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At least 73 records · Page 4

Self-Organized Stress Distributions in Polycrystalline Materials [Dissertation]

Understanding stress distributions in solid materials is complicated by the fact that most materials are polycrystalline in nature, with each crystal having an elastically anisotropic reaction to force. This study is to gain a better understanding on how external forces placed on a polycrystal are related to internal reactions within and between the grains. The hypothesis is that the stress distribution in porous to fully dense materials are self-organized based on strong contacts between and within the individual grains created by force chains. Force chains, commonly known in loaded granular materials, and could be the phenomenon that connect micro to macro deformation. Scale bridging measurements conducted through Raman spectroscopy, Atomic Force Microscopy, and Digital Image Correlation will be used to create stress maps, modulus maps, and elastic strain maps across a variety of geological and pharmaceutical polycrystals. When possible, the resulting maps will be compared to current homogenization schemes and a full field models. Finite element modeling will be used to assess whether the patterning seen in the experimental map is a reasonable approximation based on the orientation data of the samples used. A minimum of three publications is projected to be accomplished focusing each on a different method to experimentally test and analyze stress distributions.

36 MATERIALS SCIENCE↗

A FETI approach to domain decomposition for meshfree discretizations of nonlocal problems

We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem where the subdomains share “nonlocal” interfaces of the size of the nonlocal horizon. This system of nonlocal equations is first rewritten in terms of minimization of a nonlocal energy, then discretized with a meshfree approximation and finally solved via a Lagrange multiplier approach in a way that resembles the finite element tearing and interconnect method. Specifically, we propose a distributed projected gradient algorithm for the solution of the Lagrange multiplier system, whose unknowns determine the nonlocal interface conditions between subdomains. Several two-dimensional numerical tests on problems as large as 191 million unknowns illustrate the strong and the weak scalability of our algorithm, which outperforms the standard approach to the distributed numerical solution of the problem. Finally, this work is the first rigorous numerical study in a two-dimensional multi-domain setting for nonlocal operators with finite horizon and, as such, it is a fundamental step towards increasing the use of nonlocal models in large scale simulations.

42 ENGINEERING↗

On the Solution of ℓ 0 -Constrained Sparse Inverse Covariance Estimation Problems

The sparse inverse covariance matrix is used to model conditional dependencies between variables in a graphical model to fit a multivariate Gaussian distribution. Estimating the matrix from data are well known to be computationally expensive for large-scale problems. Sparsity is employed to handle noise in the data and to promote interpretability of a learning model. Although the use of a convex ℓ 1 regularizer to encourage sparsity is common practice, the combinatorial ℓ 0 penalty often has more favorable statistical properties. In this paper, we directly constrain sparsity by specifying a maximally allowable number of nonzeros, in other words, by imposing an ℓ 0 constraint. Here, we introduce an efficient approximate Newton algorithm using warm starts for solving the nonconvex ℓ 0 -constrained inverse covariance learning problem. Numerical experiments on standard data sets show that the performance of the proposed algorithm is competitive with state-of-the-art methods.

$\ell_0$-Constrained↗

Multiphysics coupling plan

In this chapter, multiphysics coupling simulations of nuclear reactor systems are reviewed. On the one hand, the mainstream methods of multiphysics coupling are demonstrated. The fundamental theory and coupling scheme of operator splitting methods, Jacobian-free Newton–Krylov methods, and approximate block Newton methods are summarized and presented. On the other hand, some significant works on neutronic and thermal-hydraulic codes coupling, and large research project, including NURESAFE European project, Multiphysics Object-Oriented Simulation Environment plan, and Consortium for the Advanced Simulation of Light Water Reactors project, are reviewed. This chapter helps the readers have a better understanding on the worldwide current status of multiphysics coupling research.

Gui, Miao↗

Electronic Coherences in Molecules: The Projected Nuclear Quantum Momentum as a Hidden Agent

Electronic coherences are key to understanding and controlling photoinduced molecular transformations. Here, we identify a crucial quantum-mechanical feature of electron-nuclear correlation, the projected nuclear quantum momenta, essential to capture the correct coherence behavior. For simulations, we show that, unlike traditional trajectory-based schemes, exact-factorization-based methods approximate these correlation terms and correctly capture electronic coherences in a range of situations, including their spatial dependence, an important aspect that influences subsequent electron dynamics and that is becoming accessible in more experiments.

74 ATOMIC AND MOLECULAR PHYSICS↗

Coupling between collective modes in the deformed 98 Zr nucleus: Insights from consistent HFB + QRPA calculations with the Gogny interaction

The zirconium isotopes exhibit structural properties that present multiple challenges to nuclear theory. Investigations of the coupling present within isoscalar modes and within isovector modes are scarce but important for advancing our understanding of the microscopic picture of nuclei. To explore some of these underlying coupling features, and to test the predictive power of a state-of-the-art nuclear structure approach, we provide a detailed analysis of the properties of 90,96,98 Zr . This region includes a benchmarking case and offers insights into nuclear deformation phenomena. Here, to investigate the coupling between collective modes in deformed nuclei, we focused our analysis on the ground and excited-state properties of these isotopes, employing a consistent approach with the axially symmetric deformed Hartree-Fock-Bogoliubov (HFB) and the quasiparticle random phase approximation (QRPA) framework, both using the Gogny D1M force. This approach effectively describes both low-lying and giant-resonance states. We devoted special attention to the deformed 98 Zr nucleus, where we confirm the existence of coupling between monopole and quadrupole excitations through the 𝐾 𝜋 = 0 + QRPA components and demonstrate an analogous dipole-octupole coupling through the 𝐾 𝜋 = 0 − and 𝐾 𝜋 = 1 − components. Intrinsic transition densities and associated radial projections illustrate the coupling. Our work complements and extends earlier studies carried out using density-functional-based methods and notably, we included the complete Coulomb interaction also in the pairing fields, i.e., we treat terms exactly that are approximated in typical calculations that use the Gogny D1 and D2 interaction families.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Coupling between collective modes in the deformed 98 Zr nucleus: Insights from consistent HFB+QRPA calculations with the Gogny interaction

The Zirconium isotopes exhibit structural properties that present multiple challenges to nuclear theory. Investigations of the coupling present within isoscalar modes and within isovector modes are scarce but important for advancing our understanding of the microscopic picture of nuclei. To explore some of these underlying coupling features, and to test the predictive power of a state-of the-art nuclear structure approach, we provide a detailed analysis of the properties of 90,96,98Zr. This region includes a benchmarking case and offers insights into nuclear deformation phenomena. To investigate the coupling between collective modes in deformed nuclei, we focused our analysis on the ground and excited-state properties of these isotopes, employing a consistent approach with the axially-symmetric deformed Hartree-Fock-Bogoliubov (HFB) and the Quasiparticle Random Phase Approximation (QRPA) framework, both using the Gogny D1M force. This approach effectively describes both low-lying and giant-resonance states. We devoted special attention to the deformed 98Zr nucleus, where we confirm the existence of coupling between monopole and quadrupole excitations through the K π = 0 + QRPA components and demonstrate an analogous dipole-octupole coupling through the K π = 0 − and K π = 1 − components. Intrinsic transition densities and associ ated radial projections illustrate the coupling. Our work complements and extends earlier studies carried out using density-functional-based methods and notably, we included the complete Coulomb interaction also in the pairing fields, i.e. we treat terms exactly that are approximated in typical calculations that use the Gogny D1 and D2 interaction families.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A fast particle-based approach for calibrating a 3-D model of the Antarctic ice sheet

We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past climate forcings. Triggering such a threshold response through anthropogenic greenhouse gas emissions would drive drastic and potentially fast sea level rise with important implications for coastal flood risks. Previous studies have combined information from ice sheet models and observations to calibrate model parameters. These studies have broken important new ground but have either adopted simple ice sheet models or have limited the number of parameters to allow for the use of more complex models. These limitations are largely due to the computational challenges posed by calibration as models become more computationally intensive or when the number of parameters increases. Here, we propose a method to alleviate this problem: a fast sequential Monte Carlo method that takes advantage of the massive parallelization afforded by modern high-performance computing systems. We use simulated examples to demonstrate how our sample-based approach provides accurate approximations to the posterior distributions of the calibrated parameters. The drastic reduction in computational times enables us to provide new insights into important scientific questions, for example, the impact of Pliocene era data and prior parameter information on sea level projections. These studies would be computationally prohibitive with other computational approaches for calibration such as Markov chain Monte Carlo or emulation-based methods. We also find considerable differences in the distributions of sea level projections when we account for a larger number of uncertain parameters. For example, based on the same ice sheet model and data set, the 99th percentile of the Antarctic ice sheet contribution to sea level rise in 2300 increases from 6.5 m to 13.1 m when we increase the number of calibrated parameters from three to 11. With previous calibration methods, it would be challenging to go beyond five parameters. Here, this work provides an important next step toward improving the uncertainty quantification of complex, computationally intensive and decision-relevant models.

54 ENVIRONMENTAL SCIENCES↗

Data-driven precision determination of the material budget in ALICE

The knowledge of the material budget with a high precision is fundamental for measurements of direct photon production using the photon conversion method due to its direct impact on the total systematic uncertainty. Moreover, it influences many aspects of the charged-particle reconstruction performance. In this article, two procedures to determine data-driven corrections to the material-budget description in ALICE simulation software are developed. One is based on the precise knowledge of the gas composition in the Time Projection Chamber. The other is based on the robustness of the ratio between the produced number of photons and charged particles, to a large extent due to the approximate isospin symmetry in the number of produced neutral and charged pions. Both methods are applied to ALICE data allowing for a reduction of the overall material budget systematic uncertainty from 4.5% down to 2.5%. Using these methods, a locally correct material budget is also achieved. The two proposed methods are generic and can be applied to any experiment in a similar fashion.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Response of hypoxia to future climate change is sensitive to methodological assumptions

Climate-induced changes in hypoxia are among the most serious threats facing estuaries, which are among the most productive ecosystems on Earth. Future projections of estuarine hypoxia typically involve long-term multi-decadal continuous simulations or more computationally efficient time slice and delta methods that are restricted to short historical and future periods. We make a first comparison of these three methods by applying a linked terrestrial–estuarine model to the Chesapeake Bay, a large coastal-plain estuary in the eastern United States. Results show that the time slice approach accurately captures the behavior of the continuous approach, indicating a minimal impact of model memory. However, increases in mean annual hypoxic volume by the mid-twenty-first century simulated by the delta approach (+ 19%) are approximately twice as large as the time slice and continuous experiments (+ 9% and + 11%, respectively), indicating an important impact of changes in climate variability. Our findings suggest that system memory and projected changes in climate variability, as well as simulation length and natural variability of system hypoxia, should be considered when deciding to apply the more computationally efficient delta and time slice methods.

54 ENVIRONMENTAL SCIENCES↗

Solving a class of infinite-dimensional tensor eigenvalue problems by translational invariant tensor ring approximations

Here, we examine a method for solving an infinite-dimensional tensor eigenvalue problem Hx = λx, where the infinite-dimensional symmetric matrix H exhibits a translational invariant structure. We provide a formulation of this type of problem from a numerical linear algebra point of view and describe how a power method applied to e -Ht is used to obtain an approximation to the desired eigenvector. This infinite-dimensional eigenvector is represented in a compact way by a translational invariant infinite Tensor Ring (iTR). Low rank approximation is used to keep the cost of subsequent power iterations bounded while preserving the iTR structure of the approximate eigenvector. We show how the averaged Rayleigh quotient of an iTR eigenvector approximation can be efficiently computed and introduce a projected residual to monitor its convergence. In the numerical examples, we illustrate that the norm of this projected iTR residual can also be used to automatically modify the time step to ensure accurate and rapid convergence of the power method.

97 MATHEMATICS AND COMPUTING↗

Optoelectronic properties of bent two-dimensional materials from first-principles methods combined with machine learning

A material’s interaction with light is highly relevant in the design of nanoelectronic devices such as photodiodes, solar cells, photocatalytic cells, phototransistors, and photodetectors. The interaction of a material with light can be altered by mechanical deformation. Fine tuning of the optical properties can be achieved by mechanical bending that alters the electronic structure. Optical properties strongly depend on band gaps, therefore any alteration in the band structure results in a changed optical response of the material. The impact of bending was explored in this project. The goal of this project was to assess the impact of mechanical bending of two-dimensional transition metal dichalcogenides on their optoelectronic properties, using first-principles methods. These first-principles approximations are largely built upon many-body theory for the optical properties of magnetic and topological nanoribbons. GW-BSE is standard for optical absorption, but it is less practical for collective excitations as it was shown in model systems. Time-dependent density functional theory, however, has better promises for collective excitations in low-dimensional materials.

36 MATERIALS SCIENCE↗

Model-Free Primal-Dual Methods for Network Optimization with Application to Real-Time Optimal Power Flow: Preprint

This paper examines the problem of real-time optimization of networked systems and develops online algorithms that steer the system towards the optimal trajectory without explicit knowledge of the system model. The problem is modeled as a dynamic optimization problem with time-varying performance objectives and engineering constraints. The design of the algorithms leverages the online zero-order primal-dual projected-gradient method. In particular, the primal step that involves the gradient of the objective function (and hence requires networked systems model) is replaced by its zero-order approximation with two function evaluations using a deterministic perturbation signal. The evaluations are performed using the measurements of the system output, hence giving rise to a feedback interconnection, with the optimization algorithm serving as a feedback controller. The paper provides some insights on the stability and tracking properties of this interconnection. Finally, the paper applies this methodology to a real-time optimal power flow problem in power systems, and shows its efficacy on the IEEE 37-node distribution test feeder for reference power tracking and voltage regulation.

61 RADIATION PROTECTION AND DOSIMETRY↗

Model-Free Primal-Dual Methods for Network Optimization with Application to Real-Time Optimal Power Flow

This paper examines the problem of real-time optimization of networked systems and develops online algorithms that steer the system towards the optimal trajectory without explicit knowledge of the system model. The problem is modeled as a dynamic optimization problem with time-varying performance objectives and engineering constraints. The design of the algorithms leverages the online zero-order primal-dual projected-gradient method. In particular, the primal step that involves the gradient of the objective function (and hence requires a networked systems model) is replaced by its zero-order approximation with two function evaluations using a deterministic perturbation signal. The evaluations are performed using the measurements of the system output, hence giving rise to a feedback interconnection, with the optimization algorithm serving as a feedback controller. The paper provides some insights on the stability and tracking properties of this interconnection. Finally, the paper applies this methodology to a real-time optimal power flow problem in power systems, and shows its efficacy on the IEEE 37-node distribution test feeder for reference power tracking and voltage regulation.

61 RADIATION PROTECTION AND DOSIMETRY↗

BUQEYE guide to projection-based emulators in nuclear physics

The BUQEYE collaboration (Bayesian Uncertainty Quantification: Errors in Your effective field theory) presents a pedagogical introduction to projection-based, reduced-order emulators for applications in low-energy nuclear physics. The term emulator refers here to a fast surrogate model capable of reliably approximating high-fidelity models. As the general tools employed by these emulators are not yet well-known in the nuclear physics community, we discuss variational and Galerkin projection methods, emphasize the benefits of offline-online decompositions, and explore how these concepts lead to emulators for bound and scattering systems that enable fast and accurate calculations using many different model parameter sets. We also point to future extensions and applications of these emulators for nuclear physics, guided by the mature field of model (order) reduction. All examples discussed here and more are available as interactive, open-source Python code so that practitioners can readily adapt projection-based emulators for their own work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Subcellular Feature-Based Classification of α and β Cells Using Soft X-ray Tomography

The dysfunction of α and β cells in pancreatic islets can lead to diabetes. Many questions remain on the subcellular organization of islet cells during the progression of disease. Existing three-dimensional cellular mapping approaches face challenges such as time-intensive sample sectioning and subjective cellular identification. To address these challenges, we have developed a subcellular feature-based classification approach, which allows us to identify α and β cells and quantify their subcellular structural characteristics using soft X-ray tomography (SXT). We observed significant differences in whole-cell morphological and organelle statistics between the two cell types. Additionally, we characterize subtle biophysical differences between individual insulin and glucagon vesicles by analyzing vesicle size and molecular density distributions, which were not previously possible using other methods. These sub-vesicular parameters enable us to predict cell types systematically using supervised machine learning. We also visualize distinct vesicle and cell subtypes using Uniform Manifold Approximation and Projection (UMAP) embeddings, which provides us with an innovative approach to explore structural heterogeneity in islet cells. This methodology presents an innovative approach for tracking biologically meaningful heterogeneity in cells that can be applied to any cellular system.

3D cell mapping↗

Extending Parsimonious Bayesian Inference

Parsimonious Bayesian inference is a theoretical framework for efficient data assimilation that seeks to balance increased consistency between predictions and training data against corresponding increases in model complexity. Within this framework, over-training is understood as optimization that encodes excessive information within model parameters while only achieving small improvements between predictions and training data. This project aims to develop practical methods of limiting excess model information during optimization. One key observation is that practical heuristics for parsimonious learning in high-dimensions must balance expressivity, i.e. the ability of the model to capture diverse predictions with only a few non-zero parameters, against discoverability, i.e. the ability to train the model with gradient-based optimization and drive parameters to low information states. As such, we developed logical activation functions that are able to adaptively approximate arbitrary truth tables that define Boolean logic operations within a probabilistic framework. These functions have demonstrated the ability to learn exclusive disjunction (XOR) and conditioned disjunction (if [condition] then [result_if_true] else [result_if_false]) within a single layer of a neural network. To efficiently exploit these activation functions to drive parsimonious learning required several other advances within the domain of variational inference. The most efficient form of complexity suppression is structured sparsification, driving most model parameters to zero while achieving the structural coherence among nonzeros needed for bandwidth reduction. Such models are not only far more efficient at suppressing information-theoretic complexity, they also reduce the other forms of complexity (computations, communication, storage, and the number of dependencies needed to evaluate predictions). Aiming to support enhanced sparsification, this project examined new approaches to high-dimensional variational inference that allow us to calibrate and control parameter uncertainty during optimization. By identifying which parameters can sustain sparsifying perturbations with little impact on prediction quality, we can develop better pruning strategies by framing them as approximate Bayesian inference. These advances also open paths to mitigate concerns with deploying advanced learning methods in resource-constrained environments, such as running models on power-limited or communication-limited devices.

97 MATHEMATICS AND COMPUTING↗