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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 19 records
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DOE OSTI2014

Phase portraits analysis of a barothropic system: The initial value problem

In this paper, we investigate the phase portraits features of a barothropic relaxing medium under pressure perturbations. In the starting point, we show within a third-order of accuracy that the previous system is modeled by a “dissipative” cubic nonlinear evolution equation. Paying particular attention to high-frequency perturbations of the system, we solve the initial value problem of the system both analytically and numerically while unveiling the existence of localized multivalued waveguide channels. Accordingly, we find that the “dissipative” term with a “dissipative” parameter less than some limit value does not destroy the ambiguous solutions. We address some physical implications of the results obtained previously.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Initial value problem in string-inspired nonlocal field theory

We consider a nonlocal scalar field theory inspired by the tachyon action in open string field theory. The Lorentz-covariant action is characterized by a parameter ξ 2 that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in ξ 2 reduces the action to a local two-derivative theory with a ξ 2 -dependent potential. This picture is supported by evidence that the redefinition maps the wildly oscillating rolling tachyon solutions of the nonlocal theory to conventional rolling in the new scalar potential. For general field configurations we exhibit an obstruction to a local Lorentz-covariant formulation, but we can still achieve a formulation local in time, as well as a light-cone formulation. These constructions provide an initial value formulation and a Hamiltonian. Their causality is consistent with a lack of superluminal behavior in the nonlocal theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Initial-Boundary Value Problem for the Non-Stationary Radiative Transfer Equation with Fresnel Reflection and Refraction Conditions

We consider the initial-boundary value problems for the nonstationary radiative transfer equation in a system of semitransparent bodies with boundary and initial data in the complete scale of Lebesgue spaces. We establish the unique solvability of the first initial-boundary value problem, the problem with “shooting conditions,” and the problem with Fresnel reflection and refraction conditions on the body boundaries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Initial-Boundary Value Problem for the Nonstationary Radiative Transfer Equation with Diffuse Reflection and Refraction Conditions

We consider the initial-boundary value problem for the nonstationary radiative transfer equation in a system of semitransparent bodies with the conditions of diffuse reflection and refraction of radiation. We establish the unique solvability of the problem with boundary and initial data in the complete scale of Lebesgue spaces. We obtain estimates for solutions.

42 ENGINEERING↗
DOE OSTI2014

Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned “least squares shadowing (LSS) problem”. The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. II. Implicit Methods

We consider specific realizations of different implicit generalized Runge–Kutta methods as applied to the numerical integration with respect to time of initial-boundary-value problems for the second-order parabolic equations and investigate their spectral stability. It is shown that all implicit generalized Runge–Kutta methods are unconditionally spectrally stable but some of them have the conditional property of monotonicity of the numerical solution with respect to time. The functions of spectral stability of the implicit generalized Runge–Kutta methods are rational. We compare the analytic solution of the nonstationary one-dimensional problem of heat conduction with the numerical solutions of this problem obtained by different implicit generalized Runge–Kutta methods. It is shown that, in this case, the application of the one-stage Radau methods with subsequent discretization of the problem with respect to the space variable leads to the classical forward finite difference scheme (Laasonen scheme), whereas the use of the one-stage Gauss–Legendre method leads to a six-point symmetric scheme (Crank–Nicolson scheme). It is shown that diagonally implicit generalized Nørsett and Burrage methods are realized in almost the same way as the one-stage Radau and Gauss–Legendre methods but their accuracy in the time step is 10–1000 times higher. On the basis of comparison of the numerical and analytic solutions, we conclude that, in order to get practically suitable numerical solutions without any restrictions on the time step, it is reasonable to use one- and three-stage generalized Radau methods or two- and four-stage Lobatto IIIC methods. All other explicit and implicit generalized Runge–Kutta methods require certain restrictions imposed on the time step.

42 ENGINEERING↗
DOE OSTI2022

Multirate Exponential Rosenbrock Methods

In this paper we propose a novel class of methods for high-order accurate integration of multirate systems of ordinary differential equation initial-value problems. The proposed methods construct multirate schemes by approximating the action of matrix φ functions within explicit exponential Rosenbrock (ExpRB) methods, thereby called multirate ExpRB (MERB) methods. They consist of the solution to a sequence of modified “fast” initial-value problems, which may themselves be approximated through subcycling any desired initial-value problem solver. In addition to proving how to construct MERB methods from certain classes of ExpRB methods, we provide rigorous convergence analysis of these methods and derive efficient MERB schemes of orders 2 through 6 (the highest-order infinitesimal multirate methods to date). Lastly, we then present numerical simulations to confirm these theoretical convergence rates and to compare the efficiency of MERB methods against other recently introduced high-order multirate methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. I. Explicit Methods

We develop a general algorithm for the analysis the spectral stability of generalized multistage Runge–Kutta methods of various orders of accuracy as applied to the numerical integration with respect to time of an initial-boundary-value problem for the second-order parabolic equation. The expression for the function of spectral stability is obtained in two alternative forms: on the basis of matrix relations and in the determinant form. We study specific realizations of various generalized explicit Runge–Kutta methods and their spectral stability. It is shown that all explicit generalized Runge–Kutta methods possess the property of conditional spectral stability and the property of conditional monotonicity of the numerical solution in time whose violation leads to the appearance of false oscillations of the approximate solution. The stability function for these methods is polynomial. It is shown that the application of two-stage generalized explicit Runge–Kutta methods leads to the appearance of predictor-corrector-type schemes. In the case of nonstationary one-dimensional heat-conduction problem, on the basis of a one-stage generalized Runge–Kutta method, we obtain the classical two-layer conditionally stable explicit finite-difference scheme on a four-point template. It is demonstrated that the five-stage generalized Runge–Kutta–Merson method is characterized by the weakest condition of spectral stability as compared with all investigated explicit generalized Runge–Kutta methods.

42 ENGINEERING↗
DOE OSTI2021

Wave-driven torques to drive current and rotation

In the classic Landau damping initial value problem, where a planar electrostatic wave transfers energy and momentum to resonant electrons, a recoil reaction occurs in the nonresonant particles to ensure momentum conservation. To explain how net current can be driven in spite of this conservation, the literature often appeals to mechanisms that transfer this nonresonant recoil momentum to ions, which carry negligible current. However, this explanation does not allow the transport of net charge across magnetic field lines, precluding E X B rotation drive. In this study, we show that in steady state, this picture of current drive is incomplete. Using a simple Fresnel model of the plasma, we show that for lower hybrid waves, the electromagnetic energy flux (Poynting vector) and momentum flux (Maxwell stress tensor) associated with the evanescent vacuum wave become the Minkowski energy flux and momentum flux in the plasma and are ultimately transferred to resonant particles. Thus, the torque delivered to the resonant particles is ultimately supplied by the electromagnetic torque from the antenna, allowing the nonresonant recoil response to vanish and rotation to be driven. We present a warm fluid model that explains how this momentum conservation works out locally, via a Reynolds stress that does not appear in the one-dimensional initial value problem. This model is the simplest that can capture both the nonresonant recoil reaction in the initial-value problem, and the absence of a nonresonant recoil in the steady-state boundary value problem, thus forbidding rotation drive in the former while allowing it in the latter.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

High-order accurate solutions of the point kinetics equations with the spectral deferred correction method

Solving initial value problems with higher-order methods can improve the accuracy of the simulation results or the efficiency of the calculation. In this paper, we apply the spectral deferred correction (SDC) method to solve the initial value problem of the point kinetics equations (PKE). SDC is a stable, robust, and efficient high-order time-integration method capable of an arbitrary order of accuracy. For our implementation we show that it is A-stable for orders up to 8 and the order of accuracy is verified for PKE problems with a range of different reactivities. A 5.-order SDC method was then implemented to solve the exact PKE (EPKE) in the Transient Multilevel (TML) method of MPACT. The error from solutions of the EPKE is shown to be negligible. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗
DOE OSTI2018

Data-driven Modeling of Hemodynamics and its Role on Thrombus Size and Shape in Aortic Dissections

Aortic dissection is a pathology that manifests due to microstructural defects in the aortic wall. Blood enters the damaged wall through an intimal tear, thereby creating a so-called false lumen and exposing the blood to thrombogenic intramural constituents such as collagen. The natural history of this acute vascular injury thus depends, in part, on thrombus formation, maturation, and possible healing within the false lumen. A key question is: Why do some false lumens thrombose completely while others thrombose partially or little at all? An ability to predict the location and extent of thrombus in subjects with dissection could contribute significantly to clinical decision-making, including interventional design. We develop, for the first time, a data-driven particle-continuum model for thrombus formation in a murine model of aortic dissection. In the proposed model, we simulate a final-value problem in lieu of the original initial-value problem with significantly fewer particles that may grow in size upon activation, thus representing the local concentration of blood-borne species. Numerical results confirm that geometry and local hemodynamics play significant roles in the acute progression of thrombus. Despite geometrical differences between murine and human dissections, mouse models can provide considerable insight and have gained popularity owing to their reproducibility. Our results for three classes of geometrically different false lumens show that thrombus forms and extends to a greater extent in regions with lower bulk shear rates. Dense thrombi are less likely to form in high-shear zones and in the presence of strong vortices. Here, the present data-driven study suggests that the proposed model is robust and can be employed to assess thrombus formation in human aortic dissections.

60 APPLIED LIFE SCIENCES↗