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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Hydrodynamic Limit of Multiple SLE

Recently del Monaco and Schleißinger addressed an interesting problem whether one can take the limit of multiple Schramm–Loewner evolution (SLE) as the number of slits N goes to infinity. When the N slits grow from points on the real line ℝ in a simultaneous way and go to infinity within the upper half plane ℍ, an ordinary differential equation describing time evolution of the conformal map g{sub t}(z) was derived in the N→∞ limit, which is coupled with a complex Burgers equation in the inviscid limit. It is well known that the complex Burgers equation governs the hydrodynamic limit of the Dyson model defined on ℝ studied in random matrix theory, and when all particles start from the origin, the solution of this Burgers equation is given by the Stieltjes transformation of the measure which follows a time-dependent version of Wigner’s semicircle law. In the present paper, first we study the hydrodynamic limit of the multiple SLE in the case that all slits start from the origin. We show that the time-dependent version of Wigner’s semicircle law determines the time evolution of the SLE hull, K{sub t}⊂ℍ∪ℝ, in this hydrodynamic limit. Next we consider the situation such that a half number of the slits start from a>0 and another half of slits start from −a<0, and determine the multiple SLE in the hydrodynamic limit. After reporting these exact solutions, we will discuss the universal long-term behavior of the multiple SLE and its hull K{sub t} in the hydrodynamic limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

Model of a rotating magnetic cloud

The possibility that magnetic clouds rotate while they propagate antisunward was investigated. Magnetic clouds are modeled as magnetic flux ropes which rotate rigidly about the axis of symmetry. An ideal magnetohydrodynamic model, in which the evolution of the magnetic structure is related to the time evolution of the angular frequency, is developed. A class of 'separable' magnetic fields is employed to reduce the problem to a nonlinear ordinary differential equation for the evolution function, and it is solved numerically. The corresponding effective potential gives rise to two modes of evolution--expansion and oscillation--depending on the energy and on the value of a dimensionless parameter, k. Parameter k depends on the gas pressure, the ratio of the magnetic field components, and the frequency of rotation. There is a critical value of k, k(sub c), above which the oscillatory regime disappears and the flux rope invariably expands, regardless of the energy. Below k(sub c) the energy determines whether the configuration is confined or unbounded. Rotation always helps expansion by lowering the potential barrier. A data example was studied and features which are interpreted as signatures of rotation are presented. The angular speed is comparable to the Alfven speed, and the core of the rotating cloud completes on average one full revolution every three days at 1 AU. The parameter k is calculated from observations, and it is found to be close to, but below, critical. Only three out of the nine clouds examined showed signatures of rotation. Theoretical analysis suggests that close to the Sun rotation effects may play a more important role in the evolution of magnetic clouds than 1 AU.

Farrugia, C. J.↗
DOE OSTI2019

Mori-Zwanzig reduced models for uncertainty quantification

In many time-dependent problems of practical interest the parameters and/or initial conditions entering the equations describing the evolution of the various quantities exhibit uncertainty. One way to address the problem of how this uncertainty impacts the solution is to expand the solution using polynomial chaos expansions and obtain a system of differential equations for the evolution of the expansion coefficients. We present an application of the Mori-Zwanzig (MZ) formalism to the problem of constructing reduced models of such systems of differential equations. In particular, we construct reduced models for a subset of the polynomial chaos expansion coefficients that are needed for a full description of the uncertainty caused by uncertain parameters or initial conditions. Even though the MZ formalism is exact, its straightforward application to the problem of constructing reduced models for estimating uncertainty involves the computation of memory terms whose cost can become prohibitively expensive. For those cases, we present a Markovian reformulation of the MZ formalism which can lead to approximations that can alleviate some of the computational expense while retaining an accuracy advantage over reduced models that discard the memory altogether. Our results support the conclusion that successful reduced models need to include memory effects.

Mori-Zwanzig, Model Reduction, Uncertainty Quantif↗
DOE OSTI2022

Modeling Dust Production, Growth, and Destruction in Reionization-era Galaxies with the CROC Simulations: Methods and Parameter Exploration

We introduce a model for the explicit evolution of interstellar dust in a cosmological galaxy formation simulation. We post-process a simulation from the Cosmic Reionization on Computers project, integrating an ordinary differential equation for the evolution of the dust-to-gas ratio along pathlines in the simulation sampled with a tracer particle technique. This model incorporates the effects of dust grain production in asymptotic giant branch star winds and supernovae, grain growth due to the accretion of heavy elements from the gas phase of the interstellar medium, and grain destruction due to thermal sputtering in the high-temperature gas of supernova remnants due to thermal sputtering. A main conclusion of our analysis is the importance of a carefully chosen dust destruction model, for which different reasonable parameterizations can predict very different values at the ∼100 pc resolution of the interstellar medium (ISM) in our simulations. We run this dust model on the single most massive galaxy in a 10 h$^{−1}$ comoving megaparsec box, which attains a stellar mass of ∼2 × 10$^{9}$ M $_{⊙}$ by z = 5. We find that the model is capable of reproducing dust masses and dust-sensitive observable quantities broadly consistent with existing data from high-redshift galaxies. The total dust mass in the simulated galaxy is somewhat sensitive to parameter choices for the dust model, especially the timescale for grain growth due to accretion in the ISM. Consequently, observable quantity observations that can constrain galaxy dust masses at these epochs are potentially useful for placing constraints on dust physics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Measuring microwave quantum states: Tomogram and moments

Two measurable characteristics of microwave one-mode photon states are discussed: a rotated quadrature distribution (tomogram) and normally and antinormally ordered moments of photon creation and annihilation operators. Extraction of these characteristics from an amplified microwave signal is presented. Relations between the tomogram and the moments are found and can be used as a cross-check of experiments. Formalism of the ordered moments is developed. The state purity and generalized uncertainty relations are considered in terms of moments. Unitary and nonunitary time evolution of moments is obtained in the form of a system of linear differential equations in contrast to partial differential equations for quasidistributions. Time evolution is specified for the cases of a harmonic oscillator and a damped harmonic oscillator which describe noiseless and decoherence processes, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Electronegativity-Guided Site Differentiation in High-Entropy Alloy for pH-universal Hydrogen Evolution Reactions

Enhancing the intrinsic activity of transition metal catalysts for the hydrogen evolution reaction (HER) remains a critical challenge in sustainable energy conversion. Herein, we report an electronegativity-guided site differentiation strategy in a single-phase CoNiCuMoW high-entropy alloy (HEA) via electrodeposition by incorporating high-electronegativity 4d/5d orbital transition metals (Mo, W) into the face-centered cubic (fcc) matrix (CoNiCu). The as-synthesized HEA demonstrates exceptional HER performance in all pH conditions, delivering an outstanding overpotential of 65 mV (alkaline), 28 mV (acidic), and 155 mV (neutral) at a current density of 100 mA cm−2, showing performance comparable to commercial Pt/C and has excellent long-term stability at high current density (1 A cm−2, 1000 h). X-Ray absorption spectroscopy (XAS) and density functional theory (DFT) calculations reveal that the incorporation of Mo/W simultaneously alters the local coordination environment and induces element-dependent charge redistribution, accompanied by a system-level d-band center downshift, thereby optimizing the hydrogen binding strength across multimetallic sites. Meanwhile, oxophilic Mo/W sites lower the water dissociation energy barrier. These synergistic effects collectively enable efficient and durable pH-universal HER performance.

Wu, Yutong↗
DOE OSTI2019

Evolution of the beam-width parameter of zeroth-order Bessel–Gaussian beams in collisional plasma with density ripple

In the present paper, we have investigated the self-focusing of zeroth-order Bessel–Gaussian beams in collisional plasma with density ripple. Based on Wentzel–Kramers–Brillouin and the paraxial ray approximations, the nonlinear differential equation governing the evolution of beam-width parameter is evaluated. The variation of beam-width parameter with propagation distance is examined for different values of ripple wave number and beam parameters. From our study, it is seen that stronger self-focusing is obtained when the density ripple is important. The results corresponding to Gaussian beams are deduced from this work as a particular case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Kinematic Flow and the Emergence of Time

Perhaps the most basic question we can ask about cosmological correlations is how their strength changes as we smoothly vary kinematic parameters. The answer is encoded in differential equations that govern this evolution in kinematic space. In this Letter, we introduce a new perspective on these differential equations. We show that, in the simplified setting of conformally coupled scalars in power-law Friedmann-Robertson-Walker spacetimes, the equations for arbitrary tree-level processes can be obtained from a small number of simple combinatorial rules. While this “kinematic flow” is defined purely in terms of boundary data, it reflects the physics of bulk time evolution. The unexpected regularity of the equations suggests the existence of an autonomously defined mathematical structure from which cosmological correlations and the time evolution of the associated spacetime emerge.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Efficient numerical algorithm for multi-level ionization of high-atomic-number gases

An efficient numerical algorithm for laser driven multi-level ionization of high-atomic-number gases is proposed and implemented in an electromagnetic particle-in-cell code SPACE. The algorithm is based on analytical solutions to the system of differential equations describing ionization evolution. Using analytical solutions resolves the multiscale issue of ionization due to different characteristic time scales of ionization processes and the main code time step. Algorithm efficiency and memory requirements are significantly improved by using a locally reduced system of differential equations. The algorithm also assigns proper orbital quantum numbers and their projections to ionization states. The algorithm is verified and validated using experimental data.

Cheng, A. (ORCID:000000021945282X)↗
NASA NTRS1995

Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma

In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a polytropic relationship and reduce the set of ideal MHD equations to a single, second-order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue -- a one-dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index gamma and a dimensionless quantity kappa the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and gamma. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for gamma greater than 1 and all values of kappa, only oscillations are possible. For gamma less than 1, however, both oscillations and expansion are allowed. For gamma less than 1 and kappa below a critical value, the energy of the nonlinear oscillator determines whether the flux rope will oscillate or expand to infinity. For gamma less than 1 and kappa above critical, however, only expansion occurs. Thus by increasing kappa while keeping gamma fixed (less than 1), a phase transition occurs at kappa = kappa(sub critical) and the oscillatory mode disappears. We illustrate the above theoretical considerations by the example of a flux rope of constant field line twist evolving self-similarly. For this example, we present the full numerical MHD solution. In an appendix to the paper we catalogue all possible evolutions when (1) either the magnetic field or (2) the gas pressure decreases monotonically toward the axis. We find that in these cases critical conditions can occur for gamma greater than 1. While in most cases the flux rope collapses, there are notable exceptions when, for certain ranges of kappa and gamma, collapse may be averted.

Osherovich, V. A.↗
DOE OSTI2022

Analytic model of dislocation density evolution in fcc polycrystals accounting for dislocation generation, storage, and dynamic recovery mechanisms

Here, an analytic model of the evolution of dislocation density in fcc polycrystals is described. The evolution equations approximately account for most known dislocation storage, dynamic recovery, and dislocation generation mechanisms in fcc polycrystals. Specifically, the model incorporates network (forest) and grain boundary storage, mobile-network and mobile–mobile annihilation, screw–screw annihilation via athermal and thermal single cross-slip, generation by double cross-slip (Koehler mechanism, including dipole formation), Frank-Read sources, grain boundary nucleation, and mobile–immobile dislocation nucleation due to shock loading. Single cross-slip is assumed to proceed through the Friedel–Escaig (FE) mechanism; the corresponding activation energy is calculated using a modified FE model. The activation energy for double cross-slip is calculated for the first time by extending the FE model. The exact evolution equations are integro-differential equations, and as such are difficult to implement in a code; hence, the evolution equations are simplified by making several approximations. Preliminary results on copper are presented, including comparisons to experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Probing putative orbital differentiation effects via Eu 2+ spin dynamics in Sr 1-x Eu x Fe 2 As 2

Here, in this work, we report x-ray powder diffraction, elemental analysis, electrical resistivity, magnetic susceptibility, specific heat, and electron spin resonance (ESR) in single crystals of Sr 1-x Eu x Fe 2 As 2 . We observed a breakdown of the previously reported scaling between the Eu 2+ Korringa relaxation rate obtained from ESR and the spin density wave temperature evolution for Sr-rich samples. This result suggests a distinct evolution of the orbital differentiation of the Fe 3d bands along the Sr-based series when compared to the Ba counterpart. We argue that this difference is related to a larger splitting between the structural (tetragonal-to-orthorhombic) and the Fe-driven spin density wave transitions induced by Eu doping in this series. In fact, our results indicate that the two transitions follow an opposite x-Eu dependence for Sr-concentrated samples. Our work shows that Sr 1-x Eu x Fe 2 As 2 series and the comparison with their Ba-based counterparts are exciting platforms to be explored for understanding the interplay among orbital differentiation, magnetism, and structural distortions in the iron pnictides

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Detailed study of the eikonal reaction theory for the breakup of one-neutron halo nuclei

Background: One-neutron removal reactions are used to study the single-particle structure of unstable nuclei, and in particular the exotic halo nuclei. The eikonal reaction theory (ERT) has been developed by Yahiro, Ogata, and Minomo [Prog. Theor. Phys. 126, 167 (2011)] to include dynamical effects, which are missing in the usual eikonal description of these reactions. Encouraging results have been obtained for total breakup cross sections in comparison to more elaborate reaction models. Purpose: Here, we extend these comparisons to more differential breakup cross sections expressed as functions of the relative energy or parallel momentum between the core and halo neutron. Method: ERT predictions of these cross sections are compared to state-of-the-art calculations. Results: The hypotheses upon which the ERT is based are confirmed and their range of validity is made clearer. The actual ordering of the evolution operators affects ERT differential cross sections and a specific choice leads to excellent agreement with the reference calculation. Dynamical effects in the treatment of the neutron-target interaction can be significant in the parallel-momentum observable. Conclusions: The role of the different interactions in the dynamics of breakup reactions of one-neutron halo nuclei are better understood and improvements to the ERT are suggested.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Strong Stability Preserving Integrating Factor Two-Step Runge-Kutta Methods

In this report, problems with components that feature significantly different time scales, where the stiff time-step restriction comes from a linear component, implicit-explicit (IMEX) methods alleviate this restriction if the concern is linear stability. However, when nonlinear non-inner-product stability properties are of interest, such as in the evolution of hyperbolic partial differential equations with shocks or sharp gradients, linear inner-product stability is no longer sufficient for convergence, and so strong stability preserving (SSP) methods are often needed. Where the SSP property is needed, IMEX SSP Runge-Kutta (SSP-IMEX) methods have very restrictive time-steps. An alternative to SSP-IMEX schemes is to adopt an integrating factor approach to handle the linear component exactly and step the transformed problem forward using some time-evolution method. The strong stability properties of integrating factor Runge-Kutta methods were established in Isherwood et al. (SIAM J Numer Anal 56(6):3276–3307, 2018), where it was shown that it is possible to define explicit integrating factor Runge-Kutta methods that preserve strong stability properties satisfied by each of the two components when coupled with forward Euler time-stepping. It was proved that the solution will be SSP if the transformed problem is stepped forward with an explicit SSP Runge-Kutta method that has non-decreasing abscissas. However, explicit SSP Runge-Kutta methods have an order barrier of p=4, and sometimes higher order is desired. In this work we consider explicit SSP two-step Runge-Kutta integrating factor methods to raise the order. We show that strong stability is ensured if the two-step Runge-Kutta method used to evolve the transformed problem is SSP and has non-decreasing abscissas. We find such methods up to eighth order and present their SSP coefficients. Adding a step allows us to break the fourth order barrier on explicit SSP Runge-Kutta methods; furthermore, our explicit SSP two-step Runge-Kutta methods with non-decreasing abscissas typically have larger SSP coefficients than the corresponding one-step methods. A selection of our methods are tested for convergence and demonstrate the design order. We also show, for selected methods, that the SSP time-step predicted by the theory is a lower bound of the allowable time-step for linear and nonlinear problems that satisfy the total variation diminishing (TVD) condition. We compare some of the non-decreasing abscissa SSP two-step Runge-Kutta methods to previously found methods that do not satisfy this criterion on linear and nonlinear TVD test cases to show that this non-decreasing abscissa condition is indeed necessary in practice as well as theory. We also compare these results to our SSP integrating factor Runge-Kutta methods designed in Isherwood et al. (2018).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Non-Wiener Dynamics of Open Systems for Nonzero Number Density of Surrounding Photons

We propose a collective decay model for a localized ensemble of identical atoms in a vacuum broadband electromagnetic field with a nonzero photon number density considering second-order terms in the atom–field interaction constant. The model is based on the stochastic differential equation for the evolution operator for the atomic ensemble and surroundings, which is controlled by the main quantum random processes and independent classical Wiener processes. It is shown that in some cases, nonzero photon number density does not influence the suppression of collective emission of atoms, and its existence is manifested as an additional mechanism of redistribution of atoms over collective sublevels.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2011

Self-focusing of cosh-Gaussian laser beam in a plasma with weakly relativistic and ponderomotive regime

This paper presents an investigation of the self-focusing of cosh-Gaussian laser beam in a plasma with linear absorption taking into account the combined effects of relativistic and ponderomotive type nonlinearities. Nonlinear parabolic partial differential equation governing the evolution of complex envelope in slowly varying envelope approximation is solved using variational approach. Self-focusing and self-phase modulation as well as self-trapping of cosh-Gaussian beam are studied at various values of decentered parameter b, with different absorption levels k{sub i}{sup '}. Numerical analysis shows that these parameters play vital role on propagation characteristics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Difference-frequency generation in the field of a few-cycle laser pulse propagating in a GaAs crystal with a domain structure

Difference-frequency generation in a GaAs crystal with a periodic domain structure in the field of a few-cycle laser pulse is considered for the case of weakly pronounced material dispersion. The straight-line method is used to solve numerically the system of coupled nonlinear partial differential equations describing the evolution of the electric field of this laser pulse in GaAs crystals with periodic and chirped domain structures. It is shown that application of a GaAs crystal with a chirped domain structure makes it possible to control the frequency-modulation law for a broadband differencefrequency pulse. (nonlinear optical phenomena)

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Black and gray box learning of amplitude equations: Application to phase field systems

Here, we present a data-driven approach to learning surrogate models for amplitude equations and illustrate its application to interfacial dynamics of phase field systems. In particular, we demonstrate learning effective partial differential equations describing the evolution of phase field interfaces from full phase field data. We illustrate this on a model phase field system, where analytical approximate equations for the dynamics of the phase field interface (a higher-order eikonal equation and its approximation, the Kardar-Parisi-Zhang equation) are known. For this system, we discuss data-driven approaches for the identification of equations that accurately describe the front interface dynamics. When the analytical approximate models mentioned above become inaccurate, as we move beyond the region of validity of the underlying assumptions, the data-driven equations outperform them. In these regimes, going beyond black box identification, we explore different approaches to learning data-driven corrections to the analytically approximate models, leading to effective gray box partial differential equations.

42 ENGINEERING↗