Modeling Adequacy of Droop-Controlled Grid-Forming Converters for Transient Studies: Singular Perturbation Analysis
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24 POWER TRANSMISSION AND DISTRIBUTION↗
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A perturbation analysis of existing resonant satellites
Perturbation analysis of existing resonant satellites
Douglas, B. C.↗
Smoothed perturbation analysis algorithms for estimating the derivatives of occupancy-related functions in serial queueing networks
The authors present smoothed perturbation analysis (SPA) estimators for the derivative of a number of occupancy-related functions in serial queuing networks with finite buffer spaces. The functions are the average number of customers at a network as seen by an arrival, the probability that a customer is blocked at a particular queue, and the probability that a customer leaves a queue empty. In all three cases, the variable is a parameter of the distribution of service times at one of the queues. The derivative estimators considered are very simple and flexible, and they easily lend themselves to analysis of unbiasedness. Unlike most of the established SPA estimators, the present ones are not based on the computation of hazard rates.
Wardi, Y.↗
Interlaminar stresses in composite laminates: A perturbation analysis
A general method of solution for an elastic balanced symmetric composite laminate subject to a uniaxial extension was developed based upon a perturbation analysis of a limiting free body containing an interfacial plane. The solution satisfies more physical requirements and boundary conditions than previous investigations, and predicts smooth continuous interlaminar stresses with no instabilities. It determines the finite maximum intensity for the interlaminar normal stress in all laminates, provides mathematical evidences for the singular stresses in angle-ply laminates, suggests the need for the experimental determination of an important problem parameter, and introduces a viable means for solving related problems of practical interest.
Hsu, P. W.↗
Nonequilibrium steady state and heat transport in nonlinear open quantum systems: Stochastic influence action and functional perturbative analysis
In this paper, we show that a nonequilibrium steady state (NESS) exists at late times in open quantum systems with weak nonlinearity by following its nonequilibrium dynamics with a perturbative analysis. We consider an oscillator chain containing three-types of anharmonicity: cubic α- and quartic β-type Fermi–Pasta–Ulam–Tsingou (FPUT) nearest-oscillator interactions and the on-site (pinned) Klein–Gordon (KG) quartic self-interaction. Assuming weak nonlinearity, we introduce a stochastic influence action approach to the problem and obtain the energy flows in different junctures across the chain. The formal results obtained here can be used for quantum transport problems in weakly nonlinear quantum systems. For α-type anharmonicity, we observe that the first-order corrections do not play any role in the thermal transport in the NESS of the configuration we considered. For KG and β-types anharmonicity, we work out explicitly the case of two weakly nonlinearly coupled oscillators, with results scalable to any number of oscillators. We examine the late-time energy flows from one thermal bath to the other via the coupled oscillators, and show that both the zeroth- and the first-order contributions of the energy flows become constant in time at late times, signaling the existence of a late-time NESS to first order in nonlinearity. Our perturbative calculations provide a measure of the strength of nonlinearity for nonlinear open quantum systems, which may help control the mesoscopic heat transport distinct from or close to linear transport. Furthermore, our results also give a benchmark for the numerical challenge of simulating heat transport. Our setup and predictions can be implemented and verified by investigating heat flow in an array of Josephson junctions in the limit of large Josephson energy with the platform of circuit QED.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Perturbation analysis of queueing systems with a time-varying arrival rate
The authors consider an M/G/1 queuing with a time-varying arrival rate. The objective is to obtain infinitesimal perturbation analysis (IPA) gradient estimates for various performance measures of interest with respect to certain system parameters. In particular, the authors consider the mean system time over n arrivals and an arrival rate alternating between two values. By choosing a convenient sample path representation of this system, they derive an unbiased IPA gradient estimator which, however, is not consistent, and investigate the nature of this problem.
Cassandras, Christos G.↗
Perturbation analysis of internal balancing for lightly damped mechanical systems with gyroscopic and circulatory forces
Approximate expressions are developed for internally balanced singular values corresponding to the modes of mechanical systems with gyroscopic forces, light damping, and small circulatory forces. A brief overview is first given of the balanced realization model reduction method, including a discussion of recent work. The models considered are defined, and a perturbation analysis is used to show that the modal representation becomes asymptotically balanced as damping reduces to zero. The approximate balanced singular values are calculated, and a simple example of a flexible, dual-spin spacecraft is given as an illustration of the results.
Blelloch, P. A.↗
Perturbative analysis of low-frequency instabilities in high-field ST40 experiments
Abstract Linear and nonlinear perturbative analyses of low-frequency instabilities are presented for ST40 spherical torus high field plasmas, with simultaneous neutral beam heating due to two tangential sources at 25 keV and 55 keV. Initial plasma profiles on which the TRANSP and NUBEAM codes were based were obtained using an integrated analysis of several diagnostics including line-of-sight integrated and volume average measurements, as well as limited profile information from a charge-exchange-recombination spectrometer. Magnetohydrodynamics (MHD) analysis using the NOVA/NOVA-K codes suggests that the modes in the experiments are core-localized n = 1 eigenmodes with mixed acoustic and electromagnetic Alfvénic polarization. The global transport combined with the perturbative mode analysis indicates that there is greater tendency for bursty chirping response as the level of background micro-turbulence decreases in time and those predictions are shown to be consistent with the experimental data. This finding is interpreted in terms of the suppression of coherent phase-space structures that support chirping when the resonant fast ion dynamics is dominated by frequent stochastic, orbit-decorrelating events.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Wind profile perturbation analysis for STS
Two case studies of the relationship between STS ascent structural loads and wind profile characteristics are described. In the first case study, a wind profile with relatively weak winds is used to demonstrate the importance of launch vehicle velocity relative to the air and its effect on loads. In the second study, a pair of wind profiles is used to show how the determination of load exceedances is strongly influenced by the wind load persistence allowances for the baseline and two day-of-launch (DOL) steering commands called I-LOADs. Characteristics of the wind profiles and associated trajectory variable and wind-sensitive load indicators are examined. Energy spectra of in-plane and out-of-plane wind component and a load indicator are presented. An analysis of load indicator sensitivity to wind perturbation energy in the 1600-6400 m wavelength band for baseline and DOL I-LOAD is described.
Adelfang, S. I.↗
Transonic perturbation analysis of wing-fuselage-nacelle-pylon configurations with powered jet exhausts
A transonic small perturbation method has been developed for the analysis of general wing-fuselage-nacelle-pylon configurations with powered jet exhausts. Finite difference successive line relaxation algorithm is used to solve the small disturbance potential equation in conservative form. The nacelle tangency condition and the jet exhaust plume contact conditions are fulfilled in a quasi-cylindrical fashion on a surface fitting the Cartesian grid. The pylon tangency condition is treated in a quasi-planar manner as for the wing. Viscous displacement effects on the wing are modeled by suitable shape changes including the placement of a viscous ramp at the base of the shock. Computed results of a transport configuration show satisfactory correlation with test data.
Wai, J. C.↗
A singular perturbation analysis of minimum time long range intercept
The application of singular perturbation theory for deriving algorithms suitable for on board real time computation of optimal aircraft trajectory control was investigated. Minimum time intercept in three dimensions was selected as a pilot problem formulation, and data for an early version F-4 aircraft was used to represent aircraft aerodynamic and propulsion characteristics. Results include the derivation of nonlinear, near optimal feedback control laws that are readily implementable in an aircraft flight computer, performance results for a variety of initial conditions (including optimal intercept at short ranges), and a point mass three dimensional simulation suitable for representing fighter aircraft under closed loop optimal control.
Calise, A.↗
Singular perturbation analysis of AOTV-related trajectory optimization problems
The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.
Calise, Anthony J.↗
Convergent perturbation analysis of intense coherent multiphoton interactions
Use has been made of flow graphs to deduce Feenberg perturbation expansions for radiative interactions. It is demonstrated that these expansions can in certain cases be summed to provide closed form expressions for the molecular response. In particular, it is shown that the coherent state response can be obtained by the summation of a continued fraction perturbation expansion for the harmonic oscillator. Anharmonicity in the lower levels is treated and its shown to introduce Rabi flopping identifiable with multiphoton transitions among isolated tightly coupled subsystems of levels. Relevance to laser induced multiphoton excitation and energy level shift calculations in the presence of a strong field are also discussed.
Gower, M. C.↗
Perturbation analysis and constants for the red system of the cyanide radical
CN radical red system molecular constants, considering degenerate perturbation effects in shifts between electronic states
Fay, T.↗
Small scale wind perturbation analysis for vertically rising launch vehicles
This paper discusses the determination of small-scale vertical wind spectra used with space flight and ballistic technology. In particular, Jimsphere, a precision balloon wind sensor with high radar reflectivity is considered. Gross wind velocity data is analyzed to subtract the steady-state wind and wind change-shear effects. A residue of small wind perturbations is left in the horizontal (scalar) along the vertical direction. An analysis leading to formulation of the covariance function with altitude is presented. The function is decoupled to yield an almost periodic representation of the vertical wind perturbations. Forcing functions are determined when the representation is coupled with the vehicle velocity characteristics.
Chenoweth, H. B.↗
A perturbation analysis of the propagation and instability of waves in ducts with varying cross sections
All publications and presented speeches are listed that discuss the various aspects of perturbed wave propagation and noise generation in ducts with varying cross sections.
Nayfeh, A. H.↗
Singular perturbation analysis of the atmospheric orbital plane change problem
A three-state model is presented for the aeroassisted orbital plane change problem. A further model order reduction to a single state model is examined using singular perturbation theory. The optimal solution for this single state model compares favorably with the exact numerical solution using a four-state model; however, a separate boundary layer solution is required to satisfy the terminal constraint on altitude. This, in general, involves the solution of a two-point boundary value problem, but for a two-state model. An approximation is introduced to obtain an analytical control solution for lift and bank angle. Included are numerical simulation results of a guidance law derived from this analysis, along with comparison to earlier work by other researchers.
Calise, A. J.↗
Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II: Perturbative analysis and all-loop resummation
We study mesonic line operators in Chern-Simons theories with bosonic or fermionic matter in the fundamental representation. In this paper, we elaborate on the classification and properties of these operators using all loop resummation of large N perturbation theory. We show that these theories possess two conformal line operators in the fundamental representation. One is a stable renormalization group fixed point, while the other is unstable. They satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two mesonic line operators. The boundary operators on which the lines can end are classified by their conformal dimension and transverse spin, which we compute explicitly at finite ’t Hooft coupling. We match the operators in the bosonic and fermionic theories. Finally, we extend our findings to the mass deformed theories and discover that the duality still holds true.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗