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DOE OSTI2025

Observation of Joule–Thomson photon-gas expansion

In recent years, a self-consistent optical thermodynamic framework has emerged that offers a systematic methodology to understand, harness and exploit the complex collective dynamics of multimode nonlinear systems. These developments now allow consideration of a series of longstanding problems in optics, including the prospect of funnelling the entire power flowing in a multimode system into its ground state, for which no methodology currently exists. Here, we demonstrate an all-optical Joule-Thomson expansion process mediated by photon-photon interactions whereby the temperature of the optical gas drops abruptly to zero. Our experiments in various configurations of coupled multicore nonlinear waveguide arrangements illustrate how light undergoing expansion-induced cooling can be channelled from arbitrary input states into the fundamental mode with near-unity efficiency. We show that the stability of the post-expansion state is ensured through an irreversible process of energy conversion. The all-optical thermodynamic phenomena explored in this study may enable innovative techniques where various uncorrelated but identical sources are merged into a unified spatially coherent state, offering a route for direct beam combining.

Kirsch, Marco S. (ORCID:0000000342798228)↗

DOE OSTI2025

ForestFlow: predicting the Lyman-α forest clustering from linear to nonlinear scales

On large scales, the Lyman-α forest provides insights into the expansion history of the Universe, while on small scales, it imposes strict constraints on the growth history, the nature of dark matter, and the sum of neutrino masses. This work introduces ForestFlow, a novel framework that bridges the gap between large- and small-scale analyses, which have traditionally relied on distinct modeling approaches. Using conditional normalizing flows, ForestFlow predicts the two Lyman-α linear biases (b δ and b η ) and six parameters describing small-scale deviations of the three-dimensional flux power spectrum (P 3D ) from linear theory as a function of cosmology and intergalactic medium physics. These are then combined with a Boltzmann solver to make consistent predictions, from arbitrarily large scales down to the nonlinear regime, for P 3D and any other statistics derived from it. Trained on a suite of 30 fixed-and-paired cosmological hydrodynamical simulations spanning redshifts from z = 2 to 4.5, ForestFlow achieves 3 and 1.5% precision in describing P 3D and the one-dimensional flux power spectrum (P 1D ) from linear scales to k = 5 Mpc −1 and k ∥ = 4 Mpc −1 , respectively. Thanks to its conditional parameterization, ForestFlow shows similar performance for ionization histories and two ΛCDM model extensions – massive neutrinos and curvature – even though none of these are included in the training set. This framework will enable full-scale cosmological analyses of Lyman-α forest measurements from the DESI survey.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Evaluation of alkali–silica reaction damage in concrete using linear and nonlinear resonance techniques

Here in this study, the initiation and development of alkali–silica reaction (ASR) in concrete prisms containing reactive coarse (RCA) and reactive fine (RFA) aggregates were monitored over one year using linear and nonlinear resonance techniques. Although the linear resonance test could detect initiation and development of ASR damage in RCA specimens, it failed in the RFA specimens. Petrographic analysis confirmed the presence of early-stage ASR damage and the presence of different microcracking patterns in the RFA and RCA specimens, which may explain differences in the linear resonance data. For both RCA and RFA specimens, the nonlinear resonance test results were able to detect the initiation of ASR damage and showed a strong correlation with the ASR expansion for all specimens from different mix designs. The results demonstrate the high sensitivity of the nonlinear resonance test and its potential for quantitative evaluation of the ASR damage state of concrete specimens without a baseline measurement.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Precision Tests of the Nonlinear Mode Coupling of Anisotropic Flow via High-Energy Collisions of Isobars

Valuable information on dynamics of expanding fluids can be inferred from the response of such systems to perturbations in their initial geometry. We apply this technique in high-energy 96 Ru+ 96 Ru and 96 Zr+ 96 Zr collisions to scrutinize the expansion dynamics of the quark-gluon plasma, where the initial geometry perturbations are sourced by the differences in deformations and radial profiles between 96 Ru and 96 Zr, and the collective response is captured by the change in anisotropic flow V n between the two collision systems. Using a transport model, we analyze how the nonlinear coupling between lower-order flow harmonics V 2 and V 3 to the higher-order flow harmonics V 4 and V 5 , expected to scale as V 4 NL = χ 4 V 2 2 and V 5NL = χ 5 V 2 V 3 , gets modified as one moves from 96 Ru+ 96 Ru to 96 Zr+ 96 Zr systems. We find that these scaling relations are valid to high precision: variations of order 20% in V 4NL and V 5NL due to differences in quadrupole deformation, octupole deformation, and nuclear skin modify χ 4 and χ 5 by about 1–2%. Percent-level deviations are however larger than the expected experimental uncertainties and could be measured. Therefore, collisions of isobars with different nuclear structures are a unique tool to isolate subtle nonlinear effects in the expansion of the quark-gluon plasma that would be otherwise impossible to access in a single collision system.

Physics↗

DOE OSTI2022

GenMod: A generative modeling approach for spectral representation of PDEs with random inputs

Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

High-Performance Electron Sources: Numerical Methods and Beam Dynamics at the Precision Frontier

Electron sources have a wide range of applications and there are many stakeholders that express continuing need for improvements and performance enhancements. Whether we consider ultra-cold, high-brightness, high-charge or high-average current source needs, there are some common themes from the point of view of the beam dynamics involved. These are the following ones: ability to model accurately the emission processes, including the presence of often complicated cathode and other boundary surfaces with a wide range of spatial scales; ability to deal accurately and efficiently with a large number of particles interacting pair-wise, including the stochastic part of these interactions with a wide range of spatial scales; and ability to propagate the particle distributions in time, including collisions with a wide range of temporal scales. These tasks require high precision and accuracy since the goal is usually generation, transport and preservation of very high-quality beams. This grant addressed one of the rem

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Chromatic Transport Models for ImpactX

This note describes the basic levels of Hamiltonian approximation (for straight-axis elements) that are used in the symplectic beam dynamics modeling code ImpactX. These include: purely linear models, models based on a paraxial (chromatic) expansion of the Hamiltonian, and models based on the exact nonlinear Hamiltonian. The focus here is on paraxial (chromatic) models.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Computing Nonlinear Power Spectra Across Dynamical Dark Energy Model Space with Neural ODEs

I show how to compute the nonlinear power spectrum across the entire $w(z)$ dynamical dark energy model space. Using synthetic ΛCDM data, I train a neural ordinary differential equation (ODE) to infer the evolution of the nonlinear matter power spectrum as a function of the background expansion and mean matter density across ∼9 Gyr of cosmic evolution. After training, the model generalises to any dynamical dark energy model parameterised by $w(z)$. With little optimisation, the neural ODE is accurate to within 4% up to $k = 5\, h\, {\mathrm Mpc}^{−1}$. Unlike simulation rescaling methods, neural ODEs naturally extend to summary statistics beyond the power spectrum that are sensitive to the growth history.

cosmology↗

DOE OSTI2023

Neural Network Enhanced RKPM for Electrochemical-Mechanical Coupled Damage Modeling of Energy Storage Materials

Energy storage materials undergo significant charge cycling, which makes understanding their reliability and durability fundamental in predicting performance and service life. Strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking, largely along material interfaces and grain boundaries. For Li-ion batteries, for example, lithium moving between electrodes during charging and discharging process causes expansion and contraction of grains, and the strongly anisotropic and nonlinearly [Li]-dependent grain material properties can cause grains to expand into and contract away from each other, leading to chemo-mechanical cracking. In the first part of this work, a RKPM based computational framework for solving the coupled solid-phase lithium conservation with Fickian diffusion and the lithium concentration dependent anisotropic mechanical problem subjected to a highly nonlinear Butler-Volmer boundary condition is introduced. The choice of RKPM completeness conditions for lithium concentration and mechanical deformation fields, and the variational consistency condition for the domain integration of the coupled problem is first determined. In the second part of this work, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1] is leveraged to accurately capture damage and crack propagation throughout the material, by learning the location, orientation, and sharpness of discontinuity while allowing for a coarser nodal distribution than that is necessary for capturing sharp solution transitions using traditional mesh-based methods. NN-RKPM is used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure.

damage modeling↗

DOE OSTI2022

Analytical benchmark solution for 1-D neutron transport coupled with thermal conduction and material expansion

In this work we present fully analytical solutions for a class of finite, homogeneous, 1-D slab benchmark problems with nonlinear temperature feedback effects. The proposed class of benchmarks include multiplicative 1-D neutron transport (limited to quasistatic S{sub 2} with μ = ±1) coupled with thermal conduction, convection, Doppler broadening, and expansion effects along the length of the slab. This class of benchmark models, along with the corresponding analytical solutions, are valuable for validating multiphysics analysis frameworks that support coupled neutronics/thermal/structural calculations. Analytical solutions for the benchmarks are obtained by introducing an ansatz that the equilibrium flux and temperature distributions in the slab have the same shape. Specific values for the total microscopic cross section, σ{sub t,0}, and conductive heat transfer coefficient, h, that satisfy the assumed ansatz are then determined. A discussion of the procedure for generating benchmark models and analytical solutions is provided, along with numerical results for an example set of model parameters and thoughts on practical applications of the benchmarks for multiphysics code validation. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Evolution of Magnetohydrodynamic Turbulence in the Expanding Solar Wind: Residual Energy and Intermittency

We conduct 3D magnetohydrodynamic simulations of decaying turbulence in the context of the solar wind. To account for the spherical expansion of the solar wind, we implement the expanding box model. The initial turbulence comprises uncorrelated counterpropagating Alfvén waves and exhibits an isotropic power spectrum. Our findings reveal the consistent generation of negative residual energy whenever nonlinear interactions are present, independent of the normalized cross helicity σc and compressibility. The spherical expansion facilitates this process. The resulting residual energy is primarily distributed in the perpendicular direction, with S 2 (b) − S 2 (u) ∝ l ⊥ or equivalently –E r ∝ k$^{–2}_{⟂}$. Here S 2 (b) and S 2 (u) are second-order structure functions of magnetic field and velocity respectively. In most runs, S 2 (b) develops a scaling relation S 2 (b) ∝ $l$$^{1/2}_{⊥}$ (E b ∝ k$^{–3/2}_{⟂}$). In contrast, S 2 (u) is consistently shallower than S 2 (b), which aligns with in situ observations of the solar wind. We observe that the higher-order statistics of the turbulence, which act as a proxy for intermittency, depend on the initial σc and are strongly affected by the expansion effect. Generally, the intermittency is more pronounced when the expansion effect is present. Finally, we find that in our simulations, although the negative residual energy and intermittency grow simultaneously as the turbulence evolves, the causal relation between them seems to be weak, possibly because they are generated on different scales.

Interplanetary turbulence↗

DOE OSTI2021

Topology optimization of 3D photonic crystals with complete bandgaps

The design of photonic crystals with complete bandgaps has recently received considerable research focus for numerous reasons. This work leverages well-known nonlinear programming techniques to alleviate the non-smoothness caused by degenerate eigenvalues such that topology optimization problems can be solved with the open-source IPOPT software. A fully-vectorial plane wave expansion technique is used with an iterative eigensolver to efficiently predict dispersion properties of candidate structures. Nonlinear programming is employed to solve the inverse problem of designing three-dimensional periodic structures that exhibit complete two-dimensional (2D) and three-dimensional (3D) photonic bandgaps. Mesh refinement is performed to alleviate the large computational burden of designing and analyzing photonic crystals, and a periodic density filter is implemented to impose a minimum feature size for manufacturability considerations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

An Integrated Computational Materials Engineering (ICME) Approach to Design Nonlinear Transition Zones Between Dissimilar Metals

Current approaches to designing graded transition joints (GTJs) between dissimilar metals often rely on linear changes in both composition profiles and thickness of each sublayer. This increases fabrication cost and may not be optimal with respect to residual stress or the formation of undesirable phases. Here, in this study, GTJs between P91 ferritic/martensitic steel and 347H austenitic stainless steel were designed using Integrated Computational Materials Engineering (ICME) principles with nonlinear composition and length profiles. Guided by inputs from classical mechanics and CALPHAD predictions of carbon chemical potential, a novel transition zone consisting of five discrete compositions was proposed, with the thickness of each sublayer varying according to a brachistochrone-inspired distribution. In addition to carbon potential gradients, CALPHAD was used to predict coefficients of thermal expansion, which were incorporated into finite element models to evaluate stress evolution. The proposed nonlinear design resulted in a smoother carbon potential gradient, lower carbon depletion at the P91 interface, and a comparable residual stress under long-term thermal exposure, compared to a conventional linear design using ten sublayers with equal thickness. This work introduces a brachistochrone-inspired distribution for GTJ design, offering a general framework for optimizing graded interfaces between dissimilar metals.

Directed Energy Deposition↗

DOE OSTI2024

Qualification and Quantification of Porosity at the Top of the Fuel Pins in Metallic Fuels Using Image Processing

Approximately 130,000 metal fuel pins were irradiated in the Experimental Breeder Reactor II (EBR-II) during its 30 years of operation to develop and characterize existing and prospective fuels. For many of the metal fuel irradiation experiments, neutron radiography imaging was performed to characterize fuel behavior, such as fuel axial expansion. While several fuel expansion results obtained from neutron radiography imaging have been published, the analysis of neutron radiography for the purpose of describing statistical properties of porous matter formed on top of the fuel pins, also referred to as fluff in previous publications, is significantly less represented in the literature with just a single paper so far. This study aims to validate and augment results reported in previous publications using automated image processing. The paper describes the statistical properties of the porous matter in terms of nine parameters derived from radiography images and correlates those parameters with such fuel properties as composition, expansion, temperature, and burnup. The reported results are based on 1097 fuel pins of eight different fuel compositions. For three major fuel types, U-10Zr, U-8Pu-10Zr, and U-19Pu-10Zr, a clear negative correlation is found between the Pu content and five parameters describing the amount of porous matter generated. The parameters describing granularity properties, however, showed either negative correlation or nonlinear dependency from fuel composition. The parameters describing the amount showed a positive correlation with fuel axial expansion, while granularity parameters showed a negative correlation with axial expansion. The dependency on cladding temperature was found to be weak. A positive correlation is demonstrated for volume parameters and fuel burnup. In general, reported results confirm and validate findings published in previous studies using a much larger number of pins and automated processing techniques, which easily lend themselves to reproducibility, thus avoiding subjective bias.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Space–time structure of weak magnetohydrodynamic turbulence

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

Physics↗

DOE OSTI2025

Capacitive response of biological membranes

We present a minimal model to analyze the capacitive response of a biological membrane subjected to a step voltage via blocking electrodes. Through a perturbative analysis of the underlying electrolyte transport equations, we show that the leading-order relaxation of the transmembrane potential is governed by a capacitive timescale, τ_{C}=λ_{D}L/D(2+Γδ^{M}/L/4+Γδ^{M}/λ_{D}), where λ_{D} is the Debye screening length, L is the electrolyte width, Γ is the ratio of the permittivity of the electrolyte to the membrane, δ^{M} is the membrane thickness, and D is the ionic diffusivity. This timescale is considerably shorter than the traditional RC timescale λ_{D}L/D for a bare electrolyte due to the membrane's low permittivity and finite thickness. Beyond the linear regime, however, salt diffusion in the bulk electrolyte drives a secondary, nonlinear relaxation process of the transmembrane potential over a longer timescale τ_{L}=L^{2}/4π^{2}D. A simple equivalent-circuit model accurately captures the linear behavior, and the perturbation expansion remains applicable across the entire range of observed physiological transmembrane potentials. Together, these findings underscore the importance of the faster capacitive timescale and nonlinear effects on the bulk diffusion timescale in determining transmembrane potential dynamics for a range of biological systems.

Farhadi, Jafar↗

DOE OSTI2025

Temperature and Strain Sensing Characteristics of a 128° YX-Cut LiNbO 3 Rayleigh-Mode SAW Sensor From Room to Cryogenic Temperatures

Accurate, passive, and wireless monitoring of cryogenic hardware is essential for high-energy physics, space propulsion, and biomedical instrumentation. Here, this study quantifies the coupled temperature-strain behavior of Rayleigh-mode surface acoustic-wave (SAW) delay-line sensors fabricated on 128° YX-cut LiNbO 3 . A nonlinear finite element (FE) model incorporating Varshni-based elastic constants, higher-order thermal expansion, and temperature-dependent piezo- and dielectric coefficients was developed and validated experimentally between 280K and 80K. Free-standing (first test condition) and bonded/wired (second test condition) devices exhibited indistinguishable thermal responses; the average temperature coefficient of delay (TCD) in the critical cryogenic range from 130K down to 80K differed by only 0.15 ppm/K (0.32%), confirming that bonding-induced stress is negligible. Over 280-80K the measured TCD was 61.77 ppm/K, while the FE model predicted an equivalent temperature coefficient of frequency (TCF) of −62.74 ppm/K with an overall coefficient of determination R2 = 0.998. In the critical cryogenic interval 130-80K the TCD fell to 47.66 ppm/K, indicating improved thermal stability at low temperature. Controlled loading (0-300 με) revealed a strain coefficient of delay (SCD) that rises from 0.53 ± 0.02 ppm/με at 300K to 1.05 ± 0.02 ppm/με at 80K. This modest sensitivity confirms that, for temperature sensing, strain is a second-order perturbation above 135K but must be compensated at deeper cryogenic levels. Overall, this work establishes a predictive multiphysics model together with repeatable wired measurements that confirm the suitability of SAW sensors for temperature and strain monitoring in extreme cryogenic environments, while also providing a baseline for future wireless implementations.

25 ENERGY STORAGE↗

DOE OSTI2023

Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration

The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a controllable way, but unfavorable combinatorics often defeats this in practice and applications with n ≥ 4 are rare. Here, we outline an algorithm to overcome this combinatorial bottleneck, based on a bottom-up approach to energy-based screening. This is implemented within a new open-source software application (“Fragme∩t”), which is integrated with a lightweight semi-empirical method that is used to cull subsystems, attenuating the combinatorial growth of higher-order terms in the graph that is used to manage the calculations. This facilitates applications of unprecedented size, and we report four-body calculations in (H2O)64 clusters that afford relative energies within 0.1 kcal/mol/monomer of the supersystem result using less than 10% of the unique subsystems. We also report n-body calculations in (H2O)20 clusters up to n = 8, at which point the expansion terminates naturally due to screening. These are the largest n-body calculations reported to date using ab initio electronic structure theory, and they confirm that high-order n-body terms are mostly artifacts of basis-set superposition error.

Chemistry↗