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All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Numerical simulation using vorticity-vector potential formulation

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Tokunaga, Hiroshi↗
DOE OSTI2016

The NonConforming Virtual Element Method for the Stokes Equations

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functions is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

On the Feynman-alpha method for reflected fissile assemblies

The Feynman-alpha method is a neutron noise technique that is used to estimate the prompt neutron period of fissile assemblies. The method and quantity are of widespread interest including in applications such as nuclear criticality safety, safeguards and nonproliferation, and stockpile stewardship; the prompt neutron period may also be used to infer the k eff multiplication factor. The Feynman-alpha method is predicated on time-correlated neutron detections that deviate from a Poisson random variable due to multiplication. Traditionally, such measurements are diagnosed with one-region point kinetics, but two-region models are required when the fissile assembly is reflected. This paper presents a derivation of the two-region point kinetics Feynman-alpha equations based on a double integration of the Rossi-alpha equations, develops novel propagation of measurement uncertainty, and validates the theory. Validation is achieved with organic scintillator measurements of weapons-grade plutonium reflected by various amounts of copper to achieve k eff values of 0.83–0.94 and prompt periods of 5–75 ns. The results demonstrate that Feynman-alpha measurements should use the two-region model instead of the one-region model. The simplified one-region model deviates from the validated two-region models by as much as 10% in the estimate of the prompt neutron period, and the two-region model reduces to the one-region model for small amounts of reflector. The Feynman-alpha estimates of the prompt neutron period are compared to those of the Rossi-alpha approach. The comparative results demonstrate that the Feynman-alpha method is more precise than the Rossi-alpha method and more accurate for k eff < 0.92, whereas the Rossi-alpha method is generally more accurate for higher multiplications. Here, the uncertainty propagation developed in this work should be used for all Feynman-alpha measurements and will therein improve fitting accuracy and appropriate precision estimates.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2019

Localization in Fractonic Random Circuits

We study the spreading of initially local operators under unitary time evolution in a one-dimensional random quantum circuit model that is constrained to conserve a U ( 1 ) charge and also the dipole moment of this charge. These constraints are motivated by the quantum dynamics of fracton phases. We discover that the charge remains localized at its initial position, providing a crisp example of a nonergodic dynamical phase of random circuit dynamics. This localization can be understood as a consequence of the return properties of low-dimensional random walks, through a mechanism reminiscent of weak localization, but insensitive to dephasing. The charge dynamics is well described by a system of coupled hydrodynamic equations, which makes several nontrivial predictions that are all in good agreement with numerics in one dimension. Importantly, these equations also predict localization in two-dimensional fractonic random circuits. We further find that the immobile fractonic charge emits nonconserved operators, whose spreading is governed by exponents that are distinct from those observed in nonfractonic circuits. These nonstandard exponents are also explained by our coupled hydrodynamic equations. Where entanglement properties are concerned, we find that fractonic operators exhibit a short time linear growth of observable entanglement with saturation to an area law, as well as a subthermal volume law for operator entanglement. The entanglement spectrum is found to follow semi-Poisson statistics, similar to eigenstates of many-body localized systems. The nonergodic phenomenology is found to persist to initial conditions containing nonzero density of dipolar or fractonic charge, including states near the sector of maximal charge. Our work implies that low-dimensional fracton systems should preserve forever a memory of their initial conditions in local observables under noisy quantum dynamics, thereby constituting ideal memories. It also implies that one- and two-dimensional fracton systems should realize true many-body localization (MBL) under Hamiltonian dynamics, even in the absence of disorder, with the obstructions to MBL in translation-invariant systems and in spatial dimensions greater than one being evaded by the nature of the mechanism responsible for localization. We also suggest a possible route to new nonergodic phases in high dimensions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Harmonic statistics

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

A composite L-band HH radar backscattering model for coniferous forest stands

The radar backscattering model developed by Richards et al. (1987), has been improved and further tested in this research. The trunk term may now be calculated from the exact solution to the electromagnetic wave equations instead of the corner reflector equation. Rough surface models have been introduced into the radar model, so that the forward reflectance and the backscattering from the ground surface are now calculated from the same model and, thus, are consistent. The number of trees in an individual pixel is assumed to be Poisson distributed, with tree height in a stand log-normally distributed. The simulated results show that the match of backscattering coefficients for eight forest stands between SIR-B image data and the simulated results are satisfying, and that the trunk term now seems to be convincingly established as the dominant term in the L-band HH radar return from coniferous forest stands.

Sun, Guoquing↗
DOE OSTI2017

Quantum groups as generalized gauge symmetries in WZNW models. Part I. The classical model

Wess-Zumino-Novikov-Witten (WZNW) models over compact Lie groups G constitute the best studied class of (two dimensional, 2D) rational conformal field theories (RCFTs). A WZNW chiral state space is a finite direct sum of integrable representations of the corresponding affine (current) algebra, and the correlation functions of primary fields are monodromy invariant combinations of left times right sector conformal blocks solving the Knizhnik-Zamolodchikov equation. However, even in this very well understood case of 2D RCFT, the “internal” (gauge) symmetry that governs the ensuing fusion rules remains unclear. On the other hand, the canonical approach to the classical chiral WZNW theory developed by Faddeev, Alekseev, Shatashvili, Gawedzki and Falceto reveals its Poisson-Lie symmetry. After a covariant quantization, the latter gives rise to an associated quantum group symmetry which naturally requires an extension of the state space. This paper contains a review of earlier work on the subject with a special emphasis, in the case G = SU(n), on the emerging chiral “WZNW zero modes” which provide an adequate algebraic description of the internal symmetry structure of the model. Combining further left and right zero modes, one obtains a specific dynamical quantum group, the structure of its Fock representation resembling the axiomatic approach to gauge theories in which a “restricted” quantum group plays the role of a generalized gauge symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

An integral transform technique for kinetic systems with collisions

The linearized Vlasov-Poisson system can be exactly solved using the G-transform, an integral transform introduced in Morrison and Pfirsch [Phys. Fluids B 4, 3038–3057 (1992)] and Morrison [Phys. Plasmas 1, 1447 (1994); Transp. Theory Stat. Phys. 29, 397 (2000)] that removes the electric field term, leaving a simple advection equation. We investigate how this integral transform interacts with the Fokker-Planck collision operator. The commutator of this collision operator with the G-transform (the “shielding term”) is shown to be negligible. We exactly solve the advection-diffusion equation without the shielding term. This solution determines when collisions dominate and when advection (i.e., Landau damping) dominates. This integral transform can also be used to simplify gyro-/drift-kinetic equations. We present new gyrofluid equations formed by taking moments of the G-transformed equation. Since many gyro-/drift-kinetic codes use Hermite polynomials as base elements, we include an explicit calculation of their G-transform

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

TH-A-18C-08: Design of a Small Animal Contrast Enhanced Dual Energy CT

Purpose: Dual energy CT has a variety of uses in a small animal setting including quantification and enhanced visualization of contrast agent. This study aims to determine the best energy combinations for contrast enhanced DECT on the XRAD 225Cx (Precision x-ray), a small animal IGRT system with a nominal energy range of 20 – 225 kVp. Focus was placed on material density accuracy and low contrast detectability. Methods: Simulations of single energy scans of an object containing concentrations of iodine varying from 0.5 to 50 mg/ml were performed using the simulation package ImaSim. Energy spectra from 50 – 220 kVp were calculated using the same software. For approximate Poisson noise modeling, mAs were chosen such that 30% of the total 10cGy dose was assigned to the low energy scan. A calibration involving projections of objects containing different thicknesses of iodine (0–0.5 mm) and water (0–50 mm) was performed for each energy and fit to a cubic equation as the calibration curve for each energy pair. Results: Contrast to noise ratios of the iodine material images and accuracies in iodine density measurements were measured. Gradual improvements in each metric were seen with increasing high energy. Larger improvements in CNR were observed for decreasing the low energy. Errors in iodine density were generally close to 5% for concentrations of iodine above 3 mg/ml but increased to around 15% for 50 kVp, likely due to its proximity to the discontinuity caused by the k-edge of iodine. Conclusion: Based on these simulations, the best energy combination for detecting low concentrations of iodine using a projection space calibration procedure is 50/200 kVp. However, if accuracy is most important 80/220 kVp is ideal, with 60/220 kVp being a good compromise to achieve both goals. Future work is necessary to verify these conclusions with physical data.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1993

Projection techniques for iterative solution of A(bar x) equals (bar b) with successive right-hand sides

Two projection techniques for computing approximate solutions to linear systems of the form A(bar x)(sup n) = (bar b)(sup n), for a sequence n = 1, 2, ..., e.g., such as arises from time discretization of a partial differential equation, are presented. The inexpensive approximate solutions can be used as initial guesses for iterative solution of the system, resulting in significantly reduced computational expense. Examples of two- and three-dimensional incompressible Navier-Stokes calculations are presented in which x represents the pressure, and A is a discrete Poisson operator. In flows containing significant dynamic activity, these projection techniques lead to as much as a two-fold reduction in solution time.

Fischer, Paul F.↗
DOE OSTI2019

Multiresolution spatiotemporal mechanical model of the heart as a prior to constrain the solution for 4D models of the heart

In several nuclear cardiac imaging applications (SPECT and PET), images are formed by reconstructing tomographic data using an iterative reconstruction algorithm with corrections for physical factors involved in the imaging detection process and with corrections for cardiac and respiratory motion. The physical factors are modeled as coefficients in the matrix of a system of linear equations and include attenuation, scatter, and spatially varying geometric response. The solution to the tomographic problem involves solving the inverse of this system matrix. This requires the design of an iterative reconstruction algorithm with a statistical model that best fits the data acquisition. The most appropriate model is based on a Poisson distribution. Using Bayes Theorem, an iterative reconstruction algorithm is designed to determine the maximum a posteriori estimate of the reconstructed image with constraints that maximizes the Bayesian likelihood function for the Poisson statistical model. The a priori distribution is formulated as the joint entropy (JE) to measure the similarity between the gated cardiac PET image and the cardiac MRI cine image modeled as a FE mechanical model. In conclusion, the developed algorithm shows the potential of using a FE mechanical model of the heart derived from a cardiac MRI cine scan to constrain solutions of gated cardiac PET images.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Poisson-Boltzmann Theory with Non-Linear Ion Correlations

The Poisson-Boltzmann (PB) theory is widely used to depict ionic systems in a mean-field manner without considering the correlations between ions. A modified theory including ion correlation effect while retaining the simplicity of the original PB theory is desired. Although recent theoretical efforts successfully incorporate ion correlations into the PB equation as the self-energy, the results deviate significantly from our molecular dynamics (MD) simulation results due to the linear form of the self-energy. We herein reinterpret the self-energy term from a physics point of view, on the basis of which we present a new way for incorporating ion correlations into the original PB equation by utilizing the Green’s function with a non-linear form of the self-energy. Justified by our MD simulation results, our modified PB theory with non-linear ion correlations surpasses linearly formed modified PB theories.

Su, Mao↗
NASA NTRS1994

Scaling, elasticity, and CLPT

The first few viewgraphs describe the general solution properties of linear elasticity theory which are given by the following two statements: (1) for stress B.C. on S(sub sigma) and zero displacement B.C. on S(sub u) the altered displacements u(sub i)(*) and the actual stresses tau(sub ij) are elastically dependent on Poisson's ratio nu alone: thus the actual displacements are given by u(sub i) = mu(exp -1)u(sub i)(*); and (2) for zero stress B.C. on S(sub sigma) and displacement B.C. on S(sub u) the actual displacements u(sub i) and the altered stresses tau(sub ij)(*) are elastically dependent on Poisson's ratio nu alone: thus the actual stresses are given by tau(sub ij) = E tau(sub ij)(*). The remaining viewgraphs describe the minimum parameter formulation of the general classical laminate theory plate problem as follows: The general CLT plate problem is expressed as a 3 x 3 system of differential equations in the displacements u, v, and w. The eighteen (six each) A(sub ij), B(sub ij), and D(sub ij) system coefficients are ply-weighted sums of the transformed reduced stiffnesses (bar-Q(sub ij))(sub k); the (bar-Q(sub ij))(sub k) in turn depend on six reduced stiffnesses (Q(sub ij))(sub k) and the material and geometry properties of the k(sup th) layer. This paper develops a method for redefining the system coefficients, the displacement components (u,v,w), and the position components (x,y) such that a minimum parameter formulation is possible. The pivotal steps in this method are (1) the reduction of (bar-Q(sub ij))(sub k) dependencies to just two constants Q(*) = (Q(12) + 2Q(66))/(Q(11)Q(22))(exp 1/2) and F(*) - (Q(22)/Q(11))(exp 1/2) in terms of ply-independent reference values Q(sub ij); (2) the reduction of the remaining portions of the A, B, and D coefficients to nondimensional ply-weighted sums (with 0 to 1 ranges) that are independent of Q(*) and F(*); and (3) the introduction of simple coordinate stretchings for u, v, w and x,y such that the process is neatly completed.

Brunelle, Eugene J.↗
DOE OSTI2013

An exact Jacobi map in the geodesic light-cone gauge

The remarkable properties of the recently proposed geodesic light-cone (GLC) gauge allow to explicitly solve the geodesic-deviation equation, and thus to derive an exact expression for the Jacobi map J{sup A}{sub B}(s,o) connecting a generic source s to a geodesic observer o in a generic space time. In this gauge J{sup A}{sub B} factorizes into the product of a local quantity at s times one at o, implying similarly factorized expressions for the area and luminosity distance. In any other coordinate system J{sup A}{sub B} is simply given by expressing the GLC quantities in terms of the corresponding ones in the new coordinates. This is explicitly done, at first and second order, respectively, for the synchronous and Poisson gauge-fixing of a perturbed, spatially-flat cosmological background, and the consistency of the two outcomes is checked. Our results slightly amend previous calculations of the luminosity-redshift relation and suggest a possible non-perturbative way for computing the effects of inhomogeneities on observations based on light-like signals.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Experimental and theoretical studies on the elasticity of tungsten to 13 GPa

Compressional (V_P) and shear wave (V_S) velocities of polycrystalline tungsten have been measured up to ~13 GPa at room temperature using ultrasonic interferometry in a multi-anvil apparatus. Using finite strain equation of state approaches, the elastic bulk and shear moduli and their pressure dependences are derived yielding $K_{S0}$= 325.9 ± 4.8 GPa, $G_0$ =164.1±2.5 GPa, $K^{'}_{S0}$ =3.65 ± 0.05 and $G^{'}_0$ =1.28 ± 0.02. On the basis of the current experimental data, the high-pressure behavior of Young’s modulus, Poisson’s ratio and ductility/brittleness for tungsten are also investigated. Complementary to the experimental data, the single crystal elastic constants, as well as the elastic anisotropy of tungsten are computed using density functional theory (DFT). The Voigt-Reuss-Hill average of the bulk and shear moduli calculated using the single crystal elastic constants from DFT are found comparable to the current experimental results within about 5%. Here, the present study offers a dataset for the elasticity of polycrystalline bcc tungsten to a maximum pressure more than 25-fold higher than other previous ultrasonic studies, which can further our understanding about the elastic, mechanical and electronic properties of tungsten under extreme conditions as well as thermodynamic modelling of its alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Covariant phase space with boundaries

The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original literature however does not systematically treat total derivatives and boundary terms, which has led to some confusion about how exactly to apply the formalism in the presence of boundaries. In particular the original construction of the canonical Hamiltonian relies on the assumed existence of a certain boundary quantity “B”, whose physical interpretation has not been clear. We here give an algorithmic procedure for applying the covariant phase space formalism to field theories with spatial boundaries, from which the term in the Hamiltonian involving B emerges naturally. Our procedure also produces an additional boundary term, which was not present in the original literature and which so far has only appeared implicitly in specific examples, and which is already nonvanishing even in general relativity with sufficiently permissive boundary conditions. The only requirement we impose is that at solutions of the equations of motion the action is stationary modulo future/past boundary terms under arbitrary variations obeying the spatial boundary conditions; from this the symplectic structure and the Hamiltonian for any diffeomorphism that preserves the theory are unambiguously constructed. We show in examples that the Hamiltonian so constructed agrees with previous results. We also show that the Poisson bracket on covariant phase space directly coincides with the Peierls bracket, without any need for non-covariant intermediate steps, and we discuss possible implications for the entropy of dynamical black hole horizons.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Evolution of the phase-space density and the Jeans scale for dark matter derived from the Vlasov-Einstein equation

We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedmann universe. We show that, after decoupling from the primordial plasma, the dark matter phase-space density indicator Q = ρ/(σ{sub 1D}{sup 2}){sup 3/2} remains constant during the expansion of the universe, prior to structure formation. This well known result is valid for non-relativistic particles and is not ''observer dependent'' as in solutions derived from the Vlasov-Poisson system. In the linear regime, the inclusion of velocity dispersion effects permits to define a physical Jeans length for collisionless matter as function of the primordial phase-space density indicator: λ{sub J} = (5π/G){sup 1/2}Q{sup −1/3}ρ{sub dm}{sup −1/6}. The comoving Jeans wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the comoving wavenumber due to free-streaming, contributing to the cut-off of the density fluctuation power spectrum at the lowest scales. We discuss the physical differences between these two scales. For dark matter particles of mass equal to 200 GeV, the derived Jeans mass is 4.3 × 10{sup −6}M{sub ⊙}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Classical mechanics on noncommutative space with Lie-algebraic structure

Highlights: > Suggest a useful method to look for new Lie-algebraic noncommutative spaces. > Find out two new Lie-algebraic noncommutative spaces. > Derive Newton and Hamilton equations that present unimaginable extra forces. > Analyse the source of unimaginable extra forces from space noncummutativity. > Provide various intriguing classical trajectories. - Abstract: We investigate the kinetics of a nonrelativistic particle interacting with a constant external force on a Lie-algebraic noncommutative space. The structure constants of a Lie algebra, also called noncommutative parameters, are constrained in general due to some algebraic properties, such as the antisymmetry and Jacobi identity. Through solving the constraint equations the structure constants satisfy, we obtain two new sorts of algebraic structures, each of which corresponds to one type of noncommutative spaces. Based on such types of noncommutative spaces as the starting point, we analyze the classical motion of the particle interacting with a constant external force by means of the Hamiltonian formalism on a Poisson manifold. Our results not only include that of a recent work as our special cases, but also provide new trajectories of motion governed mainly by marvelous extra forces. The extra forces with the unimaginable tx-dot-,(xx-dot)-, and (xx-double dot)-dependence besides with the usual t-, x-, and x-dot-dependence, originating from a variety of noncommutativity between different spatial coordinates and between spatial coordinates and momenta as well, deform greatly the particle's ordinary trajectories we are quite familiar with on the Euclidean (commutative) space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗