Showing papers on "Normal mode published in 2018"

Circuit Complexity for Coherent States

Abstract: We examine the circuit complexity of coherent states in a free scalar field theory, applying Nielsen’s geometric approach as in [1]. The complexity of the coherent states have the same UV divergences as the vacuum state complexity and so we consider the finite increase of the complexity of these states over the vacuum state. One observation is that generally, the optimal circuits introduce entanglement between the normal modes at intermediate stages even though our reference state and target states are not entangled in this basis. We also compare our results from Nielsen’s approach with those found using the Fubini-Study method of [2]. For general coherent states, we find that the complexities, as well as the optimal circuits, derived from these two approaches, are different.

Optical binding of two cooled micro-gyroscopes levitated in vacuum

Abstract: Coupling between mesoscopic particles levitated in vacuum is a prerequisite for the realization of a large-scale array of particles in an underdamped environment as well as potential studies at the classical–quantum interface. Here, we demonstrate for the first time, to the best of our knowledge, optical binding between two rotating microparticles mediated by light scattering in vacuum. We investigate autocorrelations between the two normal modes of oscillation determined by the center-of-mass and the relative positions of the two-particle system. The inter-particle coupling, as a consequence of optical binding, removes the degeneracy of the normal mode frequencies, which is in good agreement with theory. We further demonstrate that the optically bound array of rotating microparticles retains their optical coupling during gyroscopic cooling, and exhibits cooperative motion whose center-of-mass is stabilized.

Realization of Beam Steering Based on Plane Spiral Orbital Angular Momentum Wave

Abstract: A new form of plane spiral orbital angular momentum (PS-OAM) carrying wave with the spiral harmonics of exp(− $jl\varphi$ ) as a complete set of eigenmodes is proposed to realize beam steering. Such a wave possesses the fundamental characteristics of an OAM-carrying wave, i.e., a spiral phase distribution, yet propagates along transverse directions. Hence, it owes unique advantages for use in realizing desired radiation beams, while avoids the puzzles encountered by traditional OAM-carrying beams. Various OAM mode grouping using the superposition of PS-OAM waves are demonstrated here via theoretical calculations as well as experimental verifications. The generation methods for PS-OAM waves are also proposed and experimentally validated to authenticate the feasibility. Both the calculated and experimental results show that the PS-OAM grouping is capable of providing a practical realization of eigenmode beamforming.

Benchmark of gyrokinetic, kinetic MHD and gyrofluid codes for the linear calculation of fast particle driven TAE dynamics

Abstract: Fast particles in fusion plasmas may drive Alfven modes unstable leading to fluctuations of the internal electromagnetic fields and potential loss of particles. Such instabilities can have an impact on the performance and the wall-load of machines with burning plasmas such as ITER. A linear benchmark for a toroidal Alfven eigenmode (TAE) is done with 11 participating codes with a broad variation in the physical as well as the numerical models. A reasonable agreement of around 20% has been found for the growth rates. Also, the agreement of the eigenfunctions and mode frequencies is satisfying. However, they are found to depend strongly on the complexity of the used model.

Normal-mode analysis for collective neutrino oscillations

Abstract: In an interacting neutrino gas, collective modes of flavor coherence emerge that can be propagating or unstable. We derive the general dispersion relation in the linear regime that depends on the neutrino energy and angle distribution. The essential scales are the vacuum oscillation frequency ω=Δ m2/(2E), the neutrino-neutrino interaction energy μ=√2GF; nν, and the matter potential λ=√2GF ne. Collective modes require non-vanishing μ and may be dynamical even for ω=0 ("fast modes"), or they may require ω¬=0 ("slow modes"). The growth rate of unstable fast modes can be fast itself (independent of ω) or can be slow (suppressed by √|ω/μ|). We clarify the role of flavor mixing, which is ignored for the identification of collective modes, but necessary to trigger collective flavor motion. A large matter effect is needed to provide an approximate fixed point of flavor evolution, while spatial or temporal variations of matter and/or neutrinos are required as a trigger, i.e., to translate the disturbance provided by the mass term to seed stable or unstable flavor waves. We work out explicit examples to illustrate these points.

Polymer-Based Ultrasonic Motors Utilizing High-Order Vibration Modes

Abstract: Our previous studies showed that traveling-wave rotary ultrasonic motors with polymer-based vibrators yielded limited output power when operating in the commonly used low-order bending vibration modes. In this study, we employ a high-order bending mode in the polymer-based cylindrical ultrasonic motor, because this mode yields a relatively high electromechanical coupling factor, which may lead to high output power of the motor. Additionally, in contrast with the low-order modes with only vertical nodal lines, the high-order mode has both horizontal and vertical nodal lines on the circumferential outer surface of the polymer-based vibrator. With these attractive advantages, it is worth investigating basic vibration characteristics of polymer-based vibrators operating in high-order modes and their applications to ultrasonic motors. The vibrating body is made of poly phenylene sulfide, a functional polymer exhibiting low mechanical loss even under high-amplitude ultrasonic vibration and is activated by a piezoelectric ceramic element bonded on the back surface. The high-order modes are optimal for polymer-based vibrators with practical thicknesses, because their equivalent stiffnesses and masses are relatively low when operating in this mode. Polymer-based motors with the high-order modes exhibit relatively high output torques and powers, compared with not only polymer-based motors with low-order bending modes, but also metal-based motors operating in high-order vibration modes.

On the origin of spanwise vortex deformations in laminar separation bubbles

Abstract: This work investigates the three-dimensional, spatio-Temporal flow development in the aft portion of a laminar separation bubble. The bubble is forming on a flat plate geometry, subjected to an adverse pressure gradient, featuring maximum reverse flow of approximately 2Â % of the local free-stream velocity. Time-resolved velocity measurements are performed by means of planar and tomographic particle image velocimetry, in the vicinity of the reattachment region. The measurements are complemented with a numerical solution of the boundary layer equations in the upstream field. The combined numerical and measured boundary layer is used as a baseline flow for linear stability theory analysis. The results provide insight into the dynamics of dominant coherent structures that form in the separated shear layer and deform along the span. Stability analysis shows that the flow becomes unstable upstream of separation, where both normal and oblique modes undergo amplification. While the shear layer roll up is linked to the amplification of the fundamental normal mode, the oblique modes at angles lower than approximately are also amplified substantially at the fundamental frequency. A model based on the stability analysis and experimental measurements is employed to demonstrate that the spanwise deformations of rollers are produced due to a superposition of normal and oblique instability modes initiating upstream of separation. The degree of the initial spanwise deformations is shown to depend on the relative amplitude of the dominant normal and oblique waves. This is confirmed by forcing the normal mode through a controlled impulsive perturbation introduced by a spanwise invariant dielectric-barrier-discharge plasma actuator, resulting in the formation of spanwise coherent vortices. The findings elucidate the link between important features in the bubble shedding dynamics and stability characteristics and provide further clarification on the differences in the development of coherent structures seen in recent experiments. Moreover, the results present a handle on the development of effective control strategies that can be used to either promote or suppress shedding in separation bubbles, which is of interest for system performance improvement and control of aeroacoustic emissions in relevant applications.

Normal-Mode Splitting in a Weakly Coupled Optomechanical System

Abstract: Normal-mode splitting is the most evident signature of strong coupling between two interacting subsystems. It occurs when two subsystems exchange energy between themselves faster than they dissipate it to the environment. Here we experimentally show that a weakly coupled optomechanical system at room temperature can manifest normal-mode splitting when the pump field fluctuations are antisquashed by a phase-sensitive feedback loop operating close to its instability threshold. Under these conditions the optical cavity exhibits an effectively reduced decay rate, so that the system is effectively promoted to the strong coupling regime.

Nonlinear free and forced vibration analyses of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section

Abstract: Nonlinear free and forced vibrations of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section are investigated. The beam has immovable, namely clamped-clamped and pinned-pinned boundary conditions, which leads to midplane stretching in the course of vibrations. Nonlinearities occur in the system due to this stretching. Damping and forcing terms are included after nondimensionalization. The equations are solved approximately using perturbation method and mode shapes by differential quadrature method. In the linear order natural frequencies and mode shapes are computed. In the nonlinear order, some corrections arise to the linear problem; the effect of these nonlinear correction terms on natural frequency is examined and frequency –response curves are drawn to show the unstable regions. In order to confirm the validity, our results are compared with others available in literature.

H-fractal seismic metamaterial with broadband low-frequency bandgaps

Abstract: The application of metamaterial in civil engineering to achieve isolation of a building by controlling the propagation of seismic waves is a substantial challenge because seismic waves, a superposition of longitudinal and shear waves, are more complex than electromagnetic and acoustic waves. In this paper, we design a broadband seismic metamaterial based on H-shaped fractal pillars and report numerical simulation of band structures for seismic surface waves propagating. Comparative study on the band structures of H-fractal seismic metamaterials with different levels shows that a new level of fractal structure creates new band gap, widens the total band gaps and shifts the same band gap towards lower frequencies. Moreover, the vibration modes for H-fractal seismic metamaterials are computed and analyzed to clarify the mechanism of widening band gaps. A numerical investigation of seismic surface waves propagation on a 2D array of fractal unit cells on the surface of semi-infinite substrate is proposed to show the efficiency of earthquake shielding in multiple complete band gaps.

Simplified approach to the mixed time-averaging semiclassical initial value representation for the calculation of dense vibrational spectra.

Abstract: We present and test an approximate method for the semiclassical calculation of vibrational spectra. The approach is based on the mixed time-averaging semiclassical initial value representation method, which is simplified to a form that contains a filter to remove contributions from approximately harmonic environmental degrees of freedom. This filter comes at no additional numerical cost, and it has no negative effect on the accuracy of peaks from the anharmonic system of interest. The method is successfully tested for a model Hamiltonian and then applied to the study of the frequency shift of iodine in a krypton matrix. Using a hierarchic model with up to 108 normal modes included in the calculation, we show how the dynamical interaction between iodine and krypton yields results for the lowest excited iodine peaks that reproduce experimental findings to a high degree of accuracy.

Dynamically encircling an exceptional point in anti-PT-symmetric systems: asymmetric mode switching for symmetry-broken states

Abstract: Dynamically encircling an exceptional point (EP) in parity-time (PT) symmetric systems shows an interesting chiral dynamics, leading to asymmetric mode switching in which the output modes are different when the encircling direction is reversed. Here we show that the dynamical encircling of an EP in anti-PT-symmetric systems can also result in chiral dynamics if the starting/end point lies in the PT-broken phase, in contrast to PT-symmetric systems where chiral dynamics emerges if the starting/end point lies in the PT-unbroken phase. For many applications, such as signal processing using waveguides, the asymmetric mode switching of symmetry-broken modes in anti-PT-symmetric systems is more useful since each eigenmode is localized in one waveguide only. We develop an analytic theory for anti-PT-symmetric chiral dynamics and perform experiments using three waveguides to demonstrate the asymmetric mode switching. The new wave-manipulation phenomena observable in anti-PT-symmetric systems may pave the way towards designing on-chip optical systems with novel functionalities.

Bifurcation Analysis for Dust-Acoustic Waves in a Four-Component Plasma Including Warm Ions

Abstract: Investigation of linear dust-acoustic (DA) waves was analyzed in a system of collisionless, dissipative, and unmagnetized four-component dusty plasma consisting of cold positively and negatively charged particles of dust, with ions and electrons are of the Boltzmann distribution. The compatibility condition is obtained by using the normal mode analysis. The Korteweg de Vries–Burgers (KdV–Burgers) equation is obtained when the plasma system is nonlinearly analyzed by the reductive perturbation method. To study the nonlinear waves, we obtain some interesting physical solutions. These solutions are in the form of soliton, a combination between a shock and a soliton, and finally monotonic and oscillatory shock waves. Graphical illustration for these solutions was presented. The characteristics of the DA solitary and shock waves are significantly modified by the presence of positive and negative dust ions, the ratio of the ion to electron temperatures, and it is also found that the basic features are affected by the dust kinematic viscosity. The planar dynamical systems bifurcation theory, which was used to establish the existence of solitary wave solutions and periodic traveling wave solutions, has been established. Accordingly, the phase portrait topology and the potential diagram are illustrated for the KdV–Burgers equation. As a result of different phase orbits, there is an advantage to predict different classes of traveling wave solutions. The electric field is determined. Generalization of the obtained results in this paper can be used to investigate the nature of plasma waves in both laboratory and space.

The modeling of the absorption lineshape for embedded molecules through a polarizable QM/MM approach

Abstract: We present a computational strategy to simulate the absorption lineshape of a molecule embedded in a complex environment by using a polarizable QM/MM approach. This strategy is presented in two alternative formulations, one based on a molecular dynamics simulation of the structural fluctuations of the system and the other using normal modes and harmonic frequencies calculated on optimized geometries. The comparison for the case of a chromophore within a strongly inhomogeneous and structured environment, namely the intercalation pocket of DNA, shows that the MD-based approach is able to reproduce the experimental spectral bandshape. In contrast, the static approach overestimates the vibronic coupling, resulting in a much broader band.

Out-of-Equilibrium Collective Oscillation as Phonon Condensation in a Model Protein

Abstract: We describe the activation of out-of-equilibrium collective oscillations of a macromolecule as a classical phonon condensation phenomenon. If a macromolecule is modeled as an open system-that is, it is subjected to an external energy supply and is in contact with a thermal bath to dissipate the excess energy-the internal nonlinear couplings among the normal modes make the system undergo a nonequilibrium phase transition when the energy input rate exceeds a threshold value. This transition takes place between a state where the energy is incoherently distributed among the normal modes and a state where the input energy is channeled into the lowest-frequency mode entailing a coherent oscillation of the entire molecule. The model put forward in the present work is derived as the classical counterpart of a quantum model proposed a long time ago by Frohlich in an attempt to explain the huge speed of enzymatic reactions. We show that such a phenomenon is actually possible. Two different and complementary THz near-field spectroscopic techniques-a plasmonic rectenna and a microwire near-field probe-have been used in two different labs to eliminate artifacts. By considering an aqueous solution of a model protein, the bovine serum albumin, we find that this protein displays a remarkable absorption feature around 0.314 THz, when driven in a stationary out-of-thermal equilibrium state by means of optical pumping. The experimental outcomes are in very good qualitative agreement with the theory developed in the first part of the paper and in excellent quantitative agreement with the theoretical result, allowing us to identify the observed spectral feature with a collective oscillation of the entire molecule.

Modeling and dynamic analysis of bolted joined cylindrical shell

Abstract: Based on Sanders shell theory, modeling and dynamic analysis of bolted joined cylindrical shell were studied in this paper. When subjected to external excitations, contact state such as stick, slip and separation may occur at those locations of bolts. Considering these three contact states, an analytical model of cylindrical shell with a piecewise-linear boundary was established for the bolted joined cylindrical shell. First, the model was verified by the simplified line system, and the effects of stiffness in connecting interface and the number of bolts on natural frequency and mode shape were investigated. Then, through the response under instantaneous excitation, damping characteristic of the system was proved which is caused by the friction model. Last, the effects of external load frequency, response location, excitation amplitude and connecting parameters including stiffness and preload were numerically investigated and fully explained by 3-D frequency spectrum. The results indicated that periodic motion, times periodic motion and even chaotic motion were observed based on different parameters.

Anharmonic vibrational eigenfunctions and infrared spectra from semiclassical molecular dynamics

Abstract: We describe a new approach based on semiclassical molecular dynamics that allows simulating infrared absorption or emission spectra of molecular systems with inclusion of anharmonic intensities. This is achieved from semiclassical power spectra by computing first the vibrational eigenfunctions as a linear combination of harmonic states, and then the oscillator strengths associated with the vibrational transitions. We test the approach against a 1D Morse potential and apply it to the water molecule with results in excellent agreement with discrete variable representation quantum benchmarks. The method does not require any grid calculations, and it is directly extendable to high dimensional systems. The usual exponential scaling of the basis set size with the dimensionality of the system can be avoided by means of an appropriate truncation scheme. Furthermore, the approach has the advantage to provide IR spectra beyond the harmonic approximation without losing the possibility of an intuitive assignment of absorption peaks in terms of normal modes of vibration.

Saturation scalings of toroidal ion temperature gradient turbulence

Abstract: The emerging understanding of instability-driven plasma-turbulence saturation in terms of energy transfer to stable modes in the same scale range as the instability is employed to derive a saturation theory for the toroidal branch of ion temperature gradient turbulence that provides the scaling of turbulence and zonal flow levels for all physical parameters. The theory is based on the eigenmode decomposition of a nonlinear fluid model, which is subjected to a statistical closure and simplified via an ordering expansion consistent with zonal-flow catalyzed energy transfer from the unstable mode to the stable mode at large scale. Solution of the closed energy balance equations yields a turbulence level that is proportional to the ratio of the zonal flow damping rate and the inverse of the triplet correlation time of the zonal-flow catalyzed wavenumber triplet interaction. The zonal flow energy is proportional to the ratio of the growth rate and the inverse triplet correlation time. The saturation scalings a...

Theoretical Analysis of a 750-nm Bandwidth Hollow-Core Ring Photonic Crystal Fiber With a Graded Structure for Transporting 38 Orbital Angular Momentum Modes

Abstract: In this paper, a novel hollow-core ring photonic crystal fiber (HR-PCF) is proposed based on As2S3. It supports the transmission of up to 38 orbital angular momentum (OAM) modes. It is composed of a concentric ring cladding of air holes gradually increasing in diameter. In addition, the center also has a large circular air hole. A numerical simulation is accomplished using the finite-element method. Different geometrical parameters of the proposed HR-PCF include the number of air hole rings in the cladding and the background material. These parameters are varied to determine the optimal structure. The properties of the synthesized OAM vector modes are simulated and analyzed systematically and theoretically. Through the simulation of different parameters, we show that the optical fiber structure based on a three-ring cladding and As2S3 material can support 38 OAM modes. This configuration also has better eigenmode characteristics, such as the effective refractive index difference between vector modes with the same topological charge number. This difference can exceed 10−4, preventing these modes from coupling to linear polarization modes. In addition, the vector mode dispersion curve becomes smoother with increasing wavelength, and the confinement loss remains low, ranging from 10−10–10−9dB/m. Moreover, we also discuss effective mode area and nonlinear coefficients and their applications. We also investigated that various effects on the dispersions by details of the proposed HR-PCF, such as air hole spacing between adjacent rings and the diameter of the center circular air hole. This system offers some promising applications for short-distance, high-volume communications due to the increased number of OAM transfer modes.