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NASA NTRS1992

The influence of a vertical magnetic field on oscillations in an isothermal stratified atmosphere

The effect of a uniform vertical magnetic field on the modes of an isothermal stratified atmosphere is examined. The general solutions of the wave equation for an isothermal magnetized medium are given. Asymptotic expansions of these solutions are presented in the strong- and weak-field limits. For a weak field, it is found that, to lowest order of the present perturbation expansion, the oscillation spectrum can be analyzed in terms of p- and g-like modes, magnetic Lamb modes, and magnetic or slow modes. The frequency corrections for each of the modes due to coupling with the remaining modes are calculated. It is demonstrated that when the frequencies of different modes are almost identical, strong mode coupling occurs and the waves acquire a mixed character. An analysis of the solutions in the vicinity of the degenerate frequencies is carried out. The solutions reveal the presence of avoided crossings, which occur at the otherwise degenerate frequencies. Examples of different types of avoided crossings are given.

Hasan, S. S.↗

DOE OSTI2026

Geometrical optics without singularities: using the ray time as the coordinate space

Geometrical optics (GO) is widely used for reduced modelling of waves in plasmas, but it fails near reflection points, where it predicts a spurious singularity of the wave amplitude. We show how to avoid this singularity by adopting a different representation of the wave equation. Instead of the physical coordinate 𝑥 and the wavevector 𝑘, we use the ray time 𝜏 as the new canonical coordinate and the ray energy ℎ as the associated canonical momentum. To derive the envelope equation in the 𝜏-representation, we construct the Weyl symbol calculus on the (𝜏,ℎ) space and show that the corresponding Weyl symbols are related to their (𝑥,𝑘) counterparts by the Airy transform. This allows us to express the coefficients in the envelope equation through the known properties of the original dispersion operator. When necessary, solutions of this equation can be mapped to the 𝑥-space using a generalised metaplectic transform. However, the field per se might not even be needed in practice. Instead, knowing the corresponding Wigner function usually suffices for linear and quasilinear calculations. As a Weyl symbol itself, the Wigner function can be mapped analytically, using the aforementioned Airy transform. We show that the standard Airy patterns that form in regions where conventional GO fails are successfully reproduced within metaplectic GO (MGO) simply by remapping the field from the 𝜏-space to the 𝑥-space. An extension to mode-converting waves is also presented. This formulation, which we call generalised MGO, can be particularly useful, for example, for reduced modelling of the O–X conversion in inhomogeneous plasma near the critical density, an effect that is important for fusion applications and also occurs in the ionosphere. Overall, MGO can replace GO for any practical purposes, because it better handles cutoffs and is similar otherwise.

plasma waves↗

NASA NTRS1971

Nonlinear, nonlaminar-3D computation of electron motion through the output cavity of a klystron

The equations of motion used in the computation are discussed along with the space charge fields and the integration process. The following assumptions were used as a basis for the computation: (1) The beam is divided into N axisymmetric discs of equal charge and each disc into R rings of equal charge. (2) The velocity of each disc, its phase with respect to the gap voltage, and its radius at a specified position in the drift tunnel prior to the interaction gap is known from available large signal one dimensional programs. (3) The fringing rf fields are computed from exact analytical expressions derived from the wave equation assuming a known field shape between the tunnel tips at a radius a. (4) The beam is focused by an axisymmetric magnetic field. Both components of B, that is B sub z and B sub r, are taken into account. (5) Since this integration does not start at the cathode but rather further down the stream prior to entering the output cavity it is assumed that each electron moved along a laminar path from the cathode to the start of integration.

Albers, L. U.↗

DOE OSTI2021

Spatially Quasi-Periodic Water Waves of Infinite Depth

Abstract We formulate the two-dimensional gravity-capillary water wave equations in a spatially quasi-periodic setting and present a numerical study of solutions of the initial value problem. We propose a Fourier pseudo-spectral discretization of the equations of motion in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on a torus. We adopt a conformal mapping formulation and employ a quasi-periodic version of the Hilbert transform to determine the normal velocity of the free surface. Two methods of time-stepping the initial value problem are proposed, an explicit Runge–Kutta (ERK) method and an exponential time-differencing (ETD) scheme. The ETD approach makes use of the small-scale decomposition to eliminate stiffness due to surface tension. We perform a convergence study to compare the accuracy and efficiency of the methods on a traveling wave test problem. We also present an example of a periodic wave profile containing vertical tangent lines that is set in motion with a quasi-periodic velocity potential. As time evolves, each wave peak evolves differently, and only some of them overturn. Beyond water waves, we argue that spatial quasi-periodicity is a natural setting to study the dynamics of linear and nonlinear waves, offering a third option to the usual modeling assumption that solutions either evolve on a periodic domain or decay at infinity.

Wilkening, Jon (ORCID:0000000327827596)↗

NASA NTRSDate not supplied

Modelling Sonic Boom Propagation through Planetary Boundary Layer Turbulence near the Lateral Extent of the Carpet

Nonlinear acoustic propagation of sonic booms in the atmospheric boundary layer is considered in the context of a one-way solution to a third order wave equation. A split-step approach is utilized to compute different physical effects efficiently. Unlike previous approaches, the diffraction effects are computed exactly in the forward direction with no restriction on the angle of propagation. This results in more accurate modelling of sonic boom near the carpet edge. Heterogenous flow effects are incorporated with a wide-angle parabolic approximation. Nonlinear propagation is computed with a Burgers-Hayes method. Turbulence in the medium is constructed by the method of random Fourier modes. The turbulence spectra are constructed using an altitude dependent 3-dimensional von Karman spectrum. The turbulence field is considered frozen, as the eddy turnover time in the atmospheric boundary layer is generally much larger than the propagation time of the acoustic wave. Comparisons with benchmark predictions from the PCBoom software are conducted. The benchmark cases provide insight into the accuracy of the current prediction code for non-turbulent atmospheres. Future work is discussed regarding the prediction of shaped booms, boundary conditions, and predictions near the lateral extent of the boom carpet where previous approaches fail to capture the diffraction effects.

sonic boom↗

DOE OSTI2020

New Yield Estimates for Nuclear Detonations Over Water

One of the primary methods used by the United States to estimate the yields of atmospheric nuclear tests performed in the 1940’s, 50’s, and 60’s was to film each detonation with a high-speed camera, measure the blast radius as a function of time, and then use Taylor’s spherical blast wave equation to calculate the source energy (i.e., the yield). For surface detonations, the yield in Taylor’s equation was assumed to be twice as large as the actual yield to account for the energy reflected from the surface, assuming the ground was a perfect reflector. Recent simulations of surface detonations over water (referred to as barge shots) have shown that Taylor’s equation must be modified further to account for material entrainment and heat losses. We have computed this lost energy using a high-order radiation-hydrodynamics code to determine the reduction in blast radius vs. time. By analyzing simulation data in the same manner as film data, we have determined that a yield correction factor of 1.27± 0.04 should be applied to the barge shots.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

NASA NTRS2006

Airframe Noise Prediction by Acoustic Analogy: Revisited

The present work follows a recent survey of airframe noise prediction methodologies. In that survey, Lighthill s acoustic analogy was identified as the most prominent analytical basis for current approaches to airframe noise research. Within this approach, a problem is typically modeled with the Ffowcs Williams and Hawkings (FW-H) equation, for which a geometry-independent solution is obtained by means of the use of the free-space Green function (FSGF). Nonetheless, the aeroacoustic literature would suggest some interest in the use of tailored or exact Green s function (EGF) for aerodynamic noise problems involving solid boundaries, in particular, for trailing edge (TE) noise. A study of possible applications of EGF for prediction of broadband noise from turbulent flow over an airfoil surface and the TE is, therefore, the primary topic of the present work. Typically, the applications of EGF in the literature have been limited to TE noise prediction at low Mach numbers assuming that the normal derivative of the pressure vanishes on the airfoil surface. To extend the application of EGF to higher Mach numbers, the uniqueness of the solution of the wave equation when either the Dirichlet or the Neumann boundary condition (BC) is specified on a deformable surface in motion. The solution of Lighthill s equation with either the Dirichlet or the Neumann BC is given for such a surface using EGFs. These solutions involve both surface and volume integrals just like the solution of FW-H equation using FSGF. Insight drawn from this analysis is evoked to discuss the potential application of EGF to broadband noise prediction. It appears that the use of a EGF offers distinct advantages for predicting TE noise of an airfoil when the normal pressure gradient vanishes on the airfoil surface. It is argued that such an approach may also apply to an airfoil in motion. However, for the prediction of broadband noise not directly associated with a trailing edge, the use of EGF does not appear to offer any advantages over the use of FSGF at the present stage of development. It is suggested here that the applications of EGF for airframe noise analysis be continued. As an example pertinent to airframe noise prediction, the Fast Scattering Code of NASA Langley is utilized to obtain the EGF numerically on the surface of a three dimensional wing with a flap and leading edge slat in uniform rectilinear motion. The interpretation and use of these numerical Green functions are then discussed.

Farassat, F.↗

DOE OSTI2020

A note on the instability and pattern formation of shrinkage cracks in viscoplastic soils

In this work we present a theoretical study on the conditions for the onset of cracks, as well as the corresponding pattern formation, in saturated viscoplastic soils under isotropic loading (extension). The type of stress applied is left unspecified, to cover a variety of loadings including shrinkage due to desiccation, isotropic thermal expansion, mechanical loading and so forth. By treating the saturated soil as rigid viscoplastic, we obtain a 2D extension of the Cnoidal Waves equations (Veveakis and Regenauer-Lieb, 2015). By numerically solving the corresponding boundary value problem, we retrieve conditions for the onset of cracking instability in 2D loading, and identify the characteristic spacing between cracks to be a length scale combining all the hydro-mechanical parameters of the problem. Finally, we show that in a rectangular slab of clay under isotropic extension, patterns of triangular, rectangular and hexagonal cracks can tessellate the domain, with the hexagonal pattern being the energetically favored, as it minimizes the free energy of the system.

58 GEOSCIENCES↗

DOE OSTI2026

Goal-oriented real-time Bayesian inference for linear autonomous dynamical systems with application to digital twins for tsunami early warning

We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity partial differential equation (PDE) models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into a one-time-only offline phase in which the PDE model is solved a limited number of times (equal to the number of sensors), and an online phase that maps well onto GPUs and computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our ultimate goal is to apply this framework to construct digital twins for subduction zones, including Cascadia, to provide early warning for tsunamis generated by megathrust earthquakes. To this end, we demonstrate how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion (discretized with $\mathscr{O}$ (10 9 ) parameters) and forward predict the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with $\mathscr{O}$ (10 8 ) inversion parameters for which goal-oriented Bayesian inference is accomplished exactly and in real time, that is, in a matter of seconds.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Porting a 3D seismic modeling code (SW4) to CORAL machines

Seismic waves fourth order (SW4) solves the seismic wave equations on Cartesian and curvilinear grids using large compute clusters with O (100,000) cores. In this article we discuss the porting of SW4 to run on the CORAL architecture using the RAJA performance portability abstraction layer. The performances of key kernels using RAJA and CUDA are compared to estimate the performance penalty of using the portability abstraction layer. Code changes required for efficiency on GPUs and minimizing time spent in Message Passing Interface (MPI) are discussed. This article describes a path for efficiently porting large code bases to GPU-based machines while avoiding the pitfalls of a new architecture in the early stages of its deployment. Current bottlenecks in the code are discussed along with possible architectural or software mitigations. SW4 runs 28× faster on one 4-GPU CORAL node than on a CTS-1 node (Dual Intel Xeon E5-2695 v4). SW4 is now in routine use on problems of unprecedented resolution (203 billion grid points) and scale on 1,200 nodes of Summit.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Three dimensional full-wave nonlinear acoustic simulations: Applications to ultrasound imaging

Characterization of acoustic waves that propagate nonlinearly in an inhomogeneous medium has significant applications to diagnostic and therapeutic ultrasound. The generation of an ultrasound image of human tissue is based on the complex physics of acoustic wave propagation: diffraction, reflection, scattering, frequency dependent attenuation, and nonlinearity. The nonlinearity of wave propagation is used to the advantage of diagnostic scanners that use the harmonic components of the ultrasonic signal to improve the resolution and penetration of clinical scanners. One approach to simulating ultrasound images is to make approximations that can reduce the physics to systems that have a low computational cost. Here a maximalist approach is taken and the full three dimensional wave physics is simulated with finite differences. This paper demonstrates how finite difference simulations for the nonlinear acoustic wave equation can be used to generate physically realistic two and three dimensional ultrasound images anywhere in the body. A specific intercostal liver imaging scenario for two cases: with the ribs in place, and with the ribs removed. This configuration provides an imaging scenario that cannot be performed in vivo but that can test the influence of the ribs on image quality. Several imaging properties are studied, in particular the beamplots, the spatial coherence at the transducer surface, the distributed phase aberration, and the lesion detectability for imaging at the fundamental and harmonic frequencies. The results indicate, counterintuitively, that at the fundamental frequency the beamplot improves due to the apodization effect of the ribs but at the same time there is more degradation from reverberation clutter. At the harmonic frequency there is significantly less improvement in the beamplot and also significantly less degradation from reverberation. It is shown that even though simulating the full propagation physics is computationally challenging it is necessary to quantify ultrasound image quality and its sources of degradation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2015

An adaptive filtered back-projection for photoacoustic image reconstruction

Purpose: The purpose of this study is to develop an improved filtered-back-projection (FBP) algorithm for photoacoustic tomography (PAT), which allows image reconstruction with higher quality compared to images reconstructed through traditional algorithms. Methods: A rigorous expression of a weighting function has been derived directly from a photoacoustic wave equation and used as a ramp filter in Fourier domain. The authors’ new algorithm utilizes this weighting function to precisely calculate each photoacoustic signal’s contribution and then reconstructs the image based on the retarded potential generated from the photoacoustic sources. In addition, an adaptive criterion has been derived for selecting the cutoff frequency of a low pass filter. Two computational phantoms were created to test the algorithm. The first phantom contained five spheres with each sphere having different absorbances. The phantom was used to test the capability for correctly representing both the geometry and the relative absorbed energy in a planar measurement system. The authors also used another phantom containing absorbers of different sizes with overlapping geometry to evaluate the performance of the new method for complicated geometry. In addition, random noise background was added to the simulated data, which were obtained by using an arc-shaped array of 50 evenly distributed transducers that spanned 160° over a circle with a radius of 65 mm. A normalized factor between the neighbored transducers was applied for correcting measurement signals in PAT simulations. The authors assumed that the scanned object was mounted on a holder that rotated over the full 360° and the scans were set to a sampling rate of 20.48 MHz. Results: The authors have obtained reconstructed images of the computerized phantoms by utilizing the new FBP algorithm. From the reconstructed image of the first phantom, one can see that this new approach allows not only obtaining a sharp image but also showing the correct signal strength of the absorbers. The reconstructed image of the second phantom further demonstrates the capability to form clear images of the spheres with sharp borders in the overlapping geometry. The smallest sphere is clearly visible and distinguishable, even though it is surrounded by two big spheres. In addition, image reconstructions were conducted with randomized noise added to the observed signals to mimic realistic experimental conditions. Conclusions: The authors have developed a new FBP algorithm that is capable for reconstructing high quality images with correct relative intensities and sharp borders for PAT. The results demonstrate that the weighting function serves as a precise ramp filter for processing the observed signals in the Fourier domain. In addition, this algorithm allows an adaptive determination of the cutoff frequency for the applied low pass filter.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2022

Kimberlina 1.2 CCUS Geophysical Models and Synthetic Data Sets

This synthetic multi-scale and multi-physics data set was produced in collaboration with teams at the Lawrence Berkeley National Laboratory, National Energy Technology Laboratory, Los Alamos National Laboratory, and Colorado School of Mines through the Science-informed Machine Learning for Accelerating Real-Time Decisions in Subsurface Applications (SMART) Initiative. Data are associated with the following publication: Alumbaugh, D., Gasperikova, E., Crandall, D., Commer, M., Feng, S., Harbert, W., Li, Y., Lin, Y., and Samarasinghe, S., “The Kimberlina Synthetic Geophysical Model and Data Set for CO2 Monitoring Investigations”, The Geoscience Data Journal, 2023, DOI: 10.1002/gdj3.191. The dataset uses the Kimberlina 1.2 CO2 reservoir flow model simulations based on a hypothetical CO2 storage site in California (Birkholzer et al., 2011; Wainwright et al., 2013). Geophysical properties models (P- and S-wave seismic velocities, saturated density, and electrical resistivity) were produced with an approach similar to that of Yang et al. (2019) and Gasperikova et al. (2022) for 100 Kimberlina 1.2 reservoir models. Links to individual resources are provided below: [CO2 Saturation Models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-co2-saturation-models); Resistivity Models – [part 1](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-resistivity-models-part-1), [part 2](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-resistivity-models-part-2), and [part 3](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-resistivity-models-part-3); [Vp Velocity Models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-vp-velocity-models); [Vs Velocity Models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-vs-velocity-models); [Density Models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-density-models). The 3D distributions of geophysical properties for the 33 time stamps of the SIM001 model were used to generate synthetic seismic, gravity, and electromagnetic (EM) responses for 33 times between zero and 200 years. Synthetic surface seismic data were generated using 2D and 3D finite-difference codes that simulate the acoustic wave equation (Moczo et al., 2007). 2D data were simulated for six point-pressure sources along a 2D line with 10 m receiver spacing and a time spacing of 0.0005 s. 3D simulations were completed for 25 surface pressure sources using a source separation of 1 km in both the x and y directions and a time spacing of 0.001 s. Links to individual resources are provided below: [2D velocity models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-2d-velocity-models) and [2D surface seismic data](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-2d-surface-seismic-data). [3D velocity models](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-velocity-models), and 3D seismic data [year0](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year0), [year1](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year1), [year2](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year2), [year5](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year5), [year10](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year10), [year15](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year15), [year20](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year20), [year25](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year25), [year30](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year30), [year35](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year35), [year40](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year40), [year45](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year45), [year49](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year49), [year50](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year50), [year51](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year51), [year52](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year52), [year55](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year55), [year60](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year60), [year65](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year65), [year70](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year70), [year75](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year75), [year80](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year80), [year85](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year85), [year90](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year90), [year95](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year95), [year100](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year100), [year110](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year110), [year120](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year120), [year130](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year130), [year140](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year140), [year150](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year150), [year175](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year175), [year200](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-seismic-data-year200). The Python scripts to read these models and data are provided [here](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-python-scripts). EM simulations used a borehole-to-surface survey configuration, with the source located near the reservoir level and receivers on the surface using the code developed by Commer and Newman (2008). Pseudo-2D data for the source at [2500 m](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-pseudo-2d-csem-data-tz2500m) and [3025 m](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-pseudo-2d-csem-data-tz3025m), used a 2D inline receiver configuration to simulate a response over 3D resistivity models. The [3D data](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-3d-csem-data) contain electric fields generated by borehole sources at monitoring well locations and measured over a surface receiver grid. Vector gravity data, both on the surface and in boreholes, were simulated using a modeling code developed by Rim and Li (2015). The simulation scenarios were parallel to those used for the EM: [pseudo-2D data](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-gravity-data) were calculated along the same lines and within the same boreholes, and [3D data](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-gravity-data) were simulated over 3D models on the surface and in three monitoring wells. A series of [synthetic well logs](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-well-logs) of CO2 saturation, acoustic velocity, density, and induction resistivity in the injection well and three monitoring wells are also provided at 0, 1, 2, 5, 10, 15, and 20 years after the initiation of injection. These were constructed by combining the low-frequency trend of the geophysical models with the high-frequency variations of actual well logs collected in the Kimberlina 1 well that was drilled at the proposed site. Measurements of permeability and pore connectivity were made on cores of Vedder Sandstone, which forms the primary reservoir unit: [CT micro scans](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-ct-micro-scans-of-vedder-formation) and [Industrial CT Images](https://edx.netl.doe.gov/dataset/kimberlina-1-2-ccus-geophysical-models-and-synthetic-data-sets-industrial-ct-images-vedder-formation). These measurements provide the range of scales in the otherwise synthetic data set to be as close to a real-world situation as possible. References: Birkholzer, J.T., Zhou, Q., Cortis, A. and Finsterle, S., 2011. A sensitivity study on regional pressure buildup from large-scale CO2 storage projects. Energy Procedia, 4, 4371-4378. Commer, M., and Newman, G.A., 2008. New advances in three-dimensional controlled-source electromagnetic inversion, Geophysical Journal International, 172, 513-535. Gasperikova, E., Appriou, D., Bonneville, A., Feng, Z., Huang, L., Gao, K., Yang, X., Daley, T., 2022, Sensitivity of geophysical techniques for monitoring secondary CO2 storage plumes, Int. J. Greenh. Gas Control, Volume 114, 103585, ISSN 1750-5836, https://doi.org/10.1016/j.ijggc.2022.103585. Moczo, P., J.O. Robertsson and L. Eisner, 2007, The finite-difference time-domain method for modeling of seismic wave propagation: Advances in geophysics, 48, 421-516. Rim, H., and Y. Li, 2015, Advantages of borehole vector gravity in density imaging, Geophysics, 80, G1-G13. Wainwright, H. M.; Finsterle, S.; Zhou, Q.; Birkholzer, J. T., 2013. Modeling the Performance of Large-Scale CO2 Storage Systems: A Comparison of Different Sensitivity Analysis Methods. International Journal of Greenhouse Gas Control, 17, 189205. https://doi.org/10.1016/j.ijggc.2013.05.007, DOI: 10.18141/1603331. Yang, X., Buscheck, T.A., Mansoor, K., Wang, Z., Gao, K., Huang, L., Appriou, D., and Carroll, S.A., 2019. Assessment of geophysical monitoring methods for detection of brine and CO2 leakage in drinking water aquifers, International Journal of Greenhouse Gas Control, 90, 102803, https://doi.org/10.1016/j.ijggc.2019.102803.

CCUS↗

DOE OSTI2023

Physics‐Informed Machine Learning for Inverse Design of Optical Metamaterials

Optical metamaterials manipulate light through various confinement and scattering processes, offering unique advantages like high performance, small form factor and easy integration with semiconductor devices. However, designing metasurfaces with suitable optical responses for complex metamaterial systems remains challenging due to the exponentially growing computation cost and the ill‐posed nature of inverse problems. To expedite the computation for the inverse design of metasurfaces, a physics‐informed deep learning (DL) framework is used. A tandem DL architecture with physics‐based learning is used to select designs that are scientifically consistent, have low error in design prediction, and accurate reconstruction of optical responses. The authors focus on the inverse design of a representative plasmonic device and consider the prediction of design for the optical response of a single wavelength incident or a spectrum of wavelength in the visible light range. The physics‐based constraint is derived from solving the electromagnetic wave equations for a simplified homogenized model. The model converges with an accuracy up to 97% for inverse design prediction with the optical response for the visible light spectrum as input, and up to 96% for optical response of single wavelength of light as input, with optical response reconstruction accuracy of 99%.

Sarkar, Sulagna↗

DOE OSTI2025

Love symmetry in higher-dimensional rotating black hole spacetimes

We develop a method for constructing a 1-parameter family of globally-defined Love symmetry generators in rotating black hole spacetimes of general dimension. The key ingredient is to focus on the vicinity of the (physical) outer horizon, matching only the radial derivative and the outer horizon pole pieces of the Klein-Gordon operator in the black hole spacetime to the SL(2, ℝ) Casimir operator. After revisiting the 4D Kerr and 5D Myers-Perry cases, the procedure is illustrated on generalized Lense-Thirring spacetimes which describe a wide variety of slowly rotating black hole metrics in any number of dimensions. Such spacetimes are known to admit an extended tower of Killing tensor and Killing vector symmetries and, as demonstrated in this paper, allow for separability of the massive scalar wave equation in Myers-Perry-like coordinates. Interestingly, separability also occurs in the horizon-penetrating Painlevé–Gullstrand coordinates associated with the freely infalling observer who registers flat space around her all the way to singularity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

The great escape: tunneling out of microstate geometries

We compute the quasi-normal frequencies of scalars in asymptotically-flat microstate geometries that have the same charge as a D1-D5-P black hole, but whose long BTZ-like throat ends in a smooth cap. In general the wave equation is not separable, but we find a class of geometries in which the non-separable term is negligible and we can compute the quasi-normal frequencies using WKB methods. We argue that our results are a universal property of all microstate geometries with deeply-capped BTZ throats. These throats generate large redshifts, which lead to exceptionally-low-energy states with extremely long decay times, set by the central charge of the dual CFT to the power of twice the dimension of the operator dual to the mode. While these decay times are extremely long, we also argue that the energy decay is bounded, at large t , by (log( t )) – 2 and is comparable with the behavior of ultracompact stars, as one should expect for microstate geometries.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Holographic thermal correlators: a tale of Fuchsian ODEs and integration contours

We analyze real-time thermal correlation functions of conserved currents in holographic field theories using the grSK geometry, which provides a contour prescription for their evaluation. We demonstrate its efficacy, arguing that there are situations involving components of conserved currents, or derivative interactions, where such a prescription is, in fact, essential. To this end, we first undertake a careful analysis of the linearized wave equations in AdS black hole backgrounds and identify the branch points of the solutions as a function of (complexified) frequency and momentum. All the equations we study are Fuchsian with only regular singular points that for the most part are associated with the geometric features of the background. Special features, e.g., the appearance of apparent singular points at the horizon, whence outgoing solutions end up being analytic, arise at higher codimension loci in parameter space. Using the grSK geometry, we demonstrate that these apparent singularities do not correspond to any interesting physical features in higher-point functions. We also argue that the Schwinger-Keldysh collapse and KMS conditions, implemented by the grSK geometry, continue to hold even in the presence of such singularities. For charged black holes above a critical charge, we furthermore demonstrate that the energy density operator does not possess an exponentially growing mode, associated with ‘pole-skipping’, from one such apparent singularity. Our analysis suggests that the connection between the scrambling physics of black holes and energy transport has, at best, a limited domain of validity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Heavy states in 3d gravity and 2d CFT

We discuss correlators of light fields in heavy states in AdS 3 gravity and holographic 2d CFTs. In the bulk, the propagator of free fields in AdS backgrounds containing a conical defect or a BTZ black hole can be obtained by solving a wave equation, as well as by the method of images. On the boundary, these geometries are sourced by heavy operator insertions, and the propagator is dual to a heavy-light (HHLL) correlator. By matching its expansion in Virasoro blocks to our bulk results, we determine the OPE coefficients of all contributing states in both the s and t channels. In the s channel, these states are excitations of the light field on top of the heavy state, and their OPE coefficients are the amplitudes to create them. The t-channel OPE is dominated by the Virasoro vacuum block, but there is also an infinite family of light two-particle states that contribute to the correlator. The OPE coefficients that couple these states to heavy operators represent their expectation values in heavy backgrounds. We determine them exactly, derive their asymptotic form at large twist, and discuss their behavior near and above the BTZ threshold, where they become thermal one-point functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗