Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix Models”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Spinon Fermi Surface in a Cluster Mott Insulator Model on a Triangular Lattice and Possible Application to 1 T –TaS 2

1T-TaS 2 is a cluster Mott insulator on the triangular lattice with 13 Ta atoms forming a star of David cluster as the unit cell. We derive a two-dimensional XXZ spin-1/2 model with a four-spin ring exchange term to describe the effective low energy physics of a monolayer 1T-TaS 2 , where the effective spin-1/2 degrees of freedom arises from the Kramers degenerate spin-orbital states on each star of David. Here, a large scale density matrix renormalization group simulation is further performed on this effective model and we find a gapless spin liquid phase with a spinon Fermi surface at a moderate to large strength region of the four-spin ring exchange term. All peaks in the static spin structure factor are found to be located on the “2k F ” surface of a half-filled spinon on the triangular lattice. Experiments to detect the spinon Fermi surface phase in 1T-TaS 2 are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Luther-Emery liquid and dominant singlet superconductivity in the hole-doped Haldane spin-1 chain

We investigate the pairing tendencies in the hole-doped Haldane spin-1 chain. To allow for doping, we extend the original spin chain Hamiltonian into a fermionic model involving a two-orbital Hubbard chain at intermediate or strong repulsive interaction strengths U and for degenerate orbitals. At half filling and large U, the ferromagnetic Hund's coupling, J H , generates effective spin-1 moments, with antiferromagnetic correlations between sites. Using large-scale density matrix renormalization group calculations, we accurately study the system's behavior under light hole-doping. For U = 1.6 in units of the noninteracting bandwidth and for J H /U ≳ 0.275, we find that singlet pairing dominates the long-distance physics, establishing this system as a promising platform for repulsively mediated superconductivity. We provide concrete examples of materials that could realize the physics described here. We also provide evidence that the system approaches a Luther-Emery liquid state at large system sizes, reminiscent of the behavior of doped one-orbital two-leg ladders at weak coupling, which also have superconducting tendencies. The numerically calculated central charge approaches one in the thermodynamic limit, indicating a single gapless mode as is expected for the Luther-Emery state. Exponents characterizing the power-law decays of singlet pair-pair and charge density-density correlations are determined, and found to approximately satisfy the Luther-Emery identity.

1-dimensional systems↗
DOE OSTI2016

Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams

In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution formulated on the basis of the single-particle Courant-Snyder invariants has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. Here in this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations. The new generalized KV model yields spatially uniform density profiles and corresponding linear self-field forces as desired. Finally, the corresponding matrix envelope equations and beam matrix for the generalized KV model provide important new theoretical tools for the detailed design and analysis of high-intensity beam manipulations, for which previous theoretical models are not easily applicable.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Search for heavy Majorana neutrinos in same-sign dilepton channels in proton-proton collisions at $ \sqrt{s}=13 $ TeV

A search is performed for a heavy Majorana neutrino (N), produced in leptonic decay of a W boson propagator and decaying into a W boson and a lepton, with the CMS detector at the LHC. The signature used in this search consists of two same-sign leptons, in any flavor combination of electrons and muons, and at least one jet. The data were collected during 2016 in proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The results are found to be consistent with the expected standard model background. Upper limits are set in the mass range between 20 and 1600 GeV in the context of a Type-I seesaw mechanism, on |V$_{eN}$|$^{2}$, |V$_{μN}$|$^{2}$, and |V$_{eN}$V$_{μN}^{*}$ |$^{2}$/(|V$_{eN}$|$^{2}$ + |V$_{μN}$|$^{2}$), where V$_{ℓN}$ is the matrix element describing the mixing of N with the standard model neutrino of flavor ℓ = e, μ. For N masses between 20 and 1600 GeV, the upper limits on |V$_{ℓN}$|$^{2}$ range between 2.3 × 10$^{-5}$ and unity. These are the most restrictive direct limits for heavy Majorana neutrino masses above 430 GeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Preclinical tumor organoid models in personalized cancer therapy: Not everyone fits the mold

Highlights: • In personalized cancer medicine, each patient receives a specific treatment. • The tumor microenvironment and interpersonal differences can affect treatment. • Organoid culture systems fully recapitulate the tumor microenvironments. In contrast to conventional cancer treatment, in personalized cancer medicine each patient receives a specific treatment. The response to therapy, clinical outcomes, and tumor behavior such as metastases, tumor progression, carcinogenesis can be significantly affected by the heterogeneous tumor microenvironment (TME) and interpersonal differences. Therefore, using native tumor microenvironment mimicking models is necessary to improving personalized cancer therapy. Both in vitro 2D cell culture and in vivo animal models poorly recapitulate the heterogeneous tumor (immune) microenvironments of native tumors. The development of 3D culture models, native tumor microenvironment mimicking models, made it possible to evaluate the chemoresistance of tumor tissue and the functionality of drugs in the presence of cell-extracellular matrix and cell-cell interactions in a 3D construction. Various personalized tumor models have been designed to preserving the native tumor microenvironment, including patient-derived tumor xenografts and organoid culture strategies. In this review, we will discuss the patient-derived organoids as a native tumor microenvironment mimicking model in personalized cancer therapy. In addition, we will also review the potential and the limitations of organoid culture systems for predicting patient outcomes and preclinical drug screening. Finally, we will discuss immunotherapy drug screening in tumor organoids by using microfluidic technology.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Superallowed decays within and beyond the standard model

This note reviews the role of superallowed transitions in determining the strength of the weak interaction among the lightest quarks and in searching for new physics beyond the standard electroweak model. The two sets of superallowed decays in nuclei considered here are pure Fermi and mirror transitions. The first have been scrutinized for more than 50 years. Here, the most relevant results are presented and the role of the nucleus-dependent radiative correction and nucleus-independent inner radiative correction are reviewed. In this context, the systematic study of mirror transitions started about 15 years ago. Despite the significant progress made since then, the data is still limited by experimental uncertainties. Combining the results from all superallowed transitions, which are fully consistent, provides a test of unitarity of the first row of the Cabibbo-Kobayashi-Maskawa matrix, which displays a 2σ tension with the standard model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Calculating elements of matrix functions using divided differences

In this work, we introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We showcase our approach by calculating the matrix elements of the exponential of a transverse-field Ising model and evaluating quantum transition amplitudes for large many-body Hamiltonians of sizes up to 2 64 x 2 64 on a single workstation. We also discuss the application of the method to matrix inverses. We relate and compare our method to the state-of-the-art and demonstrate its advantages. We also discuss practical applications of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A scheme for a single molecule phase-shift gate in a solid matrix

We propose a feasible scheme to implement a phase-shift gate ( (table) ) based on a two-state single molecule in a solid matrix, where γ is a geometric phase controlled through a fast on-resonant laser field and a slow off-resonant radio-frequency field. In our scheme, a non-Hermitian quantum model is employed to characterize the single molecule in a solid matrix including the spontaneous decay effect. By the coupling between the radio-frequency field and the two-state permanent dipole difference resulting from the solid matrix, the spontaneous decay fatal to the preservation of geometric phase can be effectively suppressed for a considerably long waiting time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Grain detachment and transport clogging during mineral dissolution in carbonate rocks with permeable grain boundaries

In this paper, we explore the effect of permeable grain boundaries on carbonate rock dissolution in order to improve our understanding of grain detachment and migration during reactive flow. To do so we investigated the effects of grain size and enhanced reactivity along grain boundaries on global dissolution kinetics. Variations of permeability and porosity were calculated, and exponential relationships were observed in fractured rocks. Our model employed a reactive transport framework based on the Darcy-Brinkman equation to simulate calcite dissolution in carbonate rocks composed of microporous grains and, included fluid transport along grain boundaries. The model includes fluid flow, solute transport by advection–diffusion, heterogeneous reaction between fluid and minerals and grain detachment with subsequent grain transport in macropores. The migration of solid particles due to dissolution was based on cluster analysis and local movement, and the results show that grain detachment can lead to significant decreases in permeability due to the clogging of transport pathways. Microporous media with smaller grain sizes (fine grains in this study) showed a higher average reaction rate than those with coarser grains. In addition, as the overall rates of geochemical processes are commonly affected by the presence of texture heterogeneities such as fractures, a single fracture (macropore) introduced into a microporous matrix composed of permeable grains and grain boundaries was modelled as a large channel connecting the inlet and outlet of the simulation domain. It was found that macropore clogging by grain detachment temporary decreased permeability, lowering the long-term global reaction rates. Lastly, we observed that increases in flow rate can reduce detachment and fracture clogging by reducing local dissolution along grain boundaries.

58 GEOSCIENCES↗
DOE OSTI2016

Tailored Microstructure and Properties in UO{sub 2}

Advanced fuels with enhanced safety margin and accident tolerance are of vital importance for safe operation of current light water reactor fleet and the development of future reactor systems. The current UO{sub 2} fuel for LWRs has low thermal conductivity, which will be further reduced upon burn-up. The intrinsically low thermal transfer efficiency of the oxide fuels results in a large temperature gradient within the fuel pellet and high center-line temperature. Thermal swelling of the pellets and fission product accommodation and retention limit the lifetime of UO{sub 2} fuel in the reactor, presenting the great challenges for extending burn-up, effective utilization of nuclear resources and minimization of nuclear waste accumulation. Critical needs also exist in developing accident tolerant fuels that can tolerate loss of coolant accident or improve fuel performance under regular operation or beyond design scenario. Key properties of advanced fuels include high thermal conductivity, oxidation resistance, high temperature mechanical properties, fission gas retention capability and thus improved accident tolerance. The US Nuclear Energy Advanced Modeling and Simulation (NEAMS) program is developing science-based next generation fuel performance modeling capability as part its Fuel Product Line in order to facilitate the predictive capability of nuclear fuel performance and assist the design and analysis of reactor systems. Critical experimental data are needed to validate MARMOT models, particularly on effective thermal transport, fracture mechanisms, grain growth kinetics and fission gas behavior. The fabrication of sintered fuel pellets with well-controlled microstructure is prerequisite to establish the correlation of the microstructure features and fuel behavior in order to develop high fidelity fuel performance models. In this talk, recent advancements on developing advanced UO{sub 2} fuels and properties improvement are overviewed with the emphasis on different accident tolerant fuel (ATF) concepts and tailoring microstructures for MARMOT validation. Current efforts on ATFs include composite fuels and high-density fuels to improve thermal-mechanical properties and fission gas retention capabilities. Different composite UO{sub 2} fuels are fabricated with heterogeneous phases as sintering additives for microstructure and property control, and the potential application of the composites as advanced fuels with enhanced accident tolerance will be discussed. In addition, recent progresses of using field-assisted sintering technologies, specifically spark plasma sintering (SPS), in tailoring and engineering fuel matrix as the target systems for validating MARMOT physics models will be highlighted. Particularly, monolithic UO{sub 2} with tailored microstructure including grain size across multiple length scales from nano-metered to micron-sizes, porosity and stoichiometry can be sintered. The impacts of tailored microstructure on thermal-mechanical properties and grain growth kinetics are discussed within the context of the MARMOT modeling. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

The convergence of quadrupole rotational invariants from the nuclear shell model

Nuclei exhibit both single-particle and collective degrees of freedom, with the latter often subdivided into vibrational and rotational motions. Experimentally identifying the relative roles of these collective modes is extremely challenging, particularly in the face of possible shape coexistence. Model-independent, invariant quantities describing the deformation of a nucleus in the intrinsic frame have long been known but their determination potentially requires a large quantity of experimental data to achieve convergence. Through comparison with the nuclear shell model, the question of convergence is addressed. Shell-model calculations performed in the sd- and pf-shell model spaces are used to determine electric-quadrupole matrix elements for a multitude of low-lying states using the first 40 states of the relevant spins. Relative contributions to the rotationally invariant quantities from multiple states can therefore be determined. It is found that, on average, the inclusion of four intermediate states results in the leading-order invariant, $\langle\hat{Q^2}\rangle$, converging to within 10% of its true value and the triaxiality term, cos (3δ), converging to its true value, though some variance remains. Higher-order quantities relating to the softness of the nuclear shape are found to converge more slowly. The convergence of quadrupole rotationally invariant sum rules was quantified in the sd- and pf-shell model spaces and indicates the challenge inherent in a full determination of nuclear shape. The present study is limited to relatively small valence spaces. Finally, larger spaces, such as the rare-earth region, potentially offer faster convergence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but this Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Robust non-Abelian spin liquid and a possible intermediate phase in the antiferromagnetic Kitaev model with magnetic field

In this work, we investigate the non-Abelian topological chiral spin-liquid phase in the two-dimensional Kitaev honeycomb model subject to a magnetic field. By combining density matrix renormalization group and exact diagonalization we study the energy spectra, entanglement, topological degeneracy, and expectation values of Wilson loop operators, allowing for a robust characterization. While the ferromagnetic Kitaev spin liquid is already destroyed by a weak magnetic field with Zeeman energy $H^{FM}_\ast ≈ 0.02$, the antiferromagnetic (AFM) spin liquid remains robust up to a magnetic field that is an order of magnitude larger, $H^{AFM}_\ast ≈ 0.2$. Interestingly, for larger fields $H^{AFM}_\ast < H < H^{AFM}_{\ast\ast}$, an intermediate gapless phase is observed, before a second transition to the high-field partially polarized paramagnet. We attribute this rich phase diagram, and the remarkable stability of the chiral topological phase in the AFM Kitaev model, to the interplay of strong spin-orbit coupling and frustration enhanced by the magnetic field. Our findings suggest relevance to recent experiments on RuCl 3 under magnetic fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping

The one-dimensional (1D) 𝐽 1 −𝐽 2 𝑞-state Potts model is solved exactly for arbitrary 𝑞 by analytically block-diagonalizing the original 𝑞 2 ×𝑞 2 transfer matrix into a simple 2 × 2 maximally symmetric subspace, based on using OpenAI's reasoning model o3-mini-high to exactly solve the 𝑞 = 3 case. Furthermore, by matching relevant subspaces, we map the Potts model onto a simpler effective 1D 𝑞-state Potts model, where 𝐽 2 acts as the nearest-neighbor interaction and 𝐽 1 as an effective magnetic field, nontrivially generalizing a 56-year-old theorem previously limited to the simplest case (𝑞 = 2, the Ising model). Our exact results provide insights to phenomena such as atomic or electronic order stacking in layered materials and the emergence of dome-shaped phases in complex phase diagrams. In conclusion, this work is anticipated to fuel both research in 1D frustrated magnets for recently discovered finite-temperature application potentials and the fast moving topic area of AI in science.

1-dimensional spin chains↗
DOE OSTI2017

Alteration and Erosion of Rock Matrix Bordering a Carbonate-Rich Shale Fracture

A novel reactive transport model has been developed to examine the processes that affect fracture evolution in a carbonate-rich shale. An in situ synchrotron X-ray microtomography experiment, flowing CO 2 saturated water through a single fracture mini-core of Niobrara Shale provided the experimental observations for the development and testing of the model. The phenomena observed included the development of a porous altered layer, flow channeling, and increasingly limited calcite dissolution. The experimental observations cannot be explained by models that consider only mineral dissolution and development of an altered layer. The difference between the fracture volume change recorded by the microtomography images and what would be expected from mineral dissolution alone suggest that there is erosion of the altered layer as it develops. The numerical model includes this additional mechanism, with the erosion rate based on the thickness of the altered layer, and successfully captures the evolution of the geochemical reactions and morphology of the fracture. The findings imply that the abundance (with a threshold of approximately 35%) and reactivity of the rapidly reacting mineral control the development and erodibility of the altered layer on the fracture surfaces, and therefore fracture opening.

58 GEOSCIENCES↗
DOE OSTI2021

Four-Spin Terms and the Origin of the Chiral Spin Liquid in Mott Insulators on the Triangular Lattice

At strong repulsion, the triangular-lattice Hubbard model is described by s=1/2 spins with nearest-neighbor antiferromagnetic Heisenberg interactions and exhibits conventional 120° order. Using the infinite density matrix renormalization group and exact diagonalization, we study the effect of the additional four-spin interactions naturally generated from the underlying Mott-insulator physics of electrons as the repulsion decreases. Although these interactions have historically been connected with a gapless ground state with emergent spinon Fermi surface, we find that, at physically relevant parameters, they stabilize a chiral spin liquid (CSL) of Kalmeyer-Laughlin (KL) type, clarifying observations in recent studies of the Hubbard model. Finally, we present a self-consistent solution based on a mean-field rewriting of the interaction to obtain a Hamiltonian with similarities to the parent Hamiltonian of the KL state, providing a physical understanding for the origin of the CSL.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Modelling nearest neighbour distributions of biased tracers using hybrid effective field theory

ABSTRACT We investigate the application of hybrid effective field theory (HEFT) – which combines a Lagrangian bias expansion with subsequent particle dynamics from N-body simulations – to the modelling of k-nearest neighbour cumulative distribution functions (kNN-CDFs) of biased tracers of the cosmological matter field. The kNN-CDFs are sensitive to all higher order connected N-point functions in the data, but are computationally cheap to compute. We develop the formalism to predict the kNN-CDFs of discrete tracers of a continuous field from the statistics of the continuous field itself. Using this formalism, we demonstrate how kNN-CDF statistics of a set of biased tracers, such as haloes or galaxies, of the cosmological matter field can be modelled given a set of low-redshift HEFT component fields and bias parameter values. These are the same ingredients needed to predict the two-point clustering. For a specific sample of haloes, we show that both the two-point clustering and the kNN-CDFs can be well-fit on quasi-linear scales (≳ 20h−1Mpc) by the second-order HEFT formalism with the same values of the bias parameters, implying that joint modelling of the two is possible. Finally, using a Fisher matrix analysis, we show that including kNN-CDF measurements over the range of allowed scales in the HEFT framework can improve the constraints on σ8 by roughly a factor of 3, compared to the case where only two-point measurements are considered. Combining the statistical power of kNN measurements with the modelling power of HEFT, therefore, represents an exciting prospect for extracting greater information from small-scale cosmological clustering.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Higher-order triangular spectral element method with optimized cubature points for seismic wavefield modeling

The mass-lumped method avoids the cost of inverting the mass matrix and simultaneously maintains spatial accuracy by adopting additional interior integration points, known as cubature points. To date, such points are only known analytically in tensor domains, such as quadrilateral or hexahedral elements. Thus, the diagonal-mass-matrix spectral element method (SEM) in non-tensor domains always relies on numerically computed interpolation points or quadrature points. However, only the cubature points for degrees 1 to 6 are known, which is the reason that we have developed a p-norm-based optimization algorithm to obtain higher-order cubature points. In this way, we obtain and tabulate new cubature points with all positive integration weights for degrees 7 to 9. The dispersion analysis illustrates that the dispersion relation determined from the new optimized cubature points is comparable to that of the mass and stiffness matrices obtained by exact integration. Simultaneously, the Lebesgue constant for the new optimized cubature points indicates its surprisingly good interpolation properties. As a result, such points provide both good interpolation properties and integration accuracy. The Courant–Friedrichs–Lewy (CFL) numbers are tabulated for the conventional Fekete-based triangular spectral element (TSEM), the TSEM with exact integration, and the optimized cubature-based TSEM (OTSEM). A complementary study demonstrates the spectral convergence of the OTSEM. A numerical example conducted on a half-space model demonstrates that the OTSEM improves the accuracy by approximately one order of magnitude compared to the conventional Fekete-based TSEM. In particular, the accuracy of the 7th-order OTSEM is even higher than that of the 14th-order Fekete-based TSEM. Furthermore, the OTSEM produces a result that can compete in accuracy with the quadrilateral SEM (QSEM). The high accuracy of the OTSEM is also tested with a non-flat topography model. In terms of computational efficiency, the OTSEM is more efficient than the Fekete-based TSEM, although it is slightly costlier than the QSEM when a comparable numerical accuracy is required. - Highlights: • Higher-order cubature points for degrees 7 to 9 are developed. • The effects of quadrature rule on the mass and stiffness matrices has been conducted. • The cubature points have always positive integration weights. • Freeing from the inversion of a wide bandwidth mass matrix. • The accuracy of the TSEM has been improved in about one order of magnitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗