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All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Gauge structures: From stabilizer codes to continuum models

Stabilizer codes are a powerful method for implementing fault-tolerant quantum memory and in the case of topological codes, they form useful models for topological phases of matter. In this paper, we discuss the theory of stabilizer codes as a discrete version of a linear gauge structure, a concept we introduce here. A linear gauge structure captures all the familiar ingredients of U(1) gauge theory including a generalization of charge conservation, Maxwell equations and topological terms. Using this connection, we prove some important results for stabilizer codes which can be used to characterize their error-correction properties. However, this perspective does not depend on any particular Hamiltonian or Lagrangian, which as a consequence is agnostic to the source of the gauge redundancy. Based upon the connection to stabilizer codes, we view the source of the gauge redundancy as an ambiguity in the tensor product structure of the Hilbert space. That is, the gauge provides a set of equivalent but arbitrary ways to factorize the Hilbert space. We apply this formalism to the d=2 and 3 toric code as well as the paradigm fracton models, X-Cube and Haah’s cubic code. From this perspective, we are able to map all these models to some continuum version which captures all or some of the fractonic and topological features of their parent discrete models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Effect of surface loading and bulk doping of La{sup 3+} on the thermal stability and photocatalytic activity of Bi{sub 2}O{sub 2}CO{sub 3}

Graphical abstract: The Bi{sub 2}O{sub 2}O{sub 3} modified La{sup 3+} was synthesized using two methods of co-precipitation (La-Bi{sub 2}O{sub 2}O{sub 3}) and wet impregnation (La/Bi{sub 2}O{sub 2}O{sub 3}). As compared with La-Bi{sub 2}O{sub 2}O{sub 3}, Bi{sub 2}O{sub 2}CO{sub 3} can be effectively stabilized by impregnation method, as La{sup 3+} is mainly dispersed onto the surface of Bi{sub 2}O{sub 2}O{sub 3}. In photocatalytic degradation of MO, it is found that the surface modification with La{sup 3+} can enhance the photocatalytic efficiency of Bi{sub 2}O{sub 2}O{sub 3}. The surface loading La{sup 3+} could act as an effective electron scavenger to trap the CB electrons of Bi{sub 2}O{sub 2}CO{sub 3} to reduce the recombination of electrons and holes in the surface. - Highlights: • The effect of La{sup 3+} on the thermal stability of Bi{sub 2}O{sub 2}CO{sub 3} is different for the impregnation method and coprecipitation method. • Bi2O2CO3 can be effectively stabilized by impregnation method, as La3+ is mainly dispersed onto the surface of Bi2O2O3. • Surface loading La3+ is benefit for the improvement in the photocatalytic activity of Bi2O2CO3. • Surface modification of La3+ greatly suppresses the charge recombination of photogenerated electron–hole pairs in Bi2O2CO3. - Abstract: The Bi{sub 2}O{sub 2}O{sub 3} modified La{sup 3+} was synthesized using two methods of co-precipitation (La-Bi{sub 2}O{sub 2}O{sub 3}) and wet impregnation (La/Bi{sub 2}O{sub 2}O{sub 3}). The effects of the above two modification methods on the stability of Bi{sub 2}O{sub 2}CO{sub 3} after calcination and the physicochemical properties of Bi{sub 2}O{sub 2}CO{sub 3} were investigated by XRD, SEM, BET, and XPS. As compared with La-Bi{sub 2}O{sub 2}O{sub 3}, it is observed that Bi{sub 2}O{sub 2}CO{sub 3} can be effectively stabilized by impregnation method, as La{sup 3+} is mainly dispersed onto the surface of Bi{sub 2}O{sub 2}O{sub 3}. The photocatalytic activities for the methyl orange degradation for the La/Bi{sub 2}O{sub 2}CO{sub 3} and the La-Bi{sub 2}O{sub 2}CO{sub 3} samples were tested, and the results showed that surface doping (impregnation method) is benefit for the improvement in the photocatalytic activity, as compared with bulk doping (coprecipitation method). PL characterization revealed the differences in the photocatalytic process for surface doping and bulk doping. The surface modification of La{sup 3+} greatly suppresses the charge recombination of photogenerated electron−hole pairs in Bi{sub 2}O{sub 2}CO{sub 3}, which would be beneficial to improve their photocatalytic activity.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Application of linear prolongation to coarse mesh finite difference acceleration in CASMO5

The Coarse-Mesh Finite Difference (CMFD) method has been used for over a decade to accelerate the convergence of the Method of Characteristics (MOC) solution to the two- dimensional particle transport equation in CASMO5. Numerical testing, along with widespread use in production-level calculations, have shown that the current CMFD implementation provides stability and robustness for a wide range of realistic reactor physics problems. However, the recent development of linear prolongation has attracted attention from the community as a way to further improve the performance and stability of CMFD. Two interpolation methods for linear prolongation are presented in this work and implemented into a test version of CASMO5. The performance of the proposed interpolations, referred to as the bilinear and linear directional schemes, is evaluated in terms of runtime relative to the default constant or uniform scaling update. Numerical results indicate that the use of linear prolongation can reduce the transport solver runtime on average by approximately 10% when tested with two hundred randomly selected cases. The new directional linear interpolation, combined with default constant boundary updates, is found to provide the highest reduction in runtime for the cases analyzed. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

ROY Revisited, Again: The Eighth Solved Structure

X-ray powder diffraction and crystal structure prediction (CSP) algorithms were used in synergy to establish the crystal structure of the eighth polymorph of 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile (ROY), form R05. R05 crystallizes in the monoclinic space group P2_1 with lattice parameters a = 11.479(4) Å, b = 11.030(1) Å, c = 10.840(6) Å, β = 118.23(1)°. This is both the first acentric ROY polymorph, and the first with Z' > 1. The torsion angles defined by the S-C-N-C atom sequence of each molecule in the asymmetric unit are -34.0° and 44.9°. These angles fall between those previously determined for the red and orange forms of ROY. Hirshfeld surface analysis was employed to understand the crystal packing and intermolecular interactions in R05 and an updated energy stability ranking was determined using computational methods. Finally, although the application of CSP was critical to the structure solution of R05, energy stability rankings determined using a series of DFT vdW-inclusive models substantially deviate from experiment, indicating that ROY polymorphism continues to be a challenge for CSP.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Fourier Analysis of the Multilevel QD Method with {alpha}-Approximation For Time-Dependent Radiative Transfer Problems

Thermal radiation transfer (TRT) problems describe interaction of photon radiation with matter. They are defined by the time-dependent radiative transfer (RT) equation for the specific intensity I coupled with the energy balance (EB) equation. This class of problems is characterised by high dimensionality, multiple scales and strong nonlinearity. In this paper we analyze the multilevel quasi-diffusion (QD) method for solving TRT problems. This is a nonlinear method of moments with exact closures. The QD method enables one to reduce dimensionality of the original radiative transfer problem. It is formulated by a nonlinear system of equations consisting of (i) the high-order RT (HORT) equation for the intensity of photon radiation and (ii) low-order equations for the angular and energy moments of the intensity. The nonlinear closures are formulated by means of stable factors. The low-order problem brings the radiative transfer model to the level of multi-physics equations. The multilevel QD (MLQD) method possesses attractive features for efficient multi-physics coupling. To calculate the high-order RT solution we apply the {alpha}-approximation which assumes that the intensity changes exponentially in time over a time step. The {alpha}-approximation leads to the steady-state RT equation with a modified opacity and enables one to avoid storing the high-dimensional solution from the previous time step. The rate of change is evaluated by the solution of the time-dependent low-order QD (LOQD) equations for moments. We note that the HORT equation in the {alpha}-approximation contains an extra nonlinear term. It affects the iterative behaviour of the MLQD method. The obtained computational results indicated that the rate of convergence is slower compared to the rate when the time-dependent HORT is used to calculate the intensity. In this paper we perform an iterative stability analysis of the MLQD method in a discretized form and analyze convergence of outer (transport) iterations on a time step. We consider multigroup TRT problems in 1D slab geometry. The fully implicit scheme is used to discretize equations in time. The HORT equation is approximated with the method of step characteristics. A finite volume method is applied for spatial discretization of multigroup LOQD equations. The grey (one-group) LOQD equations are algebraically consistent with the multigroup LOQD equations. To perform Fourier analysis a model TRT problem in an infinite homogeneous medium is considered. The system of nonlinear equations of the MLQD method is linearized near an equilibrium solution at some given temperature. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Numerical methods for fractional Fokker–Planck equation with multiplicative Marcus Lévy noises

The Fokker–Planck equation (FPE) is an important deterministic tool for investigating stochastic dynamical systems. In this paper, we consider the space-time fractional FPE driven by multiplicative Marcus Lévy noises. Efficient numerical schemes are presented to solve the equations. Stability and convergence of the methods are also discussed. We give some numerical experiments to validate our schemes, and examine the effects of parameters on solutions. Additionally, we analyze the maximal likely trajectories and the critical time for the change of the most probability location.

Mathematics↗
DOE OSTI2018

Preparation of fluorescent carbon dots and their interaction with human-transferrin (hTf)

Highlights: • Glycine–modified Carbon dots (G-CDs) with high fluorescent quantum yield (QY = 31%) were prepared by microwave-assisted method. • G-CDs were stability at biological system, and had low cytotoxicity. • Human transferrin (hTf) had one type of binding site with G-CDs, and the fluorescence quenching mode was static quenching process. - Abstract: Luminescent carbon dots (CDs) are new fluorescent materials and widely used in biomedical fields. In this paper, CDs were prepared using citric acid and glycine (denoted G-CDs) by one-step microwave-assisted method and characterized by transmission electron microscopy (TEM), power X-ray diffraction (XRD), nuclear magnetic resonance ({sup 13}CNMR), and Fourier transform infrared (FT-IR). The results showed that glycine was better than PEG200 or hexadecyltrimethyl ammonium bromide (CTAB) as the modification in reaction. The prepared G-CDs had the sizes about 10 nm, high fluorescent quantum yield (QY) up to 31%, and stability at biological system. Moreover, G-CDs had low cytotoxicity. Our results verified that amino group (or secondary amines) had a significant effect on the QY; one-step microwave-assisted method was simple, efficient and green. The further experiments about the interaction of G-CDs with human transferrin (hTf) were also detected. Data showed that there was a strong interaction between G-CDs and hTf, and one type of binding site between them. The quenching mode of fluorescence of hTf with G-CDs was static quenching process.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Advanced Capabilities in GOMA 6.0 - Augmenting Conditions Automatic Continuation and Linear Stability Analysis

This document describes the form and use of three supplemental capabilities added to Goma during 1998 -- augmenting conditions, automatic continuation and linear stability analysis. Augmenting conditions allow the addition of constraints and auxiliary conditions which describe the relationship between unknowns, boundary conditions, material properties and post-processing extracted quantities. Automatic continuation refers to a family of algorithms (zeroth and first order here, single and multi-parameter) that allow tracking steady-state solution paths as material parameters or boundary conditions are varied. The stability analysis capability in Goma uses the method of small disturbances and superposition of normal modes to test the stability of a steady- state flow, i.e., it determines if the disturbance grows or decays in time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

An energy-stable time-integrator for phase-field models

Here, we introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Development of a high-temperature oven for the 28 GHz electron cyclotron resonance ion source

We have been developing the 28 GHz ECR ion source in order to accelerate high-intensity uranium beams at the RIKEN RI-beam Factory. Although we have generated U{sup 35+} beams by the sputtering method thus far, we began developing a high-temperature oven with the aim of increasing and stabilizing the beams. Because the oven method uses UO{sub 2}, a crucible must be heated to a temperature higher than 2000 °C to supply an appropriate amount of UO{sub 2} vapor to the ECR plasma. Our high-temperature oven uses a tungsten crucible joule-heated with DC current of approximately 450 A. Its inside dimensions are ϕ11 mm × 13.5 mm. Since the crucible is placed in a magnetic field of approximately 3 T, it is subject to a magnetic force of approximately 40 N. Therefore, we used ANSYS to carefully design the crucible, which was manufactured by machining a tungsten rod. We could raise the oven up to 1900 °C in the first off-line test. Subsequently, UO{sub 2} was loaded into the crucible, and the oven was installed in the 28 GHz ECR ion source and was tested. As a result, a U{sup 35+} beam current of 150 μA was extracted successfully at a RF power of approximately 3 kW.

43 PARTICLE ACCELERATORS↗
DOE OSTI2018

Towards a novel stellar opacity measurement scheme using stability properties of double ablation front structures

A novel method for bringing sample elements to hydrodynamic conditions relevant to the base of the solar convection zone is investigated. The method is designed in the framework of opacity measurements and exploits the temporal and spatial stability of hydrodynamic parameters in counter-propagating Double Ablation Front (DAF) structures. The physics of symmetric DAF structures is first studied in 1D geometries to assess the influence of tracer layers in the target. These results are used to propose an experimental design compatible with the OMEGA [Boehly et al., Opt. Commun. 133(1-6), 495–506 (1997)] laser. Radiative-hydrodynamic simulations conducted using the Chic code [Breil et al., Comput. Fluids 46, 161–167 (2011).] in 2D-axisymmetric geometries suggest that a Fe sample can be brought to an electron temperature of ∼160 eV and electron number density of ∼1.35 × 1023 cm−3. These parameters are reached during a 500 ps window with temporal variations of the order of 10 eV and 1022 cm−3, respectively. This allows for potential time-integrated spectral measurements. During that time, the sample is almost at local thermal equilibrium and 2D spatial gradients in the sample are less than 5% in a 360 μm diameter cylindrical volume, including the potential effects of Hot Electrons (HE) and typical uncertainties related to target fabrication and laser performances. The effects of HEs are assessed using an inline model in Chic. The HEs are found to deposit most of their energy in the cold and dense ablator between the two fronts, leading to a small efficiency loss on the DAF parameters. The calculations also suggest that negligible amounts of unabsorbed HEs are present in the probed volume, thus not affecting the atomic properties of the sample. Potential extensions of the current design to higher sample temperatures within the OMEGA capabilities are briefly discussed.

Colaïtis, A.↗
DOE OSTI2017

One-dimensional Lagrangian implicit hydrodynamic algorithm for Inertial Confinement Fusion applications

A new one-dimensional hydrodynamic algorithm, specifically developed for Inertial Confinement Fusion (ICF) applications, is presented. The scheme uses a fully conservative Lagrangian formulation in planar, cylindrical, and spherically symmetric geometries, and supports arbitrary equations of state with separate ion and electron components. Fluid equations are discretized on a staggered grid and stabilized by means of an artificial viscosity formulation. The space discretized equations are advanced in time using an implicit algorithm. The method includes several numerical parameters that can be adjusted locally. In regions with low Courant–Friedrichs–Lewy (CFL) number, where stability is not an issue, they can be adjusted to optimize the accuracy. In typical problems, the truncation error can be reduced by a factor between 2 to 10 in comparison with conventional explicit algorithms. On the other hand, in regions with high CFL numbers, the parameters can be set to guarantee unconditional stability. The method can be integrated into complex ICF codes. This is demonstrated through several examples covering a wide range of situations: from thermonuclear ignition physics, where alpha particles are managed as an additional species, to low intensity laser–matter interaction, where liquid–vapor phase transitions occur.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Electronic Structure and Phase Stability of Yb-filled CoSb 3 Skutterudite Thermoelectrics from First Principles

Filling the large voids in the crystal structure of the skutterudite CoSb$_3$ with rattler atoms $R$ provides an avenue for both increasing carrier concentration and disrupting lattice heat transport, leading to impressive thermoelectric performance. While the influence of $R$ on the lattice dynamics of skutterudite materials has been well studied, the phase stability of $R$-filled skutterudite materials and the influence of the presence and ordering of $R$ on the electronic structure remain unclear. Here, focusing on the Yb-filled skutterudite Yb$_x$Co$_4$Sb$_{12}$, we employ first-principles methods to compute the phase stability and electronic structure. Yb-filled CoSb$_3$ exhibits (1) a mild tendency for phase separation into Yb-rich and Yb-poor regions and (2) a strong tendency for chemical decomposition into Co--Sb and Yb--Sb binaries (i.e., CoSb$_3$, CoSb$_2$, and YbSb$_2$). We find that, at reasonable synthesis temperatures, configurational entropy stabilizes single-phase solid solutions with limited Yb solubility, in agreement with experiments. Filling CoSb$_3$ with Yb increases the band gap, enhances the carrier effective masses, and generates new low-energy ``emergent'' conduction band minima, which is distinct from the traditional band convergence picture of aligning the energies of existing band extrema. The explicit presence of $R$ is necessary to achieve the emergent conduction band minima, though the rattler ordering does not strongly influence the electronic structure. The emergent conduction bands are spatially localized in the Yb-rich regions, unlike the delocalized electronic states at the Brillouin zone center that form the unfilled skutterudite band edges.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Compact feature-aware Hermite-style high-order surface reconstruction

High-order surface reconstruction is now a commonly used technique for mesh generation and adaptation, geometric and physical modeling, and high-order numerical methods for solving partial differential equations (PDEs). However, surface reconstruction from a relatively coarse mesh remained a challenging problem, especially for surfaces with sharp features. Here in this paper, we introduce a new method to address this challenge by improving the previous state of the art, including continuous moving frames (CMF) and weighted averaging of local fittings (WALF) (Eng Comput 28 (2012)), in two aspects. First, we significantly improve the robustness of reconstruction from coarse meshes using a Hermite-style least squares approximation to incorporate normals of the surface and tangents of the feature curves. Second, we ensure both G 0 continuity and high-order accuracy of the reconstruction near sharp features by generating parametric surface elements with an iterative feature-aware parameterization. We present the theoretical framework of our method and compare it against point-based methods in terms of accuracy and stability. We demonstrate the use of the proposed technique in generating high-order meshes for finite element methods, and show that it enables nearly identical solutions as using the meshes generated from exact geometry, while allowing additional flexibility.

42 ENGINEERING↗
DOE OSTI2017

A single-stage flux-corrected transport algorithm for high-order finite-volume methods

We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. Here, we modify the classical algorithm by introducing a new computation for solution bounds at smooth extrema, as well as improving the preconstraint on the high-order fluxes. We compute the high-order fluxes via a method-of-lines approach with fourth-order Runge-Kutta as the time integrator. For computing low-order fluxes, we select the corner-transport upwind method due to its improved stability over donor-cell upwind. Several spatial differencing schemes are investigated for the high-order flux computation, including centered- difference and upwind schemes. We show that the upwind schemes perform well on account of the dissipation of high-wavenumber components. The new limiter method retains high-order accuracy for smooth solutions and accurately captures fronts in discontinuous solutions. Further, we need only apply the limiter once per complete time step.

97 MATHEMATICS AND COMPUTING↗