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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Integrability, normal forms, and magnetic axis coordinates

Integrable or near-integrable magnetic fields are prominent in the design of plasma confinement devices. Such a field is characterized by the existence of a singular foliation entirely consisting of invariant submanifolds. A compact regular leaf (a flux surface) of this foliation must be diffeomorphic to the two-torus. In a neighborhood of a flux surface, it is known that the magnetic field admits several exact smooth normal forms in which the field lines are straight. However, these normal forms break down near singular leaves, including elliptic and hyperbolic magnetic axes. In this work, the existence of exact smooth normal forms for integrable magnetic fields near elliptic and hyperbolic magnetic axes is established. In the elliptic case, smooth near-axis Hamada and Boozer coordinates are defined and constructed. Ultimately, these results establish previously conjectured smoothness properties for smooth solutions of the magnetohydrodynamic equilibrium equations. The key arguments are a consequence of a geometric reframing of integrability and magnetic fields: they are presymplectic systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Time evolution of ML-MCTDH wavefunctions. II. Application of the projector splitting integrator

The multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach can suffer from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of regularization of the EOMs. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here, we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement standard ML-MCTDH. We demonstrate the efficiency and stability of the PSI for large ML-MCTDH wavefunctions containing up to hundreds of thousands of nodes by considering a series of spin-boson models with up to 106 bath modes and find that for these problems, the PSI requires roughly 3–4 orders of magnitude fewer Hamiltonian evaluations and 2–3 orders of magnitude fewer Hamiltonian applications than standard ML-MCTDH and 2–3/1–2 orders of magnitude fewer evaluations/applications than approaches that use improved regularization schemes. Finally, we consider a series of significantly more challenging multi-spin-boson models that require much larger numbers of single-particle functions with wavefunctions containing up to ~1.3×10 9 parameters to obtain accurate dynamics.

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

Evaluation of the Abel inversion integral in O-mode plasma reflectometry using Chebyshev–Gauss quadrature

The Abel transform is often used to reconstruct plasma density profiles from O-Mode polarized reflectometry diagnostics. However, standard numerical trapezoidal evaluation of the Abel inversion integral can be computationally expensive for a large number of evaluation points, and an endpoint singularity exists on the upper-bound of the integral, which can result in an increased error. In this work, Chebyshev–Gauss quadrature is introduced as a new method to evaluate the Abel inversion integral for the problem of O-Mode plasma reflectometry. Here, the method does not require numerical evaluation of an integral singularity and is shown to have similar accuracy compared to existing methods while being computationally efficient.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Semantic embedding for quantum algorithms

The study of classical algorithms is supported by an immense understructure, founded in logic, type, and category theory, that allows an algorithmist to reason about the sequential manipulation of data irrespective of a computation’s realizing dynamics. As quantum computing matures, a similar need has developed for an assurance of the correctness of high-level quantum algorithmic reasoning. Parallel to this need, many quantum algorithms have been unified and improved using quantum signal processing (QSP) and quantum singular value transformation (QSVT), which characterize the ability, by alternating circuit ansätze, to transform the singular values of sub-blocks of unitary matrices by polynomial functions. However, while the algebraic manipulation of polynomials is simple (e.g., compositions and products), the QSP/QSVT circuits realizing analogous manipulations of their embedded polynomials are non-obvious. This work constructs and characterizes the runtime and expressivity of QSP/QSVT protocols where circuit manipulation maps naturally to the algebraic manipulation of functional transforms (termed semantic embedding). In this way, QSP/QSVT can be treated and combined modularly, purely in terms of the functional transforms they embed, with key guarantees on the computability and modularity of the realizing circuits. We also identify existing quantum algorithms whose use of semantic embedding is implicit, spanning from distributed search to proofs of soundness in quantum cryptography. The methods used, based in category theory, establish a theory of semantically embeddable quantum algorithms, and provide a new role for QSP/QSVT in reducing sophisticated algorithmic problems to simpler algebraic ones.

Physics↗
DOE OSTI2024

Mixed-mode oscillations in a three-timescale coupled Morris–Lecar system

Mixed-mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale systems can arise either from a canard mechanism associated with folded node singularities or a delayed Andronov–Hopf bifurcation (DHB) of the fast subsystem. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in coupled Morris–Lecar neurons with three distinct timescales. We investigate two kinds of MMOs occurring in the presence of a singularity known as canard-delayed-Hopf (CDH) and in cases where CDH is absent. In both cases, we examine how features and mechanisms of MMOs vary with respect to variations in timescales. Our analysis reveals that MMOs supported by CDH demonstrate significantly stronger robustness than those in its absence. Moreover, we show that the mere presence of CDH does not guarantee the occurrence of MMOs. This work yields important insights into conditions under which the two separate mechanisms in two-timescale context, canard and DHB, can interact in a three-timescale setting and produce more robust MMOs, particularly against timescale variations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Extended dynamic mode decomposition for model reduction in fluid dynamics simulations

High computational cost and storage/memory requirements of fluid dynamics simulations constrain their usefulness as a predictive tool. Reduced-order models (ROMs) provide a viable solution to this challenge by extracting the key underlying dynamics of a complex system directly from data. We investigate the efficacy and robustness of an extended dynamic mode decomposition (xDMD) algorithm in constructing ROMs of three-dimensional cardiovascular computations. Focusing on the ROMs' accuracy in representation and interpolation, we relate these metrics to the truncation rank of singular value decomposition, which underpins xDMD and other approaches to ROM construction. Our key innovation is to relate the truncation rank to the singular values of the original flow problem. This result establishes a priori guidelines for the xDMD deployment and its likely success as a means of data compression and reconstruction of the system's dynamics from dominant spatiotemporal structures present in the data.

Mechanics↗
DOE OSTI2021

Moiréless correlations in ABCA graphene

Atomically thin van der Waals materials stacked with an interlayer twist have proven to be an excellent platform toward achieving gate-tunable correlated phenomena linked to the formation of flat electronic bands. In this work we demonstrate the formation of emergent correlated phases in multilayer rhombohedral graphene––a simple material that also exhibits a flat electronic band edge but without the need of having a moiré superlattice induced by twisted van der Waals layers. We show that two layers of bilayer graphene that are twisted by an arbitrary tiny angle host large (micrometer-scale) regions of uniform rhombohedral four-layer (ABCA) graphene that can be independently studied. Scanning tunneling spectroscopy reveals that ABCA graphene hosts an unprecedentedly sharp van Hove singularity of 3–5-meV half-width. We demonstrate that when this van Hove singularity straddles the Fermi level, a correlated many-body gap emerges with peak-to-peak value of 9.5 meV at charge neutrality. Mean-field theoretical calculations for model with short-ranged interactions indicate that two primary candidates for the appearance of this broken symmetry state are a charge-transfer excitonic insulator and a ferrimagnet. Finally, we show that ABCA graphene hosts surface topological helical edge states at natural interfaces with ABAB graphene which can be turned on and off with gate voltage, implying that small-angle twisted double-bilayer graphene is an ideal programmable topological quantum material.

42 ENGINEERING↗
DOE OSTI2022

Defects in bent-core liquid crystals

The spatial organization of liquid crystals (LCs) is governed by molecular shapes and interactions and reveals itself at the macroscopic scale by anisotropic properties and various textures with an abundance of topological defects. LC defects, representing singular and non-singular distortions of the orientational order, carry signatures of the undistorted ground LC state and bear specific information that helps to identify phases in newly synthesized materials. The review describes defects in materials with bent-core shape of molecules.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Source term method for binary neutron stars initial data

The initial condition problem for a binary neutron star system requires a Poisson equation solver for the velocity potential with a Neumann-like boundary condition on the surface of the star. Difficulties that arise in this boundary value problem are: (a) the boundary is not known a priori, but constitutes part of the solution of the problem; (b) various terms become singular at the boundary. In this work, we present a new method to solve the fluid Poisson equation for irrotational/spinning binary neutron stars. The advantage of the new method is that it does not require complex fluid surface fitted coordinates and it can be implemented in a Cartesian grid, which is a standard choice in numerical relativity calculations. This is accomplished by employing the source term method proposed by Towers, where the boundary condition is treated as a jump condition and is incorporated as additional source terms in the Poisson equation, which is then solved iteratively. The issue of singular terms caused by vanishing density on the surface is resolved with an additional separation that shifts the computation boundary to the interior of the star. We present two-dimensional tests to show the convergence of the source term method, and we further apply this solver to a realistic three-dimensional binary neutron star problem. By comparing our solution with the one coming from the initial data solver cocal, we demonstrate agreement to approximately 1%. We report our method can be used in other problems with non-smooth solutions like in magnetized neutron stars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Elimination of MHD current sheets by modifications to the plasma wall in a fixed boundary model

Models of magnetohydrodynamic (MHD) equilibia that for computational convenience assume the existence of a system of nested magnetic flux surfaces tend to exhibit singular current sheets. These sheets are located on resonant flux surfaces that are associated with rational values of the rotational transform. We study the possibility of eliminating these singularities by suitable modifications of the plasma boundary, which we prescribe in a fixed boundary setting. We find that relatively straightforward iterative procedures can be used to eliminate weak current sheets that are generated at resonant flux surfaces by the nonlinear interactions of resonating wall harmonics. These types of procedures may prove useful in the design of fusion devices with configurations that enjoy improved stability and transport properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

On the relationship between the multi-region relaxed variational principle and resistive inner-layer theory

We show that the variational energy principle of the multi-region relaxed magnetohydrodynamic (MRxMHD) model can be used to predict finite-pressure linear tearing instabilities. In this model, the plasma volume is sliced into sub-volumes separated by 'ideal interfaces', and in each volume the magnetic field relaxes to a Taylor state, where the pressure gradient $\nabla p = 0$. The MRxMHD model is implemented in the Stepped-Pressure Equilibrium Code (SPEC) so that the equilibrium solution in each region is computed while preserving the force balance across the interfaces. As SPEC computes the Hessian matrix (a discretized stability matrix), the stability of an MRxMHD equilibrium can also be computed with SPEC. In this article, using SPEC, we investigate the effect of local pressure gradients and the $\nabla p = 0$ in the vicinity of the resonant surface of a tearing mode. For low-beta plasma, we have been able to illustrate a relationship between the resistive singular-layer theory (Coppi et al 1966 Nucl. Fusion6 101; Glasser et al 1975 Phys. Fluids18 875–88) and the MRxMHD model. Within the singular layer, the volume-averaged magnetic helicity and the flux-averaged toroidal flux are shown to be the invariants for the linear tearing modes in SPEC simulations. Our technique to compute MRxMHD stability is first tested numerically in a cylindrical tokamak and its application in toroidal geometry is demonstrated. We demonstrate an agreement between the stability boundary obtained with SPEC simulation and the resistive inner-layer theories.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Neural network-based classification and regression of magnetohydrodynamic modes in tokamaks

We present a machine learning-based magnetohydrodynamic (MHD) classifier and regressor that utilizes real or complex-valued 3D magnetic sensor array data to determine neoclassical tearing mode (NTM) onset times in tokamaks with millisecond accuracy. The input dataset consists of poloidal profiles of complex Fourier amplitudes with an n = 1 toroidal mode number from 144 human-labeled ITER Baseline Scenario discharges in the DIII-D tokamak, spanning both tearing-dominated and sawtooth-dominated regimes. Since m, n = 2,1 NTMs frequently emerge alongside sawteeth at the same frequency in this scenario, the focus is on isolating the m = 1 and m = 2 components of the n = 1 MHD mode near the tearing onset. To improve model regularization and prediction stability, singular value decomposition was applied to balance the sawtooth and tearing datasets. The enriched datasets facilitated training neural networks that learn the key distinguishing features of sawtooth and tearing modes in the poloidal profiles of their magnetic amplitude and phase. When the modes occur independently, the networks achieve perfect classification due to the modes’ distinct characteristics and low measurement noise. In the more experimentally relevant case where both modes coexist, the networks maintain exceptional performance across key metrics. Tests on synthetic data with known ground truth demonstrate the superior accuracy of the neural network trained on complex-valued input compared to models using real amplitude, phase, or pseudo-complex data, achieving both a mean time delay and standard deviation below 1 ms. Notably, standard linear regression methods fitting the dominant singular modes to the data closely match the neural network’s performance. Applying these methods across a broad range of H-mode scenarios will enable future studies to systematically identify dominant NTM triggers as scenario-specific variables, paving the way for more effective tearing mode avoidance strategies in future fusion reactor designs.

machine learning↗
DOE OSTI2025

Exploring the energy landscape of RBMs: reciprocal space insights into bosons, hierarchical learning and symmetry breaking

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Unified analysis of finite-size error for periodic Hartree-Fock and second order Møller-Plesset perturbation theory

Despite decades of practice, finite-size errors in many widely used electronic structure theories for periodic systems remain poorly understood. For periodic systems using a general Monkhorst-Pack grid, there has been no comprehensive and rigorous analysis of the finite-size error in the Hartree-Fock theory (HF) and the second order Møller-Plesset perturbation theory (MP2), which are the simplest wavefunction based method, and the simplest post-Hartree-Fock method, respectively. Such calculations can be viewed as a multi-dimensional integral discretized with certain trapezoidal rules. Due to the Coulomb singularity, the integrand has many points of discontinuity in general, and standard error analysis based on the Euler-Maclaurin formula gives overly pessimistic results. The lack of analytic understanding of finite-size errors also impedes the development of effective finite-size correction schemes. We propose a unified analysis to obtain sharp convergence rates of finite-size errors for the periodic HF and MP2 theories. Our main technical advancement is a generalization of the result of Lyness [Math. Comp. 30 (1976), pp. 1–23] for obtaining sharp convergence rates of the trapezoidal rule for a class of non-smooth integrands. Our result is applicable to three-dimensional bulk systems as well as low dimensional systems (such as nanowires and 2D materials). Our unified analysis also allows us to prove the effectiveness of the Madelung-constant correction to the Fock exchange energy, and the effectiveness of a recently proposed staggered mesh method for periodic MP2 calculations (see X. Xing, X. Li, and L. Lin [J. Chem. Theory Comput. 17 (2021), pp. 4733–4745]). In conclusion, our analysis connects the effectiveness of the staggered mesh method with integrands with removable singularities, and suggests a new staggered mesh method for reducing finite-size errors of periodic HF calculations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Kinematics and dynamics of disclination lines in three-dimensional nematics

An exact kinematic law for the motion of disclination lines in nematic liquid crystals as a function of the tensor order parameter Q is derived. Unlike other order parameter fields that become singular at their respective defect cores, the tensor order parameter remains regular. Following earlier experimental and theoretical work, the disclination core is defined to be the line where the uniaxial and biaxial order parameters are equal, or equivalently, where the two largest eigenvalues of Q cross. This allows an exact expression relating the velocity of the line to spatial and temporal derivatives of Q on the line, to be specified by a dynamical model for the evolution of the nematic. By introducing a linear core approximation for Q, analytical results are given for several prototypical configurations, including line interactions and motion, loop annihilation, and the response to external fields and shear flows. Behaviour that follows from topological constraints or defect geometry is highlighted. Finally, the analytic results are shown to be in agreement with three-dimensional numerical calculations based on a singular Maier–Saupe free energy that allows for anisotropic elasticity.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Two-component atomic Fermi superfluid with spin-orbital coupling in thin-spherical-shell geometry

We present a theory of two-component atomic Fermi superfluid with tunable pairing interaction in a thin spherical shell subject to spin-orbit coupling (SOC). By incorporating SOC into the Fermi superfluid in the BCS-Bose Einstein condensation (BEC) crossover, we obtain the energy spectrum and equations of state. While the order parameter and chemical potential are suppressed by SOC on the BCS side, the former remains positive but the latter may be pushed to negative values by SOC.Meanwhile, the compressibility exhibits kinks as the pairing interaction or SOC varies, indicating singular behavior of higher derivatives of the free energy despite the presence of the superfluid order parameter. The minimum of the energy dispersion indicates a decoupling of the energy gap from the order parameter, and the compressibility kinks occur when the energy gap approaches 0. We found the particle-hole mixing in the Fermi superfluid essential for the compressibility kinks since a Fermi gas with the same SOC but no pairing interaction only exhibits complicated dispersions but no singular behavior. Therefore, our results show that a combination of superfluid, SOC, and geometry can lead to interesting phenomena. Here, we also discuss possible experimental realizations and implications.

Fermi gases↗
DOE OSTI2020

Dynamical quantum phase transitions of quantum spin chains with a Loschmidt-rate critical exponent equal to $\frac{1}{2}$

In this work, we describe a new universality class of dynamical quantum phase transitions of the Loschmidt amplitude of quantum spin chains off equilibrium criticality. We demonstrate that in many cases it is possible to change the conventional linear singularity of the Loschmidt rate function into a smooth peak by tuning one parameter of the quench protocol. Exactly at the point when this change-over occurs, the singularity of the Loschmidt rate function persists, with a critical exponent equal to $\frac{1}{2}$. The nonequilibrium renormalization group fixed point controlling this universality class is described. An asymptotically exact renormalization group recursion relation is derived around this fixed point to obtain the critical exponent.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks

Topological states of matter are, generally, quantum liquids of conserved topological defects. We establish this by constructing and analyzing topological field theories which introduce gauge fields to describe the dynamics of singularities in the original field configurations. In this work, homotopy groups are utilized to identify topologically protected singularities, and the conservation of their protected number is captured by a topological action term that unambiguously obtains from the given set of symmetries. Stable phases of these theories include quantum liquids with emergent massless Abelian and non-Abelian gauge fields, as well as topological orders with long-range quantum entanglement, fractional excitations, boundary modes, and unconventional responses to external perturbations. This paper focuses on the derivation of topological field theories and basic phenomenological characterization of topological orders associated with homotopy groups π n (S n ), n ≥ 1 . These homotopies govern monopole and hedgehog topological defects in d = n + 1 dimensions, and enable the generalization of both weakly interacting and fractional quantum Hall liquids of vortices to d > 2 . Hedgehogs have not been in the spotlight so far, but they are particularly important defects of magnetic moments because they can be stimulated in realistic systems with spin-orbit coupling, such as chiral magnets and d = 3 topological materials. We predict topological orders in systems with U(1) × Spin(d) symmetry in which fractional electric charge attaches to hedgehogs. Monopoles, the analogous defects of charge or generic U(1) currents, may bind to hedgehogs via Zeeman effect, or effectively emerge in purely magnetic systems. The latter can lead to spin liquids with different topological orders than that of the resonant valence bond spin liquid. Charge fractionalization of quarks in atomic nuclei is also seen as possibly arising from the charge-hedgehog attachment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗