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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.

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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

SIMPLIFIED PREDICTIVE MODELS FOR CO₂ SEQUESTRATION PERFORMANCE ASSESSMENT RESEARCH TOPICAL REPORT ON TASK #3 STATISTICAL LEARNING BASED MODELS

We compare two approaches for building a statistical proxy model (metamodel) for CO₂ geologic sequestration from the results of full-physics compositional simulations. The first approach involves a classical Box-Behnken or Augmented Pairs experimental design with a quadratic polynomial response surface. The second approach used a space-filling maxmin Latin Hypercube sampling or maximum entropy design with the choice of five different meta-modeling techniques: quadratic polynomial, kriging with constant and quadratic trend terms, multivariate adaptive regression spline (MARS) and additivity and variance stabilization (AVAS). Simulations results for CO₂ injection into a reservoir-caprock system with 9 design variables (and 97 samples) were used to generate the data for developing the proxy models. The fitted models were validated with using an independent data set and a cross-validation approach for three different performance metrics: total storage efficiency, CO₂ plume radius and average reservoir pressure. The Box-Behnken–quadratic polynomial metamodel performed the best, followed closely by the maximin LHS–kriging metamodel.

Mishra, Srikanta↗
DOE OSTI2016

Coupled Neutron and Gamma Heating Calculation Based on VARIANT Nodal Transport Method

Accurate determination of temperature distributions in fuel pins and duct walls is essential for fuel-pin performance and assembly bowing analyses. Currently, the multi-assembly, sub-channel analysis code SE2-ANL is used in thermalhydraulic analysis of sodium cooled fast reactors (SFR). SE2- ANL is interfaced with the DIF3D/GAMSOR/DIF3D procedure for coupled neutron and gamma heating calculations, developed at Argonne National Laboratory (ANL). In this procedure, the neutron flux distribution is first calculated using the finite-difference diffusion theory option of the DIF3D code. Using the neutron flux solution, the GAMSOR code computes the gamma source distribution for the subsequent gamma flux calculation with DIF3D. However, in the current heating calculation scheme, the neutron and gamma flux calculations are limited to six triangular meshes per hexagonal assembly. In addition, the pin power distributions are estimated by assuming that the power distribution within an assembly is separable in the radial and axial directions. In each assembly, the axial power profile is obtained by averaging the power densities of six triangular meshes at each axial mesh interval. The radial power profile is evaluated at a single axial mesh (e.g., at the core mid-plane) by approximating the neutron and gamma flux distributions by a linear or quadratic polynomial of two variables x and y, depending on the polynomial order specified by the user. The coefficients of the linear and quadratic polynomials are determined by the least squares fit of six and 24 triangular mesh fluxes, respectively. Furthermore, the total heat generation rate in an assembly duct wall is simply determined by a user-specified fraction of the total gamma heating within that assembly. With the advancement of computer technology, the nodal transport theory code VARIANT is routinely used in core design analyses of SFR instead of DIF3D. It is therefore necessary to develop a new heating calculation procedure based on VARIANT neutron and gamma transport calculations. In this study, a new, coupled neutron and gamma heating calculation scheme has been developed to determine the pin power distributions more accurately by eliminating the aforementioned limitations of the current procedure. For this, the GAMSOR code has been extended to generate the intra-nodal gamma source distribution to be consistent with the trial functions of VARIANT. In the new heating calculation procedure, the neutron flux distribution is determined first by solving an eigenvalue transport problem using VARIANT. The obtained neutron flux is then used in GAMSOR to calculate the gamma source distribution. Using this gamma source distribution, the gamma flux distribution is determined by solving a fixed-source transport problem using VARIANT again. Using the computed neutron and gamma flux distributions, the power distribution in each fuel pin and duct wall is determined using a new utility code CURVE, which has been developed to evaluate the VARIANT flux solution at each fuel pin position and along the duct mid-wall. For each pin segment contained in a VARIANT node, the axial power shape is represented as a quadratic profile. The performance of the new heating calculation scheme based on VARIANT transport solutions has been tested against the existing method of SE2-ANL, using the ABR-1000 metal core design. The gamma source distribution and the assembly, fuel pin and duct wall power distributions were calculated and compared. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

Accessible solitons of fractional dimension

We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential. •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Stochastic modeling and statistical calibration with model error and scarce data

This paper introduces a procedure to assess the predictive accuracy of stochastic models subject to model error and sparse data. Model error is introduced as uncertainty on the coefficients of appropriate polynomial chaos expansions (PCE). The error associated with finite sample size allows us to conceive of these coefficients as statistics of the data that we describe as random variables whose influence on output quantities of interest is evaluated through the extended polynomial chaos expansion (EPCE). A Bayesian data assimilation scheme is introduced to update these expansions by considering the resulting nested chaos expansion as a hierarchical probabilistic model. Stochastic models of quantities of interest (QoI) are thus constructed and efficiently evaluated. Here, the Metropolis–Hastings Markov chain Monte Carlo procedure is used to sample the posterior. Two illustrative analytical and numerical problems are used to demonstrate the proposed approach.

Bayesian inference↗
DOE OSTI2014

Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems

We explore the relation between the development of a non-negligible probability of negative states and the instability of numerical integration of the intrusive Galerkin ordinary differential equation system describing uncertain chemical ignition. To prevent this instability without resorting to either multi-element local polynomial chaos (PC) methods or increasing the order of the PC representation in time, we propose a procedure aimed at modifying the amplitude of the PC modes to bring the probability of negative state values below a user-defined threshold. This modification can be effectively described as a filtering procedure of the spectral PC coefficients, which is applied on-the-fly during the numerical integration when the current value of the probability of negative states exceeds the prescribed threshold. We demonstrate the filtering procedure using a simple model of an ignition process in a batch reactor. This is carried out by comparing different observables and error measures as obtained by non-intrusive Monte Carlo and Gauss-quadrature integration and the filtered intrusive procedure. The filtering procedure has been shown to effectively stabilize divergent intrusive solutions, and also to improve the accuracy of stable intrusive solutions which are close to the stability limits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

GL(3,C) invariance of type B 3-fold supersymmetric systems

Type B 3-fold supersymmetry is a necessary and sufficient condition for a quantum Hamiltonian to admit three linearly independent local solutions in closed form. We show that any such a system is invariant under GL(3,C) homogeneous linear transformations. In particular, we prove explicitly that the parameter space is transformed as an adjoint representation of it and that every coefficient of the characteristic polynomial appeared in 3-fold superalgebra is algebraic invariants. In the type A case, it includes as a subgroup the GL(2,C) projective transformation studied in the literature. We argue that any N-fold supersymmetric system has a GL(N,C) invariance for an arbitrary integral N.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Mappings of open quantum systems onto chain representations and Markovian embeddings

We study systems coupled linearly to a bath of oscillators. In an iterative process, the bath is transformed into a chain of oscillators with nearest neighbour interactions. A systematic procedure is provided to obtain the spectral density of the residual bath in each step, and it is shown that under general conditions these data converge. That is, the asymptotic part of the chain is universal, translation invariant with semicircular spectral density. The methods are based on orthogonal polynomials, in which we also solve the outstanding so-called “sequence of secondary measures problem” and give them a physical interpretation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Periodic and chaotic oscillations in a tumor and immune system interaction model with three delays

In this paper, a tumor and immune system interaction model consisted of two differential equations with three time delays is considered in which the delays describe the proliferation of tumor cells, the process of effector cells growth stimulated by tumor cells, and the differentiation of immune effector cells, respectively. Conditions for the asymptotic stability of equilibria and existence of Hopf bifurcations are obtained by analyzing the roots of a second degree exponential polynomial characteristic equation with delay dependent coefficients. It is shown that the positive equilibrium is asymptotically stable if all three delays are less than their corresponding critical values and Hopf bifurcations occur if any one of these delays passes through its critical value. Numerical simulations are carried out to illustrate the rich dynamical behavior of the model with different delay values including the existence of regular and irregular long periodic oscillations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Fluid moments of the nonlinear Landau collision operator

An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary collisionality and flow.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

An Exponential Stability Result of a Timoshenko System with Thermoelasticity with Second Sound and in the Presence of Delay

In this paper, we consider a one-dimensional linear thermoelastic system of Timoshenko type with a delay, where the heat flux is given by Cattaneo’s law. We prove an exponential decay result under a smallness condition on the delay and a stability number introduced first in Santos et al. (J Diff Eqs 253:2715–2733, 2012), using a method different from that of Santos et al. (J Diff Eqs 253:2715–2733, 2012). We also reproduce the polynomial decay of Santos et al. (J Diff Eqs 253:2715–2733, 2012) using the multiplier method in the case of absence of delay. The polynomial decay issue in the presence of a small delay is an open question.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A 3D Ginibre Point Field

We introduce a family of three-dimensional random point fields using the concept of the quaternion determinant. The kernel of each field is an n-dimensional orthogonal projection on a linear space of quaternionic polynomials. We find explicit formulas for the basis of the orthogonal quaternion polynomials and for the kernel of the projection. For number of particles n→∞, we calculate the scaling limits of the point field in the bulk and at the center of coordinates. We compare our construction with the previously introduced Fermi-sphere point field process.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

On the Additive Structure and Asymptotics of Codimensions c{sub n} in the Algebra F{sup (5)}

In this paper, we investigate the additive structure of the algebra F{sup (5)}, i.e., a relatively free, associative, countably-generated algebra with the identity [x{sub 1}, . . . , x{sub 5}] = 0 over an infinite field of characteristic ≠2, 3. We study the space of proper multilinear polynomials in this algebra and means of basis construction in one of its basic subspaces. As an additional result, we obtain estimations of codimensions c{sub n} = dimP{sub n}/P{sub n}∩ T{sup (5)}, where P{sub n} is the space of multilinear polynomials of degree n in F{sup (5)} and T{sup (5)} is the T-ideal generated by the long commutator [x{sub 1}, . . . , x{sub 5}].

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Towards the Reverse Decomposition of Unipotents

Decomposition of unipotents gives short polynomial expressions of the conjugates of elementary generators as products of elementaries. It turns out that with some minor twist the decomposition of unipotents can be read backwards to give very short polynomial expressions of the elementary generators themselves in terms of elementary conjugates of an arbitrary matrix and its inverse. For absolute elementary subgroups of classical groups this was recently observed by Raimund Preusser. I discuss various generalizations of these results for exceptional groups, specifically those of types E{sub 6} and E{sub 7}, and also mention further possible generalizations and applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Electrochemical Frequency Modulation, Electrochemical Noise, and Atomic Force Microscopy Studies on Corrosion Inhibition Behavior of Benzothiazolone for Steel API X100 in 10% HCl Solution

In this work, electrochemical and surface techniques were applied to study the corrosion inhibition effects of benzothiazolone. 10% HCl was used to simulate the oil and gas well-acidizing fluid. Electrochemical frequency modulation and potentiodynamic polarization indicated that this material has excellent inhibiting features in very low concentrations. The influence of DC trend on electrochemical noise data was evaluated by polynomial fitting, and the optimum polynomial order m = 4 was obtained. After detrending, the charge of corrosion reaction obtained by electrochemical noise decreased with increasing inhibitor concentrations. In addition, the inhibition efficiencies from electrochemical noise were in agreement with data obtained by other electrochemical methods. Surface studies illustrated that the corroded surface was smoother in the presence of benzothiazolone. Electrochemical impedance and noise showed that benzothiazolone blocked the electrode surface by adsorption obeying Langmuir isotherm. According to quantum calculation, S atom in benzothiazolone indicated more tendencies for electrophilic attack in adsorption process. The main reason for high inhibition efficiencies in very low concentrations was the planar and simplicity of inhibitor structure which led to increasing the efficiency of adsorption by functional group especially sulfur.

36 MATERIALS SCIENCE↗
DOE OSTI2018

An efficient algorithm for the projection of a point on the intersection of two hyperplanes and a box in $\mathbb {R}^n$

Here, we present an efficient strongly polynomial algorithm for the projection of a point on the intersection of two hyperplanes and a box in \(\mathbb {R}^n\) . Interior point methods are the most efficient algorithm in the literature to solve this problem. While efficient in practice, the complexity of interior-point methods is bounded by a polynomial in the dimension of the problem and in the accuracy of the solution. Moreover, their efficiency is highly dependent on a series of parameters depending on the specific method chosen (especially for nonlinear problems), such as step size, barrier parameter, accuracy, among others. We propose a new method based on the KKT optimality conditions. In this method, we write the problem as a function of the Lagrangian multipliers of the hyperplanes and seek to find the pair of multipliers that corresponds to the optimal solution. We prove that the algorithm has complexity \(O(n^2 \log n)\) .

42 ENGINEERING↗
DOE OSTI2018

A new method approximating offset curve by Bézier curve using parallel derivative curves

In this paper, we present a new method for the offset approximation of an n-th degree Bézier curve by an n+1-th degree Bézier curve using parallel derivative curves. Our method is based on the Gauss map approximation of the n-th degree Bézier curve by the n+1-th degree Bézier curve whose derivative curve is parallel to that of the n-th degree Bézier curve. Thus, the convolution of the Gauss map approximation curve and n-th Bézier curve is a polynomial of degree n+1, which is our offset approximation of the n-th degree Bézier curve. Our approximation method has two advantages. One is that the offset approximation method yields a non-rational (polynomial) curve which is obtained by the simple sum of two Bézier curves. The other is that the offset approximation curve satisfying the endpoint interpolation of the given offset curve automatically has the same tangent lines as the offset curve at both endpoints. We illustrate our offset approximation method with some numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Hybridization of IMC and PID control structures based on filtered GPC using genetic algorithm

Classical and advanced hybridization methods are employed in the control literature to calibrate the tuning parameters of internal model control (IMC) and proportional-integral-derivative (PID) controllers. This paper presents an alternative tuning design for the generalized predictive controller (GPC) that is based on both the positional process model and cost function. The proposed method involves the selection of an integral polynomial weighting filter for reference and output signals to deal with reference tracking, disturbance rejection, model-plant mismatch (MPM), minimum control energy and closed-loop robustness. The filter positional GPC (FP-GPC) obtained is transformed into a two-degree-of-freedom polynomial filtered RST structure and then into filtered internal model control (F-IMC) and PID controllers. Also, a multi-objective optimization based on genetic algorithm is applied to tune the filter parameters. Numerical and experimental essays show the effectiveness of the proposed control methodology.

97 MATHEMATICS AND COMPUTING↗