Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “solution theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Spectral-partitioned Kohn-Sham density functional theory

Here we introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Global flow structure and exact formal transseries of the Gubser flow in kinetic theory

In this work we introduce the generic conditions for the existence of a non-equilibrium attractor that is an invariant manifold determined by the long-wavelength modes of the physical system. We investigate the topological properties of the global flow structure of the Gubser flow for the Israel-Stewart theory and a kinetic model for the Boltzmann equation by employing Morse-Smale theory. We present a complete classification of the invariant submanifolds of the flow and determine all the possible flow lines connecting any pair of UV/IR fixed points. The formal transseries solutions to the Gubser dynamical system around the early-time (UV) and late-time (IR) fixed points are constructed and analyzed. It is proven that these solutions are purely perturbative (or power-law asymptotic) series with a finite radius of convergence. Based on these analyses, we find that Gubser-like expanding kinetic systems do not hydrodynamize owing to the failure of the hydrodynamization process which heavily relies on the classification of (non)hydrodynamic modes in the IR regime. This is in contrast to longitudinal boost-invariant plasmas where the asymptotic dynamics is described by a few terms of the hydrodynamic gradient expansion. We finally compare our results for both Bjorken and Gubser conformal kinetic models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Resolving the ($\mathscr{g}$-2)$_μ$ discrepancy with $\mathcal{F}$–SU(5) intersecting D-branes

A discrepancy between the measured anomalous magnetic moment of the muon (g - 2) μ and computed Standard Model value now stands at a combined 4.2σ following experiments at Brookhaven National Lab (BNL) and the Fermi National Accelerator Laboratory (FNAL). A solution to the disagreement is uncovered in flipped SU(5) with additional TeV-Scale vector-like 10 +$\bar{10}$ multiplets and charged singlet derived from local F-Theory, collectively referred to as $\mathcal {F}$-SU(5). Here we engage general No-Scale supersymmetry (SUSY) breaking in $\mathcal {F}$-SU(5) D-brane model building to alleviate the (g-2)μ. tension between the Standard Model and observations. A robust Δa μ (SUSY) is realized via mixing of M 5 and M 1X at the secondary SU(5) x U(1) X unification scale in $\mathcal {F}$-SU(5) emanating from SU(5) breaking and U(1) X flux effects. Calculations unveil Δa μ (SUSY) = 19.0-22.3 x 10 -10 for gluino masses of M($\tilde{g}$ = 2.25-2.56 TeV nd higgsino dark matter, aptly residing within the BNL+FNAL 1σ mean. This (g – 2)μ favorable region of the model space also generates the correct light Higgs boson mass and branching ratios of companion rare decay processes, and is further consistent with all LHC Run 2 constraints. Finally, we also examine the heavy SUSY Higgs boson in light of recent LHC searches for an extended Higgs sector.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Growth-induced Donnan exclusion influences swelling kinetics in highly charged dynamic polymerization hydrogels

Polymeric gels crosslinked by DNA sequences can exploit DNA strand-displacement reactions to promote swelling through dynamic polymerization. The degree of swelling and the rate of swelling must be directly tunable to achieve the promise of programmable soft matter. Though the kinetics of the strand-displacement reaction provide insertion rates up to 10 4 /Molar/second as measured in bulk solution, DNA hydrogel swelling can take upwards of 30 h to complete. Computational modeling of the reaction-induced swelling of these gels with our recently-developed reactive electrochemomechanical theory (Zimmerman et al., 2024) suggests that their extraordinarily slow swelling is partly due to a scaling mismatch between the addition of charge and the addition of fluid volume, leading to a large transient increase in the fixed charge density. The significant increase in the gel’s fixed charge density, due to the binding of negatively charged DNA, sharply restricts the concentration of mobile hairpins through the phenomenon of Donnan charge exclusion, an effect commonly exploited in nanofiltration applications using polymeric membranes. The scaling problem is overcome when the mean additional swelling provided to the hydrogel by addition of a crosslink is above a critical value, thus the swelling outpaces the charge accumulation, leading the fixed charge density to drop and significantly accelerating the swelling process. This study shows that Donnan exclusion can explain the kinetics of DNA hydrogel swelling, and studies ways to modulate the reaction speed by either modifying the salt concentration or increasing or decreasing the number of base pairs in each DNA sequence.

42 ENGINEERING↗
DOE OSTI2024

Diffusion-Limited Kinetics in Reactive Systems

A proper representation of chemical kinetics is vital to understanding, modeling, and optimizing many important chemical processes. In liquid and surface phases, where diffusion is slow, the rate at which the reactants diffuse together limits the overall rate of many elementary reactions. Commonly, the textbook Smoluchowski theory is utilized to estimate effective rate coefficients in the liquid phase. On surfaces, modelers commonly resort to much more complex and expensive Kinetic Monte Carlo (KMC) simulations. Here, in this study, we extend the Smoluchowski model to allow the diffusing species to undergo chemical reactions and derive analytical formulas for the diffusion-limited rate coefficients for 3D, 2D, and 2D/3D interface cases. With these equations, we are able to demonstrate that when species react faster than they diffuse they can react orders of magnitude faster than predicted by Smoluchowski theory, through what we term “the reactive transport effect”. We validate the derived steady-state equations against particle Monte Carlo (PMC) simulations, KMC simulations, and non-steady-state solutions. Furthermore, using PMC and KMC simulations, we propose corrections that agree with all limits and the computed data for the 2D and 2D/3D interface steady-state equations, accounting for unique limitations in the associated derived equations. Additionally, we derive equations to handle couplings between diffusion-limited rate coefficients in reaction networks. We believe these equations should make it possible to run much more accurate mean-field simulations of liquids, surfaces, and liquid–surface interfaces accounting for diffusion limitations and the reactive transport effect.

Johnson, Matthew Sean↗
DOE OSTI2026

Interfacial Charge Transfer Pathways in Photoelectrochemical H 2 Evolution by a Single-Component Molecular Catalyst on a Conductive Metal Oxide

Dye-sensitized photoelectrosynthesis cells traditionally combine a photosensitizing dye to harvest light and a catalyst to generate chemical fuels on a semiconductor. Here, in this work, a photoactive catalyst capable of both light absorption and fuel formation, [Cp*Ir(4,4′-Y 2 -bpy)Cl][Cl] (Cp* = pentamethylcyclopentadienyl, bpy = 2,2′-bipyridine, Y = CH 2 PO 3 H 2 ), is anchored to a mesoporous tin-doped indium oxide (ITO) electrode and facilitates photoelectrochemical H 2 evolution in water without the need for additional photosensitizers or sacrificial reductants. Spectroelectrochemistry indicates a single-site H 2 evolution mechanism involving charge injection to ITO, in contrast to the bimetallic mechanism observed in solution. Cyclic voltammetry and variable-potential chronoamperometry under illumination probe competing pathways via interfacial electron transfer between the Ir hydride excited state and the conductive ITO electrode. A Marcus theory framework provides reorganization energies for competing interfacial electron transfer pathways from potential-dependent quantum yield measurements. The light-driven H 2 evolution catalysis on conducting oxide proceeds with high Faradaic efficiency and current densities comparable to photoelectrodes utilizing p-type semiconductors. By uncovering the principal electron transfer pathways that govern photocatalytic efficiency, this study establishes design principles for hybrid molecular photoelectrocatalysts.

catalysts↗
DOE OSTI2021

Nanoscale heterogeneity induced by nonmagnetic Zn dopants in the quantum critical metal CeCoIn 5 : 115 In NQR/NMR and 59 Co NMR study

We report antiferromagnetism in a prototypical quantum critical metal CeCoIn 5 is known to be induced by slight substitutions of nonmagnetic Zn atoms for In. In nominally 7% Zn-substituted CeCoIn 5 , an antiferromagnetic (AFM) state coexists with heavy fermion superconductivity. Heterogeneity of the electronic states is investigated in Zn-doped CeCoIn 5 by means of nuclear quadrupole and magnetic resonances (NQR and NMR). Site-dependent NQR relaxation rates 1/T 1 indicate that the AFM state is locally nucleated around Zn substituents in the matrix of a heavy fermion state, and percolates through the bulk at the AFM transition temperature T N . At lower temperatures, an anisotropic superconducting (SC) gap below the SC transition temperature Tc, and the SC state permeates through the AFM regions via a SC proximity effect. Applying an external magnetic field induces a spin-flop transition near 5T, reducing the volume of the AFM regions. Consequently, a short-ranged inhomogeneous AFM state survives and coexists with a paramagnetic Fermi liquid state at high fields.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Reversible phase transformations between Pb nanocrystals and a viscous liquid-like phase

Phase transformations have been a prominent topic of study for both fundamental and applied science. Solid-liquid reaction–induced phase transformations can be hard to characterize, and the transformation mechanisms are often not fully understood. Here, we report reversible phase transformations between a metal (Pb) nanocrystal and a viscous liquid-like phase unveiled by in situ liquid cell transmission electron microscopy. The reversible phase transformations are obtained by modulating the electron current density (between 1000 and 3000 electrons Å –2 s –1 ). The metal-organic viscous liquid-like phase exhibits short-range ordering with a preferred Pb-Pb distance of 0.5 nm. Assisted by density functional theory and molecular dynamics calculations, we show that the viscous liquid-like phase results from the reactions of Pb with the CH 3 O fragments from the triethylene glycol solution under electron beam irradiation. Such reversible phase transformations may find broad implementations.

36 MATERIALS SCIENCE↗
DOE OSTI2020

ZND Verification Tests for Reactive Burn Models in FLAG

The ZND theory, named after Zeldovich, von Neumann, and Doering, provides a simple model for one-dimensional ideal steady-state detonation. It assumes that the detonation wave front starts with a shock that is a discontinuous jump and is followed by a finite-length reaction zone. Reactive burn (also called reactive flow) models are based on ZND theory, as they model the shock initiation and detonation process with a finite reaction rate. The ZND wave propagation test is essentially the only available test case where an analytic solution exists for verification of reactive burn models in numerical codes. However, there are extensions and variants of the ZND test that have been devised for verification of multidimensional flows. The objective of this work is to provide verification of the reactive burn models currently implemented in the Lagrangian hydrocode FLAG and investigate the influence of mesh resolution, artificial viscosity models, and the Arbitrary Lagrangian-Eulerian (ALE) Euler relaxer on the simulation results. The burn models of interest are the Wescott-Stewart-Davis (WSD) model, the Scaled Uniform Reactive Flow (SURF) model (specifically with the SURFplus model extension), and the Arrhenius shock temperature state dependent WSD (AWSD) model. Previously, Ralph Menikoff has used ZND tests for verification of the SURF and SURFplus models in the Eulerian hydrocode xRAGE. The ZND tests here are somewhat different than the approach by Menikoff. In particular, we use a piston-driven ZND detonation wave (via a prescribed constant velocity boundary condition) in a Lagrangian framework whereas Menikoff had a ZND wave followed by a invariant rarefaction wave. The xRAGE simulations were carried out on uniform grids and adaptive mesh refinement (AMR) grids. Although AMR was recently implemented in FLAG and now fully functional for 2D simulations, it will not be evaluated with ZND tests at this time. Some work has been done previously for validating the reactive burn models in FLAG. For example, the validation studies of SURF with shock-to-detonation (SDT) tests, cylinder tests, and gap-stick tests. Further validation of the AWSD, WSD, and SURF models is described in for SDT, multi-shock, cylinder, and corner-turning tests. Recently, a large parameter study with approximately twenty SDT tests was performed to validate the AWSD, WSD, SURF, and SURFplus models while also investigating mesh resolution and artificial viscosity settings. To the best of our knowledge, the current work represents the first documented verification of these burn models in FLAG. The reader should note that many of the tables and figures in this report use units of cm/g/µs, which are the default units for FLAG. However, some lengths and velocities are expressed in µm and mm/µs, respectively, which are typical units for detonation analyses.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2024

Systematic discovery of new nano-scale metastable intermetallic eutectic phases in laser rapid solidified Aluminum-Germanium alloy

Laser surface remelting of as-cast Al-Ge eutectic alloy is shown to produce ultrafine lamellar eutectic morphology with interlamellar spacing refined up to ∼60 nm and composed of FCC Al solid solution and unusual Al x Ge y intermetallic phases that do not form during near-equilibrium solidification. The microstructures are characterized and analyzed using a combination of selected area electron diffraction, high-resolution scanning transmission electron microscopy, energy dispersive X-ray spectroscopy to obtain high-resolution elemental maps, and atomistic modeling using density functional theory followed by atomic-scale image simulation. Depending on the local solidification conditions, the crystallography of the Al x Ge y intermetallic phases in the eutectic microstructure is either monoclinic (C 2/c) or monoclinic (P 2 1 ), with high densities of defects in both cases. This is in sharp contrast to the as-cast alloys that showed nominally pure Al and Ge phases with significant solute partitioning and equilibrium FCC and diamond cubic crystal structures, respectively. Corresponding kinetic phase diagrams are proposed to interpret the evolution of nano-lamellar eutectic morphologies with equilibrium Al and metastable Al x Ge y phases, and to explain increased solid solubility in the Al phases manifested by precipitation of ultrafine clusters of Ge. Furthermore, the reasons for the formation of these metastable eutectics under laser rapid solidification are discussed from the perspective of the competitive growth criterion.

Al-Ge eutectic↗
DOE OSTI2024

A large deformation multiphase continuum mechanics model for shock loading of soft porous materials

A large deformation, coupled finite-element (FE) model is developed to simulate the multiphase response of soft porous materials subjected to high strain-rate loading. The approach is based on the theory of porous media (TPM) at large deformations. Simplifications to the one-dimensional regime studied in the numerical simulations follow. An overview of several different time integration schemes is presented for the purpose of solving the nonlinear dynamic coupled balance of momenta (mixture and fluid) and balance of mass of the mixture equations. Numerical examples are presented for (i) verification against closed-form analytical solutions assuming small loads, (ii) demonstrating large deformation effects at high strain-rate, and (iii) showing differences in deformations between a single-phase elastodynamics model with occluded compressible pore fluid and a multiphase poroelastodynamics model at high strain-rate. The multiphase model shows that the relative motion of the pore fluid significantly dampens the deformation response of the solid skeleton as compared to the single-phase model, and makes it possible to extract quantitative values for the stresses of the different constituents, thereby allowing one to form preliminary conclusions about the onset of damage in the solid skeleton. The novelty of the current work is developing a multiphase, large deformation, mixture theory numerical model for high strain-rate loading of soft porous materials. It was discovered that explicit, adaptive time-stepping Runge–Kutta schemes offer high accuracy at relatively low cost when compared to traditional implicit or explicit central difference time-stepping schemes for shock-like loadings. Here, shock viscosity is added to the mixture momentum balance equation to regularize the shock front, and a stabilization term is added to the mixture mass balance equation to stabilize equal order interpolation finite elements for the coupled finite element solution of multiphase materials.

Engineering↗
DOE OSTI2022

The radial action from probe amplitudes to all orders

We extract the relativistic classical radial action from scattering amplitudes, to all orders in perturbation theory, in the probe limit. Our sources include point charges and monopoles, as well as the Schwarzschild and pure-NUT gravitational backgrounds. A characteristic relativistic effect, that scattering trajectories may wind around these sources any number of times, can be recovered when all-order amplitudes are available. We show that the amplitude for scattering a probe off a pure NUT is given by the solution of a transcendental equation involving continued fractions, and explain how to solve this equation to any desired loop order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Uncovering Non-Fermi-Liquid Behavior in Hund Metals: Conformal Field Theory Analysis of an SU(2)×SU(3) Spin-Orbital Kondo Model

Hund metals have attracted attention in recent years due to their unconventional superconductivity, which supposedly originates from non-Fermi-liquid (NFL) properties of the normal state. When studying Hund metals using dynamical mean-field theory, one arrives at a self-consistent “Hund impurity problem” involving a multiorbital quantum impurity with nonzero Hund coupling interacting with a metallic bath. If its spin and orbital degrees of freedom are screened at different energy scales, T sp < T orb , the intermediate energy window is governed by a novel NFL fixed point, whose nature had not yet been clarified. We resolve this problem by providing an analytical solution of a paradigmatic example of a Hund impurity problem, involving two spin and three orbital degrees of freedom. To this end, we combine a state-of-the-art implementation of the numerical renormalization group, capable of exploiting non-Abelian symmetries, with a generalization of Affleck and Ludwig’s conformal field theory (CFT) approach for multichannel Kondo models. We characterize the NFL fixed point of Hund metals in detail for a Kondo model with an impurity forming an SU ( 2 ) × SU ( 3 ) spin-orbital multiplet, tuned such that the NFL energy window is very wide. The impurity’s spin and orbital susceptibilities then exhibit striking power-law behavior, which we explain using CFT arguments. We find excellent agreement between CFT predictions and numerical renormalization group results. Our main physical conclusion is that the regime of spin-orbital separation, where orbital degrees of freedom have been screened but spin degrees of freedom have not, features anomalously strong local spin fluctuations: the impurity susceptibility increases as χ sp imp ~ ω – γ , with γ > 1 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Cyber risk assessment and investment optimization using game theory and ML-based anomaly detection and mitigation for wide-area control in smart grids

The electric power grid is increasingly becoming susceptible to cyber attacks that exploit vulnerabilities in the smart grid control, information, and physical layers. Successful cyber attacks can have catastrophic impacts on the social and economic well-being of any nation all over the globe. It has, thus, become imperative to secure the smart grid against such adversarial actions to ensure stable, secure, and reliable operation of the grid. The existing research and industry practices prove to be inadequate in terms of providing pragmatic and effective defense methodologies and measures for long-term cybersecurity planning and real-time cybersecurity for grid operation. For example, existing works lack models that incorporate uncertain behavior of cyber-attackers and pragmatic defense measures for cyber risk assessment and cybersecurity investment optimization which often provide unreliable and strictly qualitative solutions to these problems. At the same time, with the growing number of cyber incidents in the grid, there still exists a need to develop attack-resilient algorithms for wide-area monitoring, protection, and control (WAMPAC) applications like the wide-area voltage control systems (WAVCS) for Flexible AC Transmissions Systems (FACTS) that lack in scalable and feasible solutions from the cybersecurity perspective. This dissertation proposes novel models and methodologies for: (1) Cybersecurity planning, and (2) Cybersecurity for system operation. The cybersecurity planning is achieved through cyber risk assessment and cybersecurity resource investment optimization for long-term cybersecurity of the grid using game theory and attack-defense trees. Cybersecurity for system operation consists of development of cyber anomaly detection and mitigation algorithms for flexible AC transmission system (FACTS) controller-based wide-area voltage control systems (WAVCS) using machine learning (ML), and software defined networking-based moving target defense network routing for achieving real-time cyber-physical security for grid operations. This is followed by hardware-in-the-loop (HIL) implementation and evaluation of these attack prevention, detection, and mitigation algorithms and methodologies showcasing their feasibility in a close to real-world environment. For cybersecurity planning, a novel approach involving a combination of game theory and attack defense trees (ADT) for optimal cybersecurity resource allocation in the smart grid is proposed. This methodology involves modeling of the cyber-physical smart grid substations as ADTs, defining attacker costs, defense costs, and attack probabilities for attack access points. Using game theoretical formulation, optimal defense strategies for the defender of the system to invest cybersecurity resources in the grid are obtained. Additionally, a game-theoretic framework is developed for quantitative cyber-physical risk assessment of the grid under a dynamically changing cyber threat space and uncertain behavior of cyber attackers which is further used to optimize investments in the smart grid's cybersecurity resources. The attacker, defender, and the smart grid system are modeled while incorporating attacker-stochasticity and federal guidelines for smart grid cybersecurity. This allows quantification of threat, vulnerabilities, and attack impact of the grid for quantitative risk assessment. The defender's budget to invest in the security resources in the grid is optimized based on the strategies leading to minimum system risk. The evaluation of the proposed solutions highlight the feasibility for practical implementation of these methodologies and algorithms in the smart grid, while taking the federal requirements and guidelines for smart grid security into consideration. For achieving cybersecurity for system operation, attack prevention, detection, and mitigation algorithms and methodologies are developed specifically for FACTS-based WAVCS. Anomaly detection and mitigation in the WAVCS are achieved using algorithms based on machine learning which involves offline training and testing of ML models with CPS datasets incorporating physics-based features that allow accurate distinction between system faults and cyber attacks. For attack prevention, a methodology based on software defined network (SDN)-based moving target defense (MTD) network routing is proposed that enables prevention of Denial of Service (DoS) type attacks on the smart grid communication system. Subsequently, these methodologies and algorithms are implemented and evaluated on an HIL testbed that allows for real-time attack prevention, detection, and mitigation of emulated cyber attacks on the WAVCS in a close to real-world environment. The results show highly accurate and efficient performance of the implemented algorithms and methodologies with the smart grid system operating within the NERC's system operation limits even in the presence of DoS and data integrity cyber attacks. This work opens up future research opportunities in other directions such as (1) Expanding cybersecurity planning methodologies to real-time cyber contingency analysis with different game formulations; and (2) Applying the cybersecurity for system operation algorithms to broader categories of wide-area control applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Computational modeling of grain boundary segregation: A review

Nearly all metals, alloys, ceramics, and their associated composites are polycrystalline in nature, with grain boundaries that separate well-defined crystalline regions that influence materials properties. In all but the most pure elemental systems, intentional solutes or impurities are present and can segregate to, or less commonly away from, the grain boundaries, in turn influencing boundary behavior, their stability, and associated materials properties. In some cases, grain-boundary segregation can also trigger “phase-like” structural transitions that dramatically alter the essential nature of the boundary. With the development of advanced electron microscopy techniques, researchers can directly observe grain-boundary structures and segregation with atomic precision. Despite such spatial resolution, the underlying mechanisms governing grain-boundary segregation remain difficult to characterize. As a result, computational modeling techniques such as density functional theory, molecular dynamics, mesoscale phase-field, continuum defect theory, and others are important complementary tools to experimental observations for studying grain-boundary segregation behavior. In conclusion, these computational methods offer the ability to explore the underlying formation mechanisms of grain-boundary segregation, elucidate complex segregation behavior, and provide insights into solutions to effectively controlling microstructure.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Quadrature Based Neural Network Learning of Stochastic Hamiltonian Systems

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadrature-based models according to the integral form of the SHSs’ solutions, where we denoise the loss-by-moment calculations of the solutions. The integral pattern of the models transforms the source of the essential learning error from the discrepancy between the modified Hamiltonian and the true Hamiltonian in the classical HNN models into that between the integrals and their quadrature approximations. This transforms the challenging task of deriving the relation between the modified and the true Hamiltonians from the (stochastic) Hamilton–Jacobi PDEs, into the one that only requires invoking results from the numerical quadrature theory. Meanwhile, denoising via moments calculations gives a simpler data fitting method than, e.g., via probability density fitting, which may imply better generalization ability in certain circumstances. Numerical experiments validate the proposed learning strategy on several concrete Hamiltonian systems. The experimental results show that both the learned Hamiltonian function and the predicted solution of our quadrature-based model are more accurate than that of the corrected symplectic HNN method on a harmonic oscillator, and the three-point Gaussian quadrature-based model produces higher accuracy in long-time prediction than the Kramers–Moyal method and the numerics-informed likelihood method on the stochastic Kubo oscillator as well as other two stochastic systems with non-polynomial Hamiltonian functions. Moreover, the Hamiltonian learning error εH arising from the Gaussian quadrature-based model is lower than that from Simpson’s quadrature-based model. These demonstrate the superiority of our approach in learning accuracy and long-time prediction ability compared to certain existing methods and exhibit its potential to improve learning accuracy via applying precise quadrature formulae.

Mathematics↗
DOE OSTI2022

Insight into the Fast-Rechargeability of a Novel Mo 1.5 W 1.5 Nb 14 O 44 Anode Material for High-Performance Lithium-Ion Batteries

Wadsley–Roth phased niobates are promising anode materials for lithium-ion batteries, while their inherently low electrical conductivity still limits their rate-capability. Herein, a novel doped Mo 1.5 W 1.5 Nb 14 O 44 (MWNO) material is facilely prepared via an ionothermal-synthesis-assisted doping strategy. The detailed crystal structure of MWNO is characterized by neutron powder diffraction and aberration corrected scanning transmission electron microscope, unveiling the full occupation of Mo 6+ -dopant at the t1 tetrahedral site. In half-cells, MWNO exhibits enhanced fast-rechargeability. In this work, the origin of the improved performance is investigated by ultraviolet–visible diffuse reflectance spectroscopy, density functional theory (DFT) computation, and electrochemical impedance spectroscopy, revealing that bandgap narrowing improves the electrical conductivity of MWNO. Furthermore, operando X-ray diffraction elucidates that MWNO exhibits a typical solid-solution phase conversion-based lithium-ion insertion/extraction mechanism with reversible structural evolution during the electrochemical reaction. The boosted lithium-ion diffusivity of MWNO, due to the Mo 6+ /W 6+ doping effect, is confirmed by a galvanostatic intermittent titration technique and DFT. With the simultaneously enhanced electrical conductivity and lithium-ion diffusivity, MWNO successfully demonstrates its fast-rechargeability and practicality in the LiNi 0.5 Mn 1.5 O 4 -coupled full-cells. Therefore, this work illustrates the potential of ionothermal synthesis in energy storage materials and provides a mechanistic understanding of the doping effect on improving material's electrochemical performance.

25 ENERGY STORAGE↗
DOE OSTI2025

Wormholes, branes and finite matrices in sine dilaton gravity

We compute the double trumpet in sine dilaton gravity via WdW quantization. The wormhole size is discretized. The wormhole amplitude matches the spectral correlation of a finite-cut matrix integral, where matrices have large but finite dimensions. This strongly suggests an identification of the sine dilaton gravity theory with the q-deformed JT gravity matrix integral. At the very least, it captures all universal content of that matrix model. The disk decomposes into the physical (gauge invariant) solutions of the WdW equation, which are trumpets with discrete sizes. This decomposition modifies the usual no-boundary wavefunction to a normalizable one in sine dilaton gravity.

2D Gravity↗