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A method for geometric correction data calculation is based on decomposition of image distortions into nominal distortions and perturbations, caused by deviations from the nominal spacecraft motion and sensor pointing. The maximal errors of the method are of the order of 5 m, and the average errors are less than 0.6 m (sigma).
We report the main features of a new general implementation of the Gaussian Multi-Configuration Time-Dependent Hartree model. The code allows effective computations of time-dependent phenomena, including calculation of vibronic spectra (in one or more electronic states), relative state populations, etc. Moreover, by expressing the Dirac-Frenkel variational principle in terms of an effective Hamiltonian, we are able to provide a new reliable estimate of the representation error. After validating the code on simple one-dimensional systems, we analyze the harmonic and anharmonic vibrational spectra of water and glycine showing that reliable and converged energy levels can be obtained with reasonable computing resources. The data obtained on water and glycine are compared with results of previous calculations using the vibrational second-order perturbation theory method. Additional features and perspectives are also shortly discussed.
We present a near-linear scaling formulation of the explicitly correlated coupled-cluster singles and doubles with the perturbative triples method [CCSD(T)F12¯] for high-spin states of open-shell species. The approach is based on the conventional open-shell CCSD formalism [M. Saitow et al., J. Chem. Phys. 146, 164105 (2017)] utilizing the domain local pair-natural orbitals (DLPNO) framework. The use of spin-independent set of pair-natural orbitals ensures exact agreement with the closed-shell formalism reported previously, with only marginally impact on the cost (e.g., the open-shell formalism is only 1.5 times slower than the closed-shell counterpart for the C160H322 n-alkane, with the measured size complexity of ≈1.2). Evaluation of coupled-cluster energies near the complete-basis-set (CBS) limit for open-shell systems with more than 550 atoms and 5000 basis functions is feasible on a single multi-core computer in less than 3 days. The aug-cc-pVTZ DLPNO-CCSD(T)F12¯ contribution to the heat of formation for the 50 largest molecules among the 348 core combustion species benchmark set [J. Klippenstein et al., J. Phys. Chem. A 121, 6580–6602 (2017)] had root-mean-square deviation (RMSD) from the extrapolated CBS CCSD(T) reference values of 0.3 kcal/mol. For a more challenging set of 50 reactions involving small closed- and open-shell molecules [G. Knizia et al., J. Chem. Phys. 130, 054104 (2009)], the aug-cc-pVQ(+d)Z DLPNO-CCSD(T)F12¯ yielded a RMSD of ∼0.4 kcal/mol with respect to the CBS CCSD(T) estimate.
The paper deals with extending the Lomov regularization method to classes of singularly perturbed Fredholm-type integro-differential systems, which have not so far been studied. In these the limiting operator is discretely noninvertible. Such systems are commonly known as problems with unstable spectrum. Separating out the essential singularities in the solutions to these problems presents great difficulties. The principal one is to give an adequate description of the singularities induced by 'instability points' of the spectrum. A methodology for separating singularities by using normal forms is developed. It is applied to the above type of systems and is substantiated in these systems. Bibliography: 10 titles.
Semi-analytical methods, based on Eulerian perturbation theory, are a promising tool to follow the time evolution of cosmological perturbations at small redshifts and at mildly nonlinear scales. All these schemes are based on two approximations: the existence of a smoothing scale and the single-stream approximation, where velocity dispersion of the dark matter fluid, as well as higher moments of the particle distributions, are neglected. Despite being widely recognized, these two assumptions are, in principle, incompatible, since any finite smoothing scale gives rise to velocity dispersion and higher moments at larger scales. We describe a new approach to perturbation theory, where the Vlasov and fluid equations are derived in presence of a finite coarse-graining scale: this allows a clear separation between long and short distance modes and leads to a hybrid approach where the former are treated perturbatively and the effect of the latter is encoded in external source terms for velocity, velocity dispersion, and all the higher order moments, which can be computed from N-body simulations. We apply the coarse-grained perturbation theory to the computation of the power spectrum and the cross-spectrum between density and velocity dispersion, and compare the results with N-body simulations, finding good agreement.
A method for computing geometric perturbations for probabilistic analysis. The probabilistic analysis is based on finite element modeling, in which uncertainties in the modeled system are represented by changes in the nominal geometry of the model, referred to as "perturbations". These changes are accomplished using displacement vectors, which are computed for each node of a region of interest and are based on mean-value coordinate calculations.
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
Variational approximation for ground state of perturbed Schroedinger equation with single variable wave function
Linear perturbation model used for Monte Carlo simulation of midcourse guidance problem
Recent advances in computational structural and fluid dynamics are discussed in reviews and reports. Topics addressed include fluid-structure interaction and aeroelasticity, CFD techniques for reacting flows, micromechanics, stability and eigenproblems, probabilistic methods and chaotic dynamics, and perturbation and spectral methods. Consideration is given to finite-element, finite-volume, and boundary-element methods; adaptive methods; parallel processing machines and applications; and visualization, mesh generation, and AI interfaces.
NASA's Gateway program will build a crew-tended station in an Earth-Moon Near Rectilinear Halo Orbit (NRHO) to support deep space missions to the lunar surface and heliocentric space. The station in the NRHO will be visited by crewed vehicles including lunar landers that are high mass relative to Gateway. Docking events with large vehicles induce significant thruster plume and docking contact velocity perturbations. Crewed vehicles induce significant venting perturbations that can stress the navigation filter's ability to remain converged about an estimated state. The torques that arise from venting and lunar gravity gradient require reaction control system (RCS) thruster intervention, which themselves induce a velocity perturbation. The best method to model RCS thruster perturbations is currently in development. This paper simulates different RCS perturbation models, schedules, and an increasing magnitude to investigate the navigation sensitivity to different RCS perturbation models. From the RCS perturbation models simulated, a worst-case scenario is chosen for further scrutiny. The navigation filter is further tuned to handle the most disruptive perturbation modeling and the resulting performance is analyzed.
Purpose: Small-field dosimetry is challenging due to charged-particle disequilibrium, source occlusion and more importantly finite size of detectors. IAEA/AAPM has published approach to convert detector readings to dose by k factor. Manufacturers have been trying to provide various types of micro-detectors that could be used in small fields. However k factors depends on detector perturbations and are derived using Monte Carlo simulation. PTW has introduced a microDiamond for small-field dosimetry. An experimental approach is presented to derive the k factor for this detector. Methods: PTW microDiamond is a small volume detector with 1.1 mm radius and 1.0 micron thick synthetic diamond. Output factors were measured from 1×1cm2 to 12×12 cm2 on a Varian machine at various depths using various micro-detectors with published k factors. Dose is calculated as reading * K. Assuming k factor is accurate, output factor should be identical with every micro-detectors. Hence published k values (Francescon et al Med Phys 35, 504-513,2008) were used to covert readings and then output factors were computed. Based on the converged curve from other detectors, k factor for microDiamond was computed versus field size. Results: Traditional output factors as ratio of readings normalized to 10×10 cm2 differ significantly for micro-detectors for fields smaller than 3×3 cm2 which are now being used extensively. When readings are converted to dose, the output factor is independent of detector. Based on this method, k factor for microDiamond was estimated to be nearly constant 0.993±0.007 over varied field sizes. Conclusion: Our method provides a unique opportunity to determine the k factor for any unknown detector. It is shown that even though k factor depends on machine type due to focal spot, however for fields ≥1×1 cm2 this method provides accurate evaluation of k factor. Additionally microDiamond could be used with assumption that k factor is nearly unity.
An alternative method of calculation of dense plasma effects on exchange-energy shifts {Delta}E{sub x} of highly charged ions is proposed which results in closed expressions for any plasma or perturbation potential. The method is based on a perturbation theory expansion for the inner atomic potential produced by charged plasma particles employing the Coulomb Green function method. This approach allows us to obtain analytic expressions and scaling laws with respect to the electron temperature T, density n{sub e}, and nuclear charge Z. To demonstrate the power of the present method, two specific models were considered in detail: the ion sphere model (ISM) and the Debye screening model (DSM). We demonstrate that analytical expressions can be obtained even for the finite temperature ISM. Calculations have been carried out for the singlet 1s2p{sup 1} P{sub 1} and triplet 1s2p{sup 3} P{sub 1} configurations of He-like ions with charge Z that can be observed in dense plasmas via the He-like resonance and intercombination lines. Finally we discuss recently available purely numerical calculations and experimental data.
We derive the 'separate universe' method for the inflationary bispectrum, beginning directly from a field-theory calculation. We work to tree-level in quantum effects but to all orders in the slow-roll expansion, with masses accommodated perturbatively. Our method provides a systematic basis to account for novel sources of time-dependence in inflationary correlation functions, and has immediate applications. First, we use our result to obtain the correct matching prescription between the 'quantum' and 'classical' parts of the separate universe computation. Second, we elaborate on the application of this method in situations where its validity is not clear. As a by-product of our calculation we give the leading slow-roll corrections to the three-point function of field fluctuations on spatially flat hypersurfaces in a canonical, multiple-field model.
This paper examines the problem of real-time optimization of networked systems and develops online algorithms that steer the system towards the optimal trajectory without explicit knowledge of the system model. The problem is modeled as a dynamic optimization problem with time-varying performance objectives and engineering constraints. The design of the algorithms leverages the online zero-order primal-dual projected-gradient method. In particular, the primal step that involves the gradient of the objective function (and hence requires a networked systems model) is replaced by its zero-order approximation with two function evaluations using a deterministic perturbation signal. The evaluations are performed using the measurements of the system output, hence giving rise to a feedback interconnection, with the optimization algorithm serving as a feedback controller. The paper provides some insights on the stability and tracking properties of this interconnection. Finally, the paper applies this methodology to a real-time optimal power flow problem in power systems, and shows its efficacy on the IEEE 37-node distribution test feeder for reference power tracking and voltage regulation.
Using perturbation theory methods and a variational method, we have calculated the energy of a twodimensional helium atom in its lower excited states, this energy showing itself to be practically independent of the specific characteristics of these excited states; this, together with the known value of the energy in the ground state, found earlier by one of the authors, presents the fundamental possibility of determining the frequencies of the main spectral lines of such an atom, which can be checked experimentally.
In this paper, we propose a scheme to generate highly entangled Dicke-state in circuit quantum electrodynamics (QED) system, where the quantum tunneling between local potential wells is manipulated by using Lyapunov control. We employ two different types of control Hamiltonians to generate Dicke-state: one is the local Hamiltonian that requires to individually modulate control fields; the other is the global Hamiltonian (global control) where the control fields can be modulated uniformly. Furthermore, the target Dicke-state can be obtained with arbitrary initial states when applying the average-value-based Lyapunov control. Numerical simulations demonstrate that the generation of Dicke-state is remarkably accelerated by using bang–bang Lyapunov control, and the multipartite Dicke-state is implemented at nanoseconds without accurately controlling the evolution time in ultrastrong coupling regime. In addition, the scheme is robust against some kinds of uncertainties and perturbations.
A stochastic algorithm is proposed that can compute the basis-set-incompleteness correction to the second-order many-body perturbation (MP2) energy of a polyatomic molecule. It evaluates the sum of two-, three-, and four-electron integrals over an explicit function of electron-electron distances by a Monte Carlo (MC) integration at an operation cost per MC step increasing only quadratically with size. The method can reproduce the corrections to the MP2/cc-pVTZ energies of H{sub 2}O, CH{sub 4}, and C{sub 6}H{sub 6} within a few mE{sub h} after several million MC steps. It circumvents the resolution-of-the-identity approximation to the nonfactorable three-electron integrals usually necessary in the conventional explicitly correlated (R12 or F12) methods.