete resonance contributions. At low missing masses MX, this approach leverages the Regge proton trajectory to account for the role of resonances in the cross section. Recent experimental data are used to refine model parameters, enhancing the accuracy of predictions for the differential cross section behavior in the resonance region.

Optimization of the magnetic field in the SK1000 central region model magnet

This study presents a design scheme for a central region model magnet, based on a high-intensity compact cyclotron. The objective is to ensure the long-term stable production of therapeutic radionuclides such as 211At and 225Ac, while maintaining reasonable construction and operational costs. In-depth research into the design principles and core parameters of the CRM (Central Region Model) cyclotron magnet system, guided by the concept of isochronous magnetic field design, enabled the optimization of the magnet's dimensions and magnetic field distribution. The optimization results show that the magnet system meets the acceleration and focusing requirements of the particle beam, effectively prevents particles from entering dangerous resonance regions, and aligns with the theoretical requirements of isochronous magnetic fields. This method keeps the error between the calculated magnetic field and the theoretical design field within 5 Gauss, meeting the expected physical design standards.

Validating automated resonance evaluation with synthetic data

The integrity and precision of nuclear data are crucial for a broad spectrum of applications, from national security and nuclear reactor design to medical diagnostics, where the associated uncertainties can significantly impact outcomes. A substantial portion of uncertainty in nuclear data originates from the subjective biases in the evaluation process, a crucial phase in the nuclear data production pipeline. Recent advancements indicate that automation of certain routines can mitigate these biases, thereby standardizing the evaluation process and enhancing reproducibility. This research aims to provide a methodology, framework, and metrics for the validation of automated nuclear data evaluation software leveraging high-quality synthetic data that closely mimic real experimental observables. An introduced error metric provides a scale and intuitive measure of the evaluation quality by quantifying the estimate’s accuracy and performance across the specified energy range. Synthetic data provides access to experimental observables and underlying resonance parameters, enabling comparison of different evaluations. The methodology is demonstrated using Ta-181 isotope data in the resolved resonance region. The Automated Resonance Identification Subroutine (ARIS), which operates without prior resonance information, was used to test and showcase the framework’s capabilities utilizing the proposed error metrics. The results demonstrate the effectiveness of the proposed approach and framework for optimizing software parameters and testing hypotheses through “what-if” controlled experiments, such as modifying assumptions about experimental conditions or average resonance parameters.

Plasmonic Silver Nanoparticles Facilitate Electron Emission from Diamond upon Sun‐Like Excitation

AbstractThe development of a stable, non‐toxic material that emits electrons following absorption of visible light may have a major impact on the solar photocatalysis of difficult reactions such as CO2 and N2 reduction, as well as for targeted chemical transformations in general. Diamond is a good candidate, however it is a wide bandgap material requiring deep UV photons ( <227 nm) to promote electrons from the valence band into the conduction band. Embedding silver nanoparticles under the diamond surface allows the photoconductivity of the diamond in the spectral region of the surface plasmon resonance to be increased, while also leading to an enhancement of visible light photoemission. Considering the low intensity of the light sources used in this work and the spectral properties of the enhanced photoconductivity and photoemission a mechanism based on plasmonically enhanced photoconductivity which in turn allows surface states emptied by photoemission to be recharged thus leading to enhanced photoemission in the visible range is proposed.

Research on nonlinear dynamic vertical vibration characteristics and control of roll system in cold rolling mill

In order to address the vertical vibration phenomenon of the working roll during the rolling process, taking into consideration the nonlinear factors of the rolling interface and the roll system, this study establishes a nonlinear excitation vertical vibration model based on dynamic rolling force. The impact of nonlinear factors on system stability and vibration characteristics is analyzed. The study reveals that nonlinear damping and linear stiffness exhibit significant effects through time delay characteristics. Nonlinear stiffness has a drastic impact on system stability, while increasing system damping effectively reduces the amplitude and narrows the resonance region. By employing averaging method and singular value theory, the stability of the cold rolling mill roll system is analyzed under non-autonomous and autonomous states. A combined time-delay feedback controller is proposed, which effectively suppresses the system’s large-scale vibration by adjusting the control gain and time delay parameters. MATLAB simulations are conducted to validate the accuracy of the control strategy, providing theoretical support for vibration prediction and system design in rolling mills.

Enhancing the Pressure-Sensitive Electrical Conductance of Self-Assembled Monolayers.

The inherent large HOMO-LUMO gap of alkyl thiol (CnS) self-assembled monolayers (SAMs) has limited their application in molecular electronics. This work demonstrates significant enhancement of mechano-electrical sensitivity in CnS SAMs by external compression, achieving a gauge factor (GF) of approximately 10 for C10S SAMs. This GF surpasses values reported for conjugated wires and DNA strands, highlighting the potential of CnS SAMs in mechanosensitive devices. Conductive atomic force microscopy (cAFM) investigations reveal a strong dependence of GF on the alkyl chain length in probe/CnS/Au junctions. This dependence arises from the combined influence of molecular tilting and probe penetration, facilitated by the low Young's modulus of alkyl chains. Theoretical simulations corroborate these findings, demonstrating a shift in the electrode Fermi level toward the molecular resonance region with increasing chain length and compression. Introducing a rigid graphene interlayer prevents probe penetration, resulting in a GF that is largely independent of the alkyl chain length. This highlights the critical role of probe penetration in maximizing mechano-electrical sensitivity. These findings pave the way for incorporating CnS SAMs into mechanosensitive and mechanocontrollable molecular electronic devices, including touch-sensitive electronic skin and advanced sensor technologies. This work demonstrates the potential of tailoring mechanical and electrical properties of SAMs through molecular engineering and interface modifications for optimized performance in specific applications.

Research on lateral–torsional coupled vibration induced by substantial imbalance in an overhung flexible rotor

Substantial imbalance is a real possibility in aero–engines and is usually caused by blade off, bird strikes, etc. A substantially unbalanced rotor system will exhibit extremely complicated nonlinear lateral–torsional behavior, and the related dynamics are critical to the safe design of a rotor system. In this paper, a comprehensive nonlinear model of an imbalanced flexible rotor system is proposed, in which translational–torsional coupling and angular–torsional coupling are introduced simultaneously. Based on the model, the lateral–torsional coupling features are discussed, and the lateral as well as the torsional vibration behaviors are further analyzed in detail. The results show that the lateral–torsional coupling factors only exist under the nonsynchronous whirl condition. Thus, if the imbalance is small, the lateral vibration exhibits the linear feature of a traditional unbalanced response, and the torsional vibration does not occur in steady state. However, under substantially unbalanced conditions, the vibration responses are significantly changed. In lateral vibration, many combined frequency components between rotation frequency (fu) and torsional natural frequency (ft1 and ft2) such as fu-ft1, fu-2ft1 and fu-ft2 can be induced, which can lead to combined resonance phenomena and many additional resonance peaks. The lateral–torsional coupling effect is strong at that time. Both the lateral translational–torsional coupling excitation and lateral angular–torsional coupling excitation exhibits the multiple harmonics whose frequencies are closely related to ft1 and ft2. Consequently, the torsional vibration in those combined resonance regions can be very high. The corresponding vibration exhibits the steady harmonic feature with vibration frequency being ft1 or ft2.

A magnetic pendulum for demonstrating Mathieu-type parametric resonance

Abstract We describe a magnetic pendulum apparatus designed for studying and demonstrating Mathieu-type parametric resonance. The apparatus features a T-shaped rigid arm with a neodymium (NdFeB) magnet bob, suspended by double V-shaped thread suspensions. It is parametrically driven by an alternating uniform magnetic field produced by Helmholtz coils. The pendulum is structurally simple and easy to implement, and its parameter-driven mechanism is transparent in terms of physics. The use of electromagnetic driving allows for precise control over both the frequency and amplitude of parameter modulation, enabling quantitative studying on parametric resonance. We have observed the first and second instability region of parametric resonance. We also theoretically analyze the impact of non-uniformity in the Helmholtz coils' magnetic field on the pendulum motion, revealing that the non-uniformity can significantly alter the pendulum's nonlinearity, influencing both the magnitude and the sign of the coefficients of the nonlinear terms. However, under the parameters of our experimental setup, the nonlinearity effect is mainly manifested in large swing angle motions. For small swing angle within 5\textsuperscript{$\circ$}, the impact of magnetic field non-uniformity on parametric resonance is negligible. The experiment reported here is appropriate for undergraduates to carry out experimental research, helping them develop a more intuitive and quantitative understanding of parametric resonance.