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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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

A classical and a relativistic law of motion for spherical supernovae

In this paper we derive some first order differential equations which model the classical and the relativistic thin layer approximations. The circumstellar medium is assumed to follow a density profile of the Plummer type, the Lane-Emden (n = 5) type, or a power law. The first order differential equations are solved analytically, numerically, by a series expansion, or by recursion. The initial conditions are chosen in order to model the temporal evolution of SN 1993J over 10 yr and a smaller chi-squared is obtained for the Plummer case with η = 6. The stellar mass ejected by the SN progenitor prior to the explosion, expressed in solar mass, is identified with the total mass associated with the selected density profile and varies from 0.217 to 0.402 when the central number density is 10{sup 7} particles per cubic centimeter. The FWHM of the three density profiles, which can be identified with the size of the pre-SN 1993J envelope, varies from 0.0071 pc to 0.0092 pc.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS

This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs Haarten-Lax-van-Leer-type approximate Riemann solvers and includes facilities to control the divergence of the magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Linear-algebraic bath transformation for simulating complex open quantum systems

In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly coupled multiple parallel chains. Furthermore, the transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Self-consistent initial conditions for primordial black hole formation

For an arbitrarily strong, spherically symmetric super-horizon curvature perturbation, we present analytic solutions of the Einstein equations in terms of the asymptotic expansion over the ratio of the Hubble radius to the length-scale of the curvature perturbation to set initial conditions for numerical computations of primordial black hole formation. To obtain this solution we develop a recursive method of quasi-linearization which reduces the problem to a system of coupled ordinary differential equations for the Nth order terms in the asymptotic expansion with sources consisting of a non-linear combination of the lower order terms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Excursions through KK modes

In this article we study Kaluza-Klein (KK) dimensional reduction of massive Abelian gauge theories with charged matter fields on a circle. Since local gauge transformations change position dependence of the charged fields, the decomposition of the charged matter fields into KK modes is gauge dependent. While whole KK mass spectrum is independent of the gauge choice, the mode number depends on the gauge. The masses of the KK modes also depend on the field value of the zero-mode of the extra dimensional component of the gauge field. In particular, one of the KK modes in the KK tower of each massless 5D charged field becomes massless at particular values of the extra-dimensional component of the gauge field. When the extra-dimensional component of the gauge field is identified with the inflaton, this structure leads to recursive cosmological particle productions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

The matrix product approximation for the dynamic cavity method

Stochastic dynamics of classical degrees of freedom, defined on vertices of locally tree-like graphs, can be studied in the framework of the dynamic cavity method which is exact for tree graphs. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, and other technical, biological, and social networks. The central objects in the cavity method are edge messages—conditional probabilities of two vertex variable trajectories. In this paper, we discuss a rather pedagogical derivation for the dynamic cavity method, give a detailed account of the novel matrix product edge message (MPEM) algorithm for the solution of the dynamic cavity equation as introduced, and present optimizations and extensions. Matrix product approximations of the edge messages are constructed recursively in an iteration over time. Computation costs and precision can be tuned by controlling the matrix dimensions of the MPEM in truncations. Without truncations, the dynamics is exact. Data for Glauber–Ising dynamics shows a linear growth of computation costs in time. In contrast to Monte Carlo simulations, the approach has a much better error scaling. Hence, it gives for example access to low probability events and decaying observables like temporal correlations. Here, we discuss optimized truncation schemes and an extension that allows to capture models which have a continuum time limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A canonical Hamiltonian for open quantum systems

Abstract If an open quantum system is initially uncorrelated from its environment, then its dynamics can be written in terms of a Lindblad-form master equation. The master equation is divided into a unitary piece, represented by an effective Hamiltonian, and a dissipative piece, represented by a hermiticity-preserving superoperator; however, the division of open system dynamics into unitary and dissipative pieces is non-unique. For finite-dimensional quantum systems, we resolve this non-uniqueness by specifying a norm on the space of dissipative superoperators and defining the canonical Hamiltonian to be the one whose dissipator is minimal. We show that the canonical Hamiltonian thus defined is equivalent to the Hamiltonian initially defined by Lindblad, and that it is uniquely specified by requiring the dissipator’s jump operators to be traceless, extending a uniqueness result known previously in the special case of Markovian master equations. For a system weakly coupled to its environment, we give a recursive formula for computing the canonical effective Hamiltonian to arbitrary orders in perturbation theory, which we can think of as a perturbative scheme for renormalizing the system’s bare Hamiltonian.

Physics↗
DOE OSTI2026

Analog and symbolic computation through the Koopman framework

We develop a Koopman operator framework for studying the computational structure of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ‘Koopman halting problem’ that is recursively enumerable in general. For symbolic systems, such as those defined on Cantor space, this operator formulation captures reachability between clopen sets, while for equicontinuous systems we prove that the Koopman halting problem is decidable. Our framework demonstrates that absorbing (halting) states in coarse-grained finite automata correspond to Koopman eigenfunctions with eigenvalue one, while cycles in the transition graph impose spectral constraints associated with periodic dynamics. These results provide a unifying perspective on computation in symbolic and analog systems, showing how computational universality is reflected in operator spectra, invariant subspaces, and algebraic structures. Beyond symbolic dynamics, this operator-theoretic lens opens pathways to analyze the computational properties of a broader class of dynamical systems, including polynomial and analog models, and suggests that computational hardness may admit dynamical signatures in terms of Koopman spectral structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Strategies for connecting whole-building LCA to the low-carbon design process

Abstract Decarbonization is essential to meeting urgent climate goals. With the building sector in the United States accounting for 35% of total U.S. carbon emissions, reducing environmental impacts within the built environment is critical. Whole-building life cycle analysis (WBLCA) quantifies the impacts of a building throughout its life cycle. Despite being a powerful tool, WBLCA is not standard practice in the integrated design process. When WBLCA is used, it is typically either speculative and based on early design information or conducted only after design completion as an accounting measure, with virtually no opportunity to impact the actual design. This work proposes a workflow for fully incorporating WBLCA into the building design process in an iterative, recursive manner, where design decisions impact the WBLCA, which in turn informs future design decisions. We use the example of a negative-operational carbon modular building seeking negative upfront embodied carbon using bio-based materials for carbon sequestration as a case study for demonstrating the utility of the framework. Key contributions of this work include a framework of computational processes for conducting iterative WBLCA, using a combination of an existing building WBLCA tool (Tally) within the building information modeling superstructure (Revit) and a custom script (in R) for materials, life cycle stages, and workflows not available in the WBLCA tool. Additionally, we provide strategies for harmonizing the environmental impacts of novel materials or processes from various life cycle inventory sources with materials or processes in existing building WBLCA tool repositories. These strategies are useful for those involved in building design with an interest in reducing their environmental impact. For example, this framework would be useful for researchers who are conducting WBLCAs on projects that include new or unusual materials and for design teams who want to integrate WBLCA more fully into their design process in order to ensure the building materials are consciously chosen to advance climate goals, while still ensuring best performance by traditional measures.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Linear complexity

We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the strong-admissibility-based $\mathscr{H}^{2}$ format, where strong recursive skeletonization factorization compresses remote interactions. We build upon previous implementations of $\mathscr{H}^{2}$ matrix construction for efficient factorization and solution algorithm design, which are illustrated graphically in stepwise detail. The algorithms are ‘blackbox’ in the sense that the only inputs are the matrix and right-hand side, without analytical or geometrical information about the origin of the system. We demonstrate linear complexity scaling in both time and memory on four representative families of dense matrices up to one million in size. Parallel scaling up to 16 threads is enabled by a multi-level matrix graph coloring and avoidance of dynamic memory allocations thanks to prefix-sum memory management. An experimental backward error analysis is included. We break down the timings of different phases, identify phases that are memory-bandwidth limited, and discuss alternatives for phases that may be sensitive to the trend to employ lower precisions for performance.

Boukaram, Wajih↗
DOE OSTI2018

On the Lebesgue constant of weighted Leja points for Lagrange interpolation on unbounded domains

Here, this work focuses on weighted Lagrange interpolation on an unbounded domain and analyzes the Lebesgue constant for a sequence of weighted Leja points. The standard Leja points are a nested sequence of points defined on a compact subset of the real line and can be extended to unbounded domains with the introduction of a weight function w:R → [0,1]. Due to a simple recursive formulation in one dimension, such abscissas provide a foundation for high-dimensional approximation methods such as sparse grid collocation, deterministic least squares and compressed sensing. Just as in the unweighted case of interpolation on a compact domain, we use results from potential theory to prove that the Lebesgue constant for the Leja points grows subexponentially with the number of interpolation nodes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

On decoupling the integrals of cosmological perturbation theory

ABSTRACT Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher order corrections by integration over linear statistics of the density fields weighted by kernels resulting from recursive solution of the fluid equations. These integrals quickly become high dimensional and naively require increasing computational resources the higher the order of the corrections. Here, we show how to decouple the integrands that often produce this issue, enabling PT corrections to be computed as a sum of products of independent 1D integrals. Our approach is related to a commonly used method for calculating multiloop Feynman integrals in quantum field theory, the Gegenbauer Polynomial x-Space Technique. We explicitly reduce the three terms entering the 2-loop power spectrum, formally requiring 9D integrations, to sums over successive 1D radial integrals. These 1D integrals can further be performed as convolutions, rendering the scaling of this method Nglog Ng with Ng the number of grid points used for each fast Fourier transform. This method should be highly enabling for upcoming large-scale structure redshift surveys where model predictions at an enormous number of cosmological parameter combinations will be required by Monte Carlo Markov Chain searches for the best-fitting values.

Slepian, Zachary↗
DOE OSTI2020

Combining the synergistic control capabilities of modeling and experiments: Illustration of finding a minimum-time quantum objective

A common way to manipulate a quantum system, for example spins or artificial atoms, is to use properly tailored control pulses. In order to accomplish quantum information tasks before coherence is lost, it is crucial to implement the control in the shortest possible time. Here we report the near time-optimal preparation of a Bell state with fidelity higher than 99% in an NMR experiment, which is feasible by combining the synergistic capabilities of modeling and experiments operating in tandem. In this work, the pulses preparing the Bell state are found by experiments that are recursively assisted with a gradient-based optimization algorithm working with a model. Thus, we exploit the interplay between model-based numerical optimal design and experimental-based learning control. Utilizing the balanced synergism between the dual approaches, as dictated by the case specific capabilities of each approach, should have broad applications for accelerating the search for optimal quantum controls.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Nonequilibrium renormalization group fixed points of the quantum clock chain and the quantum Potts chain

In this work, we derive an exact renormalization group recursion relation for the Loschmidt amplitude of the quantum Q-state clock model and the quantum Q-state Potts model in one dimension. The renormalization group flow is discussed in detail. The fixed points of the renormalization group flow are found to be complex in general. These fixed points control the dynamical phases of the two models, giving rise to nonanalyticities in its Loschmidt rate function, for both the pure and the disordered system. For the quench protocols studied, dynamical quantum phase transitions are found to occur in the clock model for all Qs considered, while in the Potts model, they only occur when Q < 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Dynamical quantum phase transitions of quantum spin chains with a Loschmidt-rate critical exponent equal to $\frac{1}{2}$

In this work, we describe a new universality class of dynamical quantum phase transitions of the Loschmidt amplitude of quantum spin chains off equilibrium criticality. We demonstrate that in many cases it is possible to change the conventional linear singularity of the Loschmidt rate function into a smooth peak by tuning one parameter of the quench protocol. Exactly at the point when this change-over occurs, the singularity of the Loschmidt rate function persists, with a critical exponent equal to $\frac{1}{2}$. The nonequilibrium renormalization group fixed point controlling this universality class is described. An asymptotically exact renormalization group recursion relation is derived around this fixed point to obtain the critical exponent.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Floquet dynamics of disordered bands with isolated critical energies

We investigate localization properties of driven models which exhibit a subextensive number of extended states in the static setting. We consider instances where the extended modes are or are not protected by topological considerations. To this end, we contrast the strongly driven, disordered, lowest Landau level, which we refer to as the random Landau model (RLM), with the random dimer model (RDM); the RDM also has a subextensive set of delocalized modes in the middle of the spectrum whose origin is not topological. We map the driven models on to a higher-dimensional effective model and numerically compute the localization length as a function of disorder strength, drive amplitude, and frequency using the recursive Green's function method. Our numerical results indicate that, in the presence of a strong drive (low frequency and/or large drive amplitude), the topologically protected RLM continues to exhibit a spectrum with both localized and delocalized (or critical) modes, but the spectral range of delocalized modes is enhanced by the driving. This occurs due to an admixture of the localized modes with extended modes arising due to the topologically protected critical energy in the middle of the spectrum. On the other hand, in the RDM, a weak drive immediately localizes the entire spectrum. This occurs in contrast to the naive expectation from perturbation theory that mixing between localized and delocalized modes generically enhances the delocalization of all modes. Our work highlights the importance of the origin of the delocalized modes in the localization properties of the corresponding Floquet model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Dynamics of almost strong edge modes in spin chains away from integrability

Results are presented for the dynamics of an almost strong edge mode which is the quasistable Majorana edge mode occurring in nonintegrable spin chains. The dynamics of the edge mode is studied using exact diagonalization, and compared with time evolution with respect to an effective semi-infinite model in Krylov space obtained from the recursion method. The effective Krylov Hamiltonian is found to resemble a spatially inhomogeneous Su-Schrieffer-Heeger model where the hopping amplitude increases linearly with distance into the bulk, typical of thermalizing systems, but also has a staggered or dimerized structure superimposed on it. Here, the nonperturbatively long lifetime of the edge mode is shown to be due to this staggered structure which diminishes the effectiveness of the linearly growing hopping amplitude. On taking the continuum limit of the Krylov Hamiltonian, the edge mode is found to be equivalent to the quasistable mode of a Dirac Hamiltonian on a half line, with a mass which is nonzero over a finite distance, before terminating into a gapless metallic bulk. The analytic estimates are found to be in good agreement with the numerically obtained lifetimes of the edge mode.

1-dimensional systems↗
DOE OSTI2023

Suppression of one-dimensional weak localization by band asymmetry

Herein we investigate disorder-induced localization in metals that break time-reversal and inversion symmetries through their energy dispersion, ε k ≠ε– k , but lack Berry phases. In the perturbative regime of disorder, we show that weak localization is suppressed due to a mismatch of the Fermi velocities of left and right movers. To substantiate this analytical result, we perform quench numerics on chains shorter than the Anderson localization length ξ—the latter computed and verified to be finite using the recursive Green's function method—and find a sharp rise in the saturation value of the participation ratio due to band asymmetry, indicating a tendency to delocalize. Interestingly, for weak disorder strength η, we see a better fit to the scaling behavior ξ∝1/η 2 for asymmetric bands than conventional symmetric ones.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗