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At least 505 records · Page 28

General Bayesian Inference over the Stiefel Manifold via the Givens Transform

We introduce here an approach based on the Givens representation for posterior inference in statistical models with orthogonal matrix parameters, such as factor models and probabilistic principal component analysis (PPCA). We show how the Givens representation can be used to develop practical methods for transforming densities over the Stiefel manifold into densities over subsets of Euclidean space. We demonstrate how to deal with issues arising from the topology of the Stiefel manifold and how to inexpensively compute the change-of-measure terms. We introduce an auxiliary parameter approach that limits the impact of topological issues. We provide both analysis of our methods and numerical examples demonstrating the effectiveness of the approach. We also discuss how our Givens representation can be used to define general classes of distributions over the space of orthogonal matrices. We then give demonstrations on several examples showing how the Givens approach performs in practice in comparison with other methods.

97 MATHEMATICS AND COMPUTING↗

A “Master Curve” Describing Reaction Inhomogeneity and Plating Onset during Fast-Charging of Graphite Electrodes

Lithium plating in porous graphite electrodes is a major limitation for fast charging. Theoretical evidence suggests plating during fast charging is largely due to inhomogeneous intercalation through the electrode thickness (caused by ionic/mass transfer limitations and inherent thermodynamic properties of the graphite material). Numerical and analytical predictions of plating onset during fast charging have been proposed but not compared directly with experiments. This work validates these model predictions against plating onset measurements via the “dOCV” method in graphite half-cells, for various electrode thicknesses and C-rates. Remarkably, it is shown that experimental and theoretical trends in plating onset (vs C-rate and electrode thickness) collapse to a single “master curve” using a nondimensional “reaction inhomogeneity” parameter. This observation supports the hypothesized reaction inhomogeneity mechanism for accelerating plating onset and provides practical guidance for electrode design. Furthermore, this work develops theory to quantify reaction inhomogeneity in situ directly from voltage V vs capacity Q data, using dQ / dV analysis. Here again, experiments and numerical predictions show good agreement, where peaks that correspond to LiC 6 correlate with plating onset. This work provides experimental validation of theoretical tools that can predict plating onset, aid electrode design, and give insight for plating onset mechanisms during fast charging.

25 ENERGY STORAGE↗

Scaling patch analysis of turbulent planar plume

Proper scaling in turbulent planar plumes is investigated in this study using a scaling patch approach. Based on the scaled boundary conditions, a proper velocity scale for the mean axial flow is the plume centerline velocity U ref = U ctr , and a proper temperature scale for the temperature excess is Θ ref = T ctr – T ∞ , where T ctr is the plume centerline temperature and T ∞ is the ambient fluid temperature. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity, mean momentum, and mean energy equations, respectively, the following is found: (1) a proper scale for the mean transverse flow is V ref = ( d δ / d x ) U ctr , where d δ / d x is the growth rate of the plume width. (2) A proper scale for the Reynolds shear stress is R vu , ref = U ctr V ref = ( d δ / d x ) U ctr 2 , a mix of the scales for the mean axial and transverse flows. (3) A proper scale for the turbulent heat flux is R v θ , ref = V ref Θ ctr , a mix of the scales for the mean transverse flow and mean temperature excess. The mean transverse flow thus plays a critical role in the scaling of turbulent planar plumes. Approximate functions are developed for the scaled mean transverse flow, Reynolds shear stress, and turbulent temperature flux, and are found to agree favorably with experimental and numerical simulation data. The integral analysis of the mean momentum equation yields a Richardson number Ri, which remains invariant in the axial direction. The Richardson number is defined as Ri = def g β Θ ctr δ t / ( U ctr V ref ) ≈ 1 / 2 , where g is the gravitational acceleration, β is the thermal expansion coefficient, and δ t is the plume half-width based on the mean temperature profile. This Richardson number arises directly from the scaling patch analysis of the mean momentum equation, including both the streamwise and transverse velocity scales.

42 ENGINEERING↗

Dynamical Instabilities in Systems of Multiple Short-period Planets Are Likely Driven by Secular Chaos: A Case Study of Kepler-102

We investigated the dynamical stability of high-multiplicity Kepler and K2 planetary systems. Our numerical simulations find instabilities in ∼20% of the cases on a wide range of timescales (up to 5 × 10{sup 9} orbits) and over an unexpectedly wide range of initial dynamical spacings. To identify the triggers of long-term instability in multiplanet systems, we investigated in detail the five-planet Kepler-102 system. Despite having several near-resonant period ratios, we find that mean-motion resonances are unlikely to directly cause instability for plausible planet masses in this system. Instead, we find strong evidence that slow inward transfer of angular momentum deficit (AMD) via secular chaos excites the eccentricity of the innermost planet, Kepler-102 b, eventually leading to planet–planet collisions in ∼80% of Kepler-102 simulations. Kepler-102 b likely needs a mass ≳0.1 M {sub ⊕}, hence a bulk density exceeding about half Earth’s, in order to avoid dynamical instability. To investigate the role of secular chaos in our wider set of simulations, we characterize each planetary system’s AMD evolution with a “spectral fraction” calculated from the power spectrum of short integrations (∼5 × 10{sup 6} orbits). We find that small spectral fractions (≲0.01) are strongly associated with dynamical stability on long timescales (5 × 10{sup 9} orbits) and that the median time to instability decreases with increasing spectral fraction. Our results support the hypothesis that secular chaos is the driver of instabilities in many nonresonant multiplanet systems and also demonstrate that the spectral analysis method is an efficient numerical tool to diagnose long-term (in)stability of multiplanet systems from short simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

Earthquake-induced impact of base-isolated buildings: theory, numerical modeling, and design solutions

Earthquake shaking more intense than that used to size the horizontal clearance between a base–isolated building and near–rigid perimeter moat wall will result in hard impact, producing high–frequency, high–amplitude acceleration response in the structure and supported equipment. Herein this paper provides a design solution for the damaging effects of hard impact by installing a compliant engineered element in the load path between the base–isolated building and the moat wall, resulting in soft impact and a much smaller acceleration response. The engineered element assumed herein is a commercial–off–the–shelf marine fender with mechanical properties determined by physical testing. The attachment of a flexible engineered element, with well–defined stiffness and damping, to a near–rigid moat wall, simplifies the numerical modeling of the building–moat wall system and eliminates the need to bound the lateral stiffness of the wall for impact calculations. The simple model of the engineered element can be implemented in commercial finite element codes. Theory is developed for two–sided impact of a single–degree–of–freedom oscillator. Analytical solutions are derived for the shifted first–mode frequency of the impacted oscillator and for its free–vibration response. The shifted first–mode frequency is a function of the composite lateral stiffness of the isolator–engineered element assembly and its earthquake–induced displacement. Local peaks in the spectral response of the impacted oscillator form at odd integer multiples of the shifted first–mode frequency. The analytical solutions can be used to verify, in part, the numerical model used for impact analysis.

42 ENGINEERING↗

Anisotropic yield models for lattice unit cell structures exploiting orthotropic symmetry

We report numerical homogenization enables efficient computational analysis and design of multiscale structures made of micro-architected materials including lattice unit cells. However, predicting yield is nontrivial because it requires accurate and efficient predictions of the maximum stress inside the homogenized unit cells. To address this challenge, we develop a macroscale anisotropic yield function for micro-architected materials. The yield function depends on the three-dimensional macroscale stress state and the parameters describing a family of micro-architectures, such as the radii of the struts in a lattice unit cell. To ensure accuracy, we determine the maximum stress using three-dimensional continuum finite-element analysis. To ensure efficiency, we construct surrogate models from the aforementioned high-fidelity results for yield prediction. To reduce simulation costs and surrogate modeling complexity, we leverage orthotropic symmetry commonly found in lattice unit cells. In this paper, we provide a thorough presentation of group representations and the systematic procedure to exploit orthotropic domain symmetry in homogenization and surrogate modeling. We illustrate the use of linear homogenization results to predict yield in specific unit cells without further simulations. We furthermore show that surrogate modeling presents a viable option for anisotropic yield prediction in a continuously parametrized family of micro-architectures. More specifically, despite the dimensionality and degree of nonlinearity in the maximum micro von Mises stress within the unit cell, the surrogate models can predict it with less than 5% error at least 90% of the time. Moreover, the largest under-prediction error, which is more critical than the over-prediction error, is typically less than 10%.

42 ENGINEERING↗

Development of hydrothermal corrosion model and BWR metal coating for CVD SiC in light water reactors

SiC/SiC fiber composites with CVD SiC overcoats are potential candidates for light water reactor advanced accident tolerant cladding materials. Understanding its corrosion kinetics in Light Water Reactor (LWR) conditions is essential to evaluate the concept's viability. Existing models only account for the temperature and oxygen concentration effect on the hydrothermal corrosion behavior applicable to LWR operating conditions. However, the development of a general corrosion rate for CVD SiC that accounts for the impact of irradiated microstructure, flow rate, electrical resistivity, pH, and surface roughness is critical for the practical realization of SiC/SiC-based cladding concepts. After a rigorous experimental campaign, this work updates the existing hydrothermal corrosion model to predict hydrothermal corrosion in LWRs. Numerical radiation and coolant chemistry analysis for LWRs conducted based on the updated corrosion kinetic models suggests that CVD SiC is likely a viable environmental barrier coating for Pressurized Water Reactors while questionable for Boiling Water Reactors (BWR) when the effect of irradiation damage on SiC corrosion is considered. An effective mitigation strategy for the double-layer metal coating is proposed for BWR applications. The double-layer metal coating comprising a FeCrAl overcoat with an intermediate Cr bond coating was observed to provide a stable protective barrier against SiC dissolution in BWR conditions. Finally, the proposed metal coating was also fully adherent following quench and burst tests.

36 MATERIALS SCIENCE↗

Reduced Artifact Approach for Determining Diffusion Coefficients in Time-Resolved Microscopy

Ultrafast microscopy methods traditionally assume a Gaussian profile to extract excited state diffusivities from transport measurements. Although this fitting method recovers accurate diffusion coefficients when the point spread function is well-represented by a Gaussian, even minor spatial aberrations introduced by the imaging system cause significant errors in the determined value. To provide a more accurate measure of excited state transport in nano- and microscale materials systems, in this work an alternative analysis protocol is proposed that numerically convolves the Green’s function solution to the diffusion equation with the experimentally measured point spread function. In contrast to the Gaussian fitting approach, the numerical convolution is shown to be robust against artifacts caused by nonideal point spread functions. Furthermore, the numerical convolution approach is highly effective at resolving anisotropic diffusion in modeled data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Long-time simulations for fixed input states on quantum hardware

Publicly accessible quantum computers open the exciting possibility of experimental dynamical quantum simulations. While rapidly improving, current devices have short coherence times, restricting the viable circuit depth. Despite these limitations, we demonstrate long-time, high fidelity simulations on current hardware. Specifically, we simulate an XY-model spin chain on Rigetti and IBM quantum computers, maintaining a fidelity over 0.9 for 150 times longer than is possible using the iterated Trotter method. Our simulations use an algorithm we call fixed state Variational Fast Forwarding (fsVFF). Recent work has shown an approximate diagonalization of a short time evolution unitary allows a fixed-depth simulation. fsVFF substantially reduces the required resources by only diagonalizing the energy subspace spanned by the initial state, rather than over the total Hilbert space. We further demonstrate the viability of fsVFF through large numerical simulations, and provide an analysis of the noise resilience and scaling of simulation errors.

97 MATHEMATICS AND COMPUTING↗

An investigation of Newton-Sketch and subsampled Newton methods

Sketching, a dimensionality reduction technique, has received much attention in the statistics community. In this paper, we study sketching in the context of Newton's method for solving finite-sum optimization problems in which the number of variables and data points are both large. In this work, we study two forms of sketching that perform dimensionality reduction in data space: Hessian subsampling and randomized Hadamard transformations. Each has its own advantages, and their relative tradeoffs have not been investigated in the optimization literature. Additionally, our study focuses on practical versions of the two methods in which the resulting linear systems of equations are solved approximately, at every iteration, using an iterative solver. The advantages of using the conjugate gradient method vs. a stochastic gradient iteration are revealed through a set of numerical experiments, and a complexity analysis of the Hessian subsampling method is presented.

97 MATHEMATICS AND COMPUTING↗

Elliptic multipoles and the modeling of narrow-gap bend magnets in accelerators

We highlight the virtues of 2D elliptic-multipole field expansions in modeling the magnetic fields of narrow-aperture, straight-axis bending magnets with parallel faces, addressing the limitations of the conventional circular multipole series when the beam-orbit sagitta exceeds the magnet's vertical half-gap. The elliptic multipoles provide a convenient way to represent the field in all aspects of the magnet development (design, particle-tracking simulations, measurements). We propose a numerically robust method of data analysis to determine the elliptic (or circular) multipoles from stretched-wire measurements with the wire moving on an arbitrary path.

Venturini, Marco↗

Buckling-induced interaction between circular inclusions in an infinite thin plate

Design of slender artificial materials and morphogenesis of thin biological tissues typically involve stimulation of isolated regions (inclusions) in the growing body. These inclusions apply internal stresses on their surrounding areas that are ultimately relaxed by out-of-plane deformation (buckling). Here, we utilize the Föppl-von Kármán model to analyze the interaction between two circular inclusions in an infinite plate that their centers are separated a distance of 2ℓ. In particular, we investigate a region in phase space where buckling occurs at a narrow transition layer of length ℓ D around the radius of the inclusion, $R (ℓ_D \ll R)$. We show that the latter length scale defines two regions within the system, the close separation region, $ℓ – R \sim ℓ_D$, where the transition layers of the two inclusions approximately coalesce, and the far separation region, $ℓ – R \gg ℓ_D$. While the interaction energy decays exponentially in the latter region, $E_{\text{int}} ∝ e^{– (ℓ – R)/ℓ_D}$, it presents nonmonotonic behavior in the former region. While this exponential decay is predicted by our analytical analysis and agrees with the numerical observations, the close separation region is treated only numerically. In particular, we utilize the numerical investigation to explore two different scenarios within the final configuration: The first where the two inclusions buckle in the same direction (up-up solution) and the second where the two inclusions buckle in opposite directions (up-down solution). We show that the up-down solution is always energetically favorable over the up-up solution. In addition, we point to a curious symmetry breaking within the up-down scenario; we show that this solution becomes asymmetric in the close separation region.

42 ENGINEERING↗

Leveraging Application Data Constraints to Optimize Database-Backed Web Applications

Exploiting the relationships among data is a classical query optimization technique. As persistent data is increasingly being created and maintained programmatically, prior work that infers data relationships from data statistics misses an important opportunity. We present Coco, the first tool that identifies data relationships by analyzing database-backed applications. Once identified, Coco leverages the constraints to optimize the application's physical design and query execution. Instead of developing a fixed set of predefined rewriting rules, Coco employs an enumerate-test-verify technique to automatically exploit the discovered data constraints to improve query execution. Each resulting rewrite is provably equivalent to the original query. Using 14 real-world web applications, our experiments show that Coco can discover numerous data constraints from code analysis and improve real-world application performance significantly.

Computer Science↗

Utah FORGE: Optimization of a Plug-and-Perf Stimulation (Fervo Energy)

Information around the plug-and-perf treatment design at Utah FORGE by Fervo Energy. Objective and Purpose: - Develop a multistage hydraulic stimulation approach designed specifically to target the top three factors that control the technical and commercial viability of an EGS system: i) Achieving sufficient injectivity to support high cross-well flow rates ii) Distributing flow evenly across the wellbore and reservoir to maximize heat mining efficiency, ensure sustained heat transfer, and mitigate thermal breakthrough iii) Overcoming the effects of stress heterogeneity, stress shadowing, and variations in natural fracture properties during the stimulation treatment, leading to a more predictable stimulated reservoir volume and offset well placement - The following activities will be performed: i) Design, plan, and execute a multistage plug-and-perf stimulation treatment at a Fervo site with data acquisition and well testing activities aimed at addressing key technical aspects of the issues above ii) Perform data processing and interpretation of field results to translate the results form the Fervo site to a site-specific design at the Utah FORGE site iii) Design, plan, and execute a multistage plug-and-perf stimulation treatment design at the Utah FORGE site Methods and Approach: - Design a detailed data acquisition plan to maximize learning around: i) DFIT testing ii) Petrophysical logging, image logging iii) Permanent DAS/DTS fiber optic monitoring iv) Deep borehole microseismic monitoring v) Shallow borehole induced seismicity monitoring vi) Injection/production testing (RTA analysis, tracer testing) vii) Integrated numerical modeling and production forecasting

15 GEOTHERMAL ENERGY↗

Vadose Zone Flow and Transport Parameters Data Package for the Hanford Site Composite Analysis

This report provides a description of the basis for the development and implementation of a conceptual model for vadose zone flow and transport for the Hanford Site composite analysis (CA) groundwater pathway analysis. The parameterization for a numerical model is intimately linked to the conceptual model framework. This report describes the basis for the selection of hydraulic and transport parameters for the hydrostratigraphic units (HSUs) identified in the 200 East and 200 West Areas. The following three-step process was used to develop the hydraulic properties and transport parameters for the CA modeling: 1. Breakdown of existing database on hydraulic properties by HSUs 2. Constitutive model parameters for laboratory, core-scale hydraulic properties 3. Upscaling for macroscopic, field-scale flow, and transport parameters This document provides data and information on the following items: A brief description and technical basis for the conceptual model selected to represent vadose zone flow and transport for the CA modeling. Variation in sediment particle size distribution for representative sites in the 200 East and West Areas. A summary of effective (upscaled) moisture retention, and saturated and unsaturated hydraulic conductivity estimates for the HSUs in the 200 East and West Areas. A summary of effective transport parameters, including sediment bulk density and macrodispersivity estimates for various HSUs. The 200 East Area B Complex perched water aquifer hydraulic properties

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Modeling Astrophysical Explosions and Nucleosynthesis (Final Technical Report)

The goal of this project was to further our theoretical understanding of the extreme physics and heavy element nucleosynthesis occurring in stellar explosions, in particular supernovae and neutron star mergers. To study these systems, we further developed and applied numerical simulations (radiation hydrodynamical models and nuclear reaction networks) run on high performance computers. The numerical calculations and companion theoretical analysis helped to better define the sites of astrophysical nucleosynthesis, and make predictions of the associated observables (nucleosynthetic yields and electromagnetic signals) that can be used to anticipate and interpret experimental data. This project enhances the scientific value of the nuclear data obtained from current and future experimental facilities (e.g., rare isotope beams) by improving our understanding of the astrophysical context and specific physical conditions under which we expect such reactions to take place in Nature.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Passive Ultrasonic Deterrents to Reduce Bat Mortality in Wind Farms (Final Report)

The overall objective of this project was to develop active and passive ultrasonic deterrent concepts to mitigate bat mortality at wind turbines. The research was supported by the US Department of Energy under the contract DE-EE0008731. Novel ultrasonic bat deterrents are investigated in this study. The deterrents are based on the idea of aerodynamic whistles wherein flow-acoustic resonance is used to produce high-amplitude tonal sound at desired ultrasonic frequencies. The deterrents can be grouped into active and passive. The active deterrents/whistles are driven by pressurized air supplied by an external source (e.g., an air compressor). The passive deterrents/whistles are designed to be mounted on wind turbine blades and are “powered” by the energy in the air moving past the rotor blades. Multiple active and passive deterrent ideas are proposed and investigated numerically and experimentally. The computational analysis involves solving the compressible unsteady Reynolds-averaged Navier-Stokes (URANS) equations and coupling the near-field aerodynamic solution with an integral method based on the Ffowcs Williams-Hawkings acoustic analogy to predict ultrasound in the farfield. Experiments are performed in the anechoic chamber at ISU (for the active whistles) and in the Stability wind tunnel at Virginia Tech (for the passive whistles).

17 WIND ENERGY↗