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At least 379 records · Page 21

Linear and Nonlinear Solvers for Simulating Multiphase Flow within Large-Scale Engineered Subsurface Systems

Simulation of multiphase flow in the subsurface is well-known to be computationally challenging. While there have been many studies that have explored approaches to overcoming these challenges, they often utilize relatively simple case studies. In this paper, we focus on the unique numerical challenges posed by modeling large-scale engineered subsurface systems, characterized by discrete features embedded in a heterogeneous natural subsurface setting. The man-made features such as shafts, tunnels, and barriers often cause multiple challenges in modeling the domain for multiphase porous media flow. This flow scenario can have a wide range of applications such as nuclear waste repositories, enhanced recovery of a petroleum reservoir, geothermal engineering, and carbon sequestration. An example of these severe numerical challenges is the case of performance assessment (PA) for Waste Isolation Pilot Plant (WIPP), the only operating deep geological repository in the US, which simulates extreme material properties of bedded salt rock formation and extreme contrast due to open excavation next to the formation. The models have extremes not only of permeability and porosity but also of the constitutive models needed for multiphase flow; additionally, they have process models like salt creep closure reducing porosity over time, fracturing in clay and anhydrite interbeds of the bedded salt, gas generation from the waste materials, and unintentional human borehole intrusions in some scenarios. Numerical simulations require the solution of coupled systems of nonlinear PDEs; in our work, we use the open-source simulator PFLOTRAN which is based on Finite Volume discretization. The solution of the nonlinear equations requires use of the Newton-Raphson iteration at each time step, which entails the solution of the linearized Jacobian system at each iteration. The effects of all the processes (i.e., large number of unknowns, highly nonlinear constitutive relations, large contrasts in material properties in short distances) lead to an ill-conditioned Jacobian matrix that severely challenges traditional linear solver, i.e., stabilized biconjugate gradient with block Jacobi incomplete LU preconditioner (BCGS-ILU) leading to non-convergence for traditional Newton-Raphson nonlinear solver causing unacceptably long computation time for each model. This paper presents linear solvers such as constrained pressure residual (CPR) two-stage preconditioner with alternate-block-factorization (ABF) and quasi- implicit pressure and explicit saturation (QIMPES) decouplers and flexible generalized residual solver (FGMRES). The new general-purpose nonlinear solver, Newton trust-region dogleg Cauchy (NTRDC), is also introduced to resolve extreme nonlinearities in the models. We demonstrate the effectiveness of each method relative to the default BCGS-Newton solver. The two best cases had nearly 50 times speed-up and achieved completion of a simulation in 14 hours that never completed due to non-convergence with the default solver. We also investigate the strong scalability of each method and discuss some of the deficiencies found for Block Jacobi preconditioner using parallel domain decomposition, and node packing effects of modern processor architecture.

Preconditioner, Nonlinear, Porous media, Multiphas↗

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

97 MATHEMATICS AND COMPUTING↗

Nonlinear optical diode effect in a magnetic Weyl semimetal

Diode effects are of great interest for both fundamental physics and modern technologies. Electrical diode effects (nonreciprocal transport) have been observed in Weyl systems. Optical diode effects arising from the Weyl fermions have been theoretically considered but not probed experimentally. Here, we report the observation of a nonlinear optical diode effect (NODE) in the magnetic Weyl semimetal CeAlSi, where the magnetization introduces a pronounced directionality in the nonlinear optical second-harmonic generation (SHG). We demonstrate a six-fold change of the measured SHG intensity between opposite propagation directions over a bandwidth exceeding 250 meV. Supported by density-functional theory, we establish the linearly dispersive bands emerging from Weyl nodes as the origin of this broadband effect. We further demonstrate current-induced magnetization switching and thus electrical control of the NODE. Our results advance ongoing research to identify novel nonlinear optical/transport phenomena in magnetic topological materials and further opens new pathways for the unidirectional manipulation of light.

36 MATERIALS SCIENCE↗

Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced order methods are demanded. Combining these techniques with nonlinearity, we will consider in this paper a dual-continuum model which is generalized as a multi-continuum model for a coupled system of nonlinear Richards equations as unsaturated flows, in complex heterogeneous fractured porous media; and we will solve it by a novel multiscale approach utilizing the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). In particular, such a nonlinear system will be discretized in time and then linearized by Picard iteration (whose global convergence is proved theoretically). Subsequently, we tackle the resulting linearized equations by the CEM-GMsFEM and obtain proper offline multiscale basis functions to span the multiscale space (which contains the pressure solution). More specifically, we first introduce two new sources of samples, and the GMsFEM is used over each coarse block to build local auxiliary multiscale basis functions via solving local spectral problems, that are crucial for detecting high-contrast channels. Second, per oversampled coarse region, local multiscale basis functions are created through the CEM as constrainedly minimizing an energy functional. Various numerical tests for our approach reveal that the error converges with the coarse-grid size and that only few oversampling layers as well as basis functions are needed.

97 MATHEMATICS AND COMPUTING↗

A Fast Temporal Decomposition Procedure for Long-Horizon Nonlinear Dynamic Programming

We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian provided the overlap size and penalty parameters are suitably chosen, which allows us to establish the global convergence. Moreover, we show that a unit step size is accepted locally for the approximate search direction and further establish a uniform, local linear convergence over stages. This local convergence rate matches the rate of the recent Schwarz scheme (Na et al. 2022). However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, whereas we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.

97 MATHEMATICS AND COMPUTING↗

A hybrid calibration approach to Hertz-type contact parameters for discrete element models

This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. Here, the proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.

Constitutive law↗

Perturbation theory for modeling galaxy bias: validation with simulations of the Dark Energy Survey

We describe perturbation theory (PT) models of galaxy bias for applications to photometric galaxy surveys. We model the galaxy-galaxy and galaxy-matter correlation functions in configuration space and validate against measurements from mock catalogs designed for the Dark Energy Survey (DES). We find that an effective PT model with five galaxy bias parameters provides a good description of the 3D correlation functions above scales of 4 Mpc/$h$ and $z < 1$. Our tests show that at the projected precision of the DES-Year 3 analysis, two of the non-linear bias parameters can be fixed to their co-evolution values, and a third (the $k^2$ term for higher derivative bias) set to zero. The agreement is typically at the 2 percent level over scales of interest, which is the statistical uncertainty of our simulation measurements. To achieve this level of agreement, our {\it fiducial} model requires using the full non-linear matter power spectrum (rather than the 1-loop PT one). We also measure the relationship between the non-linear and linear bias parameters and compare them to their expected co-evolution values. We use these tests to motivate the galaxy bias model and scale cuts for the cosmological analysis of the Dark Energy Survey; our conclusions are generally applicable to all photometric surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

NMPC for Mode-Switching Operation of Reversible Solid Oxide Cell Systems

Solid oxide cells (SOCs) are a promising dual-mode technology that generates hydrogen through high-temperature water electrolysis and generates power through a fuel cell reaction that consumes hydrogen. Reversible operation of SOCs requires a transition between these two modes for hydrogen production setpoints as the demand and price of electricity fluctuate. Moreover, a well-functioning control system is important to avoid cell degradation during mode-switching operation. In this work, we apply nonlinear model predictive control (NMPC) to an SOC module and supporting equipment and compare NMPC performance to classical proportional integral (PI) control strategies, while ramping between the modes of hydrogen and power production. While both control methods provide similar performance in many metrics, NMPC significantly reduces cell thermal gradients and curvatures (mixed spatial-temporal partial derivatives) during mode switching. A dynamic process flowsheet of the reversible SOC system was developed in the open-source, equation-based IDAES modeling framework. Our IDAES dynamic simulation results show that NMPC can ramp the SOC system between hydrogen and power production targets within short mode-switching times. Moreover, NMPC can comply with operating limits in the SOC system more effectively than PI, and only NMPC can directly enforce user-specified limits for mixed spatial-temporal partial derivatives of temperature. This allows for management of the trade-off be-tween operating efficiency and cell degradation, which is dependent on these temperature curvatures.

Li, Mingrui↗

Accurate parameterization of the kinetic energy functional for calculations using exact-exchange

In this report, electronic structure calculations based on Kohn-Sham density functional theory (KSDFT) that incorporate exact exchange or hybrid functionals are associated with large computational expense, a consequence of the inherent cubic scaling bottleneck and large associated prefactor, which limits the length and time scales that can be accessed. Though orbital-free density functional theory (OFDFT) calculations scale linearly with system size and are associated with significantly smaller prefactor, they are limited by the absence of accurate density-dependent kinetic energy functionals. Therefore, the development of accurate density-dependent kinetic energy functionals is important for OFDFT calculations of large realistic systems. To this end, we propose a method to train kinetic energy functional models at the exact-exchange level of theory by using a dictionary of physically relevant terms that have been proposed in the literature in conjunction with linear or nonlinear regression methods to obtain the fitting coefficients. For our dictionary, we use gradient expansion of the kinetic energy, nonlocal models proposed in the literature and their nonlinear combinations, such as a model that incorporates spatial correlations between higher order derivatives of electron density at two points. The predictive capabilities of these models are assessed by using a variety of model one-dimensional systems that exhibit diverse bonding characteristics, such as a chain of eight hydrogens, LiF, LiH, C 4 H 2 , C 4 N 2 and C 3 O 2 . We show that by using data from model one-dimensional KSDFT calculations performed using the exact-exchange functional for only a few neutral structures, it is possible to generate models with high accuracy for charged systems as well as electron and kinetic energy densities during self-consistent field iterations. In addition, we show that it possible to learn both the orbital dependent terms, i.e., the kinetic energy and the exact-exchange energy, and models that incorporate additional nonlinearities in spatial correlations, such as a quadratic model, are needed to capture subtle features of the kinetic energy density that are present in exact-exchange-based KSDFT calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

ForestFlow: predicting the Lyman-α forest clustering from linear to nonlinear scales

On large scales, the Lyman-α forest provides insights into the expansion history of the Universe, while on small scales, it imposes strict constraints on the growth history, the nature of dark matter, and the sum of neutrino masses. This work introduces ForestFlow, a novel framework that bridges the gap between large- and small-scale analyses, which have traditionally relied on distinct modeling approaches. Using conditional normalizing flows, ForestFlow predicts the two Lyman-α linear biases (b δ and b η ) and six parameters describing small-scale deviations of the three-dimensional flux power spectrum (P 3D ) from linear theory as a function of cosmology and intergalactic medium physics. These are then combined with a Boltzmann solver to make consistent predictions, from arbitrarily large scales down to the nonlinear regime, for P 3D and any other statistics derived from it. Trained on a suite of 30 fixed-and-paired cosmological hydrodynamical simulations spanning redshifts from z = 2 to 4.5, ForestFlow achieves 3 and 1.5% precision in describing P 3D and the one-dimensional flux power spectrum (P 1D ) from linear scales to k = 5 Mpc −1 and k ∥ = 4 Mpc −1 , respectively. Thanks to its conditional parameterization, ForestFlow shows similar performance for ionization histories and two ΛCDM model extensions – massive neutrinos and curvature – even though none of these are included in the training set. This framework will enable full-scale cosmological analyses of Lyman-α forest measurements from the DESI survey.

79 ASTRONOMY AND ASTROPHYSICS↗

Ghost-imaging-enhanced noninvasive spectral characterization of stochastic x-ray free-electron-laser pulses

Abstract High-intensity ultrashort X-ray free-electron laser (XFEL) pulses are revolutionizing the study of fundamental nonlinear x-ray matter interactions and coupled electronic and nuclear dynamics. To fully exploit the potential of this powerful tool for advanced x-ray spectroscopies, a noninvasive spectral characterization of incident stochastic XFEL pulses with high resolution is a key requirement. Here we present a methodology that combines high-acceptance angle-resolved photoelectron time-of-flight spectroscopy and ghost imaging to enhance the quality of spectral characterization of x-ray free-electron laser pulses. Implementation of this noninvasive high-resolution x-ray diagnostic can greatly benefit the ultrafast x-ray spectroscopy community by functioning as a transparent beamsplitter for applications such as transient absorption spectroscopy in averaging mode as well as covariance-based x-ray nonlinear spectroscopies in single-shot mode where the shot-to-shot fluctuations inherent to a self-amplified spontaneous emission (SASE) XFEL pulse are a powerful asset.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Wavelength conversion through plasmon-coupled surface states

Surface states generally degrade semiconductor device performance by raising the charge injection barrier height, introducing localized trap states, inducing surface leakage current, and altering the electric potential. We show that the giant built-in electric field created by the surface states can be harnessed to enable passive wavelength conversion without utilizing any nonlinear optical phenomena. Photo-excited surface plasmons are coupled to the surface states to generate an electron gas, which is routed to a nanoantenna array through the giant electric field created by the surface states. The induced current on the nanoantennas, which contains mixing product of different optical frequency components, generates radiation at the beat frequencies of the incident photons. We utilize the functionalities of plasmon-coupled surface states to demonstrate passive wavelength conversion of nanojoule optical pulses at a 1550 nm center wavelength to terahertz regime with efficiencies that exceed nonlinear optical methods by 4-orders of magnitude.

42 ENGINEERING↗

Mean Field Theory of Self‐Organizing Memristive Connectomes

Abstract Biological neuronal networks are characterized by nonlinear interactions and complex connectivity. Given the growing impetus to build neuromorphic computers, understanding physical devices that exhibit structures and functionalities similar to biological neural networks is an important step toward this goal. Self‐organizing circuits of nanodevices are at the forefront of the research in neuromorphic computing, as their behavior mimics synaptic plasticity features of biological neuronal circuits. However, an effective theory to describe their behavior is lacking. This study provides for the first time an effective mean field theory for the emergent voltage‐induced polymorphism of circuits of a nanowire connectome, showing that the behavior of these circuits can be explained by a low‐dimensional dynamical equation. The equation can be derived from the microscopic dynamics of a single memristive junction in analytical form. The effective model is tested on experiments of nanowire networks and show that it fits both the potentiation and depression of these synapse‐mimicking circuits. It is shown that this theory applies beyond the case of nanowire networks by formulating a general mean‐field theory of conductance transitions in self‐organizing memristive connectomes.

Caravelli, Francesco↗

Compactly‐Supported Nonstationary Kernels for Computing Exact Gaussian Processes on Big Data

The Gaussian process (GP) is a widely used method for analyzing large-scale data sets, including spatio-temporal measurements of nonlinear processes that are now commonplace in the environmental sciences. Traditional implementations of GPs involve stationary kernels (also termed covariance functions) that limit their flexibility, and exact methods for inference that prevent application to data sets with more than about 10,000 points. Modern approaches to address stationarity assumptions generally fail to accommodate large data sets, while all attempts to address scalability focus on approximating the Gaussian likelihood, which can involve subjectivity and lead to inaccuracies. In this work, we explicitly derive an alternative kernel that can discover and encode both sparsity and nonstationarity. We embed the kernel within a fully Bayesian GP model and leverage high-performance computing resources to enable the analysis of massive data sets. We demonstrate the favorable performance of our novel kernel relative to existing exact and approximate GP methods across a variety of synthetic data examples. Furthermore, we conduct space–time prediction based on more than 1 million measurements of daily maximum temperature and verify that our results outperform state-of-the-art methods in the Earth sciences. More broadly, having access to exact GPs that use ultra-scalable, sparsity-discovering, nonstationary kernels allows GP methods to truly compete with a wide variety of machine learning methods.

Gaussian processes↗

Reduced‐Order Modeling of Energetic Materials Using Physics‐Aware Recurrent Convolutional Neural Networks in a Latent Space (LatentPARC)

Physics-aware deep learning (PADL) has gained popularity for use in spatiotemporal dynamics simulations, such as those in computational modeling of energetic materials (EM). We show that the challenge PADL methods face while learning complex field evolution problems can be simplified and accelerated by decoupling it into two tasks: learning complex geometric features in evolving fields and modeling dynamics over these features in a lower-dimensional feature space. We build upon our previous work on physics-aware recurrent convolutional neural networks (PARC). PARC embeds knowledge of underlying physics into its neural network architecture for more robust and accurate prediction of evolving physical fields. PARC was shown to effectively learn complex nonlinear features such as the formation of hotspots and coupled shock fronts in various initiation scenarios of EMs, as a function of microstructures, serving effectively as a microstructure-aware burn model. Here, we further accelerate PARC and reduce its computational cost by projecting the original dynamics onto a lower-dimensional invariant manifold, or “latent space.” The projected latent representation encodes the complex geometry of evolving fields (e.g., temperature and pressure) in a set of data-driven features. The reduced dimension of this latent space allows us to learn the dynamics during the initiation of EM with a lighter and more efficient model. We observe a significant decrease in training and inference time while maintaining results comparable to PARC at inference. This work takes steps towards enabling rapid prediction of EM thermomechanics at larger scales and characterization of EM structure–property–performance linkages at a full application scale.

Mathematics and Computing↗

On the strength and fracture toughness of an additive manufactured CrCoNi medium-entropy alloy

An additively manufactured (nominally equiatomic) CrCoNi alloy was processed by laser powder bed fusion (LPBF). At ambient temperatures (298 K), this medium-entropy alloy displayed a yield strength, σ y of ~691 ± 9 MPa, and an ultimate tensile strength, σ u of ~926 ± 15.2 MPa; at cryogenic temperatures (77 K), yield and tensile strengths increased respectively to σ y ~ 944 ± 6 MPa and σ u ~ 1382 ± 11 MPa. These strength levels are 57 and 44% higher than that of the wrought alloy, due to strengthening from the solidification cellular structures intertwined with dislocations in the LPBF CrCoNi. The crack-initiation fracture toughness, K JIc was measured to be ~183.7 ± 28 MPa√m at 298 K; this value marginally decreased by ~4% to ~176 ± 11 MPa√m at 77 K. These K JIc values of the LPBF CrCoNi were 11% and 35% lower than the wrought CrCoNi alloy at 298 K and 77 K, respectively. Here, the resistance to crack growth of the LPBF CrCoNi from its hierarchical micro- and meso-structures was evaluated using nonlinear-elastic fracture mechanics by measuring R-curve behavior in the form of the J-integral as a function of crack extension. The specific features of the hierarchical microstructures at different length-scales provide a basis for the strengthening and toughening properties of this additively manufactured medium-entropy alloy. This correlation between the deformation and the hierarchical microstructures at different length-scales may provide future guidance for improving the fracture toughness properties of medium-entropy alloys.

36 MATERIALS SCIENCE↗

Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple optima in the Bayesian inverse problem. In this work, we propose a multi-variance replica exchange stochastic gradient Langevin dynamics method to tackle the challenge of the multiple local optima in the optimization and the challenge of the multiple modal posterior distribution in the inverse problem. Replica exchange methods are capable of escaping from the local traps and accelerating the convergence; two chains with different temperatures are designed where the low temperature chain aims for the local convergence, and the target of the high temperature chain is to travel globally and explore the whole loss function entropy landscape. However, it may not be efficient to solve mathematical inversion problems by using the vanilla replica method directly since the method doubles the computational cost in evaluating the forward solvers (likelihood functions) in the two chains. To address this issue, we propose to make different assumptions on the energy function estimation and this facilities one to use solvers of different fidelities in the likelihood function evaluation. More precisely, one can use a solver with low fidelity in the high temperature chain while using a solver with high fidelity in the low temperature chain. Our proposed method significantly lowers the computational cost in the high temperature chain, meanwhile preserving the accuracy and converging very fast. Here we give an unbiased estimate of the swapping rate and give an estimation of the discretization error of the scheme. To verify our idea, we design and solve four inverse problems which have multiple modes. The proposed method is also employed to train the Bayesian PINN to solve the forward and inverse problems; faster and more accurate convergence has been observed when compared to the stochastic gradient Langevin dynamics (SGLD) method and vanilla replica exchange methods.

97 MATHEMATICS AND COMPUTING↗

Two-fluid and kinetic transport physics of Kelvin–Helmholtz instabilities in nonuniform low-beta plasmas

Hall-magnetohydrodynamic (Hall-MHD) theory, two-fluid simulations, and kinetic simulations are used in this work to investigate the cross-field transport properties of Kelvin–Helmholtz instabilities in nonuniform low-beta collisionless plasmas. Hall-MHD analysis shows how the linear properties of the instability are modified by density gradients and magnetization. High-order accurate two-fluid and kinetic simulations, with complete dynamics of finite-mass electrons and ions, are applied to a suite of parameter cases to systematically assess the effects of diamagnetic drift, magnetization, charge separation, and finite Larmor motion. Initialization of exact two-species kinetic equilibria facilitates the study of isolated physical effects and enables detailed cross-comparisons between two-fluid and kinetic simulations, including for cases where ion gyroradii are comparable to gradient scale lengths. For nonuniform plasmas with significant space charge, the results of two-fluid and kinetic simulations are found to disagree with Hall-MHD predictions. Kelvin–Helmholtz instability growth rates, per unit shear, are shown to be smaller when ion diamagnetic drift and $E \times B$ drift are parallel and larger when the two drifts are antiparallel. The effect is attributed to polarization drift in the shear layer, which leads to redistribution of charge, alters the electric field that drives plasma advection, and consequently modifies growth rates. Instability-induced mass transport for different parameters is characterized in terms of the flux across the shear layer and a simplified diffusion model. Distribution functions from kinetic simulations are shown to deviate substantially from Maxwellian reconstructions, indicating the importance of kinetic physics during the nonlinear phase of the instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗