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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Gravitational waves from first-order phase transitions in Majoron models of neutrino mass

We show how the generation of right-handed neutrino masses in Majoron models may be associated with a first-order phase transition and accompanied by the production of a stochastic background of gravitational waves (GWs). We explore different energy scales with only renormalizable operators in the effective potential. If the phase transition occurs above the electroweak scale, the signal can be tested by future interferometers. We consider two possible energy scales for phase transitions below the electroweak scale. If the phase transition occurs at a GeV, the signal can be tested at LISA and provide a complementary cosmological probe to right-handed neutrino searches at the FASER detector. If the phase transition occurs below 100 keV, we find that the peak of the GW spectrum is two or more orders of magnitude below the putative NANOGrav GW signal at low frequencies, but well within reach of the SKA and THEIA experiments. We show how searches of very low frequency GWs are motivated by solutions to the Hubble tension in which ordinary neutrinos interact with the dark sector. We also present general calculations of the phase transition temperature and Euclidean action that apply beyond Majoron models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Correlating Crystallography, Magnetism, and Electronic Structure Across Anhysteretic First-Order Phase Transition in Pr 2 In

Here, temperature-dependent powder X-ray diffraction and magnetization measurements of Pr 2 In conclusively prove that the unusual anhysteretic first-order paramagnetic-ferromagnetic phase transition in the compound is related to concurrent changes in both the magnetic and crystallographic lattices. At the same time, the hexagonal Ni 2 In-type structure is stable at least between 6 and 298 K, including at T C = ~57 K. From the density functional theory calculations, the electronic structure of the compound is extraordinarily sensitive to minor changes in lattice parameters that occur across the phase transition, revealing the origin of strong magnetoelastic coupling. In the vicinity of T C , the maximum entropy change, ΔS Max = -16 J Kg -1 K -1 induced by a moderate magnetic field change of 20 kOe (ΔS Max = -20 J Kg -1 K -1 for 50 kOe magnetic field change) is comparable to other known potentially functional materials demonstrating large cryogenic magnetocaloric effect.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗
DOE OSTI2022

Anomalous electrical transport behavior in the vicinity of the first-order magnetostructural transition in the giant magnetocaloric Gd 4 ScGe 4

Here, magnetic, specific heat, and electrical transport measurements of Gd 4 ScGe 4 single crystals reveal sharp, discontinuous, nearly anhysteretic first-order magnetostructural transformation at $T_C$ = 63 K. The electrical resistivity exhibits two distinct regions where it increases with decreasing temperature: between $T_C$ and 120 K, as well as below 3 K; electronic transport remains conventionally metallic at all other measured temperatures, up to 325 K. The dispersion of charge carriers due to electron-paramagnon scattering is the likely reason for the observed anomalous transport above $T_C$. Additionally, the existence of intermediate lattice states near the transition recognized by the spike in the interslab Ge-Ge distances is expected to reduce the mean free path of the electrons contributing to the unusual behavior of the electrical resistivity between $T_C$ and 120 K. Beyond conventional electronic and lattice terms, the third component of likely magnetic origin contributes to the low-temperature heat capacity; the presence of spin waves may be responsible for the increased electron-magnon scattering below 3 K. Minor magnetocrystalline anisotropy is observed with the b axis as the easy magnetization axis in Gd 4 ScGe 4 . A negative deviation from linearity in the temperature dependence of the inverse magnetic susceptibility is detected below 150 K.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1984

A modified least squares formulation for a system of first order equations

Second order equations in terms of auxiliary variables similar to potential and stream functions are obtained by applying a weighted least squares formulation to a first order system. The additional boundary conditions which are necessary to solve the higher order equations are determined and numerical results are presented for the Cauchy-Riemann equations.

Hafez, M. M.↗
NASA NTRS1985

A modified least squares formulation for a system of first-order equations

Second order equations in terms of auxiliary variables similar to potential and stream functions are obtained by applying a weighted least squares formulation to a first order system. The additional boundary conditions which are necessary to solve the higher order equations are determined and numerical results are presented for the Cauchy-Riemann equations.

Hafez, M. M.↗
DOE OSTI2024

ALP-assisted strong first-order electroweak phase transition and baryogenesis

Axion-like particles (ALPs) can be naturally lighter than the electroweak scale. We consider an ALP that couples to the Standard Model Higgs to achieve the strong first-order electroweak phase transition. We discuss the two-field dynamics of the phase transition and the associated computation in detail and identify the viable parameter space. The ALP mass can be from the MeV to GeV scale. Baryon asymmetry can be explained by local baryogenesis without violating the current electron and atom electric dipole moment bound in most of the viable parameter space. The viable parameter space can be probed through Higgs exotic decay, rare kaon decay, the electron and atomic electric dipole moment, and the effective number of neutrinos in the cosmic microwave background in the future. The gravitational-wave signal is too weak to be detected.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Relativistic Hybrid Stars with Sequential First-order Phase Transitions in Light of Multimessenger Constraints

In this work, we consider the properties of compact stars in which quark matter has low- and high-density phases that are separated by a first-order phase transition. Thus, unlike the commonly considered case of a single phase transition from hadronic to quark matter, our models of hybrid stars contain sequential phase transitions from hadronic matter to low- and then to high-density quark matter phases. We extend our previous study of the parameter space of hybrid stars with a single phase transition to those with sequential phase transitions, taking into account the constraints on the mass and radius of neutron stars from the NICER experiment, the experimental inferences of the neutron skin thickness of the lead nucleus by the PREX-II experiment, and constraints on the tidal deformability from the gravitational-wave event GW170817. We determine the range of the masses for which both twin and triplet configurations, i.e., identical-mass stars with two and three different values of radii, arise.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1974

A minimum principle for smooth first-order distributed systems

Consideration of the problem of characterizing optimal controls for a class of distributed parameter systems. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables. Boundary conditions on the state are in the form of a finite number of algebraic relations between the state and boundary control variables. A few directions are outlined in which the results obtained may be extended further.

Johnson, T. L.↗
NASA NTRS1993

On the existence of touch points for first-order state inequality constraints

The appearance of touch points in state constrained optimal control problems with general vector-valued control is studied. Under the assumption that the Hamiltonian is regular, touch points for first-order state inequalities are shown to exist only under very special conditions. In many cases of practical importance these conditions can be used to exclude touch points a priori without solving an optimal control problem. The results are demonstrated on a simple example.

Seywald, Hans↗
DOE OSTI2021

A Semi-Analytical Solution Approach for Solving Constant-Coefficient First-Order Partial Differential Equations

Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a “time-stepping” manner, i.e. within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. Furthermore, the simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Optimal control of first order distributed systems

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

Johnson, T. L.↗
DOE OSTI2023

Two first-order phase transitions in hybrid compact stars: Higher-order multiplet stars, reaction modes, and intermediate conversion speeds

We study compact stars with hybrid equations of state consisting of a nuclear outer region and two nested quark phases, each separated from the lower density phase by a strong first-order phase transition. The stability of these models is determined by calculating their radial oscillation modes with different conversion rates between adjacent phases and hence junction conditions for the modes at the phase separation interface between them. In the case when the timescale of transition is faster than the period of oscillations, we recover the traditional stability criterion implying that ∂M/∂ρ c > 0 on the stable branch(es), where M is the mass and ρ c is the central density. In the opposite limit of slow conversion, we find stable stellar multiplets beyond triplets consisting of stars that are stable by the usual criterion plus slow-conversion (denoted by s) hybrid stars with ∂M/∂ρ c < 0 that are stabilized due to an alternative junction condition on the fluid displacement field at the interface reflecting the slow rate of conversion. We also study the properties of the reaction mode, the radial mode that only exists for stars with rapid (abbreviated by r) phase transitions, in stars with either two rapid phase transitions or alternating rapid and slow phase transitions for the first time. Here, the implications of alternative junction conditions are also examined, with these conditions generally being found to provide stability properties similar to those for a slow conversion rate.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1986

Preconditioning for first-order spectral discretization

Efficient solution of the equations from spectral discretizations is essential if the high-order accuracy of these methods is to be realized. Direct solution of these equations is rarely feasible, thus iterative techniques are required. A preconditioning scheme for first-order Chebyshev collocation operators is proposed herein, in which the central finite difference mesh is finer than the collocation mesh. Details of the proper techniques for transferring information between the meshes are given here, and the scheme is analyzed by examination of the eigenvalue spectra of the preconditioned operators. The effect of artificial viscosity required in the inversion of the finite difference operator is examined. A second preconditioning scheme, involving a high-order upwind finite difference operator of the van Leer type is also analyzed to provide a comparison with the present scheme. Finally, the performance of the present scheme is verified by application to several test problems.

Streett, C. L.↗
DOE OSTI2020

Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors

This paper presents a method for performing approximate optimal control simulations for quantum systems with multiple coupled degrees of freedom. In this work, the time evolution is simulated using the first-order Magnus expansion in the interaction picture, where the couplings between different degrees of freedom are treated as the perturbation. A numerical implementation procedure is presented that leverages upon pairwise couplings and the separability of the zeroth-order time evolution operator to achieve a reduced computational cost, which is analyzed with respect to the number of degrees of freedom. The formulation is compatible with gradient-free methods to optimize the control field, and a stochastic hill climbing algorithm is adopted for this purpose. As illustrations, optimal control simulations are performed for systems of two and three dipole-dipole-coupled molecular rotors under the influence of a control field. For the two-rotor system, the field is optimized to achieve either orientation or entanglement objectives. For the three-rotor system, the field is optimized either to orient all three rotors in the same direction or to orient one rotor in a particular direction while the other two rotors point in the opposite direction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric Time‐Dependent Nonlinear PDEs

ABSTRACT We present a model reduction approach for the real‐time solution of time‐dependent nonlinear partial differential equations (PDEs) with parametric dependencies. A major challenge in constructing efficient and accurate reduced‐order models for nonlinear PDEs is the efficient treatment of nonlinear terms. We address this by unifying the implementation of hyperreduction methods to deal with nonlinear terms. Furthermore, we introduce a first‐order empirical interpolation method (EIM) to provide an efficient approximation of the nonlinear terms in time‐dependent PDEs. We demonstrate the effectiveness of our approach on the Allen–Cahn equation, which models phase separation, and the Buckley–Leverett equation, which describes two‐phase fluid flow in porous media. Numerical results highlight the accuracy, efficiency, and stability of the proposed method compared with both the Galerkin–Newton approach and hyper‐reduced models using the standard EIM.

Nguyen, Ngoc Cuong [Center for Computational Engin↗
NASA NTRS1996

First-Order System Least-Squares for the Navier-Stokes Equations

This paper develops a least-squares approach to the solution of the incompressible Navier-Stokes equations in primitive variables. As with our earlier work on Stokes equations, we recast the Navier-Stokes equations as a first-order system by introducing a velocity flux variable and associated curl and trace equations. We show that the resulting system is well-posed, and that an associated least-squares principle yields optimal discretization error estimates in the H(sup 1) norm in each variable (including the velocity flux) and optimal multigrid convergence estimates for the resulting algebraic system.

Bochev, P.↗