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DOE OSTI2017

Multiscale analysis of the CMB temperature derivatives

We study the Planck CMB temperature at different scales through its derivatives up to second order, which allows one to characterize the local shape and isotropy of the field. The problem of having an incomplete sky in the calculation and statistical characterization of the derivatives is addressed in the paper. The analysis confirms the existence of a low variance in the CMB at large scales, which is also noticeable in the derivatives. Moreover, deviations from the standard model in the gradient, curvature and the eccentricity tensor are studied in terms of extreme values on the data. As it is expected, the Cold Spot is detected as one of the most prominent peaks in terms of curvature, but additionally, when the information of the temperature and its Laplacian are combined, another feature with similar probability at the scale of 10{sup o} is also observed. However, the p -value of these two deviations increase above the 6% when they are referred to the variance calculated from the theoretical fiducial model, indicating that these deviations can be associated to the low variance anomaly. Finally, an estimator of the directional anisotropy for spinorial quantities is introduced, which is applied to the spinors derived from the field derivatives. An anisotropic direction whose probability is <1% is detected in the eccentricity tensor.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

On the closedness and geometry of tensor network state sets

Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. Here we discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states, and the multiscale entanglement renormalization ansatz are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Multiresolution GPC-Structured Control of a Single-Loop Cold-Flow Chemical Looping Testbed

Chemical looping is a near-zero emission process for generating power from coal. It is based on a multi-phase gas-solid flow and has extremely challenging nonlinear, multi-scale dynamics with jumps, producing large dynamic model uncertainty, which renders traditional robust control techniques, such as linear parameter varying H ∞ design, largely inapplicable. This process complexity is addressed in the present work through the temporal and the spatiotemporal multiresolution modeling along with the corresponding model-based control laws. Namely, the nonlinear autoregressive with exogenous input model structure, nonlinear in the wavelet basis, but linear in parameters, is used to identify the dominant temporal chemical looping process dynamics. The control inputs and the wavelet model parameters are calculated by optimizing a quadratic cost function using a gradient descent method. The respective identification and tracking error convergence of the proposed self-tuning identification and control schemes, the latter using the unconstrained generalized predictive control structure, is separately ascertained through the Lyapunov stability theorem. The rate constraint on the control signal in the temporal control law is then imposed and the control topology is augmented by an additional control loop with self-tuning deadbeat controller which uses the spatiotemporal wavelet riser dynamics representation. The novelty of this work is three-fold: (1) developing the self-tuning controller design methodology that consists in embedding the real-time tunable temporal highly nonlinear, but linearly parametrizable, multiresolution system representations into the classical rate-constrained generalized predictive quadratic optimal control structure, (2) augmenting the temporal multiresolution loop by a more complex spatiotemporal multiresolution self-tuning deadbeat control loop, and (3) demonstrating the effectiveness of the proposed methodology in producing fast recursive real-time algorithms for controlling highly uncertain nonlinear multiscale processes. The latter is shown through the data from the implemented temporal and augmented spatiotemporal solutions of a difficult chemical looping cold flow tracking control problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

Application of an Affine Nonlinear Galerkin Reduced-order Model to Compressible Fluid Flows

Galerkin reduced-order models (ROMs) often struggle to accurately capture multiscale fluid physics in challenging flow regimes such as flows experiencing compressibility effects. This in part stems from the global nature of both the basis construction problem and the spectral formulation itself. In this work, a multi-basis ROM is developed in an affine space based on proper orthogonal decomposition (POD) by projecting the full Navier-Stokes equations expressed in terms of the specific volume, velocity, and pressure primitive variables. The model is applied to high-fidelity numerical simulation datasets obtained for a canonical compressible flow configuration: the flow over a backward facing step at different subsonic Mach numbers. It is observed that application of an eigenvalue reassignment (ER) stabilization method is required to avoid early divergence of the ROM predictions for this configuration in the three Mach numbers tested. The sensitivity of the POD-ROM results to the choice of parameters in the stabilization algorithm is discussed.

reduced-order model↗

NASA NTRSDate not supplied

Application of an Affine Nonlinear Galerkin Reduced-order Model to Compressible Fluid Flows

reduced-order model↗

DOE OSTI2022

Beyond quantum cluster theories: multiscale approaches for strongly correlated systems

The degrees of freedom that confer to strongly correlated systems their many intriguing properties also render them fairly intractable through typical perturbative treatments. For this reason, the mechanisms responsible for their technologically promising properties remain mostly elusive. Computational approaches have played a major role in efforts to fill this void. In particular, dynamical mean field theory and its cluster extension, the dynamical cluster approximation have allowed significant progress. However, despite all the insightful results of these embedding schemes, computational constraints, such as the minus sign problem in quantum Monte Carlo (QMC), and the exponential growth of the Hilbert space in exact diagonalization (ED) methods, still limit the length scale within which correlations can be treated exactly in the formalism. A recent advance aiming to overcome these difficulties is the development of multiscale many body approaches whereby this challenge is addressed by introducing an intermediate length scale between the short length scale where correlations are treated exactly using a cluster solver such QMC or ED, and the long length scale where correlations are treated in a mean field manner. At this intermediate length scale correlations can be treated perturbatively. This is the essence of multiscale many-body methods. Furthermore, we will review various implementations of these multiscale many-body approaches, the results they have produced, and the outstanding challenges that should be addressed for further advances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRSDate not supplied

Thermoviscoelastic modelling of high strain thin-ply composites by means of multiscale plate and beam model

High strain thin-ply (HS-TPC) technology is being increasingly adopted for high-performanceaerospace applications. Albeit many of these structures such as deployable booms can bemodeled as one-dimensional beam problems, there is a lack of themoviscoelastic beam mod-els to efficiently and accurately simulate HS-TPC. This work will use mechanics of struc-ture genome (MSG) to construct linear thermoviscoelastic beam models that can homogenizethree-dimensional heterogeneous materials made of constituents with time- and temperature-dependent behavior. The formulation derives the transient strain energy based on integralformulation for thermorheologically simple materials subject to finite temperature changeswith the restriction that the strain is small. A lenticular boom is used as a numerical exampleto verify the MSG-based linear thermoviscoelastic beam model against MSG-based shell/platemodel, which has already been validated against experimental data provided by NASA, anddirect numerical simulations performed in a finite element commercial package.

Orzuri Rique Garaizar↗

DOE OSTI2015

Review of the synergies between computational modeling and experimental characterization of materials across length scales

With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many applications in the development, characterization and design of complex material systems. This manuscript provides a broad and comprehensive overview of recent trends in which predictive modeling capabilities are developed in conjunction with experiments and advanced characterization to gain a greater insight into structure–property relationships and study various physical phenomena and mechanisms. The focus of this review is on the intersections of multiscale materials experiments and modeling relevant to the materials mechanics community. After a general discussion on the perspective from various communities, the article focuses on the latest experimental and theoretical opportunities. Emphasis is given to the role of experiments in multiscale models, including insights into how computations can be used as discovery tools for materials engineering, rather than to “simply” support experimental work. This is illustrated by examples from several application areas on structural materials. In conclusion this manuscript ends with a discussion on some problems and open scientific questions that are being explored in order to advance this relatively new field of research.

3-D microstructure characterization↗

DOE OSTI2020

Primal interface debonding formulation for finite strain isotropic plasticity

In this work, a framework is developed for modeling ductile damage of nonlinear materials whose plastic deformation is characterized using rate independent classical plasticity. This method relies on the assumption that the free energy can be decomposed into elastic, plastic and damage parts. A thermodynamically consistent method is derived which satisfies the second law of thermodynamics in the Clausius–Duhem inequality form. The dissipation associated with plasticity takes place in the domain only, while damage dissipation is localized to the interface. The method is developed using Variational Multiscale ideas to obtain definitions of the interface fluxes within a primal formulation analogous to the Discontinuous Galerkin method, which ensures weakly vanishing interface gap prior to reaching a damage initiation criterion. The local nonlinear problem to calculate both plastic deformation gradient and damage variable follows an incremental approach similar to classical plasticity return mapping algorithm. This elastoplastic damage formulation is developed for material undergoing finite strain, and it naturally accommodates a trapezoidal traction separation law (TSL) whose shape can be varied to model either ductile interface behavior or brittle interface behavior. The formulation's performance is assessed through modeling a patch test and a compact tension specimen.

42 ENGINEERING↗

DOE OSTI2018

Major trends and roadblocks in CFD-aided process intensification of biomass pyrolysis

Process intensification is critical to increase product yields and reduce external power consumption in biomass pyrolysis. Computational fluid dynamics offers great possibilities for fast and economical process intensification of biomass pyrolysis. This succinct but in-depth current-perspective feature article discusses the major trends and roadblocks with respect to CFD-aided process intensification of biomass pyrolysis. Major trends such as multiscale coupling, fast parametric analysis and design, and coupling between CFD and process modeling, are reviewed. Major roadblocks such as lack of accurate chemical kinetics, and difficulty in accurate description of microstructural change, are pointed out. In conclusion, it is believed that the clarification of these directions and problems will lead to a more objective but efficient application of CFD to process intensification of biomass pyrolysis.

09 BIOMASS FUELS↗

DOE OSTI2014

Multiscale Simulation Framework for Coupled Fluid Flow and Mechanical Deformation

A multiscale linear-solver framework for the pressure equation associated with flow in highly heterogeneous porous formations was developed. The multiscale based approach is cast in a general algebraic form, which facilitates integration of the new scalable linear solver in existing flow simulators. The Algebraic Multiscale Solver (AMS) is employed as a preconditioner within a multi-stage strategy. The formulations investigated include the standard MultiScale Finite-Element (MSFE) andMultiScale Finite-Volume (MSFV) methods. The local-stage solvers include incomplete factorization and the so-called Correction Functions (CF) associated with the MSFV approach. Extensive testing of AMS, as an iterative linear solver, indicate excellent convergence rates and computational scalability. AMS compares favorably with advanced Algebraic MultiGrid (AMG) solvers for highly detailed three-dimensional heterogeneous models. Moreover, AMS is expected to be especially beneficial in solving time-dependent problems of coupled multiphase flow and transport in large-scale subsurface formations.

02 PETROLEUM↗

DOE OSTI2025

A Fundamentally New Coupled Approach to Contact Mechanics via the Dirichlet‐Neumann Schwarz Alternating Method

Contact phenomena are crucial for understanding the behavior of mechanical systems. However, existing computational approaches for simulating mechanical contact often face numerical challenges, such as inaccurate physical predictions, energy conservation errors, and unwanted oscillations. Here, we introduce an alternative technique for simulating dynamic contact based on the non‐overlapping Schwarz alternating method, originally developed for domain decomposition. In multibody contact scenarios, this method treats each body as a separate, non‐overlapping domain and prevents interpenetration using an alternating Dirichlet–Neumann iterative process. This approach has a strong theoretical foundation, eliminates the need for contact constraints, and offers flexibility, making it ideal for multiscale and multiphysics applications. We conducted a numerical comparison between the Schwarz method and traditional methods, such as the Lagrange multiplier and penalty methods, focusing on a benchmark impact problem. Our results indicate that the Schwarz alternating method outperforms traditional methods in several key areas: it provides more accurate predictions for various measurable quantities and demonstrates exceptional energy conservation capabilities. To address unwanted oscillations in contact velocities and forces, we explored various algorithms and stabilization techniques, ultimately opting for the naïve‐stabilized Newmark scheme for its simplicity and effectiveness. Additionally, we validated the efficiency of the Schwarz method in a three‐dimensional impact problem, highlighting its inherent capacity to accommodate different mesh topologies, time‐integration schemes, and time steps for each interacting body.

Schwarz alternating method↗

NASA NTRS2022

Predicting Unreinforced Fabric Mechanical Behavior with Recurrent Neural Networks

Unreinforced woven fabrics are widely employed in various high-performance applications, including parachute deployment systems, airbags, and ballistic armor. The analysis of such materials is inherently complex due to the multiscale structure of these materials, and the dependence of macroscale behavior on changes that occur at lower scales. Previously, NASA’s Multiscale Analysis Tool (NASMAT) showed its capability in predicting unreinforced fabric behavior at the macroscale by capturing finite rotations that occur at the mesoscale. Though effective, the tool can face high computational cost for large, complex problems, motivating the need for the development of a surrogate model that can capture the same behavior. A recurrent neural network (RNN) was developed and trained on virtual NASMAT data to mimic the physics-based solutions while improving the computational runtime. The architecture of the RNN to best simulate the fabric behavior was carefully crafted based on heuristic knowledge of predicting physics-based temporal data, manual hyperparameter case studies, and Hyperband optimization.. The resultant model was able to predict a variety of stress-strain curves for fabrics with different mesoscale geometries, and was further validated by comparing to experimental data for the K706 style Kevlar plain-weave fabric, demonstrating the ability of the model to effectively capture the geometric changes in the fabric without explicitly calculating them, as is done in NASMAT. Furthermore, the tool showed its ability to improve on the runtime by a factor of 10 for fabric solutions compared to the multiscale tool, which would further enable the simulation of complex loading scenarios on unreinforced fabrics.

Fabric↗

DOE OSTI2015

Mathematical and Numerical Analyses of Peridynamics for Multiscale Materials Modeling

We have treated the modeling, analysis, numerical analysis, and algorithmic development for nonlocal models of diffusion and mechanics. Variational formulations were developed and finite element methods were developed based on those formulations for both steady state and time dependent problems. Obstacle problems and optimization problems for the nonlocal models were also treated and connections made with fractional derivative models.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2014

Recent Advances in Registration, Integration and Fusion of Remotely Sensed Data: Redundant Representations and Frames

In recent years, sophisticated mathematical techniques have been successfully applied to the field of remote sensing to produce significant advances in applications such as registration, integration and fusion of remotely sensed data. Registration, integration and fusion of multiple source imagery are the most important issues when dealing with Earth Science remote sensing data where information from multiple sensors, exhibiting various resolutions, must be integrated. Issues ranging from different sensor geometries, different spectral responses, differing illumination conditions, different seasons, and various amounts of noise need to be dealt with when designing an image registration, integration or fusion method. This tutorial will first define the problems and challenges associated with these applications and then will review some mathematical techniques that have been successfully utilized to solve them. In particular, we will cover topics on geometric multiscale representations, redundant representations and fusion frames, graph operators, diffusion wavelets, as well as spatial-spectral and operator-based data fusion. All the algorithms will be illustrated using remotely sensed data, with an emphasis on current and operational instruments.

Fusion↗

NASA NTRS2022

Energy Partition at Collisionless Supercritical Quasiperpendicular Shocks

Collisionless shocks in astrophysical plasmas are important thermalizers, converting some of the incident flow energy into thermal energy, and non-thermalizers, partitioning that energy in unequal ways to different particle species, sub-populations thereof, and field components. This partition problem, or equivalently the shock equation of state, lies at the heart of shock physics. Here we employ systematically a framework to capture all the incident and downstream energy fluxes at two example traversals of the Earth’s bow shock by the Magnetospheric Multiscale Mission. Here and traditionally such data has to be augmented by information from other spacecraft, e.g., to provide more accurate measurements of the cold solar wind beam. With some care and fortuitous choices, the energy fluxes are constant, including instantaneous measurements through the shock layer. The dominant incident proton ram energy is converted primarily into downstream proton enthalpy flux, the majority of which is actually carried by a small fraction of suprathermal protons. Fluctuations include both real and instrumental effects. Separating these, resolving the solar wind beam, and other considerations point the way to a dedicated mission to solve this energy partition problem across a full range of plasma and shock conditions.

Steven J Schwartz↗

NASA NTRS2009

Multiscale Failure Analysis of Laminated Composite Panels Subjected to Blast Loading Using FEAMAC/Explicit

This preliminary report demonstrates the capabilities of the recently developed software implementation that links the Generalized Method of Cells to explicit finite element analysis by extending a previous development which tied the generalized method of cells to implicit finite elements. The multiscale framework, which uses explicit finite elements at the global-scale and the generalized method of cells at the microscale is detailed. This implementation is suitable for both dynamic mechanics problems and static problems exhibiting drastic and sudden changes in material properties, which often encounter convergence issues with commercial implicit solvers. Progressive failure analysis of stiffened and un-stiffened fiber-reinforced laminates subjected to normal blast pressure loads was performed and is used to demonstrate the capabilities of this framework. The focus of this report is to document the development of the software implementation; thus, no comparison between the results of the models and experimental data is drawn. However, the validity of the results are assessed qualitatively through the observation of failure paths, stress contours, and the distribution of system energies.

Pineda, Evan J.↗

DOE OSTI2021

Split representation of adaptively compressed polarizability operator

The polarizability operator plays a central role in density functional perturbation theory and other perturbative treatment of first principle electronic structure theories. The cost of computing the polarizability operator generally scales as O(Ne4) where Ne is the number of electrons in the system. The recently developed adaptively compressed polarizability operator (ACP) formulation [L. Lin, Z. Xu and L. Ying, Multiscale Model. Simul. 2017] reduces such complexity to O(Ne 3 ) in the context of phonon calculations with a large basis set for the first time, and demonstrates its effectiveness for model problems. In this paper, we improve the performance of the ACP formulation by splitting the polarizability into a near singular component that is statically compressed, and a smooth component that is adaptively compressed. The new split representation maintains the O(Ne 3 ) complexity, and accelerates nearly all components of the ACP formulation, including Chebyshev interpolation of energy levels, iterative solution of Sternheimer equations, and convergence of the Dyson equations. For simulation of real materials, we discuss how to incorporate nonlocal pseudopotentials and finite temperature effects. In this work, we demonstrate the effectiveness of our method using one-dimensional model problem in insulating and metallic regimes, as well as its accuracy for real molecules and solids.

97 MATHEMATICS AND COMPUTING↗