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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↗

DOE OSTI2025

Relationship between microporous structure and light gas transport through glassy polymeric membranes revealed by molecular simulations

Microporous glassy polymers are attractive materials for gas separation membranes, due to their high permeability and tailorable selectivity, provided physical aging can be delayed. The archetypal microporous glassy polymer, PTMSP, can be blended with a hyper-crosslinked isatin–triptycene porous polymer network (PPN) to delay physical aging. However, while PPN is effective at reducing physical aging, it also affects the permeability of light gases through PTMSP. Molecular dynamics simulations were used here to shed fundamental light on the mechanisms responsible for these effects. Atomistic models are developed that satisfactorily reproduce experimental observations such as matrix density and cavity size distributions for neat PTMSP as well as for PTMSP–PPN blends. Analysis of the simulation results suggests that physical aging is delayed because the PPN inclusions slow down PTMSP relaxation while reducing the connectivity between free volume pockets. To understand how PPN inclusions affect light gas permeability, the atomistic models developed are used to probe CO 2 and CH 4 diffusion and sorption. These simulations are conducted for PTMSP matrices exhibiting varying density, towards reproducing experimental permeability data. Interrogating the simulation trajectories, it is discovered that while CH 4 travels preferentially through the free volume cavities, CO 2 preferentially interacts with the available surfaces, especially in the presence of PPN. These differences help interpret experimental observations. The transport of C 2 H 6 and H 2 S through PTMSP matrices was also investigated. These gases, and in particular H 2 S, were found to absorb within PTMSP, yielding very low diffusion coefficients. The ability to predict differences in diffusion pathways for various natural gas components unveils the possibility of engineering membranes to control permeability and selectivity towards large-scale applications.

Bao Le, Tran Thi [Univ. of Oklahoma, Norman, OK (U↗

DOE OSTI2022

A multisite decomposition of the tensor network path integrals

Tensor network decompositions of path integrals for simulating open quantum systems have recently been proven to be useful. However, these methods scale exponentially with the system size. This makes it challenging to simulate the non-equilibrium dynamics of extended quantum systems coupled with local dissipative environments. In this work, we extend the tensor network path integral (TNPI) framework to efficiently simulate such extended systems. The Feynman–Vernon influence functional is a popular approach used to account for the effect of environments on the dynamics of the system. In order to facilitate the incorporation of the influence functional into a multisite framework (MS-TNPI), we combine a matrix product state (MPS) decomposition of the reduced density tensor of the system along the sites with a corresponding tensor network representation of the time axis to construct an efficient 2D tensor network. The 2D MS-TNPI network, when contracted, yields the time-dependent reduced density tensor of the extended system as an MPS. The algorithm presented is independent of the system Hamiltonian. We outline an iteration scheme to take the simulation beyond the non-Markovian memory introduced by solvents. Applications to spin chains coupled to local harmonic baths are presented; we consider the Ising, XXZ, and Heisenberg models, demonstrating that the presence of local environments can often dissipate the entanglement between the sites. We discuss three factors causing the system to transition from a coherent oscillatory dynamics to a fully incoherent dynamics. The MS-TNPI method is useful for studying a variety of extended quantum systems coupled with solvents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

MICROSTRUCTURE EVOLUTION MODELING FOR SOLUTION TREATMENT OF ALUMINUM ALLOYS

The microstructure evolution during solution treatment plays an important role in mechanical properties of heat-treated aluminum alloys. In this paper, models were reviewed that can predict the microstructure evolution during the solutionizing process of the aging heat treatment of aluminum alloys. The dissolution of Mg2Si particles has been modeled as a diffusion process of Mg in the -Al matrix. The evolution of volumetric fraction of fragmented silicon as a function of time and temperature was also considered. The growth and coarsening of silicon particles during the heat treatment was considered. It was found that constitutive equations and required property data for most of the phenomena that need to be considered are available. Several model parameters that need to be obtained from material characterization were identified. Pending the availability of these model parameters, this comprehensive model can be used to describe the microstructure evolution of aluminum alloys in order to optimize the solutionizing heat treatment for energy savings.

Yin, Hebi↗

DOE OSTI2015

Equivalent Relaxations of Optimal Power Flow

Several convex relaxations of the optimal power flow (OPF) problem have recently been developed using both bus injection models and branch flow models. In this paper, we prove relations among three convex relaxations: a semidefinite relaxation that computes a full matrix, a chordal relaxation based on a chordal extension of the network graph, and a second-order cone relaxation that computes the smallest partial matrix. We prove a bijection between the feasible sets of the OPF in the bus injection model and the branch flow model, establishing the equivalence of these two models and their second-order cone relaxations. Our results imply that, for radial networks, all these relaxations are equivalent and one should always solve the second-order cone relaxation. For mesh networks, the semidefinite relaxation and the chordal relaxation are equally tight and both are strictly tighter than the second-order cone relaxation. Therefore, for mesh networks, one should either solve the chordal relaxation or the SOCP relaxation, trading off tightness and the required computational effort. Simulations are used to illustrate these results.

Bose, S↗

DOE OSTI2020

Non-Hermitian approach for quantum plasmonics

Herein, we examine the limits of applicability of a simple non-Hermitian model for exciton/plasmon interactions in the presence of dissipation and dephasing. The model can be used as an alternative to the more complete Lindblad density matrix approach and is computationally and conceptually simpler. We find that optical spectra in the linear regime can be adequately described by this approach. The model can fail, however, under continuous optical driving in some circumstances. In the case of two quantum dots or excitons interacting with a plasmon, the model can also describe coherences and entanglement qualitatively when both dissipation and dephasing are present and quantitatively in the limit with no dephasing. The approach, within a single excitation manifold, is also applied to assess the role of disorder for 50 quantum dots interacting with a plasmon, where we find that, on average, large enough disorder can help stabilize the ensemble average of the open quantum system toward a dark quasi-steady-state much faster than without disorder. Furthermore, while such single excitation manifold calculations in this size limit can readily be done with either the non-Hermitian or Lindblad forms, as one goes to larger Hilbert space sizes, the computational and storage advantages of the non-Hermitian approach can become more useful. Published under license by AIP Publishing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Optimizing Sparse Matrix-Multiple Vectors Multiplication for Nuclear Configuration Interaction Calculations

Obtaining highly accurate predictions on the properties of light atomic nuclei using the configuration interaction (CI) approach requires computing a few extremal Eigen pairs of the many-body nuclear Hamiltonian matrix. In the Many-body Fermion Dynamics for nuclei (MFDn) code, a block Eigen solver is used for this purpose. Due to the large size of the sparse matrices involved, a significant fraction of the time spent on the Eigen value computations is associated with the multiplication of a sparse matrix (and the transpose of that matrix) with multiple vectors (SpMM and SpMM-T). Existing implementations of SpMM and SpMM-T significantly underperform expectations. Thus, in this paper, we present and analyze optimized implementations of SpMM and SpMM-T. We base our implementation on the compressed sparse blocks (CSB) matrix format and target systems with multi-core architectures. We develop a performance model that allows us to understand and estimate the performance characteristics of our SpMM kernel implementations, and demonstrate the efficiency of our implementation on a series of real-world matrices extracted from MFDn. In particular, we obtain 3-4 speedup on the requisite operations over good implementations based on the commonly used compressed sparse row (CSR) matrix format. The improvements in the SpMM kernel suggest we may attain roughly a 40% speed up in the overall execution time of the block Eigen solver used in MFDn.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

A coupled thermo‐chemo‐mechanical reduced‐order multiscale model for predicting process‐induced distortions, residual stresses, and strength

Summary We study residual stresses and part distortion induced by a manufacturing process of a polymer matrix composite and its effect on the component strength. Unlike most of the thermo‐chemo‐mechanical models in the literature where governing multiphysics equations are directly formulated on the macroscale, we present a multiscale‐multiphysics approach. To address the enormous computational complexity involved, a reduced‐order homogenization was originally developed for a single physics problem is employed. The proposed reduced‐order two‐scale thermo‐chemo‐mechanical model has been validated for predicting part distortion beam strength in three‐point bending test. It is shown that while macroscopic stresses are relatively low, and therefore often ignored in practice, stresses at the scale of microconstituents are significant and may have an effect on the overall composite component strength.

Yuan, Zifeng↗