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At least 73 records · Page 4

Nonlinear Optimal Control of Electron Dynamics Within Hartree-Fock Theory

Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of motion—the time-dependent Schrödinger equation (TDSE)—is numerically intractable. Here, we present a solution of this problem within time-dependent Hartree-Fock (TDHF) theory, a mean field approximation of the TDSE. Optimality is defined in terms of minimizing the total control effort while maximizing the overlap between desired and achieved target states. We frame this problem as an optimization problem constrained by the nonlinear TDHF equations; we solve it using trust region optimization with gradients computed via a custom-built adjoint state method. For three molecular systems, we show that with very small neural network parametrizations of the control, our method yields solutions that achieve desired targets within acceptable constraints and tolerances.

97 MATHEMATICS AND COMPUTING

Generalized indical forces on deforming rectangular wings in supersonic flight

A method is presented for determining the time-dependent flow over a rectangular wing moving with a supersonic forward speed and undergoing small vertical distortions expressible as polynomials involving spanwise and chordwise distances. The solution for the velocity potential is presented in a form analogous to that for steady supersonic flow having the familiar "reflected area" concept discovered by Evvard. Particular attention is paid to indicial-type motions and results are expressed in terms of generalized indicial forces. Numerical results for Mach numbers equal to 1.1 and 1.2 are given for polynomials of the first and fifth degree in the chordwise and spanwise directions, respectively, on a wing having an aspect ratio of 4.

Lomax, Harvard

A numerically exact description of ultrafast vibrational decoherence in vibration-coupled electron transfer

Broadband pump–probe spectroscopy has been widely used to measure vibrational decoherence associated with the reaction coordinate in photoinduced ultrafast vibration-coupled electron transfer (VCET) reactions. These experiments provide insight into the interplay of intramolecular coordinates along the reaction coordinate. However, a general theoretical foundation for analyzing, and even for explaining rigorously, these data is lacking. In this work, we study vibrational decoherence in a model VCET reaction using the nearly exact time-dependent density matrix renormalization group simulation method. We explore how analyzing the density matrix with quantum information measures can help elucidate the evolution of vibrational coherence in simulations of dynamics. We examine how vibrational coherence is affected by electron transfer on the timescale of approximately 100 femtoseconds. Our results suggest that electron transfer, in the nonadiabatic model, changes the vibrational equilibrium position abruptly—an example of a “quantum quench” event. This explains the concomitant vibrational decoherence. We find that abrupt vibrational decoherence can be mitigated by wavepacket motion occurring on the timescale of the electron transfer.

Science & Technology - Other Topics

Robust Implicit Adaptive Low Rank Time-Stepping Methods for Matrix Differential Equations

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac–Frenkel time-dependent variational principle. In recent years, it has attracted a lot of attention due to its wide applicability. Our schemes are inspired by the three-step procedure used in the rank adaptive version of the unconventional robust integrator (the so called BUG integrator) (Ceruti et al. in BIT Numer Math 62(4):1149–1174, 2022) for DLRA. First, a prediction (basis update) step is made computing the approximate column and row spaces at the next time level. Second, a Galerkin evolution step is invoked using an implicit solves for the small core matrix. Finally, a truncation is made according to a prescribed error threshold. Since the DLRA is evolving the differential equation projected on to the tangent space of the low rank manifold, the error estimate of the BUG integrator contains the tangent projection (modeling) error which cannot be easily controlled by mesh refinement. This can cause convergence issue for equations with cross terms. To address this issue, we propose a simple modification, consisting of merging the row and column spaces from the explicit step truncation method together with the BUG spaces in the prediction step. In addition, we propose an adaptive strategy where the BUG spaces are only computed if the residual for the solution obtained from the prediction space by explicit step truncation method, is too large. Here, we prove stability and estimate the local truncation error of the schemes under assumptions. We benchmark the schemes in several tests, such as anisotropic diffusion, solid body rotation and the combination of the two, to show robust convergence properties.

97 MATHEMATICS AND COMPUTING

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference

Space-Time Finite Element Tensor Network Approach for the Time-Dependent Convection–Diffusion–Reaction Equation with Variable Coefficients

In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.

convection–diffusion–reaction equation

Thermal Radiation Transport with Tensor Trains

We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated by the rank of the decomposition. When the solution is “low rank,” the memory footprint of the specific intensity solution vector may be significantly compressed. The algorithm, following a step-then-truncate approach of a traditional discrete ordinates method, operates directly on the compressed state vector, thereby enabling large speedups for low-rank solutions. To achieve these speedups, we rely on a recently developed rounding approach based on the Gram-SVD. We detail how familiar S N algorithms for (gray) thermal transport can be mapped to this TT framework and present several numerical examples testing both the optically thick and thin regimes. The TT framework finds low-rank structure and supplies up to ≃60× speedups and ≃1000× compressions for problems demanding large angle counts, thereby enabling previously intractable SN calculations and supplying a promising avenue to mitigate ray effects.

79 ASTRONOMY AND ASTROPHYSICS

Sylvester-preconditioned adaptive-rank implicit time integrators for advection-diffusion equations with variable coefficients

Here, we consider the adaptive-rank integration of multi-dimensional time-dependent advection-diffusion partial differential equations (PDEs) with variable coefficients. We employ a standard finite-difference method for spatial discretization coupled with high-order diagonally implicit Runge-Kutta temporal schemes. The discrete equation is a generalized Sylvester equation (GSE), which we solve with a projection-based adaptive-rank algorithm structured around two key strategies: (i) constructing dimension-wise subspaces using a novel atypical extended Krylov strategy, and (ii) efficiently solving the basis coefficient matrix with a preconditioned GMRES solver. The low-rank decomposition is performed in 2D using SVD and with high-order SVD (HOSVD) in 3D to represent the tensor in a compressed Tucker format. For d-dimensional problems (here, d = 2 or 3), the computational complexity and memory storage of the approach are found numerically to scale as and $\mathscr{O}(Nr^2) + \mathscr{O} (r^{d+1})$ and $\mathscr{O}(Nr) + \mathscr{O} (r^{d})$, respectively, with the one-dimensional resolution and the maximal rank during the Krylov iteration (which we find to be largely independent of on our numerical examples). We present numerical examples that illustrate the advertised properties of the algorithm.

97 MATHEMATICS AND COMPUTING

Surrogate Model Integration with MOOSE XFEM for Creep Crack Growth

Ferritic-martensitic steels are key structural materials for advanced reactors but experience time-dependent deformation and damage under prolonged high temperature and irradiation, leading to creep-driven crack initiation and growth. High-fidelity models—crystal plasticity with irradiation mechanisms, phase-field for microstructural evolution, and continuum-damage viscoplasticity—capture the underlying physics but are too computationally intensive for broad design-space exploration and uncertainty quantification. This milestone advances a scalable alternative by integrating a microstructure-sensitive surrogate creep model into the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element framework and extending it to fracture via the extended finite element method (XFEM). The surrogate model, developed with collaborators at Sandia and Los Alamos National Laboratories, maps relevant microstructural descriptors to the viscoplastic response of HT9. We embed this surrogate within a coupled deformation-damage workflow in MOOSE/XFEM to simulate creep-driven crack initiation and propagation. Implementation enhancements include updates to the material interface, a plastic correction phase involving microstructure evolution, and fracture criteria to ensure numerical robustness and compatibility with the surrogate structure. Demonstrations on canonical creep benchmarks spanning uniaxial and multiaxial states show that the surrogate reproduces key trends of high-fidelity models while substantially reducing computational cost. The resulting capability bridges physics fidelity and performance, providing a practical path to a predictive, microstructure-aware assessment of creep and fracture in reactor materials.

36 - MATERIALS SCIENCE

TRUST Sensors in Environments: Thermocouples (SE-TC), Release FY25

The Delivery Environments Testbeds to Reduce Uncertainty in Simulations and Tests (TRUST) project is a broad project intended to analyze simplified problems experimentally and with modeling and simulation. The purpose of analyzing these simplified problems is to extend solution methods to more complex problems, as well as understand deficiencies and gaps in knowledge of methods currently used in more complex analyses. The TRUST project encompasses several smaller testbeds intended to isolate individual phenomena. The testbed under consideration in this report is the Sensors in Environments: Thermocouples testbed. In previous years, the purpose of this testbed was to quantify uncertainty of thermocouple sensors. To accomplish this, an aluminum plate was placed in a thermal chamber and subject to various types of thermal loading. Thermocouples were placed in various locations on the aluminum plate in various configurations (e.g., embedded in the plate, placed under Kapton tape), and an effort was made to quantify uncertainty in these measurements. Finite element simulations were performed to investigate how sensitive these measurements were to parameters such as the boundary conditions on the plate and material properties. However, a fundamental source of uncertainty in this analysis was the convective heat transfer from the plate. Convective heat transfer is a complex physical phenomenon comprised of a number of interacting sub-processes and is difficult to predict accurately a priori. As such, the main purpose of this testbed in FY25 was to better understand, both experimentally and numerically, the convective heat transfer from the plate. This is a highly applicable problem to several more complex problems, as convective heat transfer occurs in nearly all problems where a body is moving through air. Numerically, this required a two-step approach. First, the air flow in the thermal chamber was in vestigated using computational fluid dynamics. The commercial solver Fluent was used to perform these simulations. From these simulations, a heat transfer coefficient over the surface of the plate was calculated. This heat transfer was then used as boundary conditions for finite element heat transfer simulations within the plate, which were performed using Abaqus. Significant effort was devoted to automating the handoff between these two solvers. Experimentally, previous thermocouple results in the plate were used to validate the time-dependent thermal profiles produced from Abaqus. Further experimental efforts were performed both to help validate the Fluent simulations and to inform its boundary conditions. For example, hot-wire anemometers were used to measure the velocity in the chamber, which would be particularly useful in understanding the chamber inlet velocity. Thermocouple measurements were also taken in the chamber, instead of only on the plate, to serve as validation evidence for the Fluent simulations. Numerical results showed that the Fluent to Abaqus workflow matched previous plate thermocouple measurements well. This type of handoff is useful for more complex experiments, or those that are not able to be examined in as great of detail as this testbed, as it was performed without any experimental input. Experimental results, however, were more mixed. The anemometers proved unreliable, with inconsistent measurements across all anemometers, even at locations that were nearly identical. On the other hand, the thermocouples provided a relatively rich view of the temperature field in the chamber.

42 ENGINEERING

Enhanced shear stabilization of turbulence in NSTX

In studying a particular non-stationary NSTX L-mode plasma, we observed unexpectedly high levels of flux—first with quasilinear (TGLF) modeling and subsequently with nonlinear gyrokinetic simulations. Upon more detailed analysis, a novel confinement regime was discovered in which a modest increase in E x B shear (beyond baseline experimental estimates) rapidly reduced turbulent transport to levels consistent with power balance. This modest increase is plausible given the errors inherent to the estimation of shearing rates, and the added complexity of the non-stationary (time-dependent) power balance. Remarkably, an additional small increase in shear yields the familiar ion-neoclassical transport level with what appears to be the onset of high-k electron transport only. Although analyses using the TGLF-SAT2 model successfully capture numerous parametric dependencies of this plasma, TGLF does not reproduce the rapid E x B stabilization seen in CGYRO. We believe the results presented should help to better characterize the nonlinear physics of spherical tokamak confinement regimes, provide useful ST datasets for reduced model development, and motivate more accurate experimental diagnosis of E x B shearing rates.

Atomic and molecular collisions

Real-time scattering in Ising field theory using matrix product states

We study scattering in Ising field theory (IFT) using matrix product states and the time-dependent variational principle. IFT is a one-parameter family of strongly coupled nonintegrable quantum field theories in 1+1 dimensions, interpolating between massive free fermion theory and Zamolodchikov's integrable massive 𝐸 8 theory. Particles in IFT may scatter either elastically or inelastically. In the postcollision wave function, particle tracks from all final-state channels occur in superposition; processes of interest can be isolated by projecting the wave function onto definite particle sectors, or by evaluating energy density correlation functions. Using numerical simulations we determine the time delay of elastic scattering and the probability of inelastic particle production as a function of collision energy. We also study the mass and width of the lightest resonance near the 𝐸 8 point in detail. Close to both the free fermion and 𝐸 8 theories, our results for both elastic and inelastic scattering are in good agreement with expectations from form-factor perturbation theory. Using numerical computations to go beyond the regime accessible by perturbation theory, we find that the high-energy behavior of the two-to-two particle scattering probability in IFT is consistent with a conjecture of Zamolodchikov. Our results demonstrate the efficacy of tensor-network methods for simulating the real-time dynamics of strongly coupled quantum field theories in 1+1 dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Phase-space methods for neutrino oscillations: Extension to multibeams

The phase-space approach (PSA), which was originally introduced in Lacroix [] to describe neutrino flavor oscillations for interacting neutrinos emitted from stellar objects is extended to describe arbitrary numbers of neutrino beams. The PSA is based on mapping the quantum fluctuations into a statistical treatment by sampling initial conditions followed by independent mean-field evolution. A new method is proposed to perform this sampling that allows treating an arbitrary number of neutrinos in each neutrino beams. We validate the technique successfully and confirm its predictive power on several examples where a reference exact calculation is possible. We show that it can describe many-body effects, such as entanglement and dissipation induced by the interaction between neutrinos. Due to the complexity of the problem, exact solutions can only be calculated for rather limited cases, with a limited number of beams and/or neutrinos in each beam. The PSA approach considerably reduces the numerical cost and provides an efficient technique to accurately simulate arbitrary numbers of beams. Examples of PSA results are given here, including up to 200 beams with time-independent or time-dependent Hamiltonians. We anticipate that this approach will be useful to bridge exact microscopic techniques with more traditional transport theories used in neutrino oscillations. It will also provide important reference calculations for future quantum computer applications where other techniques are not applicable to classical computers. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Analysis of dynamic stall using unsteady boundary-layer theory

The unsteady turbulent boundary layer and potential flow about a pitching airfoil are analyzed using numerical methods to determine the effect of pitch rate on the delay in forward movement of the rear flow reversal point. An explicit finite difference scheme is used to integrate the unsteady boundary layer equations, which are coupled at each instant of time to a fully unsteady and nonlinear potential flow analysis. A substantial delay in forward movement of the reversal point is demonstrated with increasing pitch rate, and it is shown that the delay results partly from the alleviation of the gradients in the potential flow, and partly from the effects of unsteadiness in the boundary layer itself. The predicted delay in flow-reversal onset, and its variation with pitch rate, are shown to be in reasonable agreement with experimental data relating to the delay in dynamic stall. From the comparisons it can be concluded (a) that the effects of time-dependence are sufficient to explain the failure of the boundary layer to separate during the dynamic overshoot, and (b) that there may be some link between forward movement of the reversal point and dynamic stall.

Scruggs, R. M.

Analysis of three-dimensional unsteady flow around oscillating wings

A method based on the Navier-Stokes equations was developed for determining analytically the three-dimensional unsteady flow patterns around oscillating wings. The Helmholz vorticity transport equations were discretized in three-dimensional finite element form from a variational formulation and integrated numerically. At each time step of the numerical integration the velocity field was calculated from the representation of the three-dimensional wing by a system of optimized distribution of vortices in space. During the numerical integration of the vorticity transport equations the time-dependent boundary conditions on the wing were specified as external constraint conditions. Examples of obtained results describing the three-dimensional unsteady flow around a wing were presented.

Bratanow, T.

Numerical simulation of high Reynolds number transonic flows

A code has been developed for simulating high Reynolds number transonic flow fields of arbitrary configuration. An explicit finite-difference method with time splitting is used to solve the time-dependent equations for compressible turbulent flow. A nonorthogonal computational mesh of arbitrary configuration facilitates the description of the flow field. The code is applied to simulate the flow over an 18 percent thick circular-arc biconvex airfoil at zero angle of attack and free-stream Mach number of 0.775. A simple mixing-length model is used to describe the turbulence and chord Reynolds numbers of 1, 2, 4, and 10 million are considered. The solution describes in sufficient detail both the shock-induced and trailing-edge separation regions, and provides the profile and friction drag.

Deiwert, G. S.

Finite difference methods for transient signal propagation in stratified dispersive media

Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.

Lam, D. H.

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

Rudy, D. H.