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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

PETSc/TAO Users Manual (Rev. 3.19)

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication. PETSc/TAO includes a large suite of parallel linear solvers, nonlinear solvers, time integrators, and opti mization that may be used in application codes written in Fortran, C, C++, and Python (via petsc4py; see Getting Started). PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than packages such as MATLAB or a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++, python, or Fortran and experience using a debugger such as gdb or lldb, it may require a significant amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efficient implementation of many application codes simpler than “rolling them” yourself. For many tasks a package such as MATLAB is often the best tool; PETSc is not intended for the classes of problems for which effective MATLAB code can be written. There are several packages, built on PETSc, that may satisfy your needs without requiring directly using PETSc. We recommend reviewing these packages functionality before starting to code directly with PETSc. PETSc can be used to provide a “MPI parallel linear solver” in an otherwise sequential, or OpenMP parallel code. This approach cannot provide extremely large improvements in the application time by utilizing large numbers of MPI processes but can still improve the performance. Certainly all parts of a previously sequential code need not be parallelized but the matrix generation portion must be parallelized to expect true scalability to large numbers of MPI processes. See PCMPI for details on how to utilize the PETSc MPI linear solver server. Since PETSc is under continued development, small changes in usage and calling sequences of routines will occur. PETSc has been supported for twenty-five years; see mailing list information on our website for information on contacting support.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Parallel transport dynamics for mixed quantum states with applications to time-dependent density functional theory

Direct simulation of the von Neumann dynamics for a general (pure or mixed) quantum state can often be expensive. One prominent example is the real-time time-dependent density functional theory (rt-TDDFT), a widely used framework for the first principle description of many-electron dynamics in chemical and materials systems. Practical rt-TDDFT calculations often avoid the direct simulation of the von Neumann equation, and solve instead a set of Schrödinger equations, of which the dynamics is equivalent to that of the von Neumann equation. However, the time step size employed by the Schrödinger dynamics is often much smaller. Here, in order to improve the time step size and the overall efficiency of the simulation, we generalize a recent work of the parallel transport (PT) dynamics for simulating pure states [An, Lin, Multiscale Model. Simul. 18, 612, 2020] to general quantum states. The PT dynamics provides the optimal gauge choice, and can employ a time step size comparable to that of the von Neumann dynamics. Going beyond the linear and near adiabatic regime in previous studies, we find that the error of the PT dynamics can be bounded by certain commutators between Hamiltonians, density matrices, and their derived quantities. Such a commutator structure is not present in the Schrödinger dynamics. We demonstrate that the parallel transport-implicit midpoint (PT-IM) method is a suitable method for simulating the PT dynamics, especially when the spectral radius of the Hamiltonian is large. The commutator structure of the error bound, and numerical results for model rt-TDDFT calculations in both linear and nonlinear regimes, confirm the advantage of the PT dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Oblique instability of quasi-parallel whistler waves in the presence of cold and warm electron populations

Whistler waves propagating nearly parallel to the ambient magnetic field experience a nonlinear instability due to transverse currents when the background plasma has a population of sufficiently low energy electrons. Intriguingly, this nonlinear process may generate oblique electrostatic waves, including whistlers near the resonance cone with properties resembling oblique chorus waves in the Earth’s magnetosphere. Focusing on the generation of oblique whistlers, earlier analysis of the instability is extended here to the case where low-energy background plasma consists of both a “cold” population with energy of a few eV and a “warm” electron component with energy of the order of 100 eV. This is motivated by spacecraft observations in the Earth’s magnetosphere where oblique chorus waves were shown to interact resonantly with the warm electrons. The main new results are: 1) the instability producing oblique electrostatic waves is sensitive to the shape of the electron distribution at low energies. In the whistler range of frequencies, two distinct peaks in the growth rate are typically present for the model considered: a peak associated with the warm electron population at relatively low wavenumbers and a peak associated with the cold electron population at relatively high wavenumbers; 2) overall, the instability producing oblique whistler waves near the resonance cone persists (with a reduced growth rate) even in the cases where the temperature of the cold population is relatively high, including cases where cold population is absent and only the warm population is included; 3) particle-in-cell simulations show that the instability leads to heating of the background plasma and formation of characteristic plateau and beam features in the parallel electron distribution function in the range of energies resonant with the instability. The plateau/beam features have been previously detected in spacecraft observations of oblique chorus waves. However, they have been attributed to external sources and have been proposed to be the mechanism generating oblique chorus. In the present scenario, the causality link is reversed and the instability generating oblique whistler waves is shown to be a possible mechanism for formation of the plateau and beam features.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Detection and Perception of Sound by Eagles and Surrogate Raptors

One overarching objective of this program of study was the accumulation of objective, scientifically valid information relating to auditory performance of bald and golden eagles that may be used to guide the development of acoustic alerting/deterrence technologies intended to discourage encroachment into wind energy air spaces. To that end, analyses aimed at the characterization of sensitivity to sound in bald and golden eagles, along with findings in the supra-threshold, dynamic frequency spaces related to response latencies and amplitudes, leads us to conclude that bald, and golden eagles navigate the same basic working auditory space, as in other known and thus far characterized members of the diurnal raptor family. Specifically, bald and golden eagles, along with other raptor species within the group, operate in an auditory space characterized by a frequency band at least four octaves wide and centered on 2 kHz, with an upper frequency limit between 6 and 10 kHz at 80 dB SPL and a lower frequency limit that almost certainly extends below 0.2 kHz. Consequently, we recommend that signal designers use these data as a guideline in efforts to design effective and efficient acoustic alerting/deterrent systems. It is important to note that signal energy broadcast outside of this frequency band at moderate levels will not contribute to the efficacy of a deterrent but will add an unnecessary fraction to the overall acoustic pollution budget. The importance of this consideration is heightened by contemporaneous concerns related to the transmission of noise broadcast by wind energy farms. In addition, based on analyses of data acquired from red-tailed hawks using the same experimental paradigm and data acquisition system, we conclude that auditory function in the red-tailed hawk is sufficiently like that observed in bald and golden eagles to permit its use as a surrogate species. Response waveforms, threshold-frequency curves, and input-output characteristics match those of eagles closely. It should be noted however, that differences in sensitivity and slightly extended high-frequency limits of hearing should be taken into account when extrapolating findings from one species to the others. Although the inclusion of behavioral tests of red-tailed hawks to acoustic stimuli was beyond the scope of this investigation, future efforts to assess response parameters like signal-type preference and habituation rate will further elucidate their suitability to serve as eagle surrogates in behavioral studies; nonetheless, the species in question are well matched with respect to basic auditory performance. A second essential objective of this program of study was the acoustic characterization of a subset of calls comprising the vocal repertoires of bald and golden eagles that may be used to supplement auditory performance findings in the effort to guide the development of acoustic alerting signals. With regard to that objective, the vocal repertoires of both bald and golden eagle species are rich and varied. While similar in spectrographic structure, distinctive differences are also clear. Generally, golden eagles produce some calls with shorter durations, and similar “sounding” calls exhibit distinctively different spectrographic patterns than those of bald eagles. Both species produce calls that contain a wide variety of nonlinear elements that operate to enhance the rich and varied nature of commonly observed vocal products. Comparison of the average power spectra of commonly observed bald and golden eagle calls with threshold-frequency curves leads to the conclusion that call energies fall within the frequency bounds of hearing. Further, the acoustic energy of calls considered in this report tend to fall into overlapping, but different frequency ranges of the acoustic sensitivity curve. This condition may encourage signal designers to vary the frequency content of acoustic deterrence signals in the field. Finally, preliminary observations relating to the tendencies and proclivities of bald eagles to attend to the acoustic landscape lead to the conclusion that eagles monitor their immediate sound environment assiduously. Individuals respond to a variety of natural and synthetic sound signals reliably and, perhaps most relevant in the context of the engineering of acoustic alerting/deterrence technologies, habituation to most sounds considered in this effort was minimal. These preliminary results, while calling for extended behavioral testing, are promising and set the stage for the exportation of behavioral studies into real world scenarios.

17 WIND ENERGY↗
DOE OSTI2025

Autonomous Nanoparticle Synthesis Guided by In Situ Multiscale Structural Characterization

Autonomous synthesis platforms promise rapid exploration of vast parameter spaces; yet, integrating in situ structural characterization in closed-loop synthesis optimization remains challenging. We demonstrate a realization of such a closed-loop platform coupled with a droplet-flow microreactor, in situ X-ray scattering methods (SAXS/WAXS), and Gaussian process optimization to synthesize citrate-reduced Au nanoparticles with targeted characteristics. The system efficiently explored ∼19,000 synthesis recipes through 365 experiments, achieving precise control over size (4–60 nm) and polydispersity (σ < 0.11) across large citrate/gold ratios, exceeding traditional synthesis boundaries (1–10). Beyond confirming classical Turkevich–Frens trends, partial-dependence analysis revealed strong nonlinear coupling among precursor, citrate, and pH effects. Combining quantitative SAXS/WAXS analysis with electron microscopy characterization, we uncovered that crystallite size (d c ) and particle size (d) follow d c = 0.18d + β, where synthesis chemistry controls the intercept β while maintaining a universal slope. This parallel-band structure enables independent tuning of crystallite domain size at fixed particle diameter through a combination of chloride, gold precursor, citrate, and pH contributions (cross-validated Spearman ρ = 0.7 ± 0.1). High-resolution electron microscopy shows multiple lattice-fringe orientations within single particles, directly confirming polycrystalline domains and the ability to tune d c at the fixed d. The platform’s validation includes indistinguishable static versus flowing measurements, stable droplet transport at 100 °C, and <5% run-to-run variation, establishing a robust framework for mapping and controlling multiscale nanoparticle structure across expansive chemical spaces. In conclusion, the developed closed-loop platform can be applied to a borad range of nanosyntheis processes.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence

Abstract We identify novel structure in newly computed multi-loop amplitudes and quantum actions for even-point effective field theories, including both the nonlinear sigma model (NLSM) and double-copy gauge theories such as Born-Infeld and its supersymmetric generalizations. We exploit special properties of all even-point theories towards establishing an efficient unitarity based amplitude construction. In doing so, we find evidence that the leading IR divergence of NLSM amplitudes exponentiates when the target space is$$ \mathbbm{CP} $$ CP 1 ≅ SU(2)/U(1). We then systematically compute the two-loop anomalous behavior of Born-Infeld, and find that the counterterms needed to restore U(1) invariant behavior at loop-level can be constructed via a symmetric-structure double-copy. We also demonstrate that the divergent part of the one-minus (−+++) two-loop anomaly vanishes upon introducing an evanescent operator. In addition to these purely photonic counterterms, we verify through explicit calculation that the anomalous matrix elements that violate U(1) duality invariance can be alternatively cancelled by summing over internal$$ \mathcal{N} $$ N = 4 DBIVA superfields. Finally we find that$$ \mathcal{N} $$ N = 4 Dirac-Born-Infeld-Volkov-Akulov (DBIVA) amplitudes admit double-copy construction through two-loop order by reproducing our unitarity based result with a double copy between color-dual$$ \mathcal{N} $$ N = 4 super-Yang-Mills and our two-loop NLSM amplitudes. This result supports the possibility of color-dual representations for NLSM beyond one-loop. We conclude with an overview of howD-dimensional four-photon counterterms can be constructed in generality with the symmetric-structure double-copy, and outline a convenient way of counting evanescent operators using Hilbert series as generating functions.

Physics↗
DOE OSTI2023

Tracking Molecular Transport Across Oil/Aqueous Interfaces: Insight into “Antagonistic” Binding in Solvent Extraction

Liquid/liquid (L/L) interfaces play a key, yet poorly understood, role in a range of complex chemical phenomena where time-evolving interfacial structures and transient supramolecular assemblies act as gatekeepers to function. Here, for this study, we employ surface-specific vibrational sum frequency generation combined with neutron and X-ray scattering methods to track the transport of dioctyl phosphoric acid (DOP) and di-(2-ethylhexyl) phosphoric acid (DEHPA) ligands used in solvent extraction at buried oil/aqueous interfaces away from equilibrium. Our results show evidence for a dynamic interfacial restructuring at low ligand concentrations in contrast to expectation. These time-varying interfaces arise from the transport of sparingly soluble interfacial ligands into the neighboring aqueous phase. These results support a proposed “antagonistic” role of ligand complexation in the aqueous phase that could serve as a holdback mechanism in kinetic liquid extractions. These findings provide new insights into interfacially controlled chemical transport at L/L interfaces and how these interfaces vary chemically, structurally, and temporally in a concentration-dependent manner and present potential avenues to design selective kinetic separations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Hydration and Restructuring of Polar Polymer Interfaces: Implications in Antifouling and Responsive Materials

Manipulating polymer interfaces is crucial for understanding how structure influences function in applications spanning biofouling prevention to energy storage. Moreover, observing how polymers adapt their microscopic structure to changes in their local environment can reveal essential properties that govern their performance in such applications, providing key insights into how to design more effective interfaces. Here, in this study, a series of “grafting-from” polymer brushes with side chains varying in charge, are probed by sum frequency generation (SFG) and modeled using all-atom molecular dynamics (MD) simulations to elucidate how chemical makeup and charge mediate interfacial restructuring in dry versus hydrated states. Results show that charge, in progressing from nonpolar to cationic to zwitterionic, results in dramatic changes in interfacial structure and overall hydration. While net neutral systems, regardless of bulk phase polarity, show minimal interfacial water structuring, the cationic species exhibits strong bulk water signals from the surface potential. Meanwhile, the polymer brushes themselves restructure in water differently independent of charge, impacting the functional groups that are presented to the aqueous phase. Nonpolar and cationic species for instance undergo a change in alkyl group orientations to accommodate hydrating water molecules, whereas the zwitterionic polymer becomes completely disordered in water. Overall, the structure-based behavior trends presented herein have implications in antifouling applications and responsive material interfaces.

biointerface↗
DOE OSTI2020

Kinetic entropy-based measures of distribution function non-Maxwellianity: theory and simulations

We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e. entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function with the same density, bulk flow and temperature as the local distribution. First, we consider a form previously employed by Kaufmann & Paterson (J. Geophys. Res., vol. 114, 2009, A00D04), assessing its properties and deriving equivalent forms. To provide a quantitative understanding of it, we derive analytical expressions for three common non-Maxwellian plasma distribution functions. We show that there are undesirable features of this non-Maxwellianity measure including that it can diverge in various physical limits and elucidate the reason for the divergence. We then introduce a new kinetic entropy-based non-Maxwellianity measure based on the velocity-space kinetic entropy density, which has a meaningful physical interpretation and does not diverge. We use collisionless particle-in-cell simulations of two-dimensional anti-parallel magnetic reconnection to assess the kinetic entropy-based non-Maxwellianity measures. We show that regions of non-zero non-Maxwellianity are linked to kinetic processes occurring during magnetic reconnection. We also show the simulated non-Maxwellianity agrees reasonably well with predictions for distributions resembling those calculated analytically. These results can be important for applications, as non-Maxwellianity can be used to identify regions of kinetic-scale physics or increased dissipation in plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Recipes for when physics fails: recovering robust learning of physics informed neural networks

Abstract Physics-informed neural networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE. It also shows how physical regularizations based on continuity criteria and conservation laws fail to address this issue and rather introduce problems of their own causing the deep network to converge to a physics-obeying local minimum instead of the global minimum. We introduce Gaussian process (GP) based smoothing that recovers the performance of a PINN and promises a robust architecture against noise/errors in measurements. Additionally, we illustrate an inexpensive method of quantifying the evolution of uncertainty based on the variance estimation of GPs on boundary data. Robust PINN performance is also shown to be achievable by choice of sparse sets of inducing points based on sparsely induced GPs. We demonstrate the performance of our proposed methods and compare the results from existing benchmark models in literature for time-dependent Schrödinger and Burgers’ equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Accurately simulating nine-dimensional phase space of relativistic particles in strong fields

Next-generation high-power laser systems that can be focused to ultra-high intensities exceeding 10 23 W/cm 2 are enabling new physics regimes and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve lowest-order quantum effects. The current tool of choice for modeling these interactions is the particle-in-cell (PIC) method. In the presence of strong electromagnetic fields, the motion of charged particles and their spin is affected by radiation reaction (either the semi-classical or the quantum limit). Standard (PIC) codes usually use Boris or similar operator-splitting methods to advance the particles in standard phase space. These methods have been shown to require very small time steps in the strong-field regime in order to obtain accurate results. In addition, some problems require tracking the spin of particles, which creates a nine-dimensional (9D) particle phase space, i.e., (x, u, s). Therefore, numerical algorithms that enable high-fidelity modeling of the 9D phase space in the strong-field regime (where both the spin and momentum evolution are affected by radiation reaction) are desired. Here we present a new particle pusher that works in 9D and 6D phase space (i.e., with and without spin) based on analytical rather than leapfrog solutions to the momentum and spin advance from the Lorentz force, together with the semi-classical form of radiation reaction in the Landau-Lifshitz equation and spin evolution given by the Bargmann-Michel-Telegdi equation. Analytical solutions for the position advance are also obtained, but these are not amenable to the staggering of space and time in standard PIC codes. These analytical solutions are obtained by assuming a locally uniform and constant electromagnetic field during a time step. The solutions provide the 9D phase space advance in terms of a particle's proper time, and a mapping is used to determine the proper time step duration for each particle as a function of the lab frame time step. Due to the analytical integration of particle trajectory and spin orbit, the constraint on the time step needed to resolve trajectories in ultra-high fields can be greatly reduced. The time step required in a PIC code for accurately advancing the fields may provide additional constraints. We present single-particle simulations to show that the proposed particle pusher can greatly improve the accuracy of particle trajectories in 6D or 9D phase space for given laser fields. We have implemented the new pusher into the PIC code Osiris. Example simulations show that the proposed pusher provides improvement for a given time step. A discussion on the numerical efficiency of the proposed pusher is also provided.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Ion Pairing Mediates Molecular Organization Across Liquid/Liquid Interfaces

Liquid/liquid interfaces play a central role in scientific fields ranging from nanomaterial synthesis and soft matter electronics to nuclear waste remediation and chemical separations. This diversity of functions arises from an interface’s ability to respond to changing conditions in its neighboring bulk phases. Understanding what drives this interfacial flexibility can provide novel avenues for designing new functional interfaces. However, limiting this progress is an inadequate understanding of the subtle intermolecular and interphase interactions taking place at the molecular level. Here, we use surface-specific vibrational sum frequency generation spectroscopy combined with atomistic molecular dynamics simulations to investigate the self-assembly and structure of model ionic oligomers consisting of an oligodimethylsiloxane (ODMS) tail covalently attached to a positively charged methyl imidazolium (MIM + ) head group at buried oil/aqueous interfaces. We show how the presence of seemingly innocuous salts can impart dramatic changes to the ODMS tail conformations in the oil phase via specific ion effects and ion-pairing interactions taking place in the aqueous phase. These specific ion interactions are shown to drive enhanced amphiphile adsorption, induce morphological changes, and disrupt emergent hydrogen-bonding structures at the interface. Tuning these interactions allows for independent control over the oligomer structure in the oil phase versus interfacial population changes and represents key mechanistic insight that is needed to control chemical reactions at liquid/liquid interfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Probing lithium mobility at a solid electrolyte surface

Abstract Solid-state electrolytes overcome many challenges of present-day lithium ion batteries, such as safety hazards and dendrite formation 1,2 . However, detailed understanding of the involved lithium dynamics is missing due to a lack of in operando measurements with chemical and interfacial specificity. Here we investigate a prototypical solid-state electrolyte using linear and nonlinear extreme-ultraviolet spectroscopies. Leveraging the surface sensitivity of extreme-ultraviolet-second-harmonic-generation spectroscopy, we obtained a direct spectral signature of surface lithium ions, showing a distinct blueshift relative to bulk absorption spectra. First-principles simulations attributed the shift to transitions from the lithium 1 s state to hybridized Li- s /Ti- d orbitals at the surface. Our calculations further suggest a reduction in lithium interfacial mobility due to suppressed low-frequency rattling modes, which is the fundamental origin of the large interfacial resistance in this material. Our findings pave the way for new optimization strategies to develop these electrochemical devices via interfacial engineering of lithium ions.

25 ENERGY STORAGE↗
DOE OSTI2020

Alaskan carbon-climate feedbacks will be weaker than inferred from short-term manipulations: Alaskan Benchmark Data and Model runs

This submission aimed to assess differences in short-term step warming manipulations and long-term chronic response to climate change in Alaskan ecosystems. Briefly, climate warming is occurring fastest at high latitudes. Based on short-term field experiments, this warming is projected to stimulate soil organic matter decomposition, and promote a positive feedback to climate change. We show here that the tightly coupled, nonlinear nature of high-latitude ecosystems implies that short-term (< 10 year) warming experiments produce emergent ecosystem carbon stock temperature sensitivities inconsistent with emergent multi-decadal responses. We first demonstrate that a well-tested mechanistic ecosystem model accurately represents observed carbon cycle and active layer depth responses to short-term summer warming in four diverse Alaskan sites. We then show that short-term warming manipulations do not capture the non-linear, long-term dynamics of vegetation, and thereby soil organic matter, that occur in response to thermal, hydrological, and nutrient transformations belowground. Our results demonstrate significant spatial heterogeneity in multi-decadal Arctic carbon cycle trajectories and argue for more mechanistic models to improve predictive capabilities.The model used in the current study is available publicly (https://github.com/jinyun1tang/ECOSYS), and the current submission contains the python/ matlab codes for analyzing output from the model (includng a readme file to explain the codes). The benchmark data, also enclosed, was collected from a range of published and publicly available sources (extracted using GRABIT: https://www.mathworks.com/matlabcentral/fileexchange/7173-grabit). These sources describe warming induced changes in tundra/ boreal ecosystems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Hydrogen-Bond-Driven Chemical Separations: Elucidating the Interfacial Steps of Self-Assembly in Solvent Extraction

Chemical separations, particularly liquid extractions, are pervasive in academic and industrial laboratories, yet a mechanistic understanding of the events governing their function are obscured by interfacial phenomena that are notoriously difficult to measure. In this work, we investigate the fundamental steps of ligand self-assembly as driven by changes in the interfacial H-bonding network using vibrational sum frequency generation. Our results show how the bulk pH modulates the interfacial structure of extractants at the buried oil/aqueous interface via the formation of unique H-bonding networks that order and bridge ligands to produce self-assembled aggregates. These extended H-bonded structures are key to the subsequent extraction of Co2+ from the aqueous phase in promoting micelle formation and subsequent ejection of the said micelle into the oil phase. The combination of static and time-resolved measurements reveals the events underlying complexities of liquid extractions at high [Co2+]:[ligand] ratios by showing an evolution of interfacially assembled structures that are readily tuned on a chemical basis by altering the compositions of the aqueous phase. The results of this work point to new principles to design-applied separations through the manipulation of surface charge, electrostatic screening, and the associated H-bonding networks that arise at the interface to facilitate organization and subsequent extraction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Constrained or unconstrained? Neural-network-based equation discovery from data

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. Here, we briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.

Data-driven discovery↗
DOE OSTI2021

Analytical WKB theory for high-harmonic generation and its application to massive Dirac electrons

Here we propose an analytical approach to high-harmonic generation (HHG) for nonperturbative low-frequency and high-intensity fields based on the (Jeffreys-)Wentzel-Kramers-Brillouin (WKB) approximation. By properly taking into account Stokes phenomena of WKB solutions, we obtain wave functions that systematically include the repetitive dynamics of production and acceleration of electron-hole pairs and quantum interference due to phase accumulation between different pair production times (Stückelberg phase). Using the obtained wave functions without relying on any phenomenological assumptions, we explicitly compute electric current (including intra- and interband contributions) as the source of HHG for a massive Dirac system in (1+1) dimensions under an ac electric field. We demonstrate that the WKB approximation agrees well with numerical results obtained by solving the time-dependent Schrödinger equation and point out that the quantum interference is important in HHG. We also predict in the deep nonperturbative regime that (1) harmonic intensities oscillate with respect to electric-field amplitude E 0 and frequency Ω with a period determined by the Stückelberg phase, (2) the cutoff order of HHG is determined by 2eE 0 ℏΩ 2 , with e being the electron charge, and that (3) noninteger harmonics, controlled by the Stückelberg phase, appear as a transient effect. Our WKB theory is particularly suited for a parameter regime, where the Keldysh parameter γ = (Δ/2)Ω/eE 0 ,with Δ being the gap size, is small. This parameter regime corresponds to intense lasers in the terahertz regime for realistic massive Dirac materials. Our analysis implies that the so-called HHG plateau can be observed at the terahertz frequency within the current technology.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Ferroelectric and Charge Transport Properties in Strain-Engineered Two-Dimensional Lead Iodide Perovskites

Transitions from three-dimensional (3D) hybrid organic–inorganic perovskite (HOIP) structures to lower dimensions including 2D and quasi-2D structures open a new range of functional properties in these materials systems. Yet, the performance of solar cells made from 2D HOIP is below that of the 3D compositions due to the higher band-gap energy, low carrier concentration, and anisotropy in charge transport. Controlling ferroelectricity in 2D HOIPs is considered to be a powerful strategy to drive the spatial separation of photogenerated charge carriers to improve the photovoltaic action in this class of HOIPs. Here, we explore the strain-dependent ferroelectricity and charge carrier properties in strain-engineered 2D-layered HOIPs utilizing advanced scanning probe microscopy (SPM) techniques. Band excitation-piezoresponse force microscopy (BE-PFM) and contact Kelvin probe force microscopy (cKPFM) reveal ferroelectric domains and switchable dynamics with significantly low switching voltages in the low-strain film. Photoluminescence (PL) spectroscopy shows strain-dependent optical properties and a noncentrosymmetric structure with strong second-harmonic generation (SHG) peaks in the low-strain film. In addition, KPFM results demonstrate a higher surface potential in the low-strain films, while the photovoltage and local current are the highest on the high-strain film. Furthermore, our study demonstrates the critical role of strain engineering on the electromechanical and charge carrier dynamics in 2D HOIPs, which is important for development of 2D HOIP devices.

36 MATERIALS SCIENCE↗