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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space

We consider a truncation of the BMN matrix model to a configuration of two fuzzy spheres, described by two coupled non-linear oscillators dependent on the mass parameter μ. The classical phase diagram of the system generically (μ ≠ 0) contains three equilibrium points: two centers and a center-saddle; as μ → 0 the system exhibits a pitchfork bifurcation. We demonstrate that the system is exactly integrable in quadratures for μ = 0, while for very large values of μ, it approaches another integrable point characterized by two harmonic oscillators. The classical phase space is mixed, containing both integrable islands and chaotic regions, as evidenced by the classical Lyapunov spectrum. At the quantum level, we explore indicators of early and late time chaos. The eigenvalue spacing is best described by a Brody distribution, which interpolates between Poisson and Wigner distributions; it dovetails, at the quantum level, the classical results and reemphasizes the notion that the quantum system is mixed. We also study the spectral form factor and the quantum Lyapunov exponent, as defined by out-of-time-ordered correlators. These two indicators of quantum chaos exhibit weak correlations with the Brody distribution. We speculate that the behavior of the system as μ → 0 dominates the spectral form factor and the quantum Lyapunov exponent, making these indicators of quantum chaos less effective in the context of a mixed phase space.

AdS-CFT correspondence↗
DOE OSTI2024

Soft theorems in matrix theory

We show that the Banks-Fischler-Shenker-Susskind matrix model for M-theory obeys the leading and subleading soft theorems expected from eleven-dimensional supergravity. The subleading soft theorem implies the amplitude is Lorentz symmetric. This is argued for general four point amplitudes, but only for restricted kinematics for five and higher point amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Extracting the asymptotic behavior of S-matrix elements from their phases

The asymptotic kinematic limits of S-matrices are dominated by large logarithms which, roughly speaking, fall into two categories: those which are controlled by a renormalization group (RG) scale, which we may think of as logs involving ratios of invariant mass scales, and those which are functions of ratios of rapidities, so called “rapidity logs”. It has been pointed out by Caron-Huot and Wilhlem [1] that RG anomalous dimension can be extracted from the phase of the S-matrix, which can greatly simplify calculations via unitarity methods. In this paper we generalize the results of [1] to show that the phase can be used to reconstruct rapidity anomalous dimensions, by performing a special type of complex boost. The methodology introduced allows one to calculate without the need for a rapidity regulator which can lead to significant simplifications. We demonstrate the use of this method to derive the rapidity anomalous dimensions in the Sudakov form factor and the two parton soft function at two loops order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

hr-Adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm

In this study, we present an \(hr\) -adaptivity framework for optimization of high-order meshes. This work extends the r -adaptivity method by Dobrev et al. (Comput Fluids, 2020), where we utilized the Target-Matrix Optimization Paradigm (TMOP) to minimize a functional that depends on each element’s current and target geometric parameters: element aspect-ratio , size , skew , and rotation . Since fixed mesh topology limits the ability to achieve the target size and aspect-ratio at each position, in this paper, we augment the r -adaptivity framework with nonconforming adaptive mesh refinement to further reduce the error with respect to the target geometric parameters. The proposed formulation, referred to as \(hr\) -adaptivity, introduces TMOP-based quality estimators to satisfy the aspect-ratio target via anisotropic refinements and size target via isotropic refinements in each element of the mesh. The methodology presented is purely algebraic, extends to both simplices and hexahedra/quadrilaterals of any order, and supports nonconforming isotropic and anisotropic refinements in 2D and 3D. Using a problem with a known exact solution, we demonstrate the effectiveness of \(hr\) -adaptivity over both r - and \(h\) -adaptivity in obtaining similar accuracy in the solution with significantly fewer mesh nodes. We also present several examples that show that \(hr\) -adaptivity can help satisfy geometric targets even when \(r\) -adaptivity fails to do so, due to the topology of the initial mesh.

42 ENGINEERING↗
DOE OSTI2026

Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems

Nonconvex, nonlinear optimization problems arise naturally in parameter fitting and machine learning. While augmented Lagrangian methods have demonstrated robust convergence for classes of these problems, their convergence for block updates has been relatively unexplored outside of the context of the alternating direction method of multipliers (ADMM). ADMM has seen extensive use in these applications, but may exhibit uncertain convergence behavior in many practical nonconvex settings, and struggles with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential quadratic programming methods and interior point methods with feasibility criteria. We develop an ADMM-filter method for highly nonlinear and nonconvex problems. Here, we show convergence under mild assumptions for several types of coordinate descent schemes, and demonstrate our algorithm on nonnegative matrix factorization and completion problems in imaging and chemical spectrum analysis.

Nonconvex optimization↗
DOE OSTI2024

Investigating sol–gel matrix loading capacity toward producing surrogate nuclear explosive debris with realistic composition

Post detonation nuclear forensic materials which resemble the size, color, elemental composition, and radionuclide content of real nuclear debris would be valuable for developing and validating new nuclear forensic techniques. As nuclear fallout types vary significantly, the ability to tailor each of these parameters accurately is desired to produce materials capable of testing analytical methods under a wide array of forensic scenarios. Sol–gel synthesis techniques can provide tunability of size, shape and composition for producing a wide variety of solid nuclear forensics benchmarking materials. Further, the sol–gel process consists of forming a metal oxide material, often silica, through polymerization of a metal-alkoxy precursor. In this work, we characterize the ability to load sol–gel particles with secondary elemental components such as iron, aluminum, and calcium toward producing benchmarking materials approximating the elemental composition of historic nuclear debris from the Nevada National Security Site. We also demonstrate quantitative radionuclide encapsulation toward producing benchmarking materials with controllable radionuclide content. Finally, we employ these techniques to produce nuclear debris benchmarking materials with controllable elemental matrix composition and radionuclide content and compare these samples with the composition of a historic fallout sample previously reported from the Nevada National Security Site.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A generalized 3D elastic model for nanoscale, self-assembled oxide-metal thin films with pillar-in-matrix configurations

In recent years, functional oxide-metal based vertically aligned nanocomposite (VAN) thin films have gained interest due to their intriguing physical properties and multifunctionalities stemming from the complex interactions between the two phases in the film and the substrate. In this work, we develop a model for studying the energetics of these thin film systems, including the effects of both lattice mismatch and capillary forces due to interface curvature. Each phase is incorporated into the model using a phase indicator function, and we introduce the capillary forces as body forces using a vector density representation of the interface. The model is implemented using the finite element method to study the deformation of the thin film which is composed of Au nanopillars embedded in a La 0.7 Sr 0.3 MnO 3 (LSMO) matrix on an SrTiO 3 (STO) substrate. Further, the results suggest that the total energy is lowest for random configurations of pillars compared to ordered square and hexagonal lattice configurations, consistent with the random distribution of pillars found in experiments. Furthermore, we find that the interfacial energy dominates the total energy of each configuration, suggesting that interfacial energy in the system is an important design parameter for nanocomposite growth, along with the lattice mismatch.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Assessment the leaching characteristics and long-term leaching behavior of some radionuclides from synthesized zeolite cement matrix

Highlights: • Synthesis and characterization of zeolite cement synthesized from fly ash • Leaching tests were used to assess the release rate of {sup 85}Sr and {sup 60}Co radionuclides. • Simple mathematical models were used to detect leaching mechanisms. • Long-term leaching behavior of {sup 85}Sr and {sup 60}Co from cementitious matrix was assessed. The development of cementitious materials remains a vital goal to produce valuable products with good mechanical, physical and chemical properties suitable for the safe disposal of concentrated radionuclides resulted from the treatment of contaminated solutions. In this paper, zeolite cement with good properties was laboratory synthesized from industrial by-products fly ash and characterized using various characterization techniques. The leaching characteristics of strontium and cobalt radionuclides from the synthesized zeolite cement were scrutinized conforming with the standard leaching methodology of International Atomic Energy Authority (IAEA). A mechanical strength assessment was executed to characterize the extent of immobilization process of the solidified matrices. The cumulative leaching fraction (φ) of the two studied radionuclides was found to be less than 5% in all examined conditions, which implies the applicability of the IAEA-recommended methodology for estimating the diffusion coefficient. The experimental leaching data were regressed nonlinearly to various mathematical kinetic models to assess the controlling leaching mechanism and to determine the leaching parameters. The regression results indicated that strontium ({sup 85}Sr) and cobalt ({sup 60}Co) leaching resulted from two succeeding mechanisms: as first order kinetic reaction, and then diffusion. The calculated values of leachability indices signify that the performance of each of the studied matrices is within an acceptable range. A simplified mathematical model, rooted in the first order reaction and diffusion mechanisms, was simulated to predict the radionuclides leaching rates from zeolite cement matrices. By comparing the synthesized zeolite cement with other cementitious materials, it can be concluded that the synthesized material can be classified as an efficient material suitable to immobilize {sup 85}Sr and {sup 60}Co from radioactive wastes. The acquired findings demonstrated that the studied immobilized waste matrices have acceptable mechanical effectiveness.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Three-dimensional traction microscopy accounting for cell-induced matrix degradation

Tractions exerted by cells on the extracellular matrix (ECM) are critical in many important physiological and pathological processes such as embryonic morphogenesis, wound healing, and cancer metastasis. Three-dimensional Traction Microscopy (3DTM) is a tool to quantify cellular tractions by first measuring the displacement field in the ECM in response to these tractions, and then using this measurement to infer tractions. Most applications of 3DTM have assumed that the ECM has spatially-uniform mechanical properties, but cells secrete enzymes that can locally degrade the ECM. In this work, a novel computational method is developed to quantify both cellular tractions and ECM degradation. In particular, the ECM is modeled as a hyperelastic, Neo-Hookean solid, whose material parameters are corrupted by a single degradation parameter. The feasibility of determining both the traction and the degradation parameter is first demonstrated by showing the existence and uniqueness of the solution. An inverse problem is then formulated to determine the nodal values of the traction vector and the degradation parameter, with the objective of minimizing the difference between a predicted and measured displacement field, under the constraint that the predicted displacement field satisfies the equation of equilibrium. The inverse problem is solved by means of a gradient-based optimization approach, and the gradient is computed efficiently using appropriately derived adjoint fields. The computational method is validated in-silico using a geometrically realistic neuronal cell model and synthetic traction and degradation fields. It is found that the method accurately recovers both the traction and degradation fields. Moreover, it is found that neglecting ECM degradation can yield significant errors in traction measurements. Finally, our method can extend the range of context where tractions can be appropriately measured.

42 ENGINEERING↗
DOE OSTI2023

First-principles study of interfaces in Al/SiC metal-matrix composite system

In this work, first-principles calculations were performed on the interfaces between Al and SiC, which is a widely used strengthening agent in aluminum metal-matrix-composites (Al/MMC). C-terminated interfaces have much larger work of adhesion than Si-terminated interfaces, indicating that the former has much stronger interfacial bonding. The electron localization function shows that the chemical bonding between Al and C has a strong covalent character, while the bonding between Al and Si is largely metallic. As a result of the vastly different chemical bonding, the work of adhesion for C-terminated interfaces increases with the number of dangling bonds at the interface, while the opposite trend was observed for Si-terminated interfaces. Additionally, the interface energy for Si-terminated interfaces is comparable to that for C-terminated interfaces, suggesting both types of terminations can coexist in the Al/SiC system.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Surviving nanoscale interfacial stability in extreme thermal expansion contrast Zn(CN) 2 -epoxy resin matrix composites

Here, we report the remarkable stability at the nanoscale matrix-filler interface in a series of overall low coefficient of thermal expansion (CTE) zinc cyanide (ZC)/epoxy resin composites. These interfaces demonstrate the stability of highly contrasting materials. These composites are designed to optimize the properties of both materials: epoxy resins are valued for their high strength, superb chemical resistance, low dielectric properties, and adhesive abilities. ZC, a model flexible framework, exhibits negative thermal expansion (NTE) behavior and compensates for the epoxy resin’s detrimentally large thermal expansion values. Filled resins minimize the native 65 ppm/°C CTE values to 19 ppm/° C over a wide temperature range while maintaining linearity, yielding composites compatible with typical metal and ceramic substrates’—commonly bonded to the resin— 0–20 ppm/° C CTE values. Additionally, with significant intrinsic differences in the materials, we use wide-angle X-ray diffraction and atomic force microscopy to elucidate thermal movement. The ZC/epoxy interface is surprisingly resilient over 1,000 cycles between -55° C and 75° C, extremes typical to aerospace applications. Further, we show that the resin viscosity remains less than 21 Pa*s at up to 30 vol% ZC, an important consideration for workability. We also discuss settling distribution, glass transition temperature, flexural strength, and longevity. All results point favorably towards practical implementation in low thermal expansion application needs: filling the gap in component design.

42 ENGINEERING↗
DOE OSTI2023

Design and experimental testing of a 150 kWh thermal battery using thermosiphons embedded in a concrete matrix for power plant flexible operation

One of the options for achieving the global temperature limitation of 1.5 °C target, for the mitigation of global warming, is based on the better penetration of renewables into the electrical grid. This has imposed a burden to fossil fuel fired power plants since they are required to operate away from their baseload mode to compensate for the inherent intermittence of the renewable power. Integrating energy storage with fossil plants is an option to achieve their needed flexibility. A cost competitive energy storage option for the solution is based on storing sensible heat in concrete. Here, this paper reports research results and development of a thermal battery cell (TBC) capable of operating at temperatures up to 425 °C. A novel concept consisting of a concrete matrix for sensible heat storage, engineered to provide enhanced thermal and mechanical properties, and twenty-two thermosiphon elements, engineered for dual action were designed and fabricated into a single thermal energy storage (TES) module. Research for the development of the components for the TBC was performed in the laboratory. Efficient heat transfer, to/from the storage media, was demonstrated under several charging and discharging conditions with a thermal storage capacity of 150 kWh th and a rapid discharge, making the TBC suitable for fast ramping when integrated with a fossil fuel fired power plant. Efficient radial heat transfer to the concrete was observed due to the well designed spacing and location of thermosiphons in the radial direction. A minimal temperature difference of 2 °C, between the thermosiphons bottom and top was obtained, demonstrating the isothermicity of those elements. An overall end-to-end TBC energy-to-energy round trip efficiency of 70% was achieved.

25 ENERGY STORAGE↗
DOE OSTI2022

Thermal energy storage composites with preformed expanded graphite matrix and paraffin wax for long-term cycling stability and tailored thermal properties

Harvesting solar energy, preventing hot spots in electronics, transport of temperature-sensitive materials, and capture and repurposing of thermal energy require a latent heat thermal energy storage (TES) system to store/discharge heat repeatedly. For the practical application of phase change material (PCM) composites within TES systems, reliable thermal performance throughout its operational lifetime is essential. Nevertheless, the reliability of thermal conductivity in multi-phase composites over relevant numbers (>10 3 ) of melt/freeze cycles has barely been studied, particularly for composites containing fillers for thermal conductivity enhancement. Here, we introduce a preform-type expanded graphite (EG)/paraffin wax composite possessing highly robust heat transfer and storage properties even after 10,000 melt/freeze cycles. To achieve such excellent reliability, comparative studies on the combined influence of fabrication process, particle size, EG vol%, binder amount, and compaction on both magnitude and robustness of thermal conductivity were undertaken. Our parametric study has yielded a trade-off between thermal conductivity and latent heat. Based on our modeling, 20 vol% EG approaches the case where all EG particles are well-connected thermally while 10 vol% EG is close to loosely connected fillers in the matrix. Thermal conductivity of our paraffin composites containing 20 vol% EG (25.1 W·m -1 ·K -1 ) is highest among other EG/paraffin composites without aligned EG in the literature. After 10,000 thermal cycling, negligible conductivity fading was observed for the 10 vol% EG composite, while reduction in latent heat remained within 10% for all 10, 14, 17 and 20 vol% EG samples. Here we anticipate this work provides insight on suitable recipe for desirable magnitude and robustness of thermal conductivity of EG/paraffin composites.

25 ENERGY STORAGE↗
DOE OSTI2022

Risk matrix for legacy wells within the Area of Review (AoR) of Carbon Capture & Storage (CCS) projects

The success of CCS depends on the capacity, injectivity, and confinement by the storage medium. Thousands of wells drilled over the past century with the intention to find the trapped oil and gas may penetrate the containment seals. These wells may provide leakage pathways for the CO 2 to escape and contaminate the underground sources of drinking water (USDW) or reach the surface in the worst-case scenario. Identifying the risky wells penetrating the containment seals and predicting their current as well as future well integrity is the most challenging task when limited data is available. Here, this paper proposes a unique methodology for risk assessment of the wells penetrating the containment seals based on the proximity of these wells from the proposed injection location, mechanical integrity, and accessibility of these wells over the lifecycle of the CCS project. This helps in identifying the wells which need immediate attention from the wells that need little to no attention. It also highlights the corrective actions necessary for the success of the CCS project as well as help estimate the approximate cost required to perform the corrective actions. This methodology focuses on all wells (producers, injectors, orphan, abandoned, water, stratigraphic, etc) while the majority of the studies found in literature focused on wells with sustained casing pressure (SCP) reports and cement bond logs (CBL). The proposed risk matrix, if applied to future CCS projects across the globe, will uniformly categorize the wells within the Area of Review (AoR).

58 GEOSCIENCES↗
DOE OSTI2023

Even spheres as joint spectra of matrix models

The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can be efficiently approximated using numerical methods, but this only is possible in low dimensional example. In this paper we examine the higher-dimensional spheres that can arise from theoretical examples. We also describe a constructive method to generate five real symmetric almost commuting matrices that have a K-theoretical obstruction to being close to commuting matrices. For this, we look to matrix models of topological electric circuits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO

In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The calculation of light element impurity (α, n) yield curves in a PuO 2 matrix and associated specific yield coefficients: Influence of the reaction cross sections

Most of the Pu separated from irradiated commercial nuclear fuel is stored as PuO 2 . The primary quantitative nondestructive measurement technique used to verify the amount of Pu in storage containers is passive neutron correlation counting. An important physical property of the oxide material is the ratio, α, of the rate of (α, n) neutrons produced inside the item to the rate of neutrons produced by spontaneous fission. This ratio influences the precision of the correlated counting method and affects the interpretation of the data because of how it changes both the primary total neutron production rate and the rate of induced fission events taking place inside the item. In addition to the main O(α, n) contribution, additional contributions come from α-particle interactions with light element impurities that are inevitably present. In this work, we calculate specific (α, n) yield coefficients, expressed in units of neutrons per second per gram of α-emitting nuclide per part per million by mass of the specified impurity element distributed in a pure PuO 2 matrix, for some key α-emitting actinides commonly present in reprocessed Pu ( 238–242 Pu+ 241 Am). These coefficients are directly applicable to nuclear safeguards verification work in which the α ratio is often calculated from the Pu-isotopic composition and chemical information obtained by other means. Further, they also provide a convenient up-to-date reference set against which values generated by other methods can be compared. Results are presented for impurities with atomic number from 3 to 17 inclusive, plus K and Fe. In most cases, these coefficients are not expected to change by more than 5%–10% at any time in the future. However, as new data become available, changes as large as 20% may be needed for some targets (e.g., F). The present yield calculations are limited by the general shortage of quality experimental total (α, n) reaction cross section data, which, together with unexplained variation between determinations, means that an objective and coherent evaluation is not possible. The situation is even less satisfactory for the partial differential cross section needed to calculate neutron spectra.

(𝛼, n) reactions↗
DOE OSTI2024

Use of a deuterium-deuterium neutron generator for the Add-A-Source waste matrix correction technique

Neutron generators offer an alternative to radioactive sources in the application of active techniques for nondestructive assay of nuclear materials. The Add-A-Source technique has enabled improvements in the ability to accurately measure waste bearing nuclear materials by measuring and correcting for the non-nuclear matrix effect. The technique has historically been performed with a Cf-252 spontaneous fission source. Here, in this work, we have demonstrated the use of a Deuterium-deuterium neutron generator in place of the Cf-252 source. A DD generator enables operational advantages and allows the simplification of the instrument design, while offering equivalent corrective performance as a Cf-252 source.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗