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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.

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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Nonlinear Poisson–Boltzmann solutions for charged parallel plates: When opposite charges repel

I present an exact solution of the Poisson–Boltzmann equation for two parallel plates and discuss the solution properties. I discuss in more detail plates with opposite charges: In this case, there are two critical separations, L c,1 < L c,2 . For separations less than L c,1 , the force between plates is repulsive. It switches to attractive at L c,1 , but with the electric potential having the same sign on both plates. For L > L c,2 , the force remains attractive, and the potential at the plates has the same sign as the charge on each plate. I also describe charge regulation, determined by pK a , and provide formulas for both the critical distance where oppositely charged plates repel and their charging process. Finally, the implications of these results for the nanoparticle assembly, as driven by electrostatic interactions, are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

WeakIdent: Weak formulation for identifying differential equation using narrow-fit and trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation with two new mechanisms, narrow-fit and trimming, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise, and two new mechanisms, narrow-fit and trimming, improve the coefficient support and value recoveries respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to 100% noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Incoherent diffractive dijet production and gluon Bose enhancement in the nuclear wave function

We investigate the effect of gluon Bose enhancement in the nuclear wave function on the dijet production in incoherent diffractive processes in DIS and ultraperipheral collisions. We demonstrate that Bose enhancement leads to an enhancement of diffractive dijet production cross section when the transverse momenta of the two jets are aligned at zero relative angle. This enhancement is maximal when the magnitude of the transverse momenta of the two jets are equal, and disappears rather quickly as a function of the ratio of the two momenta. We study both the dilute limit and fully nonlinear dense regime where the nuclear wave function is evolved with the leading order JIMWLK equation. In both cases we observe a visible effect, with it being enhanced by the evolution due to the dynamical generation of the color neutralization scale.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Piecewise polyhedral formulations for a multilinear term

Herein, we present a mixed-integer linear programming (MILP) formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using its convex-hull representation. Based on the PPR’s solution, we also present a MILP formulation whose solutions are feasible for nonconvex, multilinear equations. We then present computational results showing the effectiveness of proposed formulations on standard benchmark nonlinear programs (NLPs) with multilinear terms and compare with a traditional formulation that is built using recursive bilinear groupings of multilinear terms.

42 ENGINEERING↗
DOE OSTI2020

Machine learning and serving of discrete field theories

A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the learned discrete field theory to predict new observations of the field for new boundary and initial conditions. The approach of learning discrete field theories overcomes the difficulties associated with learning continuous theories by artificial intelligence. The serving algorithm of discrete field theories belongs to the family of structure-preserving geometric algorithms, which have been proven to be superior to the conventional algorithms based on discretization of differential equations. The effectiveness of the method and algorithms developed is demonstrated using the examples of nonlinear oscillations and the Kepler problem. In particular, the learning algorithm learns a discrete field theory from a set of data of planetary orbits similar to what Kepler inherited from Tycho Brahe in 1601, and the serving algorithm correctly predicts other planetary orbits, including parabolic and hyperbolic escaping orbits, of the solar system without learning or knowing Newton’s laws of motion and universal gravitation. The proposed algorithms are expected to be applicable when the effects of special relativity and general relativity are important.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Multidimensional Coherent Spectroscopy of Molecular Polaritons: Langevin Approach

We present a microscopic theory for nonlinear optical spectroscopy of N molecules in an optical cavity. Using the Heisenberg-Langevin equation, an analytical expression is derived for the time- and frequency-resolved signals accounting for arbitrary numbers of vibrational excitations. We identify clear signatures of the polariton-polaron interaction from multidimensional projections of the signal, e.g., pathways and timescales. Cooperative dynamics of cavity polaritons against intramolecular vibrations is revealed, along with a crosstalk between long-range coherence and vibronic coupling that may lead to localization effects. Our results further characterize the polaritonic coherence and the population transfer that is slower.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Closed-Form Solutions for the Equations of Motion of the Heavy Symmetrical Top with One Point Fixed

The equations of motion (EOM) for the heavy symmetrical top with one point fixed are highly nonlinear. The literature describes the numerical methods that are used to resolve this classical system, including modern tools, such as the Runge–Kutta fourth–order method. Finding the derivate of closed-form solutions for the EOM is more difficult and, as mentioned in the literature, discovering the solution is not always possible for all the EOM. Fortunately, a few examples are available that serve as a guide to move further in this topic. The purpose of this paper is to find a methodology that will produce the solutions for a given subset of EOMs that fulfill certain requisites. This paper summarizes the literature available on this topic and then follows with the derivation of the EOM using the Euler–Lagrange method. The Routhian method will be used to reduce the size of the expression, and it continues with the formulation of the classical cubic function, ƒ(u), through a novel process. The roots of ƒ(u) are of the utmost importance in finding the EOM closed-form solution, and once the final roots are selected, the general method that will produce the closed-form solutions is presented. Two sets of examples are included to show the validity of the process, and comparisons of the results from the closed-form solutions vs. the numerical results for these examples are shown.

Laos, Hector↗
DOE OSTI2022

Quantum-inspired method for solving the Vlasov-Poisson equations

Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high-resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently, it has been proposed that matrix product state (MPS) methods, a quantum-inspired but classical algorithm, can be used to solve partial differential equations with exponential speed-up, provided that the solution can be compressed and efficiently represented as a MPS within some tolerable error threshold. Here, in this work, we explore the practicality of MPS methods for solving the Vlasov-Poisson equations for systems with one coordinate in space and one coordinate in velocity, and find that important features of linear and nonlinear dynamics, such as damping or growth rates and saturation amplitudes, can be captured while compressing the solution significantly. Furthermore, by comparing the performance of different mappings of the distribution functions onto the MPS, we develop an intuition of the MPS representation and its behavior in the context of solving the Vlasov-Poisson equations, which will be useful for extending these methods to higher-dimensional problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Non-autoregressive time-series methods for stable parametric reduced-order models

Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant interest in the use of techniques borrowed from machine learning to reduce the computational expense and/or improve the accuracy of predictions for these systems. These rely on the identification of a basis that reduces the dimensionality of the problem and the subsequent use of time series and sequential learning methods to forecast the evolution of the reduced state. Often, however, machine-learned predictions after reduced-basis projection are plagued by issues of stability stemming from incomplete capture of multiscale processes as well as due to error growth for long forecast durations. To address these issues, we have developed a non-autoregressive time series approach for predicting linear reduced-basis time histories of forward models. In particular, we demonstrate that non-autoregressive counterparts of sequential learning methods such as long short-term memory (LSTM) considerably improve the stability of machine-learned reduced-order models. Further, we evaluate our approach on the inviscid shallow water equations and show that a non-autoregressive variant of the standard LSTM approach that is bidirectional in the principal component directions obtains the best accuracy for recreating the nonlinear dynamics of partial observations. Moreover-and critical for many applications of these surrogates-inference times are reduced by three orders of magnitude using our approach, compared with both the equation-based Galerkin projection method and the standard LSTM approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Strong-field Driven Sub-cycle Band Structure Modulation and Dephasing Control

In this work, we present measurements of ultrafast electric-field observables in magnesium oxide using a non-resonant nonlinear optical interaction. Using field observables, we show that strong laser fields modulate the band structure on sub-cycle timescales, thereby altering the material’s nonlinear optical response. We perform time-dependent perturbation theory calculations using a field-dependent dispersion relation and semiconductor Bloch equation calculations, both of which agree with experimental observations. Furthermore, we extract pulse decay times from the real-time signal electric field envelope and show sub-cycle control of dephasing times. Our work offers a new perspective on strong-field-driven electron dynamics in solids through electric-field observables. The demonstrated attosecond modulation of the nonlinear response could have important implications for quantum light generation and quantum spectroscopy using nonlinear optical processes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗
DOE OSTI2023

Electron kinetics in a high- Z plasmoid

The problem of the electron dynamics on a closed magnetic field line passing through a high-Z plasmoid is considered. The electron kinetic equation is integrated over bounce motion and pitch angle, reducing the independent variables to a single adiabatic invariant plus time. Integration of the full Landau self-collision operator is carried out exactly, resulting in a nonlinear integro-differential operator in the new invariant. Conservation laws and the H theorem of the integrated self-collision operator are proven. Numerical solutions of the integrated kinetic equation are obtained with a self-consistent quasineutral electric potential, given the initial condition of a cold plasmoid immersed in a hot ambient plasma. The fact that cold electrons are deeply trapped in a potential with a parabolic peak leads to exactly 3/4 the usual rate of collisional heating by the ambient plasma, independent of any other parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning

Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff–Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ where N t is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2024

Testing and modeling of CLT-to-CLT joints made using hardwood dowels and screws with varying spacing

With the increasing popularity of mass timber, utilizing large-diameter wood screws and hardwood dowels can offer an easy and cost-efficient way to join structural elements. However, the existing research on hardwood dowels is limited to single fastener joints under monotonic loading. No research is available on the group effects of joints with multiple hardwood dowels. Here, this paper presents the results of 96 monotonic and cyclic single-shear plane CLT-to-CLT joint tests with hardwood dowels (Red Oak and Yellow Birch, 25.4 mm diameter) and self-tapping wood screws (8 mm diameter) in Grand-Fir CLT, where screws were inserted both perpendicular and at a 45-degree angle to the grain for comparison to hardwood dowels. The study evaluated the mechanical properties of the joints by changing fastener spacing. Mechanical properties such as yielding and peak strength, displacement, elastic and yielding stiffness, and ductility were evaluated. The results showed equal strength and stiffness properties for hardwood dowels comparable with large-diameter screws. Additionally, the hardwood dowel joints demonstrated moderate ductility properties. The strength and stiffness of the tested joints were compared with analytical equations found in the literature by considering the group action factor of the fasteners. Lastly, a nonlinear force-displacement model was presented and compared to the experimental results and analytical calculations, which gives the possibility to predict and optimize the mechanical behavior of hardwood dowel and screw joints with varying numbers and spacing between fasteners.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Physics constrained learning for data-driven inverse modeling from sparse observations

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Quantum Versus Classical Switching Dynamics of Driven Dissipative Kerr Resonators

Here, we report a first-principles study of the driven dissipative dynamics for Kerr oscillators in the mesoscopic regime. This regime is characterized by large Kerr nonlinearity, realized here using the nonlinear kinetic inductance of a large array of Josephson junctions. The experimentally measured nonlinear resonance lineshapes of the junction array modes show significant deviations from steady-state numerical predictions, and necessitate time-dependent numerical simulations indicative of strong measurement-induced dephasing in the system arising from the large cross-Kerr effect between array modes. Analytical and numerical calculations of switching rate corroborate this by showing the emergence of a slow time scale, which is much longer than the linear decay rate and is set by fluctuation-induced switching times in the bistable regime. Furthermore, our analysis shows that the usual quantum-activated escape treatment is inadequate for prediction of the switching rates at large frequency shifts caused by strong nonlinearities, necessitating a quantum treatment that utilizes the full system Liouvillian. Based on our analysis, we identify a universal crossover parameter that delineates the regimes of validity of semiclassical and quantum descriptions, respectively. Our work shows how dynamical switching effects in strongly nonlinear systems provide a platform to study quantum-to-classical transitions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗