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At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Complex Dependence of Calcite Crack Kinetics on Salinity: The Role of DLVO and Hydration Forces

Abstract Subcritical crack growth (SCG) plays an important role in many geological processes such as delayed earth rupture and rock weathering. The complex dependency of SCG on the in‐crack fluid chemistry, however, is still poorly understood. In this study, we utilize the newly developed surface force‐based fracture theory (SFFT) to elucidate the relative contributions of surface forces and solute transport to the crack growth kinetics of calcite in NaCl solutions. Expanding on Barenblatt's cohesive crack model, SFFT introduces an effective stress intensity at the crack tip that encompasses all the relevant intermolecular forces across the crack in addition to the external far‐field stresses. The nonlinear system of equations portraying the crack opening profile, the solute distribution in a propagating crack, and the crack growth velocity are numerically solved via an implicit scheme. After carefully calibrating the model for calcite‐water systems, the SFFT is used to predict the SCG response of calcite at different NaCl concentrations, based on various hypotheses. These predictions are then compared to existing SCG data from the literature. We demonstrate that the experimentally observed variation of SCG rate with NaCl concentration cannot be explained solely by DLVO forces (electrostatic and Van der Waals interactions). This can be remediated by introducing an exponentially decaying hydration force with a nonlinear, nonmonotonic dependence on NaCl concentration. Furthermore, we demonstrate that accounting for both diffusive and advective transport of ions is important in explaining the absence of a stage‐II SCG response for calcite in electrolyte solutions. Plain Language Summary Subcritical crack growth (SCG) refers to the slow propagation of cracks in materials under a stress below the threshold for catastrophic failure. SCG is a key process in many geological events, for example, delayed earth ruptures and rock weathering. New initiatives such as underground CO 2 and H 2 storage in carbonate reservoirs further call for better understanding of SCG in carbonate minerals subjected to varying fluid chemistry. This study examines the SCG of calcite, a key mineral found in carbonate rocks, intergranular cement in sandstones, and filling material in mineral veins and faults, determining their deformation and strength. A mathematical model is developed to describe how the crack opens and propagates, how solutes (like salts) distribute within the crack, and how the crack surfaces interact with each other. We used the model to predict calcite SCG in water at different salt concentrations and compared it with experimental data. Our results revealed that the hydration force is the dominating factor in determining the complex, non‐linear dependency of SCG on salinity. We also found that both the movement of ions by diffusion and by bulk water flow are crucial for explaining the SCG rates, especially when the cracks grow quickly. Key Points Surface Force‐Based Fracture Theory predicts the complex subcritical crack growth patterns of calcite crystals immersed in NaCl solutions Results highlight the dominant role of hydration forces in altering the fracture behavior of calcite compared to VdW and electric double‐layer forces Advective solute transport explains the absence of stages‐II and ‐III subcritical crack growth responses in solid‐liquid systems

DLVO↗
DOE OSTI2023

A phase-field model for hydraulic fracture nucleation and propagation in porous media

Many geo-engineering applications, for example, enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase-field method has grown in popularity as a valid approach to modeling hydraulic fracturing because of the ease of handling complex fracture propagation geometries. However, existing phase-field methods cannot appropriately capture nucleation of hydraulic fractures because their formulations are solely energy-based and do not explicitly take into account the strength of the material. Thus, in this work, we propose a novel phase-field formulation for hydraulic fracturing with the main goal of modeling fracture nucleation in porous media, for example, rocks. Built on the variational formulation of previous phase-field methods, the proposed model incorporates the material strength envelope for hydraulic fracture nucleation through two important steps: (i) an external driving force term, included in the damage evolution equation, that accounts for the material strength; (ii) a properly designed damage function that defines the fluid pressure contribution on the crack driving force. In conclusion, the comparison of numerical results for two-dimensional test cases with existing analytical solutions demonstrates that the proposed phase-field model can accurately model both nucleation and propagation of hydraulic fractures. Additionally, we present the simulation of hydraulic fracturing in a three-dimensional domain with various stress conditions to demonstrate the applicability of the method to realistic scenarios.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

Q-balls meet fuzzballs: non-BPS microstate geometries

We construct a three-parameter family of non-extremal microstate geometries, or “microstrata”, that are dual to states and deformations of the D1-D5 CFT. These families are non-extremal analogues of superstrata. We find these microstrata by using a Q-ball-inspired Ansatz that reduces the equations of motion to solving for eleven functions of one variable. We then solve this system both perturbatively and numerically and the results match extremely well. We find that the solutions have normal mode frequencies that depend upon the amplitudes of the excitations. We also show that, at higher order in perturbations, some of the solutions, having started with normalizable modes, develop a “non-normalizable” part, suggesting that the microstrata represent states in a perturbed form of the D1-D5 CFT. This paper is intended as a “Proof of Concept” for the Q-ball-inspired approach, and we will describe how it opens the way to many interesting follow-up calculations both in supergravity and in the dual holographic field theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Modeling the influence of the solid electrolyte interphase on the sand’s time and dendrite formation on lithium metal electrodes

Lithium metal is a sought after battery material for its high energy density due to the low electrochemical potential and density. However, lithium metal is also highly reactive, which results in a strong propensity for dendrite formation. The Sand’s time has previously been used to predict the time of dendrite initiation on metals that do not form a solid-electrolyte interphase (SEI), but it has been shown that the Sand’s time is not accurate for lithium electrodes when using transport parameters associated with the electrolyte. Thus, we built a numerical model to simulate lithium ion transport through a growing SEI to predict the Sand’s time. The numerical model is shown to be more accurate than previous analytical solutions, especially for low current densities. We then analyze the sensitivity of the Sand’s time to different SEI properties and the chemical potential gradients present in the SEI, driving lithium transport. The results showed that high lithium concentration has a greater impact at high current density, while fast diffusivity is more important at low current density. Lastly, we modeled the influence of surface roughness on the plating evolution and chemical potential gradients when an SEI is present in comparison to the electrolyte. As a result, we demonstrate that the SEI plays a critical role in lithium electrode stability, and that improved characterization techniques are needed to better understand transport through the SEI and increase lithium metal utilization in energy storage devices.

Chemistry↗
DOE OSTI2024

Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data. An integral component in addressing this challenge is model reduction, which reduces both the data dimensionality and problem size. In this paper, we utilize low-dimensional nonlinear structures in model reduction by investigating Auto-Encoder-based Neural Network (AENet). AENet first learns the latent variables of the input data and then learns the transformation from these latent variables to corresponding output data. Our numerical experiments validate the ability of AENet to accurately learn the solution operator of nonlinear partial differential equations. Furthermore, we establish a mathematical and statistical estimation theory that analyzes the generalization error of AENet. Finally, our theoretical framework shows that the sample complexity of training AENet is intricately tied to the intrinsic dimension of the modeled process, while also demonstrating the robustness of AENet to noise.

Auto-encoder↗
DOE OSTI2021

Bayesian sparse learning with preconditioned stochastic gradient MCMC and its applications

Deep neural networks have been successfully employed in an extensive variety of research areas, including solving partial differential equations. Despite its significant success, there are some challenges in effectively training DNN, such as avoiding overfitting in over-parameterized DNNs and accelerating the optimization in DNNs with pathological curvature. Here, we propose a Bayesian type sparse deep learning algorithm. The algorithm utilizes a set of spike-and-slab priors for the parameters in the deep neural network. The hierarchical Bayesian mixture will be trained using an adaptive empirical method. That is, one will alternatively sample from the posterior using preconditioned stochastic gradient Langevin Dynamics (PSGLD), and optimize the latent variables via stochastic approximation. The sparsity of the network is achieved while optimizing the hyperparameters with adaptive searching and penalizing. A popular SG-MCMC approach is Stochastic gradient Langevin dynamics (SGLD). However, considering the complex geometry in the model parameter space in nonconvex learning, updating parameters using a universal step size in each component as in SGLD may cause slow mixing. To address this issue, we apply a computationally manageable preconditioner in the updating rule, which provides a step-size parameter to adapt to local geometric properties. Moreover, by smoothly optimizing the hyperparameter in the preconditioning matrix, our proposed algorithm ensures a decreasing bias, which is introduced by ignoring the correction term in the preconditioned SGLD. According to the existing theoretical framework, we show that the proposed algorithm can asymptotically converge to the correct distribution with a controllable bias under mild conditions. Numerical tests are performed on both synthetic regression problems and learning solutions of elliptic PDE, which demonstrate the accuracy and efficiency of the present work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems

Abstract Predicting complex dynamics in physical applications governed by partial differential equations in real-time is nearly impossible with traditional numerical simulations due to high computational cost. Neural operators offer a solution by approximating mappings between infinite-dimensional Banach spaces, yet their performance degrades with system size and complexity. We propose an approach for learning neural operators in latent spaces, facilitating real-time predictions for highly nonlinear and multiscale systems on high-dimensional domains. Our method utilizes the deep operator network architecture on a low-dimensional latent space to efficiently approximate underlying operators. Demonstrations on material fracture, fluid flow prediction, and climate modeling highlight superior prediction accuracy and computational efficiency compared to existing methods. Notably, our approach enables approximating large-scale atmospheric flows with millions of degrees, enhancing weather and climate forecasts. Here we show that the proposed approach enables real-time predictions that can facilitate decision-making for a wide range of applications in science and engineering.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Active SOC Balancing for a Multi-Chemistry Battery Pack with Reduced Number of Converters

In energy storage systems using second-life or multi-chemistry cells, an active state of charge (SOC) balancing system can prolong pack life and enhance performance by utilizing the healthier cells more than those which are heavily degraded. However, the high cost of the active balancing system, particularly in converter-based solutions, prevents their widespread usage. Considering this, existing research has proposed numerous balancing systems utilizing only one converter. However, such systems may compromise the balancing speed too much. Therefore, this work proposes two active balancing systems with a reduced number of converters for 14-16 series-connected cells. One system uses two converters for direct cell-to-cell balancing. The other uses a time-multiplexed approach to exchange energy via an auxiliary low-voltage (LV) bus using four converters. The proposed balancing systems are compared to two baseline systems, a single converter cell-to-cell balancing system, and a 14 converter balancing system with an auxiliary LV bus.

battery pack↗
DOE OSTI2021

Inverse Biot–Savart Optimization for Superconducting Accelerator Magnets

Superconducting (SC) magnets for accelerator concepts are often synthesized by numerically optimizing magnetic field waveforms, a process that requires a subsequent solution of a constrained inverse problem to identify suitable SC magnet windings. When the desired field distribution is intuitive, the inverse process is facilitated by seeding preconceived coil distributions into design optimization methods for refinement. With more complex magnetic field distributions, an initial design may be unknown, and topology optimization tools are required to synthesize current distributions without a priori guidance from a subject matter expert. In this work, we develop a constrained inverse Biot-Savart topology optimization methodology that synthesizes optimal distributions of current density in racetrack-like SC coils. The problem structure is exploited through a computationally efficient quadratic programming formulation, and the method is applied to recently published magnetic field waveforms for a recirculating proton phase shifter, a proton therapy gantry, and dipole magnets with sharp field transitions. The method and results herein identify novel winding configurations that can help magnet designers bring accelerator concepts to fruition.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Decentralized Failure-Tolerant Optimization of Electric Vehicle Charging

We present a decentralized failure-tolerant algorithm for optimizing electric vehicle (EV) charging, using charging stations as computing agents. The algorithm is based on the alternating direction method of multipliers (ADMM) and it has the following features: (i) It handles capacity, peak demand, and ancillary services coupling constraints. (ii) It does not require a central agent collecting information and performing coordination (e.g. an aggregator), instead all agents exchange information and computations are carried out in a fully decentralized fashion. (iii) It can withstand the failure of any number of computing agents, as long as the remaining computing agents are in a connected communications network. We construct this algorithm by reformulating the optimal EV charging problem in a decomposable form, amenable to ADMM, and then developing efficient decentralized solution methods for the subproblems dealing with coupling constraints. We conduct numerical experiments on industry-scale synthetic EV charging datasets, with up to 1,152 charging stations, using a high performance computing cluster. The experiments demonstrate that the proposed algorithm can solve the optimal EV charging problem fast enough to permit the integration of EV charging with real-time electricity markets, even in the presence of failures.

42 ENGINEERING↗
DOE OSTI2020

Statistical Treatment of Inverse Problems Constrained by Differential Equations-based Models with Stochastic Terms

This paper introduces a statistical treatment of inverse problems constrained by models with stochastic terms. The solution of the forward problem is given by a distribution represented numerically by an ensemble of simulations. The goal is to formulate the inverse problem, in particular the objective function, to find the closest forward distribution (i.e., the output of the stochastic forward problem) that best explains the distribution of the observations in a certain metric. We use proper scoring rules, a concept employed in statistical forecast verification, namely energy, variogram, and hybrid (i.e., combination of the two) scores. We study the performance of the proposed formulation in the context of two applications: a coefficient field inversion for subsurface flow governed by an elliptic partial differential equation with a stochastic source and a parameter inversion for power grid governed by differential-algebraic equations. In both cases we show that the variogram and the hybrid scores produce better parameter inversion results than does the energy score, whereas the energy score leads to better probabilistic predictions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Binary Quantum Control Optimization with Uncertain Hamiltonians

Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum controls under uncertainties. In this paper, we consider a stochastic discrete optimization formulation of a discretized binary optimal quantum control problem involving Hamiltonians with predictable uncertainties. We propose a sample-based reformulation that optimizes both risk-neutral and risk-averse measurements of control policies, and solve these with two gradient-based algorithms using sum-up-rounding approaches. Furthermore, we discuss the differentiability of the objective function and prove upper bounds of the gaps between the optimal solutions to binary control problems and their continuous relaxations. We conduct numerical simulations on various sized problem instances based on two applications of quantum pulse optimization; we evaluate different strategies to mitigate the impact of uncertainties in quantum systems. In conclusion, we demonstrate that the controls of our stochastic optimization model achieve significantly higher quality and robustness compared with the controls of a deterministic model.

conditional value-at-risk (CVaR)↗
DOE OSTI2024

Comparing the MELCOR Aerosol Deposition Model with Exact Analytical Solutions

Exact analytical solutions are presented for the evolution of the aerosol particle mass density function in a control volume for particle deposition due to gravitational settling, thermophoresis, and diffusion. The solutions are for arbitrary initial mass density functions and are applied for an initial lognormal density function. Integration of these solutions provides the suspended mass in the control volume as a function of time. These solutions serve as an exact benchmark to assess the accuracy of numerical methods. For the numerical algorithm used in MELCOR, excellent agreement is obtained for gravitational settling, diffusive deposition, and thermophoretic deposition for the suspended aerosol mass. In all cases, the default number of discrete particle size bins of 10 is shown to converge, with hardly any advantage to using 20 size bins.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

On the energy landscape of symmetric quantum signal processing

Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given polynomial f , the parameters (called phase factors) can be obtained by solving an optimization problem. However, the cost function is non-convex, and has a very complex energy landscape with numerous global and local minima. It is therefore surprising that the solution can be robustly obtained in practice, starting from a fixed initial guess Φ 0 that contains no information of the input polynomial. To investigate this phenomenon, we first explicitly characterize all the global minima of the cost function. We then prove that one particular global minimum (called the maximal solution) belongs to a neighborhood of Φ 0 , on which the cost function is strongly convex under the condition ‖ f ‖ ∞ = O ( d − 1 ) with d = d e g ( f ) . Our result provides a partial explanation of the aforementioned success of optimization algorithms.

Wang, Jiasu↗
DOE OSTI2025

An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications

In this paper, we explore using the Harrow–Hassidim–Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations of the accuracy of quantum phase estimation, along with various properties of coefficient matrices, on the final solution and quantum resource cost in iterative and non-iterative numerical methods such as the Newton–Raphson method and finite difference method, as well as their impacts on quantum error correction costs using the Microsoft Azure Quantum resource estimator. We summarize the exponential resource cost from quantum phase estimation before and after quantum error correction and illustrate a potential way to reduce the demands on physical qubits. This work lays down a preliminary step for future investigations, urging a closer examination of quantum algorithms’ scalability and efficiency in domain applications.

hybrid software for QC-HPC↗
DOE OSTI2020

Scaling Turbulent Combustion Fields in Explosions

We considered the topic of explosions from spherical high-explosive (HE) charges. We studied how the turbulent combustion fields scale. On the basis of theories of dimensional analysis by Bridgman and similarity theories of Sedov and Barenblatt, we found that all fields scaled with the explosion length scale r0. This included the blast wave, the mean and root mean squared (RMS) profiles of thermodynamic variables, combustion variables, velocities, vorticity, and turbulent Reynolds stresses. This was a consequence of the formulation of the problem and our numerical method, which both satisfied the similarity conditions of Sedov. We performed numerical simulations of 1 g charges and 1 kg charges; the solutions were identical (within roundoff error) when plotted in scaled variables. We also explored scaling laws related to three-phase pyrotechnic explosions. We show that although the scaling formally broke down, the fireball still essentially scaled with the explosion length scale r0. However, the discrete Lagrange particles (DLP) (phase 2) and the heterogeneous continuum model (HCM) of the DLP wakes (phase 3) did not scale with r0, and mean and RMS profiles could differ by a factor of 10 in some regions. This was because the DLP particles and wakes introduced an additional scale that broke the similarity conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations

In this study, we present a data-driven approach for approximating entropy-based closures of moment systems from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment system, and thus does not depend on the spacetime discretization of the moment system or specific problem configurations such as initial and boundary conditions. With convex and C 2 approximations, this data-driven closure inherits several structural properties from entropy-based closures, such as entropy dissipation, hyperbolicity, and H-Theorem. We construct convex approximations to the Maxwell–Boltzmann entropy using convex splines and neural networks, test them on the plane source benchmark problem for linear transport in slab geometry, and compare the results to the standard, entropy-based systems which solve a convex optimization problem to find the closure. Numerical results indicate that these data-driven closures provide accurate solutions in much less computation time than that required by the optimization routine.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

CICE on a C-grid: new momentum, stress, and transport schemes for CICEv6.5

Abstract. This article presents the C-grid implementation of the CICE sea ice model, including the C-grid discretization of the momentum equation, the boundary conditions (BCs), and the modifications to the code required to use the incremental remapping transport scheme. To validate the new C-grid implementation, many numerical experiments were conducted and compared to the B-grid solutions. In idealized experiments, the standard advection method (incremental remapping with C-grid velocities interpolated to the cell corners) leads to a checkerboard pattern. A modal analysis demonstrates that this computational noise originates from the spatial averaging of C-grid velocities at corners. The checkerboard pattern can be eliminated by adjusting the departure regions to match the divergence obtained from the solution of the momentum equation. We refer to this novel approach as the edge flux adjustment (EFA) method. The C-grid discretization with edge flux adjustment allows for transport in channels that are one grid cell wide – a capability that is not possible with the B-grid discretization nor with the C-grid and standard remapping advection. Simulation results match the predicted values of a novel analytical solution for one-grid-cell-wide channels.

Lemieux, Jean-François (ORCID:0000000320845759)↗