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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 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Mechanical Actuation via Homeomorphic Transformations of Topological Solitons within Polymer Coatings

Abstract Topological solitons are currently under investigation for their exotic properties, especially in nonlinear physics, optics, and material sciences. However, challenges of robust generation and limited stability over time have hindered their practical uses. To address this issue, an approach is developed to form structured arrays of solitons in films of polymerizable liquid crystals. Their complex molecular architecture is preserved by in situ photopolymerization forming a stable liquid crystal network. Most excitingly, their properties are advanced to include responsiveness functions. When thermally actuated, these topological solitons mediate the reconfiguration of surface topographies. Complex shape changes occur depending on the intrinsic complex spatial distribution of the director, which may even lead to full shape inversion and topographical changes as high as ≈40% of the initial thickness. Conversely, the shape changes provide information on the initial director profile, which is consistent with the mathematical model. The soliton‐containing polymer coatings are applicable in multiple domains, ranging from tunable optics to haptics, and from shape‐coupled sensing systems to temperature‐coupled heat management.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Orientation reversal and the Chern-Simons natural boundary

We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals a deeper rigidity aspect of resurgence in a quantum field theory path integral. The physical context here is the non-perturbative completion of complex Chern-Simons theory that associates to a 3-manifold a collection of q-series invariants labeled by Spinc structures, for which crossing the natural boundary corresponds to orientation reversal of the 3-manifold. Our new resurgent perspective leads to a practical numerical algorithm that generates q-series which are dual to unary q-series composed of false theta functions. Until recently, these duals were only known in a limited number of cases, essentially based on Ramanujan’s mock theta functions, and the common belief was that the duals might not even exist in the general case. Resurgence analysis identifies as primary objects Mordell integrals: up to changes of variables, they are Laplace transforms of resurgent functions. Their unique Borel summed transseries decomposition on either side of the Stokes line is simply the unique decomposition into real and imaginary parts. In turn, the latter are combinations of unary q-series in terms of q and its modular counterpart $\overset{\sim }{q}$ , and are resurgent by construction. The Mordell integral is analytic across the natural boundary of the q and $\overset{\sim }{q}$ series, and uniqueness of a similar decomposition which preserves algebraic relations on the other side of the boundary defines the unique boundary crossing of the q series. We demonstrate that this continuation can be efficiently implemented numerically. In the cases where unique mock modular identities are known, they are found by this numerical procedure, but the procedure can go well beyond the known list of identities. A particularly interesting feature of the resurgent approach is that it reveals new aspects, and is very different from other known approaches based on indefinite theta series, Appell-Lerch sums, and representation theory of logarithmic vertex operator algebras.

Chern-Simons theories↗
DOE OSTI2023

Discussion on “Saving Storage in Climate Ensembles: A Model-Based Stochastic Approach”

Abstract We thank the authors for this interesting paper that highlights important ideas and concepts for the future of climate model ensembles and their storage, as well as future uses of stochastic emulators. Stochastic emulators are particularly relevant because of the statistical nature of climate model ensembles, as discussed in previous work of the authors (Castruccio et al. in J Clim 32:8511–8522, 2019; Hu and Castruccio in J Clim 34:8409–8418, 2021). We thank the authors for sharing of some of their data with us in order to illustrate this discussion. In the following, in Sect. 1 we discuss alternative techniques currently used and studied, namely lossy compression and ideas emerging from the climate modeling community, that could feed the discussion on ensemble and storage. In that section, we also present numerical results of compression performed on the data shared by the authors. In Sect. 2, we discuss the current statistical model proposed by the authors and its context. We discuss other potential uses of stochastic emulators in climate and Earth modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type

Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the main concerns for the use of nonlocal models in real world engineering applications. Here, we present a domain decomposition solver that is inspired by substructuring methods for classical local equations. In numerical experiments involving finite element discretizations of scalar and vectorial nonlocal equations of integrable and fractional type, we observe improvements in solution time of up to 14.6x compared to commonly used solver strategies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A low-rank power iteration scheme for neutron transport criticality problems

Computing effective eigenvalues for neutron transport often requires a fine numerical resolution. Here, the main challenge of such computations is the high memory effort of classical solvers, which limits the accuracy of chosen discretizations. In this work, we derive a method for the computation of effective eigenvalues when the underlying solution has a low-rank structure. This is accomplished by utilizing dynamical low-rank approximation (DLRA), which is an efficient strategy to derive time evolution equations for low-rank solution representations. The main idea is to interpret the iterates of the classical inverse power iteration as pseudo-time steps and apply the DLRA concepts in this framework. In our numerical experiment, we demonstrate that our method significantly reduces memory requirements while achieving the desired accuracy. Analytic investigations show that the proposed iteration scheme inherits the convergence speed of the inverse power iteration, at least for a simplified setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A high-order finite difference method for moving immersed domain boundaries and material interfaces

Here, we present a high-order sharp treatment of immersed moving domain boundaries and material interfaces, and apply it to the advection-diffusion equation in two and three dimensions. The spatial discretization combines dimension-split finite difference schemes with an immersed boundary treatment based on a weighted least-squares reconstruction of the solution, providing stable discretizations with up to sixth order accuracy for diffusion terms and third order accuracy for advection terms. The temporal discretization relies on a novel strategy for maintaining high-order temporal accuracy in problems with moving boundaries that minimizes implementation complexity and allows arbitrary explicit or diagonally-implicit Runge-Kutta schemes. The approach is broadly compatible with popular PDE-specialized Runge-Kutta time integrators, including low-storage, strong stability preserving, and diagonally implicit schemes. Through numerical experiments we demonstrate that the full discretization maintains high-order spatial and temporal accuracy in the presence of complex 3D geometries and for a range of boundary conditions, including Dirichlet, Neumann, and flux conditions with large jumps in coefficients.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Rotor blade imbalance fault detection for variable-speed marine current turbines via generator power signal analysis

Marine hydrokinetic (MHK) turbines extract renewable energy from oceanic environments. However, due to the harsh conditions that these turbines operate in, system performance naturally degrades over time. Thus, ensuring efficient condition-based maintenance is imperative towards guaranteeing reliable operation and reduced costs for marine hydrokinetic power. This work proposes a novel framework aimed at identifying and classifying the severity of rotor blade pitch imbalance faults experienced by marine current turbines (MCTs). In the framework, a Continuous Morlet Wavelet Transform (CMWT) is first utilized to acquire the wavelet coefficients encompassed within the 1P frequency range of the turbine's rotor shaft. From these coefficients, several statistical indices are tabulated into a six-dimensional feature space. Next, Principle Component Analysis (PCA) is employed on the resulting feature space for dimensionality reduction, and then the application of a K-Nearest Neighbor (KNN) machine learning algorithm is utilized for fault detection and severity classification. The effectiveness of the proposed framework is validated using a high-fidelity MCT numerical simulation platform, where results demonstrate that the presence of a pitch imbalance fault can be accurately detected 100% of the time and correctly classified based upon severity more than 97% of the time.

42 ENGINEERING↗
DOE OSTI2022

A deterministic gradient-based approach to avoid saddle points

Abstract Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning (ML) models efficiently. First-order methods such as gradient descent (GD) are usually the methods of choice for training ML models. However, these methods converge to saddle points for certain choices of initial guesses. In this paper, we propose a modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher et al., arXiv:1806.06317 ], called modified LSGD (mLSGD), and demonstrate its potential to avoid saddle points without sacrificing the convergence rate. Our analysis is based on the attraction region, formed by all starting points for which the considered numerical scheme converges to a saddle point. We investigate the attraction region’s dimension both analytically and numerically. For a canonical class of quadratic functions, we show that the dimension of the attraction region for mLSGD is $\lfloor (n-1)/2\rfloor$ , and hence it is significantly smaller than that of GD whose dimension is $n-1$ .

Mathematics↗
DOE OSTI2026

Multiscale Modeling and Experimental Insights into High-Temperature Soil Biodegradation Dynamics of Semi-Crystalline Poly(Lactic Acid) Nonwoven Fabrics

This study investigates the biodegradation of semi-crystalline poly(lactic acid) (PLA) nonwovens (NWs) in soil at 58 °C using both experimental and mathematical modeling approaches. The model utilizes a system of parabolic diffusion-reaction partial differential equations (PDEs) to elucidate chemical transformations over time and in space. It accounts for phenomena such as the diffusion of water and lactic acid monomers through the polymer matrix and into the surrounding soil, along with their microbial breakdown. It also accounts for the initial PLA crystallinity and predicts its evolution in time. The model is solved numerically for a single filament, and the results were used to shed light on PLA NW transformations observed in soil over a 180-day incubation period. Various characterization techniques, including scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and Raman spectroscopy, were employed to assess morphological changes, crystallinity, and molecular changes in the NWs throughout the experiment. By comparing the experimental data with the model predictions, the hydrolysis rate coefficient was found to be 3.37 × 10 -7 s -1 , while the rate of microbial degradation of lactic acid monomers was faster, of the order of 9.63 × 10 -7 s -1 . The findings highlight the significant role of crystallinity in the biodegradation process. The PLA degradation ceases when no amorphous material remains, and the crystallinity reaches 0.8, as observed in the experiments by day 120. Furthermore, this research contributes to a deeper understanding of PLA biodegradation dynamics and offers insights for effectively managing biodegradable materials in environmental settings.

Diffusion−reaction modeling↗
DOE OSTI2024

Exponential concentration in quantum kernel methods

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Theoretical guarantees for permutation-equivariant quantum neural networks

Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Recently, the nascent field of geometric quantum machine learning (GQML) has emerged as a potential solution to some of those issues. The key insight of GQML is that one should design architectures, such as equivariant QNNs, encoding the symmetries of the problem at hand. Here, we focus on problems with permutation symmetry (i.e., symmetry group $S_n$), and show how to build $S_n$-equivariant QNNs We provide an analytical study of their performance, proving that they do not suffer from barren plateaus, quickly reach overparametrization, and generalize well from small amounts of data. To verify our results, we perform numerical simulations for a graph state classification task. Our work provides theoretical guarantees for equivariant QNNs, thus indicating the power and potential of GQML.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Efficient quantum algorithm for dissipative nonlinear differential equations

Significance Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution time, we give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to nonlinear and forcing terms and the solution does not decay too rapidly. We also establish a lower bound showing that differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics. Furthermore, numerical results for the Burgers equation suggest that our algorithm may potentially address complex nonlinear phenomena even in regimes with weaker dissipation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Forward Analytic Model of Neutron Time-of-Flight Signals for Inferring Ion Temperatures from MagLIF Experiments

A forward analytic model is required to rapidly simulate the neutron time-of-flight (nToF) signals that result from magnetized liner inertial fusion (MagLIF) experiments at Sandia’s Z Pulsed Power Facility. Various experimental parameters, such as the burn-weighted fuel-ion temperature and liner areal density, determine the shape of the nToF signal and are important for characterizing any given MagLIF experiment. Extracting these parameters from measured nToF signals requires an appropriate analytic model that includes the primary deuterium-deuterium neutron peak, once-scattered neutrons in the beryllium liner of the MagLIF target, and direct beamline attenuation. Here, mathematical expressions for this model were derived from the general-geometry time- and energy-dependent neutron transport equation with anisotropic scattering. Assumptions consistent with the time-of-flight technique were used to simplify this linear Boltzmann transport equation into a more tractable form. Models of the uncollided and once-collided neutron scalar fluxes were developed for one of the five nToF detector locations at the Z-Machine. Numerical results from these models were produced for a representative MagLIF problem and found to be in good agreement with similar neutron transport simulations. Twenty experimental MagLIF data sets were analyzed using the forward models, which were determined to only be significantly sensitive to the ion temperature. The results of this work were also found to agree with values obtained separately using a zero scatter analytic model and a high-fidelity Monte Carlo simulation. Finally, inherent difficulties in this and similar techniques are identified, and a new approach forward is suggested.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Efficient Streaming Dynamic Mode Decomposition

We propose a reformulation of the streaming dynamic mode decomposition method that requires maintaining a single orthonormal basis, thereby reducing computational redundancy. The proposed efficient streaming dynamic mode decomposition method results in a constant-factor reduction in computational complexity and memory storage requirements. Numerical experiments on representative canonical dynamical systems show that the enhanced computational efficiency does not compromise the accuracy of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A Numerical Scheme for Wave Turbulence: 3-Wave Kinetic Equations

Here, we introduce a finite volume scheme to solve a special case of isotropic 3-wave kinetic equations. We test our numerical solution against theoretical results concerning the long time behavior of the energy and observe that our solutions verify the energy cascade phenomenon. To our knowledge, this is the first numerical scheme that can capture the long time asymptotic behavior of solutions to those isotropic 3-wave kinetic equations, where the energy cascade can be observed. Our numerical energy cascade rates are in good agreement with previously obtained theoretical results. The finite volume scheme given here relies on a new identity, allowing one to reduce the number of terms needed in the collision operators.

3-wave equation↗
DOE OSTI2023

LANL contribution to ryujin, an open source finite element solver

Ryujin (https://github.com/conservation-laws/ryujin) is a high-performance finite-element software for solving mathematical partial differential equations (PDEs) with dominant hyperbolic structures. The author of this request, Eric Tovar, is using Ryujin as a high-performance tool for his Mark Kac postdoctoral fellowship research at LANL. Eric would like to contribute openly to the ryujin software without changing its core functionality. This includes: (i) bug fixes; (ii) re-organization of code for performance and syntactic updates including documentation; (iii) implementation of new PDE numerical methods that align with the core solver; (iv) implementation of new initial state configurations for target applications.

Tovar, Eric↗
DOE OSTI2020

SIERRA Multimechanics Module: Aria User Manual - Version 4.58

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( %3C 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newtons method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic -adaptivity and dynamic load balancing are some of Arias more advanced capabilities.

97 MATHEMATICS AND COMPUTING↗