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Results for “Analytic linearization”

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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Gravitational lens equation for embedded lenses; magnification and ellipticity

We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches the observer. We call this deflector an embedded lens because the deflecting mass is part of the mean density. The embedded lens equation differs from the conventional lens equation because the deflector mass is not simply an addition to the cosmic mean. We prescribe an iteration scheme to solve this new lens equation and use it to compare our results with standard linear lensing theory. We also compute analytic expressions for the lowest order corrections to image amplifications and distortions caused by incorporating the lensing mass into the mean. We use these results to estimate the effect of embedding on strong lensing magnifications and ellipticities and find only small effects, <1%, contrary to what we have found for time delays and for weak lensing, {approx}5%.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Temporal enhancement of super-horizon curvature perturbations from decays of two curvatons and its cosmological consequences

If more than one curvaton dominate the Universe at different epochs from each other, curvature perturbations can be temporarily enhanced to a value much larger than the observed one 10{sup -5}. The traces of the enhancement may be left as higher order correlation functions, that is, as non-Gaussianity, the stochastic gravitational waves that are sourced by scalar-scalar mode couplings, as well as the primordial black holes that are formed by the gravitational collapse of the enhanced curvature perturbations. We first confirm that such a temporal enhancement indeed occurs by solving the linearized perturbation equations both numerically and analytically. We then derive an analytic expression of the full-order curvature perturbation which does not rely on the frequently used sudden decay approximation and is exact on superhorizon scales. By using this analytic formula, we provide expressions of the nonlinearity parameters f{sub NL}, {tau}{sub NL} and g{sub NL}. If both two curvatons contribute to the final curvature perturbations, the strong non-Gaussianity appears in the trispectrum rather than in the bispectrum. We also find a unique consistency relation between {tau}{sub NL} and g{sub NL} without f{sub NL}. By using the second-order perturbation theory, we numerically show that the spectrum of the induced gravitational waves has a plateau corresponding to duration of the enhancement and such gravitational waves can be probed by ultimate-DECIGO and space-based atomic interferometers. We finally calculate the abundance of the primordial black holes and put a constraint on the amplitude of the enhanced curvature perturbations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Entanglement Entropy in Lifshitz Theories

We discuss and compute entanglement entropy (EE) in (1+1)-dimensional free Lifshitz scalar field theories with arbitrary dynamical exponents. We consider both the subinterval and periodic sublattices in the discretized theory as subsystems. In both cases, we are able to analytically demonstrate that the EE grows linearly as a function of the dynamical exponent. Furthermore, for the subinterval case, we determine that as the dynamical exponent increases, there is a crossover from an area law to a volume law. Lastly, we deform Lifshitz field theories with certain relevant operators and show that the EE decreases from the ultraviolet to the infrared fixed point, giving evidence for a possible c c -theorem for deformed Lifshitz theories.

He, Temple↗
DOE OSTI2011

Neoclassical Transport Including Collisional Nonlinearity

In the standard {delta}f theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction {delta}f is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlueter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Testing the Delayed Gamma Capability in MCNP6 - Paper 86

The mission of the Domestic Nuclear Detection Office (DNDO) is to quickly and reliably detect unauthorized attempts to import or transport special nuclear material (SNM) for use against the United States. Developing detection equipment to meet this objective requires accurate simulation of both the detectable signature and detection mechanism. MCNP6 is capable of transporting the various types of radiation encountered in these scenarios; however, the accuracy of MCNP6 must be quantified such that we can be confident in the results of the simulations. Delayed gamma transport is one important component of these detection scenarios. Delayed gamma transport is defined as the combination of gamma emission from radioactive and subsequent transport through matter. MCNP always possessed the ability to emit delayed neutrons from fission; however, these delayed neutron spectra and intensity were functional fits and not directly sampled from the created fission products. Furthermore, there existed no method to emit the decay photons from radioactive fission products (or any radioactive nucleus) A delayed particle capability was initially added to MCNPX 2.6.A in 2005 to sample the radioactive fission product parents and emit decay particles resulting from the decay chain. At the point of capture, a residual nucleus is created and decayed using the CINDER90 depletion code. MCNP only sends CINDER90 a residual radioactive nucleus and not a flux (i.e. capture rate). As a result, the Bateman equations for the solution are coupled first order differential equations with constant coefficients. Theoretically, these equations could be solved analytically; however, CINDER90 employs a numerical Markov linear chain scheme to solve these equations. This paper addresses a more simplified approach to benchmarking in order to best assess: (1) whether or not deficiencies exist in the current methodology for certain types of decay chains; and (2) paths forward for improving the delayed particle emission capability. We utilize closed form analytic solutions to the granddaughter equations for particular sets of isotope systems to compare the accuracy of the delayed gamma capability in MCNP6. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2014

Gradient of molecular Hartree–Fock–Bogoliubov energy with a linear combination of atomic orbital quasiparticle wave functions

The analytical gradient for the atomic-orbital-based Hartree–Fock–Bogoliubov (HFB) energy functional, the modified form of which was proposed by Staroverov and Scuseria to account for the static electron correlation [J. Chem. Phys. 117, 11107 (2002)], is derived. Interestingly, the Pulay force for the HFB energy is expressed with the same formula as that for the Hartree–Fock method. The efficiency of the present HFB energy gradient is demonstrated in the geometry optimizations of conjugated and biradical systems. The geometries optimized by using the HFB method with the appropriate factor ζ, which controls the degree of static correlation included, are found to show good agreement with those obtained by using a complete active-space self-consistent field method, although they are significantly dependent on ζ.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Large-Area Graphene Films as Target Surfaces for Highly Reproducible Matrix-Assisted Laser Desorption Ionization Suitable for Quantitative Mass Spectrometry

Due to the known sweet-spot issues that intrinsically arise from inhomogeneous formation of matrix-analyte crystals utilized as samples in matrix-assisted laser desorption ionization (MALDI) mass spectrometry, its reproducibility and thus its applications for quantification have been somewhat limited. In this paper, we report a simple strategy to improve the uniformity of matrix-analyte crystal spots, which we realized by adapting large-area graphene films, i.e., non-inert, interacting surfaces, as target surfaces. In this example, the graphitic surfaces of the graphene films interact with excess matrix molecules during the sample drying process, which induces spontaneous formation of optically uniform MALDI sample crystal layers on the film surfaces. Further, mass spectrometric imaging reveals that the visible uniformity is indeed accompanied by reproducible MALDI ionization over an entire sample spot, which greatly suppresses the appearance of sweet spots. The results of this study confirm that the proposed method achieves good linear responses of ion intensity to the analyte concentration (R{sup 2} > 0.99) with small relative standard deviations (σ < 10%), which is a range applicable for quantitative measurements using MALDI mass spectrometry. .

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2016

Dynamics of atoms in strong laser fields I: A quasi analytical model in momentum space based on a Sturmian expansion of the interacting nonlocal Coulomb potential

In this study we present a model that we have formulated in the momentum space to describe atoms interacting with intense laser fields. As a further step, it follows our recent theoretical approach in which the kernel of the reciprocal-space time-dependent Schrödinger equation (TDSE) is replaced by a finite sum of separable potentials, each of them supporting one bound state of atomic hydrogen (Tetchou Nganso et al. 2013). The key point of the model is that the nonlocal interacting Coulomb potential is expanded in a Coulomb Sturmian basis set derived itself from a Sturmian representation of Bessel functions of the first kind in the position space. As a result, this decomposition allows a simple spectral treatment of the TDSE in the momentum space. In order to illustrate the credibility of the model, we have considered the test case of atomic hydrogen driven by a linearly polarized laser pulse, and have evaluated analytically matrix elements of the atomic Hamiltonian and dipole coupling interaction. For various regimes of the laser parameters used in computations our results are in very good agreement with data obtained from other time-dependent calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model

We present a semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite difference method deals with the spatial coordinate. This semi-numerical scheme is not restricted by space discretization and allows the computation of a solution at any time without compromising numerical stability or the mass conservation principle. Our formulation results in a non-analytically-solvable second-order differential equation whose spatial discretization yields a tridiagonal linear algebraic system. Moreover, we describe comparisons between semi-numerical and semi-analytical solutions for particular cases. Results agree well with those from semi-analytic solutions. Furthermore, we expose a parametric analysis from the coupled model in order to show the effects of relevant parameters on pressure profiles and flow rates for the case where neither analytic nor semi-analytic solutions are available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Particle simulation of radio frequency waves with fully-kinetic ions and gyrokinetic electrons

A toroidal particle-in-cell (PIC) code, suitable for investigating nonlinear phenomena in radio frequency (RF) heating and current drive, is developed and verified thereafter through a series of fidelity tests for field solvers and single particle motions in toroidal geometry, where simulation results show good coincidence with analytical prediction. The RF capability is then demonstrated through the integrated benchmarks with linear lower hybrid wave and ion Bernstein wave theory in cylindrical geometry, where the analytic result is easily available. The frequency and mode structure in the simulations agree well with the theoretical prediction.

Lin, Jingbo↗
DOE OSTI2022

Leading-color two-loop amplitudes for four partons and a $\textit{W}$ boson in QCD

We present the leading-color two-loop QCD corrections for the scattering of four partons and a W boson, including its leptonic decay. The amplitudes are assembled from the planar two-loop helicity amplitudes for four partons and a vector boson decaying to a lepton pair, which are also used to determine the planar two-loop amplitudes for four partons and a $Z/γ^\ast$ boson with a leptonic decay. The analytic expressions are obtained by setting up a dedicated Ansatz and constraining the free parameters from numerical samples obtained within the framework of numerical unitarity. The large linear systems that must be solved to determine the analytic expressions are constructed to be in Vandermonde form. Such systems can be very efficiently solved, bypassing the bottleneck of Gaussian elimination. Our results are expressed in a basis of one-mass pentagon functions, which opens the possibility of their efficient numerical evaluation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Nonlinear fan instability of electromagnetic waves

This paper studies the linear and nonlinear stages of the fan instability, considering electromagnetic waves of the whistler frequency range interacting resonantly with energetic electron fluxes in magnetized plasmas. The main attention is paid to determine the wave-particle interaction processes that can lead to the excitation of intense electromagnetic waves by nonequilibrium particle distributions involving suprathermal tails, and to explain under what conditions and through what mechanisms they can occur, develop, and saturate. This paper presents and discusses two main processes: (i) the linear fan instability and (ii) the nonlinear process of dynamical resonance merging, which can significantly amplify the energy carried by linearly destabilized waves after they saturate due to particle trapping. This study consists of (i) determining analytically and numerically, for parameters typical of space and laboratory plasmas, the linear growth rates of whistlers excited by suprathermal particle fluxes through the fan instability, as well as the corresponding thresholds and the physical conditions at which the instability can appear, (ii) building a theoretical self-consistent 3D model and a related numerical code for describing the nonlinear evolution of the wave-particle system, and (iii) performing numerical simulations to reveal and characterize the nonlinear amplification process at work, its conditions of development, and its consequences, notably in terms of electromagnetic wave radiation. The simulations show that when the waves have reached sufficient energy levels owing to the linear fan instability, they saturate by trapping particles and due to the complex dynamics of these particles in the electromagnetic fields, the resonant velocities' domains of the waves overlap and merge, meanwhile a strong increase of the wave energy occurs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2010

Analytic treatment of vortex states in cylindrical superconductors in applied axial magnetic field

We solve the linear Ginzburg-Landau (GL) equation in the presence of a uniform magnetic field with cylindrical symmetry and we find analytic expressions for the eigenfunctions in terms of the confluent hypergeometric functions. The discrete spectrum results from an implicit equation associated to the boundary conditions and it is resolved in analytic form using the continued fractions formalism. We study the dependence of the spectrum and the eigenfunctions on the sample size and the surface conditions for solid and hollow cylindrical superconductors. Finally, the solutions of the nonlinear GL formalism are constructed as expansions in the linear GL eigenfunction basis and selected by minimization of the free energy. We present examples of vortex states and their energies for different samples in enhancing/suppressing superconductivity surroundings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Approximate solutions to a nonintegrable problem of propagation of elliptically polarised waves in an isotropic gyrotropic nonlinear medium, and periodic analogues of multisoliton complexes

Using the linearization method, we obtain approximate solutions to a one-dimensional nonintegrable problem of propagation of elliptically polarised light waves in an isotropic gyrotropic medium with local and nonlocal components of the Kerr nonlinearity and group-velocity dispersion. The consistent evolution of two orthogonal circularly polarised components of the field is described analytically in the case when their phases vary linearly during propagation. The conditions are determined for the excitation of waves with a regular and 'chaotic' change in the polarisation state. The character of the corresponding nonlinear solutions, i.e., periodic analogues of multisoliton complexes, is analysed. (nonlinear optical phenomena)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

On the interaction between turbulence and a planar rarefaction

The modeling of turbulence, whether it be numerical or analytical, is a difficult challenge. Turbulence is amenable to analysis with linear theory if it is subject to rapid distortions, i.e., motions occurring on a timescale that is short compared to the timescale for nonlinear interactions. Such an approach (referred to as rapid distortion theory) could prove useful for understanding aspects of astrophysical turbulence, which is often subject to rapid distortions, such as supernova explosions or the free-fall associated with gravitational instability. As a proof of principle, a particularly simple problem is considered here: the evolution of vorticity due to a planar rarefaction in an ideal gas. Analytical solutions are obtained for incompressive modes having a wave vector perpendicular to the distortion; as in the case of gradient-driven instabilities, these are the modes that couple most strongly to the mean flow. Vorticity can either grow or decay in the wake of a rarefaction front, and there are two competing effects that determine which outcome occurs: entropy fluctuations couple to the mean pressure gradient to produce vorticity via baroclinic effects, whereas vorticity is damped due to the conservation of angular momentum as the fluid expands. Whether vorticity grows or decays depends upon the ratio of entropic to vortical fluctuations at the location of the front; growth occurs if this ratio is of order unity or larger. In the limit of purely entropic fluctuations in the ambient fluid, a strong rarefaction generates vorticity with a turbulent Mach number on the order of the rms of the ambient entropy fluctuations. The analytical results are shown to compare well with results from two- and three-dimensional numerical simulations. Analytical solutions are also derived in the linear regime of Reynolds-averaged turbulence models. This highlights an inconsistency in standard turbulence models that prevents them from accurately capturing the physics of rarefaction-turbulence interaction. In addition to providing physical insight, the solutions derived here can be used to verify algorithms of both the Reynolds-averaged and direct numerical simulation variety. Finally, dimensional analysis of the equations indicates that rapid distortion of turbulence can give rise to two distinct regimes in the turbulent spectrum: a distortion range at large scales where linear distortion effects dominate, and an inertial range at small scales where nonlinear effects dominate.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Mass spectrometric identification of the N ‐monosubstituted N ‐hydroxylamino functionality in protonated analytes via ion/molecule reactions in tandem mass spectrometry

Rationale N ‐Monosubstituted hydroxylamines correspond to an important class of metabolites for many bioactive molecules. In this study, a tandem mass spectrometric method based on ion/molecule reactions was developed for the identification of compounds with the N ‐monosubstituted hydroxylamino functionality. Methods The diagnostic ion/molecule reaction occurs between protonated analytes with 2‐methoxypropene (MOP) inside a linear quadrupole ion trap mass spectrometer. Results Most protonated compounds with N ‐monosubstituted and disubstituted hydroxylamino and oxime functional groups react with MOP via proton transfer and formation of a stable adduct in a linear quadrupole ion trap mass spectrometer. However, only protonated compounds with N ‐monosubstituted hydroxylamino groups form the characteristic MOP adduct–MeOH product. Possible mechanisms of this reaction are discussed. Conclusions A method based on functional group‐selective ion/molecule reactions in a linear quadrupole ion trap mass spectrometer has been demonstrated to allow the identification of protonated compounds with the N ‐monosubstituted hydroxylamino functionality. Only N ‐monosubstituted hydroxylamines react with MOP via formation of an adduct that has eliminated methanol. Copyright © 2015 John Wiley & Sons, Ltd.

Sheng, Huaming↗
DOE OSTI2013

A convergence study for SPDEs using combined Polynomial Chaos and Dynamically-Orthogonal schemes

We study the convergence properties of the recently developed Dynamically Orthogonal (DO) field equations [1] in comparison with the Polynomial Chaos (PC) method. To this end, we consider a series of one-dimensional prototype SPDEs, whose solution can be expressed analytically, and which are associated with both linear (advection equation) and nonlinear (Burgers equation) problems with excitations that lead to unimodal and strongly bi-modal distributions. We also propose a hybrid approach to tackle the singular limit of the DO equations for the case of deterministic initial conditions. The results reveal that the DO method converges exponentially fast with respect to the number of modes (for the problems considered) giving same levels of computational accuracy comparable with the PC method but (in many cases) with substantially smaller computational cost compared to stochastic collocation, especially when the involved parametric space is high-dimensional.

97 MATHEMATICS AND COMPUTING↗