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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 1,441 records · Page 80
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Stability of linear systems in second-order form based on structure preserving similarity transformations

This paper deals with two stability aspects of linear systems of the form I ¨ x +B˙ x +Cx = 0 given by the triple (I;B;C). A general transformation scheme is given for a structure and Jordan form preserving transformation of the triple. We investigate how a system can be transformed by suitable choices of the transformation parameters into a new system (I;B1;C1) with a symmetrizable matrix C1. This procedure facilitates stability investigations. We also consider systems with a Hamiltonian spectrum which discloses marginal stability after a Jordan form preserving transformation.

Stoustrup, Jakob↗
DOE OSTI2015

Subcellular-level resolution MALDI-MS imaging of maize leaf metabolites by MALDI-linear ion trap-Orbitrap mass spectrometer

A significant limiting factor in achieving high spatial resolution for matrix-assisted laser desorption ionization-mass spectrometry (MALDI-MS) imaging is the size of the laser spot at the sample surface. We present modifications to the beam-delivery optics of a commercial MALDI-linear ion trap-Orbitrap instrument, incorporating an external Nd:YAG laser, beam-shaping optics, and an aspheric focusing lens, to reduce the minimum laser spot size from ~50 μm for the commercial configuration down to ~9 μm for the modified configuration. This improved system was applied for MALDI-MS imaging of cross sections of juvenile maize leaves at 5-μm spatial resolution using an oversampling method. There are a variety of different metabolites including amino acids, glycerolipids, and defense-related compounds were imaged at a spatial resolution well below the size of a single cell. Such images provide unprecedented insights into the metabolism associated with the different tissue types of the maize leaf, which is known to asymmetrically distribute the reactions of C4 photosynthesis among the mesophyll and bundle sheath cell types. The metabolite ion images correlate with the optical images that reveal the structures of the different tissues, and previously known and newly revealed asymmetric metabolic features are observed.

47 OTHER INSTRUMENTATION↗
DOE OSTI2013

Linear Integro-differential Schroedinger and Plate Problems Without Initial Conditions

Via Carleman's estimates we prove uniqueness and continuous dependence results for the temporal traces of solutions to overdetermined linear ill-posed problems related to Schroedinger and plate equation. The overdetermination is prescribed in an open subset of the (space-time) lateral boundary.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Kalman Duality Principle for a Class of Ill-Posed Minimax Control Problems with Linear Differential-Algebraic Constraints

In this paper we present Kalman duality principle for a class of linear Differential-Algebraic Equations (DAE) with arbitrary index and time-varying coefficients. We apply it to an ill-posed minimax control problem with DAE constraint and derive a corresponding dual control problem. It turns out that the dual problem is ill-posed as well and so classical optimality conditions are not applicable in the general case. We construct a minimizing sequence <##> } } u }&#x005E;<!-- ^ --> } &#x03B5;<!-- ?? --> $ /hat{u}{sub {/varepsilon}} $ u-hat {sub ε} </##> for the dual problem applying Tikhonov method. Finally we represent <##> } } u }&#x005E;<!-- ^ --> } &#x03B5;<!-- ?? --> $ /hat{u}{sub {/varepsilon}} $ u-hat {sub ε} </##> in the feedback form using Riccati equation on a subspace which corresponds to the differential part of the DAE.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource

We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Scale-bridging with the extended/generalized finite element method for linear elastodynamics

This paper presents an extended/generalized finite element method for bridging scales in linear elastodynamics in the absence of scale separation. More precisely, the GFEMgl framework is expanded to enable the numerical solution of multiscale problems through the automated construction of specially-tailored shape functions, thereby enabling high-fidelity finite element modeling on simple, fixed finite element meshes. Furthermore, this introduces time-dependencies in the shape functions in that they are subject to continuous adaptation with time. The temporal aspects of the formulation are investigated by considering the Newmark-β time integration scheme, and the efficacy of mass lumping strategies is explored in an explicit time-stepping scheme. This method is demonstrated on representative wave propagation examples as well as a dynamic fracture problem to assess its accuracy and flexibility.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Exploring the use of dynamic linear panel data models for evaluating energy/economy/environment models — an application for the transportation sector

This paper evaluates the RoSE transportation sector scenarios of the GCAM and REMIND models for the U.S. region by comparing these models’ projected future final energy use levels (1) to historical trends and (2) across each other. To estimate and compare the intrinsic model elasticities, we explore the use of dynamic linear panel data models. On the basis of 26 scenarios (panels) from each of the two energy system models, our analysis suggests that most intrinsic model elasticities with respect to final energy use are roughly comparable to each other and to those observed historically. The key difference is the income elasticity of final energy use, which is significantly smaller for the two energy models than that derived from the historical development. This difference and other minor inconsistencies are interpreted through key assumptions underlying both energy system models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Donor-Acceptor Conjugated Linear Polyenes: A Study of Excited State Intramolecular Charge Transfer, Photoisomerization and Fluorescence Probe Properties

Numerous studies of donor-acceptor conjugated linear polyenes have been carried out with the goal to understand the exact nature of the excited state electronic structure and dynamics. In this article we discuss our endeavours with regard to the excited state intramolecular charge transfer, photoisomerization and fluorescence probe properties of various donor-acceptor substituted compounds of diphenylpolyene [Ar(CH = CH){sub n}Ar] series and ethenylindoles.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2014

Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows

A new class of compact-reconstruction weighted essentially non-oscillatory (CRWENO) schemes were introduced (Ghosh and Baeder in SIAM J Sci Comput 34(3): A1678–A1706, 2012) with high spectral resolution and essentially non-oscillatory behavior across discontinuities. The CRWENO schemes use solution-dependent weights to combine lower-order compact interpolation schemes and yield a high-order compact scheme for smooth solutions and a non-oscillatory compact scheme near discontinuities. The new schemes result in lower absolute errors, and improved resolution of discontinuities and smaller length scales, compared to the weighted essentially non-oscillatory (WENO) scheme of the same order of convergence. Several improvements to the smoothness-dependent weights, proposed in the literature in the context of the WENO schemes, address the drawbacks of the original formulation. This paper explores these improvements in the context of the CRWENO schemes and compares the different formulations of the non-linear weights for flow problems with small length scales as well as discontinuities. Simplified one- and two-dimensional inviscid flow problems are solved to demonstrate the numerical properties of the CRWENO schemes and its different formulations. Canonical turbulent flow problems—the decay of isotropic turbulence and the shock-turbulence interaction—are solved to assess the performance of the schemes for the direct numerical simulation of compressible, turbulent flows

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. Additionally, a uniform numerical stability with respect to the Knudsen number ϵ, and a uniform in ϵ error estimate is given. For temporal and spatial discretizations, we apply the implicit–explicit scheme under the micro–macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048–2072, 2014) for deterministic problem. Lastly, we provide a rigorous proof of the stochastic asymptotic-preserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Positivity Limiters for Filtered Spectral Approximations of Linear Kinetic Transport Equations

We analyze the properties and compare the performance of several positivity limiters for spectral approximations with respect to the angular variable of linear transport equations. It is well-known that spectral methods suffer from the occurrence of (unphysical) negative spatial particle concentrations due to the fact that the underlying polynomial approximations are not always positive at the kinetic level. Positivity limiters address this defect by enforcing positivity of the polynomial approximation on a finite set of preselected points. With a proper PDE solver, they ensure positivity of the particle concentration at each step in a time integration scheme. We review several known positivity limiters proposed in other contexts and also introduce a modification for one of them. We give error estimates for the consistency of the positive approximations produced by these limiters and compare the theoretical estimates to numerical results. We then solve two benchmark problems with these limiters, make qualitative and quantitative observations about the solutions, and then compare the efficiency of the different limiters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. In this report we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate speed-up over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Linear Light Amplifier and Amplification of N-Photon States

We consider a linear quantum amplifier consisting of NA two-level atoms and study the problem of amplification of N-photon states. The N-photon states are associated with N-quantum states of the harmonic oscillator. We show that the process of interaction of the electromagnetic field with atoms can be associated with some transformation of the phase space and functions defined on this phase space. We consider the Husimi functions QN(q, p) of N-quantum states of the harmonic oscillator, which are defined on the phase space, investigate transformation of these functions, and find an explicit form of the density matrix of the amplified N-photon state. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad’s angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543–1608, 2004), (Bull Inst Math Acad Sin 1:1–78, 2006), (Bull Inst Math Acad Sin 6:151–243, 2011) and Lee et al. (Commun Math Phys 269:17–37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The Hurwitz Product, p-Adic Topology on ℤ, and Fundamental Solution to Linear Differential Equation in the Ring ℤ[[x]]

We study the linear inhomogeneous first order differential equation by′ + f(x) = y in the ring of formal power series with integer coefficients. Using the p-adic topology on the ring of integers, we construct a counterpart of the Hurwitz product of the Euler series and an arbitrary formal power series with integer coefficients. It is shown that the Euler series can be interpreted as the fundamental solution to the equation under consideration. Bibliography: 8 titles.

97 MATHEMATICS AND COMPUTING↗