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DOE OSTI2026

Long-Range Dispersion Governs the Behavior of Near-Critical Fluids: Universal Scaling and Implications for Accurate Molecular Simulation

Computer simulations of near-critical and supercritical fluids often deviate from experimental results, a discrepancy commonly attributed to force-field resolutions and inaccuracies. We demonstrate that these errors primarily stem from using finite cutoff schemes for dispersion interactions, which become effectively long-range as the correlation length grows near the critical point. By employing the smooth particle-mesh Ewald method to account for full long-range dispersion, we show that coarse-grained models can also achieve high quantitative accuracy for n-undecane and propylbenzene. This approach enables the precise determination of density fluctuations and correlation lengths, which exhibit universal critical scaling and depend on the molecular size and shape. Our findings resolve a longstanding debate in molecular simulations of near-critical fluids, establishing that capturing long-wavelength fluctuations is essential for bridging the gap between the microscopic behavior and macroscopic critical phenomena.

Chen, Guang↗

DOE OSTI2025

Deciphering supramolecular and polymer-like behavior in metallogels: real-time insights into temperature-modulated gelation and rapid self-assembly dynamics

Bis(pyridyl) urea-based gelators, namely L2 and its isomeric mixture ( L1 + L2 ), are known to self-assemble into 1D architectures capable of inducing supramolecular gelation. Coordination with metal ions such as Ag( I ), Cu( II ), and Fe( III ) introduces structural reinforcement, enabling the formation of distinct 3D networks governed by metal-specific coordination geometries. Here, we present a comprehensive investigation into the temperature-responsive behavior (20–60 °C) of L2 and L1 + L2 , both in the absence and presence of Ag( I ), Dy( III ), Fe( III ), Cu( II ), and Ho( III ), using real-time small-angle neutron scattering (SANS). To probe long-term structural evolution/kinetics of self-assembly, real-time small-angle X-ray scattering (SAXS) was employed on L2 + Ag gels, complemented by differential scanning calorimetry (DSC) to evaluate thermal transitions. Our results reveal strikingly divergent gelation behaviors: L2 forms a highly rigid, covalent polymer-like network, while L1 + L2 exhibits remarkable thermal adaptability. Upon metal coordination, the assemblies exhibit pronounced crystallinity and exceptional thermal stability, as evidenced by persistent Bragg reflections and invariant d-spacings. Intriguingly, L2 : Fe (2 : 1) and L1 : L2 : Fe (0.5 : 0.5 : 1) in acetonitrile-d 3 (ACN-d 3 ) deviate from this trend, forming thermally labile amorphous gels. These systems show a complete loss of crystalline order, reduced Porod exponents—indicative of collapsed or branched fiber morphologies—and prominent melting and glass transition events in DSC. Fitting SANS and SAXS data to the correlation length model unveiled insightful nanostructural features. While most systems displayed minimal temperature-induced variation in mesh size or surface morphology, L2 : Ag in dimethyl sulfoxide-d 6 (DMSO-d 6 )/D 2 O and L2 : Fe (1 : 1) in ACN-d 3 exhibited a rare combination of thermally stable correlation lengths and increasing high- q exponents—strongly suggesting progressive fiber densification or surface smoothing within a robust gel framework. These findings highlight the tunability and structural resilience of supramolecular gels through precise control of ligand architecture, metal coordination, and temperature, offering valuable design principles for functional soft materials.

Pajoubpong, Jinnipha [Univ. of Cincinnati, OH (Uni↗

NASA NTRS1977

ALTKAL: An optimum linear filter for GEOS-3 altimeter data

ALTKAL is a computer program designed to smooth sea surface height data obtained from the GEOS 3 altimeter, and to produce minimum variance estimates of sea surface height and sea surface slopes, along with their standard derivations. The program operates by processing the data through a Kalman filter in both the forward and backward directions, and optimally combining the results. The sea surface height signal is considered to have a geoid signal, modeled by a third order Gauss-Markov process, corrupted by additive white noise. The governing parameters for the signal and noise processes are the signal correlation length and the signal-to-noise ratio. Mathematical derivations of the filtering and smoothing algorithms are presented. The smoother characteristics are illustrated by giving the frequency response, the data weighting sequence and the transfer function of a realistic steady-state smoother example. Based on nominal estimates for geoidal undulation amplitude and correlation length, standard deviations for the estimated sea surface height and slope are 12 cm and 3 arc seconds, respectively.

Fang, B. T.↗

DOE OSTI2025

Equilibrium expectations for non-Gaussian fluctuations near a QCD critical point

With the highly anticipated results from the Beam Energy Scan II program at RHIC being recently revealed, an understanding of particle-number fluctuations and their significance as a potential signature of a possible QCD critical point is crucial. Early works that embarked on this endeavor sought to estimate the fluctuations due to the presence of a critical point assuming they stay in equilibrium. From these results came the proposal to focus efforts on higher, non-Gaussian, moments of the event-by-event distributions, in particular of the number of protons. These non-Gaussian moments are especially sensitive to critical fluctuations, as their magnitudes are proportional to high powers of the critical correlation length. As the equation of state provides key input for hydrodynamical simulations of heavy-ion collisions, we estimate equilibrium fluctuations from the BEST equation of state (EoS) that includes critical features from the 3D Ising Model. In particular, the proton factorial cumulants and their dependence on non-universal mapping parameters is investigated within the BEST EoS. Furthermore, the correlation length, as a central quantity for the assessment of fluctuations in the vicinity of a critical point, is also calculated in a consistent manner with the scaling equation of state. An understanding of the equilibrium estimates of proton factorial cumulants will be useful for further comparison to estimates of out-of-equilibrium fluctuations in order to determine the magnitude of the observable fluctuations to be expected in heavyion collision experiments, in which the time spent near a critical point is short.

Karthein, Jamie M. [Massachusetts Institute of Tec↗

NASA NTRS1988

On the universality of the two-point galaxy correlation function

The behavior of the two-point galaxy correlation function in volume-limited subsamples of three complete redshift surveys is investigated. The correlation length is shown to scale approximately as the square root of the distance limit in both the CfA and Southern Sky catalogs, but to be independent of the distance limit in the IRAS sample. This effect is found to be due to factors such as the large positive density fluctuations in the foreground of the optically selected catalogs biasing the correlation length estimate downward, and the brightest galaxies appearing to be more strongly clustered than the mean.

Davis, Marc↗

DOE OSTI2020

Scaling Law Describes the Spin-Glass Response in Theory, Experiments, and Simulations

The correlation length ξ, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields or close to the glass temperature. We solve this problem by introducing a scaling law that takes into account both the magnetic field and the time-dependent spin-glass correlation length. Here, the scaling law is successfully tested against experimental measurements in a CuMn single crystal and against large-scale simulations on the Janus II dedicated computer.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Fluctuation dynamics near the QCD critical point

The evolution of nonhydrodynamic slow processes near the QCD critical point is explored with the novel hydro+ framework, which extends the conventional hydrodynamic description by coupling it to additional explicitly evolving slow modes describing long wavelength fluctuations. Here, their slow relaxation is controlled by critical behavior of the correlation length and is independent from gradients of matter density and pressure that control the evolution of the hydrodynamic quantities. In this exploratory study, we follow the evolution of the slow modes on top of a simplified QCD matter background, allowing us to clearly distinguish and study, both separately and in combination, the main effects controlling the dynamics of critical slow modes. In particular, we show how the evolution of the slow modes depends on their wave number, the expansion of and advection by the fluid background, and the behavior of the correlation length. Nonequilibrium contributions from the slow modes to bulk matter properties that affect the bulk dynamics (entropy, pressure, temperature, and chemical potential) are discussed and found to be small.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2022

Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems

Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic partial differential equations. This loss of variance has been attributed to reduced-rank representations of the covariance matrix, as in ensemble methods for example, or else to the use of dissipative numerical methods. Through a combination of analytical work and numerical experiments, we demonstrate that significant variance loss, as well as gain, typically occurs during covariance propagation, even at full rank. The cause of this unusual behavior is a discontinuous change in the continuum covariance dynamics as correlation lengths become small, for instance in the vicinity of sharp gradients in the velocity field. This discontinuity in the covariance dynamics arises from hyperbolicity: the diagonal of the kernel of the covariance operator is a characteristic surface for advective dynamics. Our numerical experiments demonstrate that standard numerical methods for evolving the state are not adequate for propagating the covariance, because16they do not capture the discontinuity in the continuum covariance dynamics as correlations lengths tend to zero. Our analytical and numerical results show that this leads to significant, spurious variance loss in certain regions, and gain in others. The results suggest that developing local covariance propagation methods designed specifically to capture covariance evolution near the diagonal may prove a useful alternative to current methods of covariance propagation.

covariance propagation↗

DOE OSTI2024

Revealing Mesoscale Ionomer Membrane Structure by Tender Resonant X-ray Scattering

Nafion, a perfluorosulfonic acid ionomer, has been well-studied for decades due to its key role as an ion-conductive membrane in electrochemical energy conversion and storage applications. When hydrated, this membrane phase separates into a complex hierarchical nanostructure with hydrophilic domains that facilitate ion transport. Hard X-ray scattering has been a powerful technique in understanding Nafion due to its capabilities in capturing the ionomer’s nanophase separated structure, which gives rise to contrast between polymer and water domains. More recently, resonant X-ray scattering, which tunes to elemental absorption edges to provide specificity on constituent elements, has been explored to highlight key interactions related to the sulfonic acid groups within its structure. Here, in this work, we study the Nafion nanostructure by combining hard X-ray scattering and tender resonant X-ray scattering (TReXS) at the sulfur K-edge to reveal a mesoscopic feature corresponding to a correlation length of approximately 40 nm that has been challenging to resolve with hard X-ray studies. Additionally, we study the effect of the dispersion solvent composition that plays a key role in the formation of this mesoscale feature. Notably, TReXS can attain high contrast to decipher this mesoscale morphology even for dry polymer membranes under a vacuum, which typically have reduced contrast for hard X-rays. We find that the correlation length of this mesoscale feature decreases with increasing water fraction in the dispersion, which is the opposite trend exhibited by the smaller intercrystalline feature in the same membranes. This study showcases the utility of TReXS to uncover multiscale morphological details in functional polymers that are not always revealed by other methods like hard X-ray scattering. We illustrate this with Nafion, which is a relevant ion-conducting polymer for electrochemical technologies.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Continuum covariance propagation for understanding variance loss in advective systems

At the heart of modern data assimilation schemes is covariance propagation.Loss of variance experienced in large-scale applications such as numerical weather prediction is problematic, and the development of auxiliary methods to mitigate this issue is an active research area. The focus of this work is to understand the root causes of variance loss and show that for advective dynamics, the covariance propagation by itself typically causes significant, spurious loss of variance, even at full rank. To demonstrate this, we first study continuum covariance propagation by analyzing the covariance evolution equation for advective dynamics. The behavior of this evolution equation changes abruptly as the correlation length tends to zero, for example in the vicinity of sharp gradients in the advection field. This happens because the diagonal of the kernel of the covariance operator is a characteristic surface for advective dynamics. Our numerical experiments then confirm that the variance lost during numerical propagation greatly exceeds that due to numerical dissipation alone. The variance loss is driven primarily by inaccurate variance propagation resulting from standard, full-rank covariance propagation schemes, which have difficulty capturing the abrupt change in dynamics as the correlation length tends to zero. These results suggest that developing local covariance propagation methods may prove useful in ameliorating the variance loss observed in data assimilation schemes

Covariance Propagation↗

DOE OSTI2024

Constant-Depth Preparation of Matrix Product States with Adaptive Quantum Circuits

Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices limited to shallow-depth circuits. Matrix product states (MPS) comprise a significant class of many-body entangled states, efficiently describing the ground states of one-dimensional gapped local Hamiltonians and finding applications in a number of recent quantum algorithms. Recently, it has been shown that the Affleck-Kennedy-Lieb-Tasaki state—a paradigmatic example of an MPS—can be exactly prepared with an adaptive quantum circuit of constant depth, an impossible feat with local unitary gates alone due to its nonzero correlation length [Smith , PRX Quantum 4, 020315 (2023)]. In this work, we broaden the scope of this approach and demonstrate that a diverse class of MPS can be exactly prepared using constant-depth adaptive quantum circuits, outperforming theoretically optimal preparation with unitary circuits. We show that this class includes short- and long-ranged entangled MPS, symmetry-protected topological (SPT) and symmetry-broken states, MPS with finite Abelian, non-Abelian, and continuous symmetries, resource states for MBQC, and families of states with tunable correlation length. Moreover, we illustrate the utility of our framework for designing constant-depth sampling protocols, such as for random MPS or for generating MPS in a particular SPT phase. We present sufficient conditions for particular MPS to be preparable in constant time, with global on-site symmetry playing a pivotal role. Altogether, this work demonstrates the immense promise of adaptive quantum circuits for efficiently preparing many-body entangled states and provides explicit algorithms that outperform known protocols to prepare an essential class of states. Published by the American Physical Society 2024

Smith, Kevin C. (ORCID:0000000223971518)↗

DOE OSTI2024

Not all that is β0 is β-function: the DGLAP resummation and the running coupling in NLO JIMWLK

Abstract We reanalyze the origin of the large transverse logarithms associated with the QCD one loopβfunction coefficient in the NLO JIMWLK Hamiltonian. We show that some of these terms are not associated with the running of the QCD coupling constant but rather with the DGLAP evolution. The DGLAP-like resummation of these logarithms is mandatory within the JIMWLK Hamiltonian, as long as the color correlation length in the projectile is larger than that in the target. This regime in fact covers the whole range of rapidities at which JIMWLK evolution is supposed to be applicable. We derive the RG equation that resums these logarithms to all orders inα s in the JIMWLK Hamiltonian. This is a nonlinear equation for the eikonal scattering matrixS(x). We solve this equation, and perform the DGLAP resummation in two simple cases: the dilute limit, where both the projectile and the target are far from saturation, and the saturated regime, where the target correlation length also determines its saturation momentum.

Physics↗

DOE OSTI2020

Finite-size effects in lead scandium tantalate relaxor thin films

Large electromechanical effects in relaxor ferroelectrics are generally attributed to the collective response of an ensemble of correlated, nanometer-sized polar structures induced by chemical and charge disorder. Here, we study finite-size effects on such polar order (i.e., how it evolves when sample dimensions approach the polarization correlation length) in 7–70-nm-thick films of the relaxor ferroelectric PbSc 0.5 Ta 0.5 O 3 . Temperature-dependent polarization studies reveal a linear suppression of the polarization and nonlinearity associated with relaxor order as the film thickness decreases to ≈ 30 nm. Below this thickness, however, the suppression rapidly accelerates, and polarization is completely absent by film thicknesses of ≈ 7 nm, despite the continued observation of a broad peak in dielectric permittivity and frequency dispersion. Diffuse-scattering measurements reveal the diffuse-scattering symmetry, and analysis suggests the films have a polarization correlation length of ≈ 23 nm. Finally, taken together, it is apparent that reduction of sample size and the resulting distribution of polar structures drive suppression and eventual quenching of the electrical response of relaxors, which may be attributed to increasing dipole-dipole and dipole-interface interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1980

Cycle II.5 aircraft aero-optical turbulent boundary-layer/shear-layer measurements

The aero-optical effects associated with propagating a laser beam through aircraft turbulent boundary layers and shear layers were examined. Observed laser optical performance levels were compared with those inferred from aerodynamic measurements of unsteady densities and correlation lengths within these random flows. Optical instrumentation included a fast shearing interferometer (FSI). A 9 cm diameter collimated helium neon laser beam made a double pass through the aircraft random flow via an airfoil mirror located one meter from the fuselage. Typical aircraft turbulent boundary layer thickness measured 0.3 meters. Averaging many FSI generated modulation transfer functions (MTFs) and Fourier transforming, this average yields the expected far field intensity degradation associated with an aircraft mounted laser system. Aerodynamic instrumentation included fine wire probes to measure unsteady temperature and mass flux. A laser doppler velocimeter measured unsteady velocity within the flows. An analysis of these data yielded point measurements of unsteady density and correlation length.

Gilbert, K.↗

NASA NTRS2017

Experimental Verification of Buffet Calculation Procedure Using Unsteady Pressure-Sensitive Paint

Typically, a limited number of dynamic pressure sensors is employed to determine the unsteady aerodynamic forces on large, slender aerospace structures. This paper describes a robust calculation procedure based on frequency-specific correlation lengths and validation from an experiment conducted on a flat panel coated with fast response pressure-sensitive paint. The first part of the paper describes the procedure used to analyze the pressure sensitive paint images and a calibration method using dynamic pressure transducers. Excellent comparison in spectra, coherence, and phase, measured via pressure-sensitive paint and dynamic pressure sensors, validates the pressure-sensitive paint data. The second part of the paper describes the buffet validation process, the first step of which was to use pressure histories from all pixels to determine the true force fluctuations. In the next step, only a selected number of pixels was chosen as virtual sensors, and a correlation-length-based buffet calculation procedure was applied to determine modeled force fluctuations. By progressively decreasing the number of virtual sensors, it was observed that the present calculation procedure was able to make a close estimate of the true unsteady forces only from eight sensors. It is believed that the present work provides the first validation of a buffet calculation procedure.

Buffet↗

DOE OSTI2020

Suppression of superconducting parameters by correlated quasi-two-dimensional magnetic fluctuations

In this work, we consider a clean layered magnetic superconductor in which a continuous magnetic transition takes place inside a superconducting state. We assume that the exchange interaction between superconducting and magnetic subsystems is weak so that superconductivity is not destroyed at the magnetic transition. A representative example of such material is Rb Eu Fe 4 As 4 . We investigate the suppression of the superconducting gap and superfluid density by correlated magnetic fluctuations in the vicinity of the magnetic transition. The influence of nonuniform exchange field on superconducting parameters is very sensitive to the relation between the magnetic correlation length ξ h and superconducting coherence length ξ s defining the ‘scattering’ ( ξ h < ξ s ) and ‘smooth’ ( ξ h > ξ s ) regimes. As a small uniform exchange field does not affect the superconducting gap and superfluid density at zero temperature, smoothening of the spatial variations of the exchange field reduces its effects on these parameters. We develop a quantitative description of this ‘scattering-to-smooth’ crossover for the case of quasi-two-dimensional magnetic fluctuations realized in Rb Eu Fe 4 As 4 . Since the magnetic-scattering energy scale is comparable with the gap in the crossover region, the standard quasiclassical approximation is not applicable and full microscopic treatment is required. We find that the corrections to both the gap and superfluid density increase proportionally to ξ h until it remains much smaller than ξ s . In the opposite limit, when the correlation length exceeds the coherence length both parameters have much weaker dependence on ξ h . Moreover, the gap correction may decrease with increasing of ξ h in the immediate vicinity of the magnetic transition if it is located at temperature much lower than the superconducting transition. We also find that the crossover between the two regimes is unexpectedly broad: The standard scattering approximation becomes sufficient only when ξ h is substantially smaller than ξ s .

36 MATERIALS SCIENCE↗

NASA NTRS2017

Comparison of Commonly-Used Microwave Radiative Transfer Models for Snow Remote Sensing

This paper reviews four commonly-used microwave radiative transfer models that take different electromagnetic approaches to simulate snow brightness temperature (T(sub B)): the Dense Media Radiative Transfer - Multi-Layer model (DMRT-ML), the Dense Media Radiative Transfer - Quasi-Crystalline Approximation Mie scattering of Sticky spheres (DMRT-QMS), the Helsinki University of Technology n-Layers model (HUT-nlayers) and the Microwave Emission Model of Layered Snowpacks (MEMLS). Using the same extensively measured physical snowpack properties, we compared the simulated T(sub B) at 11, 19 and 37 GHz from these four models. The analysis focuses on the impact of using different types of measured snow microstructure metrics in the simulations. In addition to density, snow microstructure is defined for each snow layer by grain optical diameter (Do) and stickiness for DMRT-ML and DMRT-QMS, mean grain geometrical maximum extent (D(sub max)) for HUT n-layers and the exponential correlation length for MEMLS. These metrics were derived from either in-situ measurements of snow specific surface area (SSA) or macrophotos of grain sizes (D(sub max)), assuming non-sticky spheres for the DMRT models. Simulated T(sub B) sensitivity analysis using the same inputs shows relatively consistent T(sub B) behavior as a function of Do and density variations for the vertical polarization (maximum deviation of 18 K and 27 K, respectively), while some divergences appear in simulated variations for the polarization ratio (PR). Comparisons with ground based radiometric measurements show that the simulations based on snow SSA measurements have to be scaled with a model-specific factor of Do in order to minimize the root mean square error (RMSE) between measured and simulated T(sub B). Results using in-situ grain size measurements (SSA or D(sub max), depending on the model) give a mean T(sub B) RMSE (19 and 37 GHz) of the order of 16-26 K, which is similar for all models when the snow microstructure metrics are scaled. However, the MEMLS model converges to better results when driven by the correlation length estimated from in-situ SSA measurements rather than D(sub max) measurements. On a practical level, this paper shows that the SSA parameter, a snow property that is easy to retrieve in-situ, appears to be the most relevant parameter for characterizing snow microstructure, despite the need for a scaling factor.

Snow↗

NASA NTRS2016

Experimental Verification of Buffet Calculation Procedure Using Unsteady PSP

Typically a limited number of dynamic pressure sensors are employed to determine the unsteady aerodynamic forces on large, slender aerospace structures. The estimated forces are known to be very sensitive to the number of the dynamic pressure sensors and the details of the integration scheme. This report describes a robust calculation procedure, based on frequency-specific correlation lengths, that is found to produce good estimation of fluctuating forces from a few dynamic pressure sensors. The validation test was conducted on a flat panel, placed on the floor of a wind tunnel, and was subjected to vortex shedding from a rectangular bluff-body. The panel was coated with fast response Pressure Sensitive Paint (PSP), which allowed time-resolved measurements of unsteady pressure fluctuations on a dense grid of spatial points. The first part of the report describes the detail procedure used to analyze the high-speed, PSP camera images. The procedure includes steps to reduce contamination by electronic shot noise, correction for spatial non-uniformities, and lamp brightness variation, and finally conversion of fluctuating light intensity to fluctuating pressure. The latter involved applying calibration constants from a few dynamic pressure sensors placed at selective points on the plate. Excellent comparison in the spectra, coherence and phase, calculated via PSP and dynamic pressure sensors validated the PSP processing steps. The second part of the report describes the buffet validation process, for which the first step was to use pressure histories from all PSP points to determine the "true" force fluctuations. In the next step only a selected number of pixels were chosen as "virtual sensors" and a correlation-length based buffet calculation procedure was applied to determine "modeled" force fluctuations. By progressively decreasing the number of virtual sensors it was observed that the present calculation procedure was able to make a close estimate of the "true" unsteady forces only from four sensors. It is believed that the present work provides the first validation of the buffet calculation procedure which has been used for the development of many space vehicles.

Buffet↗