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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↗

NASA NTRSDate not supplied

Informing the Space Launch System Booster Separation Initial CFD Run Matrix with Observed Parametric Sensitivity

It currently requires significant computational cost to simulate the flow physics of the booster separation event on the Space Launch System. This comes from the large parametric space in which the event occurs, as pre-separation flight conditions and separated booster core-relative trajectories can vary. Functionally removing the risk of core-booster collision mandates careful assessment of the fluid dynamics in terms of several trajectory parameters. However, simulating the entire trajectory envelope is computationally intractable given the high parametric dimension. In order to reduce the uncertainty in the resulting low-parametric-resolution aerodynamic booster separation database, a data-driven approach was developed to select which breakpoints should be studied by simulations and experiments and which should be relegated to a regression-based interpolation procedure. This technique works by simulating cases where the flow physics are most sensitive to changes in the parameters and leaving the less parametrically sensitive regions for interpolation. The result is a booster separation run matrix whose computational cost is comparable to that of previous database generations but has lower interpolation errors.

SLS↗

NASA NTRSDate not supplied

Informing the Space Launch System Booster Separation Initial CFD Run Matrix with Observed Parametric Sensitivity

SLS↗

NASA NTRS2023

New Seawater Dielectric Constant Parametrization and Application to SMOS Retrieved Salinity

The accuracy of the Sea Surface Salinity (SSS) retrieved from L-Band radiometer measurements is strongly dependent on the reliability of the dielectric constant model. Two new parametrizations were recently developed based on one hand on the Soil Moisture and Ocean Salinity (SMOS) satellite multi-angular brightness temperature measurements by Boutin et al. (2021) (BV), and on the other hand, on new George Washington University laboratory measurements by Zhou et al. (2021) (GW2020). These two approaches are fully independent. For most SSS and Sea Surface Temperature (SST) conditions commonly observed over the open ocean, the relative variations of brightness temperatures Tb simulated through the BV and GW2020 parametrizations agree particularly well, and better than with earlier parametrizations previously used in the SMOS, Soil Moisture Active Passive (SMAP) and Aquarius SSS retrievals. Nevertheless, uncertainty remains, especially below 10 °C where a ∼ 0.1 K relative difference between the two models is observed. This motivates the development of a revised parameterization, BVZ, based on a methodology similar to that used to derive BV but using GW2020 instead of SMOS measurements. Compared to the GW2020 parameterization, BVZ is derived with a reduced number of degrees of freedom, it relies on the TEOS10 PSS78 conductivity-salinity relationship, and on the previously derived static permittivity of fresh water. One month per season of SMOS data have been reprocessed in 2018 using BV, GW2020, and BVZ. We find the best overall agreement between SMOS SSS and Argo SSS with BVZ parametrization, with noticeable improvement in the 5 °C–15 °C SST range.

sea measurements↗

DOE OSTI2022

Parametric dynamic mode decomposition for reduced order modeling

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by singular value decomposition of the temporal data sets. For parameter-dependent models, as found in many multi-query applications such as uncertainty quantification or design optimization, the only parametric DMD technique developed was a stacked approach, with data sets at multiple parameter values were aggregated together, increasing the computational work needed to devise low-rank dynamical reduced-order models. Here in this paper, we present two novel approach to carry out parametric DMD: one based on the interpolation of the reduced-order DMD eigen-pair and the other based on the interpolation of the reduced DMD (Koopman) operator. Numerical results are presented for diffusion-dominated nonlinear dynamical problems, including a multiphysics radiative transfer example. All three parametric DMD approaches are compared.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

The use of idealised experiments in testing a new convective parametrization: Performance of CoMorph-A

CoMorph is a new mass-flux convection parametrization under development at the Met Office designed for use within the Unified Model and its successor model, LFRic. Use of a three-dimensional idealised model enables controlled tests of the performance of the scheme across different regimes. This includes the interaction between the physical parametrizations and the resolved dynamics, allowing study of the emergent organisation of convection on the resolved scale. A selection of well-known cases is revisited here, with the purpose of documenting the extent to which CoMorph captures a range of important, but challenging, behaviour such as the diurnal cycle and sensitivity to tropospheric moisture. Simulations using CoMorph-A, a new physics package, that has been demonstrated to perform well at numerical weather prediction (NWP) and climate scales, are compared against the current global atmosphere configuration and high-resolution results. In addition to an entirely new convection scheme, the package of changes includes significant changes to the cloud, microphysics, and boundary-layer parametrizations. Recognising that CoMorph-A is the first version of a scheme that will continue to be substantially developed and to obtain good performance, compromises in tuning have had to be made. These idealised tests therefore show what works well in this configuration, and what areas will require further work. As such, it is quite a demanding testbed and could be viewed as some of the equipment required for a “convective playground”.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

A multi-dimensional parametric study of variability in multi-phase flow dynamics during geologic CO 2 sequestration accelerated with machine learning

Successful geologic CO 2 storage projects depend on numerical simulations to predict reservoir performance during site selection, injection verification, and post-injection monitoring phases of the project. These numerical simulations solve non-linear sets of coupled partial differential equations, while accounting for multi-phase fluid dynamics on the basis of constitutive equations that are embedded into the solution scheme. As a consequence, individual simulations often require tens to hundreds of hours to complete on high-performance computing clusters. Moreover, laboratory experiments reveal that parametric functions for capillary pressure and relative permeability exhibit substantial variability, even within the same rock type. This combination of computational expense and wide-ranging parametric variability means that there remains substantial uncertainty in the behavior of multi-phase CO 2 -water systems, particularly in the context of feedbacks between relative permeability and capillary pressure. To bridge this knowledge gap, here we develop a novel workflow that utilizes physics-based numerical simulation to train an artificial neural network (ANN) emulator for interrogating the multivariate parameter space that governs both capillary pressure and relative permeability. With this approach, the ANN is trained to emulate both fluid pressure distribution and CO 2 saturation, which are then interrogated quantitatively to generate parametric response surface mappings with high-fidelity resolution. Results from this study initially show that capillary entry pressure is the dominant control on both CO 2 plume geometry and fluid pressure propagation when considering the combined effects of capillary pressure and relative permeability, particularly when phase interference is low and residual CO 2 saturation is high. Moreover, the ANN emulator provides tremendous computational speed-up by computing 2691 individual simulations in several minutes; whereas, the same simulation ensemble would have required ~3 years of simulation time using only physics-based simulation methods (25,000 times speed up).

58 GEOSCIENCES↗

DOE OSTI2021

Numerical simulation of parametric resonance in point absorbers using a simplified model

Abstract Parametric resonance is a non‐linear phenomenon in which a system can oscillate at a frequency different from its exciting frequency. Some wave energy converters are prone to this phenomenon, which is usually detrimental to their performance. Here, a computationally efficient way of simulating parametric resonance in point absorbers is presented. The model is based on linear potential theory, so the wave forces are evaluated at the mean position of the body. However, the first‐order variation of the body's centres of gravity and buoyancy is taken into account. This gives essentially the same result as a more rigorous approach of keeping terms in the equation of motion up to second order in the body motions. The only difference from a linear model is the presence of non‐zero off‐diagonal elements in the mass matrix. The model is benchmarked against state‐of‐the‐art non‐linear Froude–Krylov and computational fluid dynamics models for free decay, regular wave, and focused wave group cases. It is shown that the simplified model is able to simulate parametric resonance in pitch to a reasonable accuracy even though no non‐linear wave forces are included. The simulation speed on a standard computer is up to two orders of magnitude faster than real time.

16 TIDAL AND WAVE POWER↗

DOE OSTI2021

Non-degenerate parametric mixing and Q-enhancement in ALN Lamb wave resonator

In this Letter, we explore a non-degenerate phase independent parametric quality factor (Q)-enhancement technique for aluminum nitride (AlN) Lamb wave resonators. Unlike other active Q-enhancement techniques which require precise phase control of the electronic feedback loop, this technique is implemented by parametrically pumping AlN material stiffness to realize a negative resistance seen at the signal path. The negative resistance is dependent on the nonlinear material modulation and multi-resonance coupling in the device. A nonlinear circuit model is developed to simulate the parametric coupling of each resonance and extract the nonlinearity of AlN from experimental data. With proper pump frequency and pump power, the device quality factor is boosted in both simulation and experiment. The demonstrated Q-enhancement method is simple to implement and can be applied to other types of resonators that have nonlinear behavior and support multi-resonance operation.

42 ENGINEERING↗

DOE OSTI2026

Parametrically amplified Josephson plasma waves in YBa 2 Cu 3 O 6+ x : Evidence for local superconducting fluctuations up to the pseudogap temperature T ∗

Experiments that subject underdoped YBa 2 Cu 3 O 6+x (YBCO) to intense terahertz pulses at temperatures between the transition temperature T c and the pseudogap scale T ∗ have revealed a reflectivity edge that resembles that of the superconducting state, together with second harmonic generation of a probe pulse modulated at a similar frequency. These have been interpreted in terms of parametric amplification of the lower Josephson plasmon mode. Since this mode is often associated with coherent oscillations between bilayers in the YBCO structure, these experiments have led to the suggestion that the intense pump has created (or revealed) in-plane pair coherence up to T ∗ ≈ 400 K. In this paper we propose an alternative explanation by assuming the existence of local pair amplitude and phase at equilibrium for T c < T < T ∗ . The phase correlation spans only a few lattice constants and we do not assume any pump-induced enhancement of this correlation, either in-plane or between bilayers. Instead, the coherent drive, via a parametric amplification process, induces coherence in the Josephson currents between members of bilayers. When combined with a Floquet framework, the reflectivity data can be explained. The key point is that in the lower Josephson plasmon, the coupling between bilayers is mainly capacitive; the Josephson current between bilayers can be set to zero without strongly affecting the parametric amplification process. Importantly, while superconducting coherence may not be created by the pump, the pseudogap phase must possess a local pairing amplitude at equilibrium. Consequently, these experiments have strong implications for the understanding of the pseudogap phase.

parametric amplification↗

DOE OSTI2026

Parametric amplification of spin-motion coupling in three-dimensional trapped-ion crystals

Three-dimensional (3D) crystals offer a route to scaling up trapped-ion systems for quantum sensing and quantum simulation applications; however, engineering coherent spin-motion couplings and effective spin-spin interactions in large crystals poses technical challenges associated with decoherence and prolonged timescales to generate appreciable entanglement. Here, we explore the possibility of speeding up these interactions in 3D crystals via parametric amplification. For this purpose, we derive a general Hamiltonian for the parametric amplification of spin-motion coupling that is broadly applicable to normal modes with motion transverse to or along the spatial extent of the crystal. Unlike in lower-dimensional crystals, we find that the ability to faithfully (uniformly) amplify the spin-spin interactions in 3D crystals depends on the physical implementation of the spin-motion coupling. We consider the light-shift gate, and the so-called phase-insensitive and phase-sensitive Mølmer-Sørensen (MS) gates, and we find that only the phase-sensitive MS gate can be faithfully amplified in general 3D crystals. We discuss a situation where nonuniform amplification can be advantageous. We also reconsider the effect of counter-rotating terms on parametric amplification and find that they are not as detrimental as previous studies suggest.

Optical parametric oscillators & amplifiers↗

DOE OSTI2021

Enhancement of Parametric Effects in Polariton Waveguides Induced by Dipolar Interactions

Exciton-polaritons are hybrid light-matter excitations arising from the nonperturbative coupling of a photonic mode and an excitonic resonance. Behaving as interacting photons, they show optical third-order nonlinearities providing effects such as optical parametric oscillation or amplification. It has been suggested that polariton-polariton interactions can be greatly enhanced by inducing aligned electric dipoles in their excitonic part. However, direct evidence of a true particle-particle interaction, such as superfluidity or parametric scattering, is still missing. In this Letter, we demonstrate that dipolar interactions can be used to enhance parametric effects such as self-phase modulation in waveguide polaritons. By quantifying these optical nonlinearities, we provide a reliable experimental measurement of the direct dipolar enhancement of polariton-polariton interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Hybrid Symbolic-Numerical Modeling and Parametric Stability Analysis of DC–AC Power Systems

Hybrid DC-AC power systems integrating diverse inverter-based resources (IBRs) and multi-terminal high-voltage direct current (MTDC) networks represent a promising architecture for future power grids, while introducing challenges for modeling, stability analysis, and control design. This paper develops a hybrid symbolic-numerical modeling framework and tool to characterize the parametric small-signal stability of DC-AC coupled power systems. The proposed approach constructs parametric state-space models to enable efficient representation of system dynamics under varying control parameters and network configurations, with target parameters retained as symbolic variables and the remainder treated numerically. The stability analysis framework covers eigenvalue, sensitivity, and stability boundary and region characterization. Enhanced linear matrix inequality (LMI) techniques are proposed to directly certify small-signal stability over regions of parameter space while also reducing the conservativeness and computational burden. The resulting tools and frameworks enable rapid parametric model construction across diverse grid conditions, thereby facilitating stability-informed control and operation in complex DC–AC power systems.

DC–AC power systems↗

DOE OSTI2020

Affine Approximation of Parametrized Kernels and Model Order Reduction for Nonlocal and Fractional Laplace Models

In this work, we consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels. In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by the fractional power $s\in(0,1)$, are studied. Furthermore, in order to provide an efficient and reliable approximation of the solution for different values of the parameters, we develop the reduced basis method as a parametric model order reduction approach. Major difficulties arise since the kernels are not affine in the parameters, singular, and discontinuous. Moreover, the spatial regularity of the solutions depends on the varying fractional power $s$. To address this, we derive regularity and differentiability results with respect to $\delta$ and $s$, which are of independent interest for other applications such as optimization and parameter identification. We then use these results to construct affine approximations of the kernels by local polynomials. Finally, we certify the method by providing reliable a posteriori error estimators, which account for all approximation errors, and support the theoretical findings by numerical experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Parametric Study to Assess Technical Prospect Feasibility for Offshore CO 2 Storage

This report is a white paper on the parametric study to assess technical prospect feasibility for CO 2 storage with and without CO 2 -EOR. The SECARB Offshore GOM team reviewed key parameters that previous modeling experience suggests have the largest impact on CO 2 plume size and CO 2 -EOR performance (SSEB, 2019) These parameters include tectonic impacts (reservoir dip and fault block size), reservoir properties (permeability) and development strategies (well field payout, waterflood, and CO 2 flooding strategies). These parameters are further evaluated in this study in order to identify upper and lower boundary conditions for the parametric values. The boundary conditions are needed to set constraints for key parameters when performing modeling assessments. Understanding the key parametric values for the GOM will facilitate locating successful offshore carbon capture utilization and storage (CCUS) projects in terms of plume size, CO 2 stored and, in the case of EOR, oil recovery. Importantly, this white paper focuses on both technical factors (geologic and engineering), but does not address economic, commercial, or stakeholder considerations. The report is organized into four sections and includes a review of the datasets used to define the parameter ranges, the results of a full-physics reservoir simulation, a summary of a reduced order modeling approach to evaluate the impact of the study parameters, and, finally, a discussion of the work that will occur during the next phase of the project.

02 PETROLEUM↗

DOE OSTI2021

Parametrizations of the spin density matrix

Highlights: • Proposed two methods for parametrizing the SDM of spinning, unstable particles. • All non-negativity conditions fulfilled; adaptability to various constraints. • First method: based on a theorem; applicable in a simple and flexible way. • Second method: particularly suitable for especial conditions. • Applications: two of them interesting in the search for new physics. We propose for the spin density matrix two parametrizations which automatically fulfill the non-negativity conditions, without setting any bound on the parameters. The first one relies on a theorem, that we prove, and it is rather simple and easily adaptable to some specific reactions, where, for example, parity is conserved or angular momentum conservation entails selection rules. Moreover, in the case when the rank is less than the order of the density matrix, we show how to improve the fits to the data, either by implementing previous suggestions, or by elaborating an alternative method, for which we prove a second theorem. Our second parametrization is a variant of previous treatments, it appears suitable for some particular processes. Moreover, we discuss about the possibility of inferring the elements of the density matrix from the differential decay width. Last, we illustrate various examples of current interest, both in strong and weak decays; some of them may be helpful in the investigation of physics beyond the standard model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

A parametric finite element study for determining burst strength of thin and thick-walled pressure vessels

To accurately predict the burst strength of both thin and thick-walled pressure vessels (PVs), a parametric study of PV burst strength was performed for a wide range of vessel geometries and materials using elastic-plastic finite element analysis (FEA). A valid FEA model was established through a detailed study of 2D versus 3D FEA models, the critical stress failure criterion versus the limit load criteria, and the thick-wall effect on the FEA simulations. Here, the results show that the stresses and strains at the mean diameter, rather than outside diameter, determines a more accurate burst strength for both thin and thick-walled PVs. On this basis, a parametrized FEA script using the ABAQUS Python application programming interface (API) was used to create a large database of PV burst strengths for a variety of vessel geometries and materials, demonstrating that Python scripting is a powerful technique for performing parametric studies or generating large databases. From the FEA results, using the regression method, a new burst pressure model was developed as a function of the vessel geometry (D/t ratio) and material properties (UTS and n). As validated by a large number of full-scale burst test data, the proposed burst model can very accurately predict the burst strength for both thin and thick-walled PVs.

42 ENGINEERING↗

DOE OSTI2025

Direct local parametrization of nuclear state densities using the back-shifted Bethe formula

Level densities are often parametrized using the back-shifted Bethe formula (BBF) for nuclei that possess experimental data for s-wave neutron resonance average spacings and a complete discrete level sequence at low excitation energies. However, these parametrizations require the additional modeling of the dependence of the spin-cutoff parameter on excitation energy. Here, in this work, we avoid the need to model the spin distribution of level densities by using the experimental data to parametrize directly the state densities, for which the BBF does not depend on the spin-cutoff parameter. This approach allows for a local parameterization of state densities that is independent of the spin-cutoff parameter. We provide these parameters in a tabulated form for applications in nuclear reaction calculations and for testing microscopic approaches to state densities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗