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DOE OSTI2012

GCG parametrization for growth function and current constraints

We study the linear growth function f for large scale structures in a cosmological scenario where Generalised Chaplygin Gas (GCG) serves as dark energy candidate. We parametrize the growth index parameter as a function of redshift and do a comparative study between the theoretical growth rate and the proposed parametrization. Moreover, we demonstrate that growth rates for a wide range of dark energy models can be modeled accurately by our proposed parametrization. Finally, we compile a data set consisting of 28 data points within redshift range (0.15,3.8) to constrain the growth rate. It includes direct growth data from various projects/surveys including the latest data from the Wiggle-Z measurements. It also includes data constraining growth indirectly through the rms mass fluctuation σ{sub 8}(z) inferred from Ly-α measurements at various redshifts. By fitting our proposed parametrization for f to these data, we show that growth history of large scale structures of the universe although allows a transient acceleration, one cannot distinguish it at present with an eternally accelerating universe.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2012

A new class of parametrization for dark energy without divergence

A new class of parametrization of the equation of state of dark energy is proposed in this paper. In contrast with the famous CPL parametrization, the equation of state with this new kind of parametrization does not divergent during the evolution of the Universe even in the future. By using the Markov Chain Monte Carlo (MCMC) method, we perform an observational constraint on two simplest dark energy models belonging to this new class of parametrization with the combined latest observational data from the type Ia supernova compilations including Union2(557), cosmic microwave background, and baryon acoustic oscillation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Parametric resonance in the early Universe—a fitting analysis

Particle production via parametric resonance in the early Universe, is a non-perturbative, non-linear and out-of-equilibrium phenomenon. Although it is a well studied topic, whenever a new scenario exhibits parametric resonance, a full re-analysis is normally required. To avoid this tedious task, many works present often only a simplified linear treatment of the problem. In order to surpass this circumstance in the future, we provide a fitting analysis of parametric resonance through all its relevant stages: initial linear growth, non-linear evolution, and relaxation towards equilibrium. Using lattice simulations in an expanding grid in 3+1 dimensions, we parametrize the dynamics' outcome scanning over the relevant ingredients: role of the oscillatory field, particle coupling strength, initial conditions, and background expansion rate. We emphasize the inaccuracy of the linear calculation of the decay time of the oscillatory field, and propose a more appropriate definition of this scale based on the subsequent non-linear dynamics. We provide simple fits to the relevant time scales and particle energy fractions at each stage. Our fits can be applied to post-inflationary preheating scenarios, where the oscillatory field is the inflaton, or to spectator-field scenarios, where the oscillatory field can be e.g. a curvaton, or the Standard Model Higgs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Parametrizations of coupled betatron motion for strongly coupled lattices

The coupling of transverse motion is a natural occurrence in particle accelerators, either in the form of a residual coupling arising from imperfections or originating by design from strong systematic coupling fields. While the first can be treated perturbatively, the latter requires a robust approach adapted to strongly coupled optics, and a parametrization of the linear optics must be performed to explore beam dynamics in such peculiar lattices. This work highlights the key physical interpretations of the main parametrization formalisms to describe linear coupled optics, along with explicit links and comparisons of these parametrizations. Concepts rarely illustrated in other works, such as forced mode flips and local coupling, are explored in detail, clarifying some anomalies that can arise in lattice functions. The analytical methods have been implemented in a reference Python package and connected with ray-tracing and integration codes to explore examples of strongly coupled lattices, which are discussed in detail to highlight the key physical interpretations of the parametrizations and characteristics of the lattices.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Analysis of parton distributions in a pion with Bézier parametrizations

We explore the role of parametrizations for nonperturbative QCD functions in global analyses, with a specific application to extending a phenomenological analysis of the parton distribution functions (PDFs) in the charged pion realized in the xFitter fitting framework. The parametrization dependence of PDFs in our pion fits substantially enlarges the uncertainties from the experimental sources estimated in the previous analyses. We systematically explore the parametrization dependence by employing a novel technique to automate generation of polynomial parametrizations for PDFs that makes use of Bézier curves. This technique is implemented in a ++ module that is included in the xFitter program. Our analysis reveals that the sea and gluon distributions in the pion are not well disentangled, even when considering measurements in leading-neutron deep inelastic scattering. For example, the pion PDF solutions with a vanishing gluon and large quark sea are still experimentally allowed, which elevates the importance of ongoing lattice and nonperturbative QCD calculations, together with the planned pion scattering experiments, for conclusive studies of the pion structure. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Broadband coplanar-waveguide-based impedance-transformed Josephson parametric amplifier

Quantum-limited Josephson parametric amplifiers play a pivotal role in advancing the field of circuit quantum electrodynamics by enabling the fast and high-fidelity measurement of weak microwave signals. Therefore, it is necessary to develop robust parametric amplifiers with low noise, broad bandwidth, and reduced design complexity for microwave detection. However, current broadband parametric amplifiers either have degraded noise performance or rely on complex designs. Here, we present a device based on the broadband impedance-transformed Josephson parametric amplifier that integrates a hornlike coplanar waveguide transmission line, which significantly decreases the design and fabrication complexity while keeping comparable performance. The device shows an instantaneous bandwidth of 700 (200) MHz for 15 (20) dB gain with an average input saturation power of − 110 dBm and near quantum-limited added noise. The operating frequency can be tuned over 1.4 GHz using an external flux bias. We further demonstrate the negligible backaction from our device on a transmon qubit. The amplification performance and simplicity of our device promise its wide adaptation in quantum metrology, quantum communication, and quantum information processing. Published by the American Physical Society 2024

Qing, Bingcheng (ORCID:0000000345227017)↗

DOE OSTI2025

Fundamental limits to the generation of highly displaced bright squeezed light using linear optics and parametric amplifiers

High-quality squeezed light is an important resource for a variety of applications. Multiple methods for generating squeezed light are known, having been demonstrated theoretically and experimentally. However, the effectiveness of these methods—in particular, the inherent limitations to the signals that can be produced—has received little consideration. Here we present a comparative theoretical analysis for generating a highly displaced squeezed light from a linear optical method—a beamsplitter mixing a squeezed vacuum and a strong coherent state—and well-studied parametric amplification methods including an optical parametric oscillator, an optical parametric amplifier, and a dissipative optomechanical squeezer seeded with coherent states. We show that the quality of highly displaced squeezed states that can be generated using these methods is limited on a fundamental level by the physical mechanism utilized; across all methods there are significant trade-offs between displacement, squeezing, and overall uncertainty. We explore the nature and extent of these trade-offs specific to each mechanism and identify the optimal operation modes for each. Finally, we identify the conditions for minimum-uncertainty squeezing in arbitrary parametric amplifying systems and show that displacing the output signal will in general violate these conditions, adding noise and degrading squeezing. Published by the American Physical Society 2025

Young, Steve M. (ORCID:0000000173839366)↗

DOE OSTI2016

Dynamic PET simulator via tomographic emission projection for kinetic modeling and parametric image studies

Purpose: To develop and evaluate a fast and simple tool called dPETSTEP (Dynamic PET Simulator of Tracers via Emission Projection), for dynamic PET simulations as an alternative to Monte Carlo (MC), useful for educational purposes and evaluation of the effects of the clinical environment, postprocessing choices, etc., on dynamic and parametric images. Methods: The tool was developed in MATLAB using both new and previously reported modules of PETSTEP (PET Simulator of Tracers via Emission Projection). Time activity curves are generated for each voxel of the input parametric image, whereby effects of imaging system blurring, counting noise, scatters, randoms, and attenuation are simulated for each frame. Each frame is then reconstructed into images according to the user specified method, settings, and corrections. Reconstructed images were compared to MC data, and simple Gaussian noised time activity curves (GAUSS). Results: dPETSTEP was 8000 times faster than MC. Dynamic images from dPETSTEP had a root mean square error that was within 4% on average of that of MC images, whereas the GAUSS images were within 11%. The average bias in dPETSTEP and MC images was the same, while GAUSS differed by 3% points. Noise profiles in dPETSTEP images conformed well to MC images, confirmed visually by scatter plot histograms, and statistically by tumor region of interest histogram comparisons that showed no significant differences (p < 0.01). Compared to GAUSS, dPETSTEP images and noise properties agreed better with MC. Conclusions: The authors have developed a fast and easy one-stop solution for simulations of dynamic PET and parametric images, and demonstrated that it generates both images and subsequent parametric images with very similar noise properties to those of MC images, in a fraction of the time. They believe dPETSTEP to be very useful for generating fast, simple, and realistic results, however since it uses simple scatter and random models it may not be suitable for studies investigating these phenomena. dPETSTEP can be downloaded free of cost from https://github.com/CRossSchmidtlein/dPETSTEP.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2024

Interplay between gain and loss in arrays of nonlinear plasmonic nanoparticles: toward parametric downconversion and amplification

With the help of a theoretical model and finite-difference time-domain (FDTD) simulations based on the hydrodynamic–Maxwell model, we examine the effect of difference-frequency generation (DFG) in an array of L-shaped metal nanoparticles (MNPs) characterized by intrinsic plasmonic nonlinearity. The outcomes of the calculations reveal the spectral interplay between gain and loss in the vicinity of the fundamental frequency of the localized surface plasmon resonances. Subsequently, we identify different array thicknesses and pumping regimes facilitating parametric amplification and spontaneous parametric downconversion. Our results suggest that the parametric amplification regime becomes feasible on a scale of hundreds of nanometers and spontaneous parametric downconversion on the scale of tens of nanometers, opening up new exciting opportunities for developing building blocks of photonic metasurfaces.

Shah, Syed A.↗

DOE OSTI2016

From neutron star observables to the equation of state. I. An optimal parametrization

The increasing number and precision of measurements of neutron star masses, radii, and, in the near future, moments of inertia offer the possibility of precisely determining the neutron star equation of state (EOS). One way to facilitate the mapping of observables to the EOS is through a parametrization of the latter. We present here a generic method for optimizing the parametrization of any physically allowed EOS. We use mock EOS that incorporate physically diverse and extreme behavior to test how well our parametrization reproduces the global properties of the stars, by minimizing the errors in the observables of mass, radius, and the moment of inertia. We find that using piecewise polytropes and sampling the EOS with five fiducial densities between ∼1–8 times the nuclear saturation density results in optimal errors for the smallest number of parameters. Specifically, it recreates the radii of the assumed EOS to within less than 0.5 km for the extreme mock EOS and to within less than 0.12 km for 95% of a sample of 42 proposed, physically motivated EOS. Such a parametrization is also able to reproduce the maximum mass to within 0.04 M{sub ⊙} and the moment of inertia of a 1.338 M{sub ⊙} neutron star to within less than 10% for 95% of the proposed sample of EOS.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Direct Estimation of Kinetic Parametric Images for Dynamic PET

Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1980

Parametric instabilities of rotor-support systems with application to industrial ventilators

Rotor support systems interaction with parametric excitation is considered for both unequal principal shaft stiffness (generators) and offset disc rotors (ventilators). Instability regions and types of instability are computed in the first case, and parametric resonances in the second case. Computed and experimental results are compared for laboratory machine models. A field case study of parametric vibrations in industrial ventilators is reported. Computed parametric resonances are confirmed in field measurements, and some industrial failures are explained. Also the dynamic influence and gyroscopic effect of supporting structures are shown and computed.

Parszewski, Z.↗

NASA NTRS1984

Extended parametric representation of compressor fans and turbines. Volume 1: CMGEN user's manual

A modeling technique for fans, boosters, and compressors has been developed which will enable the user to obtain consistent and rapid off-design performance from design point input. The fans and compressors are assumed to be multi-stage machines incorporating front variable stators. The boosters are assumed to be fixed geometry machines. The modeling technique has been incorporated into time sharing program to facilitate its use. Because this report contains a description of the input output data, values of typical inputs, and examples cases, it is suitable as a user's manual. This report is the first of a three volume set describing the parametric representation of compressors, fans, and turbines. The titles of the three volumes are as follows: (1) Volume 1 CMGEN USER's Manual (Parametric Compressor Generator); (2) Volume 2 PART USER's Manual (parametric Turbine); (3) Volume 3 MODFAN USER's Manual (Parametric Modulating Flow Fan).

Converse, G. L.↗

NASA NTRS1989

Robustness analysis for real parametric uncertainty

Some key results in the literature in the area of robustness analysis for linear feedback systems with structured model uncertainty are reviewed. Some new results are given. Model uncertainty is described as a combination of real uncertain parameters and norm bounded unmodeled dynamics. Here the focus is on the case of parametric uncertainty. An elementary and unified derivation of the celebrated theorem of Kharitonov and the Edge Theorem is presented. Next, an algorithmic approach for robustness analysis in the cases of multilinear and polynomic parametric uncertainty (i.e., the closed loop characteristic polynomial depends multilinearly and polynomially respectively on the parameters) is given. The latter cases are most important from practical considerations. Some novel modifications in this algorithm which result in a procedure of polynomial time behavior in the number of uncertain parameters is outlined. Finally, it is shown how the more general problem of robustness analysis for combined parametric and dynamic (i.e., unmodeled dynamics) uncertainty can be reduced to the case of polynomic parametric uncertainty, and thus be solved by means of the algorithm.

Sideris, Athanasios↗

NASA NTRS1994

Parametric robust control and system identification: Unified approach

Despite significant advancement in the area of robust parametric control, the problem of synthesizing such a controller is still a wide open problem. Thus, we attempt to give a solution to this important problem. Our approach captures the parametric uncertainty as an H(sub infinity) unstructured uncertainty so that H(sub infinity) synthesis techniques are applicable. Although the techniques cannot cope with the exact parametric uncertainty, they give a reasonable guideline to model the unstructured uncertainty that contains the parametric uncertainty. An additional loop shaping technique is also introduced to relax its conservatism.

Keel, Leehyun↗

NASA NTRS2008

Parametric-Studies and Data-Plotting Modules for the SOAP

"Parametric Studies" and "Data Table Plot View" are the names of software modules in the Satellite Orbit Analysis Program (SOAP). Parametric Studies enables parameterization of as many as three satellite or ground-station attributes across a range of values and computes the average, minimum, and maximum of a specified metric, the revisit time, or 21 other functions at each point in the parameter space. This computation produces a one-, two-, or three-dimensional table of data representing statistical results across the parameter space. Inasmuch as the output of a parametric study in three dimensions can be a very large data set, visualization is a paramount means of discovering trends in the data (see figure). Data Table Plot View enables visualization of the data table created by Parametric Studies or by another data source: this module quickly generates a display of the data in the form of a rotatable three-dimensional-appearing plot, making it unnecessary to load the SOAP output data into a separate plotting program. The rotatable three-dimensionalappearing plot makes it easy to determine which points in the parameter space are most desirable. Both modules provide intuitive user interfaces for ease of use.

Source record↗

NASA NTRS2008

Parametrically disciplined operation of a vibratory gyroscope

Parametrically disciplined operation of a symmetric nearly degenerate mode vibratory gyroscope is disclosed. A parametrically-disciplined inertial wave gyroscope having a natural oscillation frequency in the neighborhood of a sub-harmonic of an external stable clock reference is produced by driving an electrostatic bias electrode at approximately twice this sub-harmonic frequency to achieve disciplined frequency and phase operation of the resonator. A nearly symmetric parametrically-disciplined inertial wave gyroscope that can oscillate in any transverse direction and has more than one bias electrostatic electrode that can be independently driven at twice its oscillation frequency at an amplitude and phase that disciplines its damping to zero in any vibration direction. In addition, operation of a parametrically-disciplined inertial wave gyroscope is taught in which the precession rate of the driven vibration pattern is digitally disciplined to a prescribed non-zero reference value.

Shcheglov, Kirill V.↗

NASA NTRS2009

Ultra-Broad-Band Optical Parametric Amplifier or Oscillator

A concept for an ultra-broad-band optical parametric amplifier or oscillator has emerged as a by-product of a theoretical study in fundamental quantum optics. The study was originally intended to address the question of whether the two-photon temporal correlation function of light [in particular, light produced by spontaneous parametric down conversion (SPDC)] can be considerably narrower than the inverse of the spectral width (bandwidth) of the light. The answer to the question was found to be negative. More specifically, on the basis of the universal integral relations between the quantum two-photon temporal correlation and the classical spectrum of light, it was found that the lower limit of two-photon correlation time is set approximately by the inverse of the bandwidth. The mathematical solution for the minimum two-photon correlation time also provides the minimum relative frequency dispersion of the down-converted light components; in turn, the minimum relative frequency dispersion translates to the maximum bandwidth, which is important for the design of an ultra-broad-band optical parametric oscillator or amplifier. In the study, results of an analysis of the general integral relations were applied in the case of an optically nonlinear, frequency-dispersive crystal in which SPDC produces collinear photons. Equations were found for the crystal orientation and pump wavelength, specific for each parametric-down-converting crystal, that eliminate the relative frequency dispersion of collinear degenerate (equal-frequency) signal and idler components up to the fourth order in the frequency-detuning parameter

Strekalov, Dmitry↗