Showing papers on "Normal mode published in 2019"

Visualizing vibrational normal modes of a single molecule with atomically confined light

Abstract: The internal vibrations of molecules drive the structural transformations that underpin chemistry and cellular function. While vibrational frequencies are measured by spectroscopy, the normal modes of motion are inferred through theory because their visualization would require microscopy with angstrom-scale spatial resolution—nearly three orders of magnitude smaller than the diffraction limit in optics1. Using a metallic tip to focus light and taking advantage of the surface-enhanced Raman effect2 to amplify the signal from individual molecules, tip-enhanced Raman spectromicroscopy (TER-SM)3,4 reaches the requisite sub-molecular spatial resolution5, confirming that light can be confined in picocavities6–10 and anticipating the direct visualization of molecular vibrations11–13. Here, by using TER-SM at the precisely controllable junction of a cryogenic ultrahigh-vacuum scanning tunnelling microscope14–16, we show that angstrom-scale resolution is attained at subatomic separation between the tip atom and a molecule in the quantum tunnelling regime of plasmons6,8,9,17. We record vibrational spectra within a single molecule, obtain images of normal modes and atomically parse the intramolecular charges and currents driven by vibrations. Our analysis provides a paradigm for optics in the atomistic near-field. The vibrational normal modes in a single molecule are imaged using tip-enhanced Raman spectromicroscopy performed in the atomistic near-field.

Quantum absorption refrigerator with trapped ions.

Abstract: In recent years substantial efforts have been expended in extending thermodynamics to single quantum systems. Quantum effects have emerged as a resource that can improve the performance of heat machines. However in the fully quantum regime their implementation still remains a challenge. Here, we report an experimental realization of a quantum absorption refrigerator in a system of three trapped ions, with three of its normal modes of motion coupled by a trilinear Hamiltonian such that heat transfer between two modes refrigerates the third. We investigate the dynamics and steady-state properties of the refrigerator and compare its cooling capability when only thermal states are involved to the case when squeezing is employed as a quantum resource. We also study the performance of such a refrigerator in the single shot regime made possible by coherence and demonstrate cooling below both the steady-state energy and a benchmark set by classical thermodynamics. Studying quantum heat machines would extend our fundamental understanding of thermodynamics. Here, the authors report on absorption refrigeration within three normal modes of motion of a three-ion chain, studying performances using either thermal or squeezed states, also in the single-shot regime.

Dynamically encircling an exceptional point in anti-parity-time symmetric systems: asymmetric mode switching for symmetry-broken modes.

Abstract: Dynamically encircling an exceptional point (EP) in parity-time (PT) symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes. The counterpart symmetry-broken modes (i.e., each eigenmode is localized in one waveguide only), which are more useful for applications such as on-chip optical signal processing, exhibit only non-chiral dynamics and therefore cannot be used for asymmetric mode switching. Here, we solve this problem by resorting to anti-parity-time (anti-PT) symmetric systems and utilizing their unique topological structure, which is very different from that of PT-symmetric systems. We find that the dynamical encircling of an EP in anti-PT-symmetric systems with the starting point in the PT-broken phase results in chiral dynamics. As a result, symmetry-broken modes can be used for asymmetric mode switching, which is a phenomenon and application unique to anti-PT-symmetric systems. We perform experiments to demonstrate the new wave-manipulation scheme, which may pave the way towards designing on-chip optical systems with novel functionalities. By steering microwaves in an anti-parity-time symmetric system, Chinese scientists have explored the topological physics and their wave-manipulation applications in optics and photonics. Recent developments in non-Hermitian systems, i.e., open systems that can exchange energy with surroundings, have given rise to new optical devices such as isolators, sensors, and absorbers. Such systems exhibit the so-called exceptional points, where two or more resonances have equal frequencies and dissipations. By sending microwaves along a waveguide with specially designed boundaries, which is equivalent to looping the waveguide resonance around an exceptional point in a parameter space, Xu-Lin Zhang from Jilin University and Che Ting Chan from the Hong Kong University of Science and Technology have demonstrated a new method for manipulating electromagnetic waves in waveguides. Their work could pave the way for on-chip optical devices with new functionalities.

A novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium under the effect of gravity with three-phase-lag model

Abstract: In the present paper, the three-phase-lag (3PHL) model, Green-Naghdi theory without energy dissipation (G-N II) and Green-Naghdi theory with energy dissipation (G-N III) are used to study the influence of the gravity field on a two-temperature fiber-reinforced thermoelastic medium.,The analytical expressions for the displacement components, the force stresses, the thermodynamic temperature and the conductive temperature are obtained in the physical domain by using normal mode analysis.,The variations of the considered variables with the horizontal distance are illustrated graphically. Some comparisons of the thermo-physical quantities are shown in the figures to study the effect of the gravity, the two-temperature parameter and the reinforcement. Also, the effect of time on the physical fields is observed.,To the best of the author’s knowledge, this model is a novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium, and gravity plays an important role in the wave propagation of the field quantities. It explains that there are significant differences in the field quantities under the G-N II theory, the G-N III theory and the 3PHL model because of the phase-lag of temperature gradient and the phase-lag of heat flux.

A novel method of vibration modes selection for improving accuracy of frequency-based damage detection

Abstract: Frequency-based damage detection techniques have been widely applied to structural health monitoring. By analysing the changes (shifts) in natural frequencies in a structure with and without damage, these techniques solve the inverse problem of determining size and location of damage. In the existing literature, the first few or random modes of frequency shifts are given to the inverse algorithms as inputs in order to predict the damage parameters. These frequency shifts can be either numerical or measured. While the accuracy of prediction in the former (numerical) case has been found to be satisfactory, the use of measured frequencies has often shown large errors. This can be attributed to unavoidable noise in frequencies, including the mismatch between FEM model and real structure, as well as the noise in the measurement itself. Previous research has shown that the noise in frequency will actually be magnified in the discrepancy of frequency shifts, and thus affect the damage prediction accuracy. And moreover, the same noise added to different modes of frequency of a damaged case will lead to the different levels of deviation in different modes of frequency shifts. This observation indicates that potentially some modes of frequency shifts are less affected by the noise than others for a given case. However, so far, there has been no studies that attempt to identify particular vibration modes of frequency shifts that are (a) less affected by the noise for all damage cases and (b) result in a more accurate prediction of damage. In this study, a novel concept of Noise Response Rate (NRR) is proposed to evaluate the sensitivity of each mode of the frequency shift to noise. Further, it is shown that selecting the vibration modes with low NRR values improves the prediction accuracy of frequency-based damage detection. The efficacy of NRR is demonstrated through a case study on a composite curved plate compared with the conventional method for damage detection.

Topological bands and localized vibration modes in quasiperiodic beams

Abstract: We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground springs at locations determined by projecting from a circle onto an underlying periodic system. A family of periodic and quasiperiodic structures is obtained by smoothly varying a parameter defining such projection. Numerical simulations show the existence of vibration modes that first localize at a boundary, and then migrate into the bulk as the projection parameter is varied. Explicit expressions predicting the change in the density of states of the bulk define topological invariants that quantify the number of modes spanning a gap of a finite structure. We further demonstrate how modulating the phase of the ground springs distribution causes the topological states to undergo an edge-to-edge transition. The considered configurations and topological studies provide a framework for inducing localized modes in continuous elastic structural components through globally spanning, deterministic perturbations of periodic patterns defined by the considered projection operations.

On the frequency response computation of geometrically nonlinear flat structures using reduced-order finite element models

Abstract: This paper presents a general methodology to compute nonlinear frequency responses of flat structures subjected to large amplitude transverse vibrations, within a finite element context. A reduced-order model (ROM)is obtained by an expansion onto the eigenmode basis of the associated linearized problem, including transverse and in-plane modes. The coefficients of the nonlinear terms of the ROM are computed thanks to a non-intrusive method, using any existing nonlinear finite element code. The direct comparison to analytical models of beams and plates proves that a lot of coefficients can be neglected and that the in-plane motion can be condensed to the transverse motion, thus giving generic rules to simplify theROM. Then, a continuation technique, based on an asymptotic numerical method and the harmonic balance method, is used to compute the frequency response in free (nonlinear mode computation) or harmonically forced vibrations. The whole procedure is tested on a straight beam, a clamped circular plate and a free perforated plate for which some nonlinear modes are computed, including internal resonances. The convergence with harmonic numbers and oscillators is investigated. It shows that keeping a few of them is sufficient in a range of displacements corresponding to the order of the structure’s thickness, with a complexity of the simulated nonlinear phenomena that increase very fast with the number of harmonics and oscillators.

Radial Force Density Analysis of Switched Reluctance Machines: The Source of Acoustic Noise

Abstract: Closer attention has been given to the acoustic noise performance of electric motors as electrified powertrains penetrate into our transportation system. In particular, switched reluctance machine introduces a new challenge to acoustic noise aspect given that the temporal harmonics of high amplitudes on the radial direction can excite the natural frequencies of the main circumferential modes. A practical understanding of the radial force density decomposition is crucial in identifying the primary source of acoustic noise at different operating points, and it is the main contribution of this paper. An analytical expression is introduced to identify the temporal harmonic orders that excite different spatial mode shapes. The combination of the circumferential and temporal harmonic orders results in a force density surface wave that travels in the clockwise (CW) or counter CW direction. The mode excitation is investigated along with the sound pressure level produced by the primary vibrating mode shapes. Acoustic noise characteristics for each mode and the corresponding natural frequency at different speeds have been analyzed by using a waterfall plot.

Exact dynamic characteristic analysis of a double-beam system interconnected by a viscoelastic layer

Abstract: As an important composite beam structure, the double-beam system with a viscoelastic connection layer has a wide range of applications in engineering. Accurate analysis of its dynamic characteristics is an imperative requirement for the design, monitoring and evaluation, or vibration control of these structures. Existing researches usually introduce some simplifications or assumptions, and ignore the damping characteristics of the structure in most cases, which results in inaccurate dynamic analysis results of such double-beam structures and cannot meet the actual requirements. For this reason, a generalized mechanical model that can consider the damping factor is established in this paper to accurately simulate the double-beam system with a viscoelastic connection layer, and its dynamic characteristics are accurately analyzed by dynamic stiffness method. On this basis, the effects of structural parameters on the modal frequencies and mode shapes of the system are studied. The results show that the stiffness of the connection layer has little effect on the system mode; the modal frequencies of the double-beam system can be reduced by increasing the mass or damping coefficient of the connection layer, where the influence of damping on the low-order modes of the system is very significant, but its effect on the higher-order modes are clearly inferior to that of mass.

Free vibration analysis of laminated composite elliptic cylinders with general boundary conditions

Abstract: In this paper, a unified analysis model is proposed for the first time to study the free vibration of laminated composite elliptic cylinders with general boundary conditions including the classical boundary, elastic boundary and their combinations. The theoretical model is established by means of the modified variational principle and multilevel partition technique based on the first-order shear deformation theory. The interface continuity and boundary constraints are enforced by using the coupling and boundary spring technique. On the basis of that, the displacement components of each shell domain are expanded in the form of double Jacobi polynomials along the meridional and circumferential direction. The convergence and comparison analysis for laminated composite elliptic cylinders subject to different classical boundary conditions is conducted to show the reliability and accuracy of the present method. To make the research topic understood better, some mode shapes are also depicted. The present solutions show stable and rapid convergence characteristics, and the natural frequencies and mode shapes agree well with the Finite Element Analysis results. Some new vibration results and parameterized results are presented and may be as the reference data by other researchers in the future.

Anisotropy of the high‐power piezoelectric properties of Pb(Zr,Ti)O3

Abstract: Piezoceramics are widely‐used in high‐power applications, whereby the material is driven in the vicinity of the resonance frequency with high electric fields. Evaluating material's performance at these conditions requires the consideration of inherent nonlinearity, anisotropy, and differences between individual vibration modes. In this work, the relation between electromechanical properties at large vibration velocity and the utilized vibration mode is investigated for a prototype hard piezoceramic. The nonlinear behavior is determined using a combined three‐stage pulse drive method, which enables the analysis of resonant and antiresonant conditions and the calculation of electromechanical parameters. The deviations of coupling coefficients, compliances, and piezoelectric coefficients at high‐power drive were found to be strongest for the transverse length vibration mode. Differences in the mechanical quality factors were observed only between the planar and transverse length modes, which were rationalized by the different strain distribution profiles and the contribution of different loss tensor components. In addition, the influence of the measurement configuration was investigated and a correction method is proposed. The differences between vibration modes are further confirmed by heat generation measurements under continuous drive, which revealed that the strongest heat generation appears in the radial mode, while transverse and longitudinal length modes show similar temperature increase.

Dense active matter model of motion patterns in confluent cell monolayers

Abstract: Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described within the framework of dense active matter, and argue that persistent uncoordinated cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce swirl-like correlations. We obtain this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based cell models, soft elastic particles and the self-propelled Voronoi model together with in-vitro experiments of confluent corneal epithelial cell sheets. Simulations and normal mode analysis perfectly match when tissue-level reorganisation occurs on times longer than the persistence time of cell motility. Our analytical model quantitatively matches measured velocity correlation functions over more than a decade with a single fitting parameter.

Negative refraction in quasicrystalline multilayered metamaterials

Abstract: Inspired by some recent results in elastodynamics of layered composites, we address here the problem of an antiplane elastic wave obliquely incident at the interface between a substrate and a periodic laminate with a quasicrystalline structure (generated by the Fibonacci substitution rule). The angles of refraction of the transmitted modes are computed by combining the transfer matrix method with the normal mode decomposition and evaluating the direction of the average Poynting vector. It is shown that, with respect to a periodic classical bilayer, on the one hand, beyond a certain frequency threshold, high order Fibonacci laminates can provide negative refraction for a wider range of angles of incidence, on the other, they allow negative wave refraction at lower frequencies. The outcome strongly relies on the Floquet-Bloch dynamic analysis of this class of laminates that is performed thoroughly. It is revealed that the corresponding spectra have a self-similar character linked to the specialisation of the Kohmoto’s invariant, a function of the frequency that was recently studied by the authors for periodic one-dimensional quasicrystalline-generated waveguides. This function is able to explain two types of scaling occurring in dispersion diagrams. The attained results represent an important advancement towards the realisation of multilayered quasicrystalline metamaterials with the aim to control negatively refracted elastic waves.

Detection of Rossby Waves in the Sun using Normal-mode Coupling

Abstract: Rossby waves play a fundamental role in angular momentum processes in rotating fluids. In addition to the potential to shed light on physical mechanisms operating in the solar convection zone, the recent detection of Rossby waves in the Sun (Loptien et al. 2018; Liang et al. 2018) also serves as a means of comparison between different helioseismic methods. Time-distance helioseismology, ring-diagram analysis and other techniques have all proven successful in recovering the Rossby-wave dispersion relation from analyses of Helioseismic and Magnetic Imager data (HMI; Schou et al. 2012). In this article, we demonstrate that analyses of two years of HMI global-mode-oscillation data using the technique of normal-mode coupling also show signatures of Rossby waves. In addition to providing an independent means of inferring Rossby waves, this detection lends credence to the methodology of mode coupling and encourages a more complete exploration of its possibilities.

Observation of dressed states of distant atoms with delocalized photons in coupled-cavities quantum electrodynamics.

Abstract: In a cavity quantum electrodynamics (QED) system, where atoms coherently interact with photons in a cavity, the eigenstates of the system are the superposition states of atoms and cavity photons, the so-called dressed states of atoms. When two cavities are connected by an optical fiber with negligible loss, the coherent coupling between the cavities gives rise to photonic normal modes. One of these normal modes is the fiber-dark mode, in which photons are delocalized in the two distant cavities. Here we demonstrate the setting of coupled-cavities QED, where two nanofiber cavity-QED systems are coherently connected by a meter-long low-loss channel in an all-fiber fashion. Specifically, we observe dressed states of distant atoms with delocalized photons of the fiber-dark normal mode. Our system will provide a platform for the study of delocalized atomic and photonic states, photonic many-body physics, and distributed quantum computation.

Voigt Exceptional Points in an Anisotropic ZnO-Based Planar Microcavity: Square-Root Topology, Polarization Vortices, and Circularity.

Abstract: Voigt points represent propagation directions in anisotropic crystals along which optical modes degenerate, leading to a single circularly polarized eigenmode. They are a particular class of exceptional points. Here, we report the fabrication and characterization of a dielectric, anisotropic optical microcavity based on nonpolar ZnO that implements a non-Hermitian system and mimics the behavior of Voigt points in natural crystals. We prove the exceptional-point nature by monitoring the complex-square-root topology of the mode eigenenergies (real and imaginary parts) around the Voigt points. Polarization state analysis shows that these artificially engineered Voigt points behave as vortex cores for the linear polarization and sustain chiral modes. Our findings apply to any planar microcavity with broken cylindrical symmetry and, thus, pave the way for exploiting exceptional points in widespread optoelectronic devices such as vertical cavity surface emitting lasers and resonant cavity light emitting diodes.

Observation of dressed states of distant atoms with delocalized photons in coupled-cavities quantum electrodynamics

Abstract: In a cavity quantum electrodynamics (QED) system, where atoms coherently interact with photons in a cavity, the eigenstates of the system are the superposition states of atoms and cavity photons, the so-called dressed states of atoms. When two cavities are connected by an optical fiber with negligible loss, the coherent coupling between the cavities gives rise to photonic normal modes. One of these normal modes is the fiber-dark mode, in which photons are delocalized in the two distant cavities. Here we demonstrate the setting of coupled-cavities QED, where two nanofiber cavity-QED systems are coherently connected by a meter-long low-loss channel in an all-fiber fashion. Specifically, we observe dressed states of distant atoms with delocalized photons of the fiber-dark normal mode. Our system will provide a platform for the study of delocalized atomic and photonic states, photonic many-body physics, and distributed quantum computation.

Highly sensitive and wide-range resonant pressure sensor based on the veering phenomenon

Abstract: We report a highly sensitive wide-range resonant pressure sensor. The concept is based on tracking multiple modes of vibration of an electrothermally heated initially curved micro-beam experiencing the veering phenomenon between its first and third vibration modes. For low values of pressure, the third resonance frequency is very sensitive, and thus its variation with pressure is monitored and recorded. As increasing pressure, the resonance frequency of the third mode decreases until reaching the veering phenomenon. At that point, the first mode exchanges role with the third mode, becoming very sensitive, and hence its frequency is tracked afterward as varying pressure. We show that using this concept, the sensitivity of the resonant pressure micro-sensor is significantly enhanced. Finite element method (FEM) simulations and experimental data show that the proposed micro-sensor becomes highly sensitive for wide-range of pressure from 38 mTorr to 200 Torr. The effect of various parameters on the performance of the proposed pressure sensor is investigated including the thickness of the micro-beam, the vacuum chamber size, and the thermal actuation load.