Eigenvalues Of Modes Research Articles

A New Code for Relativistic Hydrodynamics and its Application to FR II Radio Jets

AbstractTo study the dynamics of relativistic flows in astrophysical objects such as radio jets, we have developed a new special relativistic hydrodynamic (RHD) code based on the weighted essentially non-oscillatory (WENO) scheme, a high-order finite difference scheme. The code includes different WENO versions, and high-order time integration methods such as the 4th-order accurate Runge-Kutta (RK4) and strong stability preserving RK (SSPRK), as well as the equations of state (EOSs) that closely approximate the EOS of the single-component perfect gas in relativistic regime. Additionally, it is optimized for the reproduction of complex structures in multi-dimensional flows, and implements a modification of eigenvalues for the acoustic modes to effectively control carbuncle instability. As the first application of the code, we have simulated ultra-relativistic jets of FR II radio galaxies, and studied the nonlinear flow structures, such as shocks, velocity shear, and turbulence, through large-scale.

An optimal modal coordination strategy based on modal superposition theory to mitigate low frequency oscillation in FCWG penetrated power systems

Full converter-based wind power generation (FCWG, e.g. permanent magnet synchronous generator (PMSG)) becomes prevalent in power electronics dominated multi-machine power system (MMPS). With flexibly modified FCWG oscillation modes (FOMs), FCWG has the potential to actuate conducive dynamic interactions with electromechanical oscillation modes (EOMs) of MMPS. In this paper, a mathematical model of FCWG and MMPS is firstly derived to examine the dynamic interactions. Then a novel modal superposition theory is proposed to classify the modal interactions between FOMs and EOMs in the complex plane for the first time. The modal coupling mechanism is graphically visualized to investigate the dynamic interactions, and the eigenvalue shift index is proposed to quantify the dynamic interaction impact on critical EOM. Based on different manifestos in modal coupling mechanism and eigenvalue shift index, a novel methodology to optimize the dynamic interactions between the FCWG and MMPS is designed within the existing control frame. The optimized dynamic interactions (i.e. modal counteraction) can significantly enhance the LFO stability of MMPS, effectiveness of which is verified by both modal analysis and time domain simulations.

Analysis of scattering by finite sonic crystals in free field with infinite elements and normal modes

Acoustic exterior problems are in this paper solved numerically using the Astley-Leis infinite element method (IFEM). Normal modes can be determined thanks to the frequency independence of the system matrices. Convergence properties of the harmonic sound pressure solution as well as of normal mode eigenvalues are investigated for two-dimensional elliptical computational domains to estimate the essential requirements of accuracy. A relationship between the half-axis ratio of the ellipses and the eigenvalues is identified. By solving half-space problems, symmetry of the computational domains is utilized, which is shown for the first time for frequency-independent normal modes in exterior acoustics. This paper discusses applicability of the modes in the example of sonic crystals—periodic arrays of scatterers, in this context denoted as acoustic meta-atoms—that have recently attracted attention for their possible use as noise barriers. It can be shown that the sound-insulating effect of finite sonic crystals and individual meta-atoms in the free field can be related to normal modes in exterior acoustics. With the help of this approach, the absorption by Helmholtz resonators and due to a boundary admittance inside are studied. This work provides a new point of view and physical insights into the effects and underlying physics of sound insulation by finite sonic crystals and acoustic meta-atoms in free field. Although it is not the intention of this article to optimize the arrays, the method of normal modes in exterior acoustics is presented as an appropriate and novel tool for their dimensioning and design.

Payload Parameter Identification of a Flexible Space Manipulator System via Complex Eigenvalue Estimation

Manipulator systems are widely used in payload capture and movement in the ground/space operation due to their dexterous manipulation capability. In this study, a method for identifying the payload parameters of a flexible space manipulator using the estimated system of complex eigenvalue matrix is proposed. The original nonlinear dynamic model of the manipulator is linearized at a selected working point. Subsequently, the system state-space model and corresponding complex eigenvalue parameters are determined by the observer/Kalman filter identification algorithm using the torque input signal of the motor and the vibration output signals of the link. Therefore, the inertia parameters of the payload, that is, the mass and the moment of inertia, can be derived from the identified complex eigenvalue system and mode shapes by solving a least-squares problem. In numerical simulations, the proposed parameter identification method is implemented and compared with the classical recursive least-squares and affine projection sign algorithms. Numerical results demonstrate that the proposed method can effectively estimate the payload parameters with satisfactory accuracy.

Vibration analysis of a free moving thin plate with fully covered active constrained layer damping treatment

A comprehensive dynamic model for a free moving thin plate with fully covered active constrained layer damping (ACLD) treatment is developed. The discrete equations of motion of the moving ACLD plate are derived by using Ritz method and Lagrange’s equations. Free vibration analysis of the composite plate undergoing large rotational or translational motions are performed by solving the complex modal eigenvalue problem of the system in open-loop and closed-loop cases. Interesting frequency curve veering, mode shape switching as well as damping ratio jumping phenomena are observed and discussed for the plate rotating around two different axes. It is demonstrated that the flexible plate undergoing rigid motions can not only generate dynamic stiffening effect but also dynamic softening effect. Effects of parameters such as angular velocity, acceleration, and control gain on the modal and damping characteristics of the ACLD plate are also investigated.

Slender-body theory for plasmonic resonance.

We develop a slender-body theory for plasmonic resonance of slender metallic nanoparticles, focusing on a general class of axisymmetric geometries with locally paraboloidal tips. We adopt a modal approach where one first solves the plasmonic eigenvalue problem, a geometric spectral problem which governs the surface-plasmon modes of the particle; then, the latter modes are used, in conjunction with spectral-decomposition, to analyse localized-surface-plasmon resonance in the quasi-static limit. We show that the permittivity eigenvalues of the axisymmetric modes are strongly singular in the slenderness parameter, implying widely tunable, high-quality-factor, resonances in the near-infrared regime. For that family of modes, we use matched asymptotics to derive an effective eigenvalue problem, a singular non-local Sturm-Liouville problem, where the lumped one-dimensional eigenfunctions represent axial voltage profiles (or charge line densities). We solve the effective eigenvalue problem in closed form for a prolate spheroid and numerically, by expanding the eigenfunctions in Legendre polynomials, for arbitrarily shaped particles. We apply the theory to plane-wave illumination in order to elucidate the excitation of multiple resonances in the case of non-spheroidal particles.

Estimation of Parameters of a Dynamic Generator Model From Modal PMU Measurements

This paper introduces a novel methodology of parameter estimation for the power system models using the values of modes and mode shapes extracted from the phasor measurement unit (PMU) measurements. The main idea is to force the state matrix A, which is a function of the unknown parameters, to satisfy as closely as possible the eigenequation linking the state matrix, the modes (eigenvalues of A) and the mode shapes (eigenvectors of A). The methodology is derived and analyzed for a general case of any model's parameters. The applications to the estimation of generator inertia M coefficients are then discussed in detail. The proposed methodology has been tested using two different system models. The results confirm the efficiency of estimating M using the PMU data, while the estimation of D is shown to be very sensitive to the measurement noise.

A pseudospectral approach applicable for time integration of linearized N‐S operator that removes pole singularity and physically spurious eigenmodes

SummaryThis paper addresses a modified singularity removal technique for the eigenvalue or optimal mode problems in pipe flow using a pseudospectral method. The current approach results in the linear stability operator to be devoid of any unstable physically spurious modes, and thus, it provides higher numerical stability during time‐based integration. The correctness of the numerical operator is established by calculating the known eigenvalues of pipe Poiseuille flow. Subsequently, the optimal modes are determined with Farrell's approach and compared with the existing literature. The usefulness of this approach is further demonstrated in the time‐based numerical integration of the linearized Navier‐Stokes operator for the adjoint method–based optimal mode determination. The numerical scheme is implemented with the radial velocity‐radial vorticity formulation. Even number of Chebyshev‐Lobatto grid points are distributed over the domain r∈[−1,1] omitting the centerline, which also efficiently provides higher resolution near the wall boundary. The boundary conditions are imposed with homogeneous wall boundary conditions, whereas the analytic nature of a proper set of base functions enforces correct centerline conditions. The resulting redundancy introduced in the process is eliminated with the proper usage of parity.

Stability analysis of bicycles by means of analytical models with increasing complexity

Abstract. The basic Whipple-Carvallo bicycle model for the study of stability takes into account only geometric and mass properties. Analytical bicycle models of increasing complexity are now available, they consider frame compliance, tire properties, and rider posture. From the point of view of the designer, it is important to know if geometric and mass properties affect the stability of an actual bicycle as they affect the stability of a simple bicycle model. This paper addresses this problem in a numeric way by evaluating stability indices from the real parts of the eigenvalues of the bicycle's modes (i.e., weave, capsize, wobble) in a range of forward speeds typical of city bicycles. The sensitivity indices and correlation coefficients between the main geometric and mass properties of the bicycle and the stability indices are calculated by means of bicycle models of increasing complexity. Results show that the simpler models correctly predict the effect of most of geometric and mass properties on the stability of the single modes of the bicycle. Nevertheless, when the global stability indices of the bicycle are considered, often the simpler models fail their prediction. This phenomenon takes place because with the basic model some design parameters have opposite effects on the stability of weave and capsize, but, when tire sliding is included, the capsize mode is always stable and low speed stability is chiefly determined by weave stability.

Analytic solution to a waveguide featuring caustics and shadow zones

Exact solutions to waveguides are useful tools for validating numerical waveguide models. In this paper, a modal solution to an unbounded waveguide with a range-independent but depth-dependent profile is described. The sound speed profile utilized is a symmetric, piecewise n2-linear profile matched above and below to a homogenous half-layer with density and sound speeds that prevent any reflections at the interface. In this environment, caustics and shadow zones are formed. A nearly exact solution to this environment could help improve other numerical methods' accuracy near caustics and shadow zones. In this mathematical analysis, both proper (trapped) and improper (leaky) modes are included. Arbitrarily high frequencies are permitted through the use of numerically well-conditioned approximations to Airy functions, particularly for the dispersion relations and mode-shape evaluations. The proper (real) and improper (complex) modal eigenvalues are found approximately, with root-finding algorithms used for eigenvalues near cut-off to improve the approximation. Mathematical details are presented along with a brief discussion of how well a few common numerical solvers agree with the analytic solution derived.

Edge and bulk dissipative solitons in modulated PT-symmetric waveguide arrays.

We address dissipative soliton formation in modulated parity-time (PT)-symmetric continuous waveguide arrays composed from waveguides with amplifying and absorbing sections, whose density gradually increases (due to decreasing waveguide separation) either towards the center of the array or towards its edges. In such a structure, the level of gain/loss at which PT-symmetry gets broken depends on the direction of increase of waveguide density. Breakup of PT-symmetry occurs when eigenvalues of modes localized in the region where waveguide density is largest collide and move into a complex plane. In this regime of broken symmetry, the inclusion of focusing Kerr-type nonlinearity of the material and weak two-photon absorption allows to arrest the growth of amplitude of amplified modes and may lead to the appearance of stable attractors either in the center or at the edge of the waveguide array, depending on the type of array modulation. Such solitons can be stable; they acquire specific triangular shapes and notably broaden with increase of gain/loss level. Our results illustrate how spatial array modulation that breaks PT-symmetry "locally" can be used to control the specific location of dissipative solitons forming in the array.

Identification of multiple eigenmode growth rates in DIII-D and EAST tokamak plasmas

The successful application of three-dimensional (3D) magnetohydrodynamic (MHD) spectroscopy in the stable DIII-D and EAST plasmas enables to directly extract the multi-mode plasma transfer function in tokamak experiments. The transfer function not only reveals the contribution of each dominant MHD eigenmode in the multi-model plasma response, but also quantifies the corresponding eigenvalue which is the critical stability index of MHD mode. The method performs the active detection of stable plasma by utilizing the upper and lower rows of internal coils to scan the frequency and poloidal spectrum of the applied 3D field, and reconstructing the multi-mode transfer functions model through the least square fitting of the plasma response measured by 3D-field magnetic sensors distributed at different poloidal locations. The results point to the potential development of an advanced strategy for tracking the plasma stability based on the extracted eigenvalues of stable modes. The improved understanding of the dominant eigenmodes’ behavior in multi-mode plasma response through transfer function can also help to optimize the applied 3D fields for the purposes, such as the type-I edge localized mode suppression and the core stability control in future fusion reactors.

A magneto – thermo-elastic problem for a half-space without energy dissipation subjected to rotation and gravity field

The prime objective of the present paper is to analyze the effects of the rotation, magnetic field and gravity in a thermo-elastic half-space containing heat source on the boundary of the half-space. The medium assumed under consideration is traction free, homogeneous, isotropic, as well as without energy dissipation. The normal mode analysis and eigenvalue approach technique are used to solve the resulting non-dimensional coupled equations. The comparisons for the physical quantities are established numerically and represented graphically in different cases with respect to the used effects. A comparative and remarkable study has been carried out through various graphs to deliberate the consequences of different parameter on the displacement components, stress components and temperature.

Impact of Integration on Straining Modes and Shear-Locking for Plane Stress Finite Elements

Stiffness matrix of the four-node quadrilateral plane stress element is decomposed into normal and shear components. A computer program is developed to obtain the straining modes using adequate and reduced integration. Then a solution for the problem of mixing straining modes is found. Accuracy of the computer program is validated by a closed-form stiffness matrix, derived for the plane rectangular as well as square element. It is shown that method of integration has no effect on the straining modes, but it influences the eigenvalues of the bending modes. This effect is intensified by increasing the element aspect ratio, confirming the occurrence of shear locking.

Further evidence that suicide risk is categorical: A taxometric analysis of data from an inpatient sample.

Recent research by Witte and colleagues (2017) revealed a taxonic structure for classifying suicide risk using a sample of predominantly military outpatients. The authors sought to replicate the Witte et al. (2017) findings using data from a sample of 2,385 psychiatric inpatients who completed measures of suicidal ideation and behavior upon admission to the hospital. The comparison curve fit index values for means above minus below a cut (.80), maximum eigenvalue (.71), and latent mode (.52) showed a similar taxonic structure (i.e., dichotomous rather than continuous). Consistent with Witte et al. (2017), differences between the taxon and complement groups were larger for variables conceptually directly related to suicide risk than to broader constructs such as hopelessness or depression. Support for this categorical distinction among a sample of long-term psychiatric inpatients, who are uniformly high in symptom severity, emphasizes the need for additional research on this high-risk group and development of further assessment methods. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Influence of Nonaxisymmetric Confinement on the Hydrodynamic Stability of Multinozzle Swirl Flows

Interaction between coherent flow oscillations and the premixed flame sheet in combustors can result in coherent unsteadiness in the global heat release response. These coherent flow oscillations can either be self-excited (e.g., the precessing vortex core) or result from the hydrodynamic response of the flow field to acoustic forcing. Recent work has focused on understanding the various instability modes and fundamental mechanisms that control hydrodynamic instability in single nozzle swirl flows. However, the effect of multiple closely spaced nozzles as well as the nonaxisymmetric nature of the confinement imposed by the combustor liner on swirl nozzle flows remains as yet unexplored. We study the influence of internozzle spacing and nonaxisymmetric confinement on the local temporal and spatiotemporal stability characteristics of multinozzle flows in this paper. The base flow model for the multinozzle case is constructed by superposing contributions from a base flow model for each individual nozzle. The influence of the flame is captured by specifying a spatially varying base flow density field. The nonaxisymmetric local stability problem is posed in terms of a parallel base flow with spatial variations in the two directions perpendicular to the streamwise direction. We investigate the case of a single nozzle and three nozzles arranged in a straight line within a rectangular combustor. The results show that geometric confinement imposed by the combustor walls has a quantitative impact on the eigenvalues of the hydrodynamic modes. Decreasing nozzle spacing for a given geometric confinement configuration makes the flow more unstable. The presence of an inner shear layer (ISL) stabilized flame results in an overall stabilization of the flow instability. We also discuss qualitatively, the underlying vorticity dynamics mechanisms that influence the characteristics of instability modes in triple nozzle flows.

Linear Stability of Moist Convecting Atmospheres. Part I: From Linear Response Functions to a Simple Model and Applications to Convectively Coupled Waves

Abstract A procedure is presented to systematically construct simple models for the linear stability of moist convecting atmospheres. First, linear response functions of a cumulus ensemble constructed from cloud-system-resolving models are coupled with matrices expressing two-dimensional large-scale linear wave dynamics. For a radiative–convective equilibrium reference state, this model gives two branches of unstable modes: a propagating convectively coupled wave branch and a stationary branch related to storage of column-integrated moist static energy (MSE). The stationary branch is unstable only when radiative feedback is included, while the convectively coupled wave branch is less affected by radiative feedback. With a modular order-reduction procedure from control theory, the linear-response-function-based model is reduced to a system of six ordinary differential equations while still capturing the essential features of the unstable modes (eigenvalues and structures). The six-dimensional system is then split into a slow and a fast manifold. The slow manifold (again, reflecting column MSE storage) is essential for the stationary mode but not for the convectively coupled waves. The fast manifold is then transformed into a form similar to that of prior simple models of convectively coupled waves, thus placing those models and the insights derived from them on a firmer footing. The procedure also better quantifies the parameters of such simple models and allows the stability difference between different reference states to be better understood.

Synthesis of Im-Bessel correlated beams via coherent modes.

We present the first high-quality experimental realization of a random optical beam as a linear superposition of its coherent modes. The individual modes are generated by passing a laser beam through a phase-only spatial light modulator. A random stationary beam is obtained by using a temporally randomized sequence of its coherent modes, each contributing, on average, with a weight proportional to the corresponding mode eigenvalue. As an example, the new method is applied to a Im-Bessel correlated beam which was originally introduced in theory via the coherent mode decomposition, but could not have been experimentally generated so far by any other method.

Cuckoo Search Optimization Algorithm for Designing of a Multimachine Power System Stabilizer

In this paper, new metaheuristic technique cuckoo search optimization (CSO) is explored for an optimal and robust power system stabilizer (PSS) designing for multimachine power systems and performance is evaluated by comparing with well-established techniques, i.e., genetic algorithm (GA), particle swarm optimization (PSO), and new harmony search optimization (HSO). An eigenvalue-based multiobjective function is implemented for simultaneous control of damping factor and damping ratio to damp out low-frequency local and interarea modes of oscillations. The PSS parameters are so intended that unstable and/or lightly damped mode eigenvalues are shifted to a specified D-shape zone in the left half of the s-plane. The selected metaheuristic techniques GA, PSO, HSO, and CSO are used to obtain PSS parameters for 10-machines, 39-bus New England Power System and the controllers designed are named as GAPSS, PSOPSS, HSOPSS, and CSOPSS, respectively. The performance of all designed PSSs controllers is evaluated by eigenvalues analysis, nonlinear simulations, and performance indices for various operating conditions under different scenarios of severe disturbances and their comparative analysis is observed. The robustness of all designed PSSs controllers is observed by testing them on unseen operating conditions and results are compared for the same. The performance of CSOPSS is found to be better than other controllers designed.

Effect of higher harmonics in the area-ratio pulsed neutron source technique

The area-ratio pulsed neutron source technique, which can yield a subcriticality in dollar units, is given by Ap/Ad, the area ratio of the prompt neutron component to the delayed neutron component. In this paper, both components are reconstructed by the summation of the spatial harmonics that are obtained by solving the α–mode eigenvalue equations based on the neutron transport and diffusion theories. Monte Carlo simulations for the area-ratio method in a one-dimensional slab are performed. The reconstructed prompt and delayed components agree well with the simulation results. The areas Ap and Ad contain a higher harmonic effect, and the ratio Ap/Ad differs from the true subcriticality. The effect of the higher harmonics in Ap can be reduced by the extrapolated area-ratio method if the earlier period after the pulse generation is successfully excluded from the fitting period. However, there is no way to remove the effect of the higher harmonics from the delayed neutron component, but it alleviates itself because it is given by the subtraction of the prompt component from the total (delayed and prompt) component. The subcriticality in dollar units adjusted by the extrapolated area-ratio method is considerably improved compared with the unadjusted Ap/Ad. The improvement is remarkable for a near-critical system in which the denominator Ad is relatively large, and the effect of the higher harmonics in Ad is minor.