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At least 127 records · Page 7

Finite state modelling of unsteady aerodynamics and its application to a rotor dynamic problem

The paper presents a method for formulating finite state unsteady aerodynamic models in the time domain from frequency domain unsteady aerodynamics. The method is based on recognizing that the lift deficiency function represents an aerodynamic transfer function and utilizes the Bode plot technique, used in control systems engineering, to construct approximation to the lift deficiency function. Indicial response functions for both fixed wing and rotary wing applications are obtained, using these finite state unsteady aerodynamic models. It is shown that the rotary wing indicial response function is oscillatory and thus it is fundamentally different when compared to the fixed wing indicial response function which is nonoscillatory. Certain aspects of the finite state aerodynamic model are demonstrated by applying it to the flapping dynamics of an articulated helicopter rotor blade. The influence of unsteady aerodynamics on the damping characteristics of the rotor is examined. The same problem is also treated by using a different unsteady aerodynamic model, namely dynamic inflow. Based on a comparison of the results obtained with these two unsteady aerodynamic models, useful conclusions are drawn regarding some fundamental features of these theories.

Friedmann, P. P.↗

Green’s Function Perspective on the Nonlinear Density Response of Quantum Many-Body Systems

We derive equations of motion for higher order density response functions using the theory of thermodynamic Green’s functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin–Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures.

Density Functional Theory↗

Recent Developments in Tolerancing Methods for Imaging Spectrometers

We discuss detailed tolerancing methods developed for imaging spectrometers at NASA Jet Propulsion Laboratory, California Institute of Technology using the Earth Surface Mineral Dust Source Investigation (EMIT) imaging spectrometer as an illustrative example. We tolerance five metrics simultaneously: along-track response function, cross-track response function, spectral response function, spectral centroid uniformity, and spatial centroid uniformity. A method to calculate tolerancing sensitivities for each metric directly, a method to statistically combine Monte Carlo files from multiple tolerancing runs, and an example summary error budgets that communicate the key and driving tolerances for each metric are discussed. These methods facilitate rapid and semi-automated assessment of the predicted performance of imaging spectrometer systems from design through to assembly and launch life cycle, using metrics that are directly relevant to the extraction of accurate spectroscopic data from these instruments.

Mouroulis, Pantazis↗

Electrodynamic Shaker Capability Estimation Through Experimental Dynamic Substructuring [Thesis]

Electrodynamic shaker systems are an essential tool in shock and vibration testing of dynamic environments. However, the specific performance capability of these systems is difficult to characterize. The dynamics of the shaker itself, the device under test and the specific test configuration used all couple to create a dynamic response unique to each test. Poorly predicted limitations in shaker capability affect the ability to achieve test specifications, delay testing schedules, and create difficulties for choosing test equipment. To predict shaker capability for a specific test configuration prior to setup, a lumped parameter model of the shaker system and a modal model of a device under test was developed. These models were then analytically coupled using LaGrange multiplier frequency based substructuring to estimate their coupled frequency response functions. The coupled frequency response functions were used to predict electrical inputs required to meet a given test specification. These input requirements were finally compared to a validation test using the specification and setup. Input requirements estimated using the substructuring estimated frequency response functions showed significant error. However, results using an ideal frequency response function showed very little error. These results indicate that with a better method of experimental dynamic substructuring employed it would be possible to accurately predict shaker capability for a given test configuration prior to setup.

42 ENGINEERING↗

A Gaussian field approach to the planar electric double layer structures in electrolyte solutions

Here, in this work, the planar, electric, double-layer structures of non-polarizable electrodes in electrolyte solutions are studied with Gaussian field theory. A response function with two Yukawa functions is used to capture the electrostatic response of the electrolyte solution, from which the modified response function in the planar symmetry is derived analytically. The modified response function is further used to evaluate the induced charge density and the electrostatic potential near an electrode. The Gaussian field theory, combined with a two-Yukawa response function, can reproduce the oscillatory decay behavior of the electric potentials in concentrated electrolyte solutions. When the exact sum rules for the bulk electrolyte solutions and the electric double layers are used as constraints to determine the parameters of the response function, the Gaussian field theory could at least partly capture the nonlinear response effect of the surface charge density. Comparison with results for a planar electrode with fixed surface charge densities from molecular simulations demonstrates the validity of Gaussian field theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

G-Function Library for Modeling Vertical Bore Ground Heat Exchanger

This library contains g-functions (thermal response functions) for standard, regularly spaced vertical borehole ground heat exchangers. In total, it contains 34, 321 configurations. To permit interpolation, each configuration has g-functions for heights of 24, 48, 96, 192, and 384 m. All the g-functions were calculated with burial depths of 2m, and borehole diameters of 15 to 17.5 cm, depending on height. In configurations with uniform spacing, the spacing between the boreholes is set to 5m, though it can be scaled to other horizontal spacings.

15 GEOTHERMAL ENERGY↗

Comparison of Response Surface Construction Methods for Derivative Estimation Using Moving Least Squares, Kriging and Radial Basis Functions

Response construction methods using Moving Least Squares (MLS), Kriging and Radial Basis Functions (RBF) are compared with the Global Least Squares (GLS) method in three numerical examples for derivative generation capability. Also, a new Interpolating Moving Least Squares (IMLS) method adopted from the meshless method is presented. It is found that the response surface construction methods using the Kriging and RBF interpolation yields more accurate results compared with MLS and GLS methods. Several computational aspects of the response surface construction methods also discussed.

Krishnamurthy, Thiagarajan↗

A Gaussian field approach to the solvation of spherical ions in electrolyte solutions

In this paper, the electrostatic response of an electrolyte solution to a spherical ion is studied with a Gaussian field theory. In order to capture the ionic correlation effect in concentrated solutions, the bulk dielectric response function is described by a two-Yukawa response function. The modified response function of the solution is solved analytically in the spherical geometry, from which the induced charge density and the electrostatic energy are also derived analytically. Comparisons with results for small ions in electrolyte solutions from the hyper-netted chain theory demonstrate the validity of the Gaussian field theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multi-Beam Approach for Accelerating Alignment and Calibration of HyspIRI-Like Imaging Spectrometers

A paper describes an optical stimulus that produces more consistent results, and can be automated for unattended, routine generation of data analysis products needed by the integration and testing team assembling a high-fidelity imaging spectrometer system. One key attribute of the system is an arrangement of pick-off mirrors that provides multiple input beams (five in this implementation) to simultaneously provide stimulus light to several field angles along the field of view of the sensor under test, allowing one data set to contain all the information that previously required five data sets to be separately collected. This stimulus can also be fed by quickly reconfigured sources that ultimately provide three data set types that would previously be collected separately using three different setups: Spectral Response Function (SRF), Cross-track Response Function (CRF), and Along-track Response Function (ARF), respectively. This method also lends itself to expansion of the number of field points if less interpolation across the field of view is desirable. An absolute minimum of three is required at the beginning stages of imaging spectrometer alignment.

Eastwood, Michael L.↗

Resolving Wave-Particle Duality Could Accelerate the Mass Production of Quantum Computers

Quantum computers, hypothesized in 1980s, use concepts of superposition and entanglement phenomena. Although theoretical propositions and associated search algorithms for accurate measurements are being generated, the development of practical quantum computers themselves are advancing very slowly requiring enormous time and investments. The underlying concepts of a quantum computer are not new to the optical domain. However, the crucial enabling concepts of Entanglement and Superposition Principle are remaining clouded under the unresolved postulates, Wave-Particle Duality (WPD), and Wave Packet Reduction (WPR), implicating incompleteness in the interpretations of the mathematical formalism behind Quantum Mechanics. The WPD debate started during late1600 between Newton and Huygens. Young’s resolution of WPD through his double-slit experiment in 1802 was effectively overturned by Einstein’s interpretation of photoelectric effect as due to “indivisible light quanta”. However, Einstein disowned his “light quanta” postulate shortly before his death in1955, even though it had earned him the Nobel Prize. We resolve WPD by synthesizing Newton’s and Maxwell’s concepts and assume atoms do emit quanta but propagate as time-finite exponential pulses. This assumption also resolves WPR for light-matter interaction with the assumption that Schrodinger’s ψ represents atom’s internal dipolar amplitude stimulations. This over-turns Born’s interpretation that ψ only represents the abstract mathematical probability amplitude, rather than the physical “internal amplitude stimulation” of the quantum entity. However, our concept of atomic pulse emission forces us to re-derive the expression for the N-slit grating-spectrometer response since the classical derivation uses CW light, which does not exist. This pulsespectrometric response function strengthens our postulate since the grating response to the exponential pulse appears to be the convolution of a Lorentzian spectrum with the classical CW response function of the grating. The Fourier Transform of an exponential function is Lorentzian and QM predicts spontaneous emission line width to be Lorentzian. Then, conceptually one can extend the grating-expression (with N=2) to get the double-slit pattern. This approach preserves the classical causality that each of the two slits, like the N-signals out of a grating, are physically real and jointly stimulate the quantum detector array at the far field to generate the “Local” cosine fringes. The detector array executes the square modulus operation on its imposed dipolar amplitude stimulation and absorbs the necessary energy to fill up their quantum cups. Hence the double-slit pattern must also be “Local”, just as the N-slit grating spectrum is generated locally at the exit spectral-plane of the spectrometer. This removes the need to believe that “single photons” mysteriously generate the double slit pattern. Quantum computers, hypothesized in 1980s, use concepts of superposition and entanglement phenomena. Although theoretical propositions and associated search algorithms for accurate measurements are being generated, the development of practical quantum computers themselves are advancing very slowly requiring enormous time and investments. The underlying concepts of a quantum computer are not new to the optical domain. However, the crucial enabling concepts of Entanglement and Superposition Principle are remaining clouded under the unresolved postulates, Wave-Particle Duality (WPD), and Wave Packet Reduction (WPR), implicating incompleteness in the interpretations of the mathematical formalism behind Quantum Mechanics. The WPD debate started during late1600 between Newton and Huygens. Young’s resolution of WPD through his double-slit experiment in 1802 was effectively overturned by Einstein’s interpretation of photoelectric effect as due to “indivisible light quanta”. However, Einstein disowned his “light quanta” postulate shortly before his death in1955, even though it had earned him the Nobel Prize. We resolve WPD by synthesizing Newton’s and Maxwell’s concepts and assume atoms do emit quanta but propagate as time-finite exponential pulses. This assumption also resolves WPR for light-matter interaction with the assumption that Schrodinger’s ψ represents atom’s internal dipolar amplitude stimulations. This over-turns Born’s interpretation that ψ only represents the abstract mathematical probability amplitude, rather than the physical “internal amplitude stimulation” of the quantum entity. However, our concept of atomic pulse emission forces us to re-derive the expression for the N-slit grating-spectrometer response since the classical derivation uses CW light, which does not exist. This pulsespectrometric response function strengthens our postulate since the grating response to the exponential pulse appears to be the convolution of a Lorentzian spectrum with the classical CW response function of the grating. The Fourier Transform of an exponential function is Lorentzian and QM predicts spontaneous emission line width to be Lorentzian. Then, conceptually one can extend the grating-expression (with N=2) to get the double-slit pattern. This approach preserves the classical causality that each of the two slits, like the N-signals out of a grating, are physically real and jointly stimulate the quantum detector array at the far field to generate the “Local” cosine fringes. The detector array executes the square modulus operation on its imposed dipolar amplitude stimulation and absorbs the necessary energy to fill up their quantum cups. Hence the double-slit pattern must also be “Local”, just as the N-slit grating spectrum is generated locally at the exit spectral-plane of the spectrometer. This removes the need to believe that “single photons” mysteriously generate the double slit pattern.

Quantum Computer↗

Simplified spin dependence in dark matter direct detection

The interactions of dark matter with Standard Model particles can be systematically studied in the language of effective field theories. We investigate dark matter interactions with Standard Model particles, including spin-dependent interactions, for direct detection experiments and demonstrate that, although the scattering rate generally depends on multiple types of material response functions, certain linear combinations of these material response functions vanish if the initial and final electronic states share the same Hamiltonian. We also find that several other response functions vanish in parity-symmetric materials, making these systems as simple as isotropic detectors in some respects. Finally, we present the scattering rate for an anisotropic, possibly chiral detector, for generic dark matter-electron spin interactions. These relations reduce the number of independent response functions needed, thereby simplifying the computational complexity for a broad class of dark matter models. Our results provide a complete and efficient toolkit for analyzing electron recoil signals in diverse detector materials.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The electrical conductivity of the upper mantle as estimated from satellite magnetic field data

The electrical conductivity of the upper mantle is estimated from low-latitude magnetic field variations caused by large fluctuations in the equatorial ring current. The data base is derived from magnetic field magnitude data measured by satellites OGO 2, 4, and 6, which offer better global coverage than land-based observatories. The procedures of analysis consist of: (1) separation of the disturbance field into internal and external parts relative to the surface of the earth, (2) estimation of an electromagnetic response function Q(omega) which relates the internally generated magnetic field variations to the external variations due to the ring current, and (3) interpretation of the estimated response function using theoretical response functions for assumed conductivity profiles. Special consideration is given to possible oceanic and ionospheric effects. Best estimates of the geomagnetic response function Q(omega) for 0.2 to 2.0 cpd indicate an upper mantle conductivity of the order of 0.01 S/m.

Didwall, E. M.↗

Hybrid NN/SVM Computational System for Optimizing Designs

A computational method and system based on a hybrid of an artificial neural network (NN) and a support vector machine (SVM) (see figure) has been conceived as a means of maximizing or minimizing an objective function, optionally subject to one or more constraints. Such maximization or minimization could be performed, for example, to optimize solve a data-regression or data-classification problem or to optimize a design associated with a response function. A response function can be considered as a subset of a response surface, which is a surface in a vector space of design and performance parameters. A typical example of a design problem that the method and system can be used to solve is that of an airfoil, for which a response function could be the spatial distribution of pressure over the airfoil. In this example, the response surface would describe the pressure distribution as a function of the operating conditions and the geometric parameters of the airfoil. The use of NNs to analyze physical objects in order to optimize their responses under specified physical conditions is well known. NN analysis is suitable for multidimensional interpolation of data that lack structure and enables the representation and optimization of a succession of numerical solutions of increasing complexity or increasing fidelity to the real world. NN analysis is especially useful in helping to satisfy multiple design objectives. Feedforward NNs can be used to make estimates based on nonlinear mathematical models. One difficulty associated with use of a feedforward NN arises from the need for nonlinear optimization to determine connection weights among input, intermediate, and output variables. It can be very expensive to train an NN in cases in which it is necessary to model large amounts of information. Less widely known (in comparison with NNs) are support vector machines (SVMs), which were originally applied in statistical learning theory. In terms that are necessarily oversimplified to fit the scope of this article, an SVM can be characterized as an algorithm that (1) effects a nonlinear mapping of input vectors into a higher-dimensional feature space and (2) involves a dual formulation of governing equations and constraints. One advantageous feature of the SVM approach is that an objective function (which one seeks to minimize to obtain coefficients that define an SVM mathematical model) is convex, so that unlike in the cases of many NN models, any local minimum of an SVM model is also a global minimum.

Rai, Man Mohan↗

A new approach to finite state modelling of unsteady aerodynamics

This paper presents a novel technique for formulating a high quality finite state unsteady aerodynamic model by applying Bode plot methods, used in control engineering. Indicial response functions for both fixed wing and rotary wing applications are obtained using these finite state unsteady aerodynamic models. It is shown that the rotary wing indicial response function has a fundamentally different characteristic when compared to fixed wing indicial response. The rotary wing indicial response function is oscillatory in nature while the fixed wing indicial response function is nonoscillatory. Furthermore it should be emphasized that this is the first that a rotary-wing indicial response function has been presented in the literature.

Venkatesan, C.↗

Machine-learning-based inversion of nuclear responses

A microscopic description of the interaction of atomic nuclei with external electroweak probes is required for elucidating aspects of short-range nuclear dynamics and for the correct interpretation of neutrino oscillation experiments. Nuclear quantum Monte Carlo methods infer the nuclear electroweak response functions from their Laplace transforms. Inverting the Laplace transform is a notoriously ill-posed problem; and Bayesian techniques, such as maximum entropy, are typically used to reconstruct the original response functions in the quasielastic region. In this work, we present a physics-informed artificial neural network architecture suitable for approximating the inverse of the Laplace transform. Utilizing simulated, albeit realistic, electromagnetic response functions, we show that this physics-informed artificial neural network outperforms maximum entropy in both the low-energy transfer and the quasielastic regions, thereby allowing for robust calculations of electron scattering and neutrino scattering on nuclei and inclusive muon capture rates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Gauge invariance and Ward identities in nonlinear response theory

We present a formal analysis of nonlinear response functions in terms of correlation functions in real- and imaginary-time domains. In particular, we show that causal nonlinear response functions, expressed in terms of nested commutators in real time, can be obtained from the analytic continuation of time-ordered response functions, which are more easily amenable to diagrammatic calculation. This generalizes the well-known result of linear response theory. We then use gauge invariance arguments to derive exact relations between second-order response functions in density and current channels. These identities, which are non-perturbative in the strength of inter-particle interactions, allow us to establish exact connections between nonlinear optics calculations done in different electromagnetic gauges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Nuclear two point correlation functions on a quantum computer

The calculation of dynamic response functions is expected to be an early application benefiting from rapidly developing quantum hardware resources. The ability to calculate real-time quantities of strongly correlated quantum systems is one of the most exciting applications that can easily reach beyond the capabilities of traditional classical hardware. Response functions of fermionic systems at moderate momenta and energies corresponding roughly to the Fermi energy of the system are a potential early application because the relevant operators are nearly local, and the energies can be resolved in moderately short real time, reducing the spatial resolution and gate depth required. This is particularly the case in quasielastic electron and neutrino scattering from nuclei, a topic of great interest in the nuclear and particle physics communities and directly related to experiments designed to probe neutrino properties. In this paper we use current quantum hardware and error mitigation protocols to calculate response functions for a highly simplified nuclear model through calculations of a 2-point real time correlation function for a modified Fermi-Hubbard model in two dimensions with three distinguishable nucleons on four lattice sites.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗