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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 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

3D full core BEAVRS using OpenMOC with transport equivalence

Using an optimized implementation of the three-dimension method of characteristics for neutron transport, as well as a novel equivalence method for transport calculations de- signed to recover self-shielding errors from neglecting the angular dependence of reso- nant group absorption, a 3D full core light water reactor hybrid stochastic-deterministic eigenvalue calculation was achieved. This paper presents the optimizations developed and compares the transport solutions obtained. It realizes a runtime near 6,000 CPU hours for the statepoint, an improvement of an order of magnitude on previous works, with less than 1% error on pin fission/U-238 capture ratios and a few dozen pcms on the eigenvalue.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Development of a Representative Molten Chloride Fast Reactor Model to Assess the Impact of Nuclear Data

The SCALE code system was employed to conduct a preliminary investigation of nuclear data impacts for a fast spectrum molten chloride salt reactor. A computationally effective depletion model that is representative of the reactor system was successfully developed and used to conduct fuel depletion simulations. Development of this model draws from the SLICE method that was developed at Oak Ridge National Laboratory to enable generation of fuel compositions for an advanced reactor core at equilibrium operation. Eigenvalue uncertainty calculations using the ENDF/B-VII.1 nuclear data library were performed for the reactor in the fresh fuel state and an irradiated fuel state. It was determined that the primary driver of eigenvalue uncertainty was the uncertainty in the 235U (n, 𝛾) cross section. Uncertainty calculation results from this study were compared to results available for a different fast system, a sodium-cooled fast reactor, to confirm similarities and identify differences with respect to nuclear data impacts between the two fast advanced reactor systems.

Hirji, Rakim [Georgia Institute of Technology]↗
DOE OSTI2018

Real Space Renormalization Group Investigation of the Mixed Spins S = 1/2 and S = 3/2 Model

Using a real-space renormalization approach, namely the Migdal-Kadanoff one, we study the mixed Ising system with spins S = 1/2 and S = 3/2 on d-dimensional hypercubic lattice. We have determined the phase diagram in the plane (Δ/|J|, 1/|J|) as well as the eigenvalues of the transformation of the group in the vicinity of the critical points. A comparison with the results of other techniques was carried out.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Theory of Green’s Functions of Nambu-Goldstone and Higgs Modes in Superconductors

We examine fundamental properties of Green’s functions of Nambu-Goldstone and Higgs modes in superconductors with multiple order parameters. Nambu-Goldstone and Higgs modes are determined once the symmetry of the system and that of the order parameters are specified. Multiple Nambu-Goldstone modes and Higgs modes exist when we have multiple order parameters. The Nambu-Goldstone Green function D(ω, q) has the form 1/(gN(0)){sup 2}⋅(2Δ){sup 2}/(ω{sup 2}−c{sub s}{sup 2}q{sup 2}) with the coupling constant g and c{sub s}=v{sub F}/√3 for small ω and q, with a pole at ω = 0 and q = 0 indicating the existence of a massless mode. It is shown, based on the Ward-Takahashi identity, that the massless mode remains massless in the presence of intraband scattering due to non-magnetic and magnetic impurities. The pole of D(ω, q), however, disappears as ω increases as large as 2Δ: ω∼2Δ. The Green function H(ω, q) of the Higgs mode is given by H(ω,q)∝(2Δ){sup 2}/((2Δ){sup 2}−(1/3)ω{sup 2}+(1/3)c{sub s}{sup 2}q{sup 2}) for small ω and q, and H(ω, q) is proportional to 1/(gN(0)){sup 2}⋅Δ/√((2Δ){sup 2}+c{sub s}{sup 2}q{sup 2}−ω{sup 2}) for ω∼2Δ with the cut in the interval − ω(q) ≤ z ≡ q{sub 0} ≤ ω(q) where ω(q)=√((2Δ){sup 2}+c{sub s}{sup 2}q{sup 2}). The constant part of the action for the Higgs modes is important since it determines the coherence length of a superconductor. There is the case that it has a large eigenvalue, indicating that the large upper critical field H{sub c2} may be realized in a superconductor with multiple order parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2018

Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality

We prove tail triviality of determinantal point processes μ on continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for Sine{sub 2},Airy{sub 2},Bessel{sub 2}, and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Resonances in a Chaotic Attractor Crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle–Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The ϵ Expansion and Universality in Three Dimensions

It has been observed that the classification into universality classes of critical behavior, as established by perturbative renormalization group in the vicinity of four or six dimensions of space by the epsilon expansion, remains valid down to three dimensions in all known cases, even when perturbative renormalization group fails in lower dimensions. In this paper we argue that this classification into universality classes remains true in lower dimensions of space, even when perturbative renormalization group fails, because of the well known phenomenon of eigenvalue repulsion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Systems of Functions Orthogonal Over the Domain and Their Application in Boundary-Value Problems of Mathematical Physics

We formulate a boundary-value problem for eigenvalues and eigenfunctions of the Helmholtz equation in a complex domain with the use of mutually conjugated complex variables. The obtained systems of functions are orthogonal in this domain and constructed by using the Bessel functions and powers of the conformal mappings of the analyzed domains onto a circle. The solutions of boundary-value problems for the principal equations of mathematical physics (hyperbolic, parabolic and elliptic types) are obtained in the form of the sums of series in the systems of functions orthogonal over the domain.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Oscillation, Rotation, and Wandering of Solutions to Linear Differential Systems

For solutions of a linear system on the semi-axis, we introduce a series of Lyapunov exponents that describe the oscillation, rotation, and wandering properties of these solutions. In the case of systems with constant matrices, these exponents are closely related to the imaginary parts of the eigenvalues. We examine the problem on the existence of a similar relationship in the case of piecewise constant of arbitrary systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Cliffed Cape Does Not Trap Water Waves in the Sea of Constant Depth

The water wave problem is considered for a class of semi-infinite domains each having its shore shaped as a cliffed cape. In particular, the free surface of a water domain is supposed to be an infinite sector whose vertex angle is greater than π, whereas the water layer lying under the free surface is of constant depth. Under these assumptions it is shown that there are no trapped mode solutions of the problem for all values of a non-dimensional spectral parameter; in other words, no point eigenvalues are embedded in the continuous spectrum of the problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

On the Determinantal Range of Matrix Products

Let matrices A,C ∈ M{sub n} have eigenvalues α{sub 1}, . . ., α{sub n} and γ{sub 1}, . . . , γ{sub n}, respectively. The set of complex numbers D{sub C}(A) = {det(A−UCU*) : U ∈ M_n, U*U = I_n} is called the C-determinantal range of A. The paper studies various conditions under which the relation D{sub C}(R S) = D{sub C}(S R) holds for some matrices R and S.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

On Some Degenerate Elliptic Equations Arising in Geometric Problems

We consider some fully nonlinear degenerate elliptic operators and we investigate the validity of certain properties related to the maximum principle. In particular, we establish the equivalence between the sign propagation property and the strict positivity of a suitably defined generalized principal eigenvalue. Furthermore, we show that even in the degenerate case considered in the present paper, the well-known condition introduced by Keller–Osserman on the zero-order term is necessary and sufficient for the existence of entire weak subsolutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Localized Pisot Matrices and Joint Approximations of Algebraic Numbers

A development of the simplex-module algorithm for expansion of algebraic numbers in multidimensional continued fractions is proposed. To this end, localized Pisot matrices are constructed, whose eigenvalues with moduli less than one are contained in an interval of small length. Such Pisot matrices generate continued fractions whose convergents are arbitrarily close to the best approximations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Asymptotics of the Resonant Tunneling of High-Energy Electrons in Two-Dimensional Quantum Waveguides of Variable Cross-Section

A waveguide occupies a strip in ℝ{sup 2} having two identical narrows of small diameter ε. An electron wave function satisfies the Helmholtz equation with the homogeneous Dirichlet boundary condition. The energy of electrons may be rather high, i.e., any (fixed) number of waves can propagate in the strip far from the narrows. As ε → 0, a neighborhood of a narrow is assumed to transform into a neighborhood of the common vertex of two vertical angles. The part of the waveguide between the narrows as ε = 0 is called the resonator. An asymptotics of the transmission coefficient is obtained in the waveguide as ε → 0. Near a degenerate eigenvalue of the resonator, the leading term of the asymptotics has two sharp peaks. Positions and shapes of the resonant peaks are described.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Analyzing honeycomb photonic crystal waveguides by Dirichlet-to-Neumann maps

As an analog to graphene, honeycomb photonic crystals (PhCs) have attracted a great deal of interest in recent years. The additional degrees of freedom in a honeycomb PhC are useful in designing and optimizing waveguides, can be used to control the symmetry of the system and to realize novel optical devices. In this paper, we present an efficient numerical method for analyzing two-dimensional honeycomb PhC waveguides. Our method is based on a special supercell that covers one period of the honeycomb PhC waveguide and the so-called Dirichlet-to-Neumann map of the supercell. The method gives rise to a linear eigenvalue value problem with relatively small matrices, and it is validated by comparing with previous works. As an application of the method, we calculate edge modes for a few different PhCs. For a honeycomb PhC with dielectric rods in air, we found an edge mode at the zigzag edge, without using special modified rods at the edge. For a honeycomb PhC with air holes, we found a new edge mode when the PhC is bounded by a perfectly electric conductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Alternative trajectories of electron density to plot the atomic connectivity graph in the region of nondirectional interactions

Model supramolecular associates possessing nondirectional intermolecular interactions were investigated in order to demonstrate the opportunity of plotting of an atomic connectivity graph based on trajectories of Hessian eigenvector of electron density corresponding to the largest eigenvalue. Such trajectories are a reasonable alternative to the gradient bond paths in the case of proximity of the latter to the T-shaped form upon the presence of parallel surface of the zero-flux of electron density in the neighborhood of gradient-based trajectory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A new relaxed splitting preconditioner for the generalized saddle point problems from the incompressible Navier–Stokes equations

Based on the modified relaxed splitting (MRS) preconditioner proposed by Fan and Zhu (Appl Math Lett 55:18–26, 2016), a new relaxed splitting preconditioner is proposed for the generalized saddle point problems arising from the incompressible Navier–Stokes equations. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are analyzed. Numerical results show that the proposed preconditioner is superior to the MRS preconditioner when they are used as preconditioners to accelerate the convergence rate of the Krylov subspace methods, such as GMRES.

97 MATHEMATICS AND COMPUTING↗