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DOE OSTI2024

Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations

Abstract In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.

Mathematics↗

DOE OSTI2020

Interference of electrical double layers: Confinement effects on structure, dynamics, and screening of ionic liquids

Ionic liquids are widely used as electrolytes in electronic devices in which they are subject to nanoconfinement within nanopores or nanofilms. Because the intrinsic width of an electrical double layer is on the order of several nanometers, nanoconfinement is expected to fundamentally alter the double layer properties. Furthermore, in confined systems, a large portion of the ions are interfacial, e.g., at the electrode interface, leading to significant deviations of electrostatic screening and ion dynamics as compared to bulk properties. In this article, we systematically investigate the interference between electrical double layers for nanoconfined ionic liquids and the resulting influence on the structure, dynamics, and screening behavior. We perform molecular dynamics simulations for the ionic liquids [BMIm + ][BF$^-_4$] and [BMIm + ][PF$^-_6$] confined between two flat electrodes at systematic separation distances between 1.5 nm and 4.5 nm for both conducting and insulating boundary conditions. We find that while ion dynamics is expectedly slower than in the bulk (by ~2 orders of magnitude), there is an unexpected non-linear trend with the confinement length that leads to a local maximum in dynamic rates at ~3.5–4.5 nm confinement. We show that this nonlinear trend is due to the ion correlation that arises from the interference between opposite double layers. We further evaluate confinement effects on the ion structure and capacitance and investigate the influence of electronic polarization of the ionic liquid on the resulting properties. This systematic evaluation of the connection between electrostatic screening and structure and dynamics of ionic liquids in confined systems is important for the fundamental understanding of electrochemical supercapacitors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Time scales for nonlinear processes in preheating after multifield inflation with nonminimal couplings

We have conducted extensive lattice simulations to study the postinflation dynamics of multifield models involving nonminimal couplings. In this work, we explore the parameter dependence of preheating in these models and describe the various time scales that control such nonlinear processes as energy transfer, rescattering, and the approach to radiation domination and thermalization. In the limit of large nonminimal couplings ($ξ_I$ ~ 100), we find that efficient transfer of energy from the inflaton condensate to radiative degrees of freedom, emergence of a radiation-dominated equation of state, and the onset of thermalization each consistently occur within $N_{\text{reh}} ≲ 3 e$-folds after the end of inflation, largely independent of the values of the other couplings in the models. The exception is the case of negative ellipticity, in which there is a misalignment between the dominant direction in field space along which the system evolves and the larger of the nonminimal couplings $ξ_I$. In those cases, the field-space-driven parametric resonance is effectively shut off. More generally, the competition between the scalar fields’ potential and the field-space manifold structure can yield interesting phenomena such as two-stage resonances. Across many regions of parameter space, we find efficient re-scattering between the distinct fields, leading to a partial memory loss of the shape of the initial fluctuation spectrum. Despite the explosive particle production, which can lead to a quick depletion of the background energy density, the nonlinear processes do not induce any superhorizon correlations after the end of inflation in these models, which keeps predictions for cosmic microwave background observables unaffected by the late-time amplification of isocurvature fluctuations. Hence the excellent agreement between primordial observables and recent observations is preserved for this class of models, even when we consider postinflation dynamics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Determination of acoustic nonlinearity parameters using thermal modulation of ultrasonic waves

This study presents a test method and its theoretical framework to determine the acoustic nonlinearity parameters (α, β, δ) of material using thermal modulation of ultrasonic waves. Temperature change-induced thermal strain excites the nonlinear response of the material and modulates the ultrasonic wave propagating in it. Experimental results showed a strong correlation between the relative wave velocity change and the temperature change. With a quadratic polynomial model, the acoustic nonlinearity parameters were obtained from the polynomial coefficients by curve fitting the experimental data. Their effects on thermal-induced velocity change were discussed. The parameters α, β, and δ govern the hysteretic gap, average slope, and curvature of the correlation curve, respectively. The proposed theory was validated on aluminum, steel, intact and damaged concrete samples. The obtained nonlinear parameters show reasonable agreement with values reported in the literature. Compared to other nonlinear acoustic methods using vibration or acoustic excitation, the thermal modulation method generates more uniform, slow changing, and larger strain field in the test sample. Employing the thermal effect as the driving force for nonlinearity instead of an undesired influencing factor, this method can measure the absolute values of α, β, and δ with good accuracy using a simple ultrasonic test setup.

Physics↗

DOE OSTI2022

Phenomenological Model of Nonlinear Dynamics and Deterministic Chaotic Gas Migration in Bentonite: Experimental Evidence and Diagnostic Parameters

Understanding gas migration in compacted clay materials, e.g., bentonite and claystone, is important for the design and performance assessment of an engineered barrier system of a radioactive waste repository system, as well as many practical applications. Existing field and laboratory data on gas migration processes in low-permeability clay materials demonstrate the complexity of flow and transport processes, including various types of instabilities, caused by nonlinear dynamics of coupled processes of liquid–gas exchange, dilation, fracturing, fracture healing, etc., which cannot be described by classical models of fluid dynamics in porous media. We here show that the complexity of gas migration processes can be explained using a phenomenological concept of nonlinear dynamics and deterministic chaos theory. To do so, we analyzed gas pressure and gas influx (i.e., input) and outflux (i.e., output), recorded during the gas injection experiment in the compact Mx80-D bentonite sample, and calculated a set of the diagnostic parameters of nonlinear dynamics and chaos, such a global embedding dimension, a correlation dimension, an information dimension, and a spectrum of Lyapunov exponents, as well as plotted 2D and 3D pseudo-phase-space strange attractors, based on the univariate influx and outflux time series data. These results indicate the presence of phenomena of low-dimensional deterministic chaotic behavior of gas migration in bentonite. In particular, during the onset of gas influx in the bentonite core, before the breakthrough, the development of gas flow pathways is characterized by the process of chaotic gas diffusion. After the breakthrough, with inlet-to-outlet movement of gas, the prevailing process is chaotic advection. During the final phase of the experiment, with no influx to the sample, the relaxation pattern of gas outflux is resumed back to a process of chaotic diffusion. The types of data analysis and a proposed phenomenological model can be used to establish the basic principles of experimental data-gathering, modeling predictions, and a research design.

36 MATERIALS SCIENCE↗

DOE OSTI2026

A new effective theory for stochastic relativistic hydrodynamics

Thermal fluctuations are a fundamental feature of dissipative systems that are essential for understanding physics near the expected critical point of QCD and in small systems. When such fluctuations are modeled naively in relativistic systems, strange features can appear such as negative self-correlation functions. We construct an effective theory for nonlinear stochastic relativistic hydrodynamics that ensure a well-posed mathematical formulation. Using Crooks fluctuation theorem, we derive a symmetry of the effective action that incorporates fluctuations through a suitable free energy functional. For divergence type theories, the action can then be fully specified using a single vector generating current. The equations of motion obtained using this procedure are guaranteed to be flux conservative and symmetric hyperbolic when the dynamics is causal. This ensures that these equations are well-posed (for suitable initial data) and are in a form that can easily be simulated, including with Metropolis techniques.

Mullins, Nicki [University of Illinois at Urbana-C↗

DOE OSTI2025

A Measurement of the Largest-scale CMB E -mode Polarization with CLASS

We present measurements of large-scale cosmic microwave background E-mode polarization from the Cosmology Large Angular Scale Surveyor 90 GHz data. Using 115 det-yr of observations collected through 2024 with a variable-delay polarization modulator, we achieved a polarization sensitivity of 82 μK arcimin, comparable to Planck at similar frequencies (100 and 143 GHz ). The analysis demonstrates effective mitigation of systematic errors and addresses challenges to large-angular-scale power recovery posed by time-domain filtering in maximum-likelihood map-making. A novel implementation of the pixel-space transfer matrix is introduced, which enables efficient filtering simulations and bias correction in the power spectrum using the quadratic cross-spectrum estimator. Overall, we achieved an unbiased time-domain filtering correction to recover the largest angular scale polarization, with the only power deficit, arising from map-making nonlinearity, being characterized as <3%. Through cross-correlation with Planck, we detected the cosmic reionization at 99.4% significance and measured the reionization optical depth τ = $0.053^{+0.018}_{-0.019}$, marking the first ground-based attempt at such a measurement. At intermediate angular scales (ℓ > 30), our results, both independently and in cross-correlation with Planck, remain fully consistent with Planck’s measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Brighter-fatter Effect in Near-infrared Detectors—III. Fourier-domain Treatment of Flat Field Correlations and Application to WFIRST

Weak gravitational lensing has emerged as a leading probe of the growth of cosmic structure. However, the shear signal is very small and accurate measurement depends critically on our ability to understand how non-ideal instrumental effects affect astronomical images. The Wide-Field Infrared Survey Telescope (WFIRST) will fly a focal plane containing 18 Teledyne H4RG-10 near-infrared detector arrays, which present different instrument calibration challenges from previous weak lensing observations. Previous work [Paper I: Hirata & Choi, PASP, 132, 014501 (2020); and Paper II: Choi & Hirata, PASP, 132, 014502 (2020)] has shown that correlation functions of flat field images, including cross-correlations between different time slices that are enabled by the non-destructive read capability of the infrared detectors, are effective tools for disentangling linear and nonlinear inter-pixel capacitance (IPC) and the brighter-fatter effect (BFE). Here we present a Fourier-domain treatment of the flat field correlations, which allows us to expand the previous formalism to all orders in IPC, BFE, and classical nonlinearity. We show that biases in simulated flat field analyses in Paper I are greatly reduced through the use of this formalism. We then apply this updated formalism to flat field data from three WFIRST flight candidate detectors, and explore the robustness to variations in the analysis. We find that the BFE is present in all three detectors, and that its contribution to the flat field correlations dominates over the nonlinear IPC, in accordance with the results from Paper II on a development detector. The magnitude of the BFE is such that the effective area of a pixel is increased by (3.54 ± 0.03) × 10 -7 for every electron deposited in a neighboring pixel (sensor chip assembly [SCA] 20829, statistical error, not IPC-deconvolved). We compare IPC maps from flat field autocorrelation measurements to those obtained from the single pixel reset method and find a median difference of 0.113% for SCA 20829. After further diagnosis of this difference, we ascribe it largely to an additional source of cross-talk, the vertical trailing pixel effect, and recommend further work to develop a model for this effect. These results represent a significant step toward calibration of the non-ideal effects in WFIRST detectors.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

An Atom-Precise Approach to Damp First-Order Phase Transitions and Its Implications for Neuromorphic Signal Processing

Neuromorphic computing inspired by mammalian intelligence aims to emulate the nonlinear dynamics of biological neurons and synapses to achieve fast, low-energy, and highly efficient information processing. Brain-inspired computing relies on the design and discovery of materials exhibiting nonlinear current–voltage profiles, frequently underpinned by electronic state transitions, to achieve spiking neurons and dynamically tunable synapses. A signature challenge in the design of artificial neurons is controlling the steepness of first-order transitions in active elements, as abrupt transitions are at risk of driving unstable voltage and temperature oscillations, which result in catastrophic device failure. A critical knowledge gap is the lack of structure–function correlations mapping the composition and atomistic structure of crystalline solids to nonlinear dynamical response characteristics. Here, we address the key question of how modification of atomistic structure correlates with alteration of neuron-like functionality. Constructing oscillator circuits from millimeter-scale single crystals enables high-resolution atomic structure solutions, which we use to demonstrate that the selective positioning of Pb cations modifies charge ordering along a one-dimensional CuxV2O5 framework even at low insertion stoichiometries, thereby providing an atom-precise design parameter for damping first-order transitions. We use temperature-variant X-ray diffraction and X-ray spectroscopy to elucidate the suppression of Cu-ion shuttling based on the precise positioning of Pb ions in seven-coordinated tunnel interstitial sites as the mechanistic basis for transition broadening, thus bridging a critical gap between statistical mechanics and quantum chemical descriptions of phase transitions. Such mechanistic understanding thus paves the way to site-selective modification strategies for modulating the sharpness of first-order transitions, with an exemplary demonstration here in tuning neuronal signal processing.

Crystal structure↗

DOE OSTI2020

Nonlinear spectroscopy in the condensed phase: The role of Duschinsky rotations and third order cumulant contributions

First-principles modeling of nonlinear optical spectra in the condensed phase is highly challenging because both environment and vibronic interactions can play a large role in determining spectral shapes and excited state dynamics. In this work, we compute two dimensional electronic spectroscopy (2DES) signals based on a cumulant expansion of the energy gap fluctuation operator, with specific focus on analyzing mode mixing effects introduced by the Duschinsky rotation and the role of the third order term in the cumulant expansion for both model and realistic condensed phase systems. We show that for a harmonic model system, the third order cumulant correction captures effects introduced by a mismatch in curvatures of ground and excited state potential energy surfaces, as well as effects of mode mixing. We also demonstrate that 2DES signals can be accurately reconstructed from purely classical correlation functions using quantum correction factors. We then compute nonlinear optical spectra for the Nile red and methylene blue chromophores in solution, assessing the third order cumulant contribution for realistic systems. We show that the third order cumulant correction is strongly dependent on the treatment of the solvent environment, revealing the interplay between environmental polarization and the electronic-vibrational coupling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model

Determining the range of validity of Migdal’s approximation for electron-phonon (e-ph) coupled systems is a long-standing problem. Many attempts to answer this question employ the Holstein Hamiltonian, where the electron density couples linearly to local lattice displacements. When these displacements are large, however, nonlinear corrections to the interaction must also be included, which can significantly alter the physical picture obtained from this model. Using determinant quantum Monte Carlo and the self-consistent Migdal approximation, we compared superconducting and charge-density-wave correlations in the Holstein model with and without second-order nonlinear interactions. We find a disagreement between the two cases, even for relatively small values of the e-ph coupling strength, and, importantly, that this can occur in the same parameter regions where Migdal’s approximation holds. Our results demonstrate that questions regarding the validity of Migdal’s approximation go hand in hand with questions of the validity of a linear e-ph interaction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

A Flexible Quasi-Static Mooring Design Optimization Method for Floating Structures

This paper presents a flexible and efficient design method for optimizing the mooring systems of floating structures. Mooring system optimization is challenging because of the strong nonlinearity of mooring system behavior and the many technical constraints that must be satisfied. Furthermore, different mooring configurations can have very different design spaces. While some successful examples of mooring design optimization exist in the literature, developing an optimization approach that can work across various mooring design problems is a larger challenge. We present such a method based on a flexible parameterization that allows a wide variety of mooring designs to be described by a list of variables, a quasi-static mooring model that provides efficient evaluation of a mooring design without directly considering mooring system dynamics, and an optimization framework that generates, evaluates, and adjusts the mooring design while considering user-specified constraints such as offset limits, strength safety factors, and seabed contact limits. We demonstrate the design optimization framework on four mooring design problems, each for a different type of mooring system. We compare the use of different design modes to simplify the optimization problem, showing that they can reduce the computation time by up to 75%. We also compare different optimization algorithms and find that the resulting computational speed can vary by up to 51 times. We perform a sensitivity study on one design and find that the local sensitivity of anchoring radius to water depth has a positive correlation of 0.29, but the global sensitivity shows large nonlinearities. Lastly, we perform a coupled dynamic analysis on one of the optimized designs and find that the predicted mean platform motions and mooring line tensions are within 1% of dynamic results and the extreme motions and tensions are within 14%. Lastly, we show that a DEA-Chain-Polyester mooring configuration is cost-optimal for the given design problem of the demonstrations, which aligns with general industry practice.

16 TIDAL AND WAVE POWER↗

DOE OSTI2025

Investigating the broadening phenomenon in two-particle correlations induced by gluon saturation

It has been found that the gluon density inside the proton grows rapidly at small momentum fractions. Quantum chromodynamics (QCD) predicts that this growth can be regulated by nonlinear effects, ultimately leading to gluon saturation. Within the color glass condensate framework, nonlinear QCD effects are predicted to suppress and broaden back-to-back angular correlations in collisions involving heavy nuclei. While suppression has been observed in various experiments in 𝑑/𝑝 + A collisions compared to 𝑝 + 𝑝 collisions, the predicted broadening remains unobserved. This study investigates the contributions of intrinsic transverse momentum (𝑘 𝑇 ), which is associated with saturation physics, as well as parton showers and transverse motion from fragmentation (𝑝$^{frag}_{𝑇}$), which are not saturation dependent, to the width of the correlation function. Our findings show that the non-saturation dependent effects, especially the initial-state parton shower and 𝑝$^{frag}_{𝑇}$, which occur independently of the collision system, smear the back-to-back correlation more than gluon saturation does, making the broadening phenomenon difficult to observe.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Charged Ferroelectric Domain Walls for Deterministic ac Signal Control at the Nanoscale

The direct current (dc) conductivity and emergent functionalities at ferroelectric domain walls are closely linked to the local polarization charges. Depending on the charge state, the walls can exhibit unusual dc conduction ranging from insulating to metallic-like, which is leveraged in domain-wall-based memory, multilevel data storage, and synaptic devices. In contrast to the functional dc behaviors at charged walls, their response to alternating currents (ac) remains to be resolved. Here, we reveal ac characteristics at positively and negatively charged walls in ErMnO 3 , distinctly different from the response of the surrounding domains. By combining voltage-dependent spectroscopic measurements on macroscopic and local scales, we demonstrate a pronounced nonlinear response at the electrode-wall junction, which correlates with the domain-wall charge state. The dependence on the ac drive voltage enables reversible switching between uni- and bipolar output signals, providing conceptually new opportunities for the application of charged walls as functional nanoelements in ac circuitry.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2020

Comparative Analysis of Thrombin Calibration Algorithms and Correction for Thrombin-α2macroglobulin Activity

Background: The thrombin generation (TG) test is useful for characterizing global hemostasis potential, but fluorescence substrate artifacts, such as thrombin-α2macroglobulin (T-α2MG) signal, inner filter effect (IFE), substrate consumption, and calibration algorithms have been suggested as sources of intra- and inter-laboratory variance, which may limit its clinical utility. Methods: Effects of internal vs. external normalization, IFE and T-α2MG on TG curves in normal plasma supplemented with coagulation factors, thrombomodulin, and tissue factor were studied using the Calibrated Automated Thrombinography (CAT; Diagnostica Stago, Parsippany, NJ, USA) and in-house software. Results: The various calibration methods demonstrated no significant difference in producing TG curves, nor increased the robustness of the TG assay. Several TG parameters, including thrombin peak height (TPH), produced from internal linear calibration did not differ significantly from uncalibrated TG parameters. Further, TPH values from internal linear and nonlinear calibration with or without T-α2MG correction correlated well with TPH from external calibration. Higher coefficients of variation (CVs) for TPH values were observed in both platelet-free and platelet-rich plasma with added thrombomodulin. Conclusions: Our work suggests minimal differences between distinct computational approaches toward calibrating and correcting fluorescence signals into TG levels, with most samples returning similar or equivalent TPH results.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Satellite-Based Observations of Nonlinear Relationships between Vertical Wind Shear and Intensity Changes during the Life Cycle of Hurricane Joaquin (2015)

A CIMSS vertical wind shear (VWS-C) dataset based on reprocessed GOES-East atmospheric motion vectors (AMVs) at 15-min intervals has a −0.36 correlation with the CIMSS Satellite Consensus (SATCON) intensity changes at 30-min intervals over the life cycle of Hurricane Joaquin (2015). Correlations are then calculated for four intensity change events including two rapid intensifications (RIs) and two decays, and four intensity change segments immediately before or after these events. During the first RI, the peak intensity increase of 16 kt (6 h) −1 (1 kt ≈ 0.51 m s −1 ) follows a small VWS-C decrease to a moderate 8 m s −1 value (negative correlation). A 30-h period of continued RI following the first peak RI occurred under moderate magnitude VWS-C (negative correlation), but with a rotation of the VWS-C direction to become more aligned with the southwestward heading of Joaquin. During the second RI, the peak intensity increase of 15 kt (6 h) −1 leads the rapid VWS-C increase (positive correlation), which the horizontal plots of VWS-C vectors demonstrate is related to an upper-tropospheric cyclone to the northeast of Joaquin. A conceptual model of ocean cooling within the anticyclonic track loop is proposed to explain a counterintuitive decreasing intensity when the VWS-C was also decreasing (positive correlation) during the Joaquin track reversal. These alternating negative and positive correlations during the four events and four segments of intensity change demonstrate the nonlinear relationships between the VWS-C and intensity changes during the life cycle of Joaquin that must be understood, analyzed, and modeled to improve tropical cyclone intensity forecasts, and especially RI events.

Elsberry, Russell L.↗

DOE OSTI2022

Unraveling the Correlation between Raman and Photoluminescence in Monolayer MoS 2 through Machine‐Learning Models

Abstract 2D transition metal dichalcogenides (TMDCs) with intense and tunable photoluminescence (PL) have opened up new opportunities for optoelectronic and photonic applications such as light‐emitting diodes, photodetectors, and single‐photon emitters. Among the standard characterization tools for 2D materials, Raman spectroscopy stands out as a fast and non‐destructive technique capable of probing material's crystallinity and perturbations such as doping and strain. However, a comprehensive understanding of the correlation between photoluminescence and Raman spectra in monolayer MoS 2 remains elusive due to its highly nonlinear nature. Here, the connections between PL signatures and Raman modes are systematically explored, providing comprehensive insights into the physical mechanisms correlating PL and Raman features. This study's analysis further disentangles the strain and doping contributions from the Raman spectra through machine‐learning models. First, a dense convolutional network (DenseNet) to predict PL maps by spatial Raman maps is deployed. Moreover, a gradient boosted trees model (XGBoost) with Shapley additive explanation (SHAP) to bridge the impact of individual Raman features in PL features is applied. Last, a support vector machine (SVM) to project PL features on Raman frequencies is adopted. This work may serve as a methodology for applying machine learning to characterizations of 2D materials.

Lu, Ang‐Yu↗

DOE OSTI2023

Influence of doping and thickness on domain avalanches in lead zirconate titanate thin films

In undoped lead zirconate titanate films of 1–2 μm thick, domain walls move in clusters with a correlation length of approximately 0.5–2 μm. Band excitation piezoresponse force microscopy mapping of the piezoelectric nonlinearity revealed that niobium (Nb) doping increases the average concentration or mobility of domain walls without changing the cluster area of correlated domain wall motion. In comparison, manganese (Mn) doping reduces the contribution of mobile domain walls to the dielectric and piezoelectric responses without changing the cluster area for correlated motion. In both Nb and Mn doped films, the cluster area increases and the cluster density drops as the film thickness increases from 250 to 1250 nm. This is evident in spatial maps generated from the analysis of irreversible to reversible ratios of the Rayleigh coefficients.

36 MATERIALS SCIENCE↗