Search NASA⌕ Search

SEARCH · Search NASA

Results for “Relaxation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Convex Relaxations of Maximal Load Delivery for Multi-Contingency Analysis of Joint Electric Power and Natural Gas Transmission Networks

Recent increases in gas-fired power generation have engendered increased interdependencies between natural gas and power transmission systems. These interdependencies have amplified existing vulnerabilities in gas and power grids, where disruptions can require the curtailment of load in one or both systems. Although typically operated independently, coordination of these systems during severe disruptions can allow for targeted delivery to lifeline services, including gas delivery for residential heating and power delivery for critical facilities. To address the challenge of estimating maximum joint network capacities under such disruptions, we consider the task of determining feasible steady-state operating points for severely damaged systems while ensuring the maximal delivery of gas and power loads simultaneously, represented mathematically as the nonconvex joint Maximal Load Delivery (MLD) problem. To increase its tractability, we present a mixed-integer convex relaxation of the MLD problem. Then, to demonstrate the relaxation’s effectiveness in determining bounds on network capacities, exact and relaxed MLD formulations are compared across various multi-contingency scenarios on nine joint networks ranging in size from 25 to 1191 nodes. The relaxation-based methodology is observed to accurately and efficiently estimate the impacts of severe joint network disruptions, often converging to the relaxed MLD problem’s globally optimal solution within ten seconds.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2023

Halted-pendulum Relaxation: Application to White Dwarf Binary Initial Data

Studying compact-star binaries and their mergers is integral to determining progenitors for observable transients. Today, compact-star mergers are typically studied via state-of-the-art computational fluid dynamics codes. One such numerical technique, smoothed particle hydrodynamics (SPH), is frequently chosen for its excellent mass, energy, and momentum conservation. The natural treatment of vacuum and the ability to represent highly irregular morphologies make SPH an excellent tool for the study of compact-star binaries and mergers. For many scenarios, including binary systems, the outcome of simulations is only as accurate as the initial conditions. For SPH, it is essential to ensure that the particles are distributed regularly, representing the initial density profile but without long-range correlations. Particle noise in the form of high-frequency local motion and low-frequency global dynamics must be damped out. Damping the latter can be as computationally intensive as the actual simulation. We discuss a new and straightforward relaxation method, halted-pendulum relaxation (HPR), to remove global oscillation modes of SPH particle configurations. In combination with effective external potentials representing gravitational and orbital forces, we show that HPR has an excellent performance in efficiently relaxing SPH particles to the desired density distribution and removing global oscillation modes. We compare the method to frequently used relaxation approaches and test it on a white dwarf binary model at its Roche-lobe overflow limit. We highlight the importance of our method in achieving accurate initial conditions and its effect on achieving circular orbits and realistic accretion rates when compared with other general relaxation methods.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Measurements of Electron Beam-Induced Spin-Relaxation in Frozen-Spin Hydrogen-Deuteride (HD)

Targets of solid hydrogen-deuteride (HD) can be prepared in a frozen-spin state with spin relaxation times (T1) in excess of a year. The present work has studied their potential use in experiments with electron beams. Polarization relaxation rates have been measured during exposure to sub-nanoAmp currents of 9.7 MeV electron beams from the recently commissioned Upgraded Injector Test Facility (UITF) at Jefferson Lab (JLab). These UITF measurements can be used to anticipate the expected performance at the GeV energies typical of JLab experiments, since the energy deposition in a target is almost independent of beam energy. An in-beam dilution refrigerator equipped with superconducting solenoids has been used to maintain solid HD samples at ?0.1 K and ?1 tesla, and internal NMR coils have been used to monitor hydrogen polarization. Spin-relaxation in two frozen-spin targets, with initial H-polarizations of 40% and 34%, have been tracked while exposed to beams under varying conditions of current, dose, beam duty factor and temperature. At a fixed accumulated dose, the spin-relaxation rates drop with current, suggesting depolarization by the charge cloud of the beam. Imposing a duty factor on the otherwise continuous UITF beam, with forced millisecond scale gaps, has shown no obvious correlation to polarization loss rates. After an accumulated dose of ?2 ?C/cm2, beam-off spin-relaxation rates drop from their immeasurably long pre-irradiation values to the order of weeks (with beam-on T1 values typically an order of magnitude shorter), reflecting a buildup of paramagnetic charge centers within the HD lattice. The accumulated polarization loss was approximately proportional to dose in both targets, dropping to 1/e of their initial values after ?6 ?C/cm2. Thermal equilibrium polarizations of targets not in the frozen-spin state (with intentionally short T1) have been used to deduce the in situ temperature of solid HD while under electron bombardment. A model for depolarization by beam-associated paramagnetic impurities largely accounts for the data, and suggests that improvements in heat removal could lead to significant increases in the in-beam T1.

O'Connell, Thomas↗
DOE OSTI2023

Surface oxygen exchange kinetics of mixed conducting oxides: Dilatometric vs electrical conductivity relaxation study

The surface oxygen exchange kinetics of mixed ionic-electronic conducting (MIEC) oxides play a crucial role in a variety of applications, including solid oxide fuel/electrolysis cells (SOFCs/SOECs), permeation membranes and sensors. To date, a variety of methods, including isotope exchange, electrical conductivity, optical absorptivity and thermogravimetry relaxation, and impedance spectroscopy have been used to measure the oxygen exchange coefficient of MIEC oxides. Each of these methods have their advantages and limitations, depending on the physical and chemical properties of the investigated materials and their sample dimensions and densities. Here, we demonstrate the ability to precisely measure the surface oxygen exchange coefficient (k chem ) of MIEC model material Pr 0.1 Ce 0.9 O 2-δ (PCO) by use of dilatometric relaxation measurements, particularly of interest for materials that exhibit larger chemical expansion coefficients. This is achieved by use of porous bulk specimens to ensure that the contribution of oxygen exchange to the overall kinetics is dominant. We demonstrate that k chem values extracted from chemical expansion relaxation measurements on PCO are nearly identical to those derived from electrical conductivity relaxation measurements. As a result, this provides the opportunity to precisely investigate the oxygen exchange and chemical expansion kinetics of a wide range of materials used in high-temperature applications, particularly where more conventional methods are difficult or inappropriate to apply.

(Pr,Ce)O2-x↗
DOE OSTI2022

Reconsidering spin-phonon relaxation in magnetic molecules

Because of the larger intra-molecular distortion, optical phonons usually have stronger spin-phonon coupling than acoustic phonons in molecular magnets. This property may pose problems to the theory of spin relaxation in ordinary paramagnetic materials, which have served as the basis for the understanding of spin dynamics in molecular magnets for decades. In this review, we explain why the Raman processes driven by optical phonons can play a dominant role at low temperature and provide unconventional dependence between relaxation time and temperature. Especially, we emphasize that the sub-barrier relaxation and anomalously low Raman exponents are two common signatures of the dominance. Here, we also present the algorithm and implementation for calculating spin-phonon relaxation in molecular solids with density functional theory codes.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Identifying electrochemical processes by distribution of relaxation times in proton exchange membrane electrolyzers

Distribution of relaxation time (DRT) is used to interpret electrochemical impedance spectroscopy (EIS) for proton exchange membrane (PEM) water electrolyzers, with an attempt to separate overlapped relaxation processes in Nyquist plots. By varying operating conditions and catalyst loadings, four main relaxation peaks arising from EIS can be identified and successfully separated from low to high frequencies as (P1) mass transport, (P2) oxygen evolution reaction kinetics, (P3) reaction kinetics (with faster time constant than P2), and (P4) ionic transport. Here, the shape, height, and frequency of the DRT peaks change with different membrane electrode assembly (MEA) configurations. Electron microscopy reveals distinct features from the cross-sectioned MEAs which verify critical DRT results in that increasing the iridium (Ir)-anode loading from 0.2 mgIr/cm 2 to 1.5 mgIr/cm 2 reduces kinetic losses due to higher site-access; a thick and compacted anode, however, also triggers higher ohmic resistances from membrane/catalyst layer hydration and increases transport losses due to longer ionomer pathways. DRT provides higher resolution to EIS for deconvoluting processes with different relaxation times and the quantification of DRT peaks improves the accounting of total losses from each process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

On relaxations of the max k -cut problem formulations

Here, a tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max k-cut problem is a fundamental combinatorial optimization problem with multiple notorious mixed integer optimization formulations. In this paper, we explore four existing mixed integer optimization formulations of the max k-cut problem. Specifically, we show that the continuous relaxation of a binary quadratic optimization formulation of the problem is: (i) stronger than the continuous relaxation of two mixed integer linear optimization formulations and (ii) at least as strong as the continuous relaxation of a mixed integer semidefinite optimization formulation. We also conduct a set of experiments on multiple sets of instances of the max k-cut problem using state-of-the-art solvers that empirically confirm the theoretical results in item (i). Furthermore, these numerical results illustrate the advances in the efficiency of global non-convex quadratic optimization solvers and more general mixed integer nonlinear optimization solvers. As a result, these solvers provide a promising option to solve combinatorial optimization problems. Our codes and data are available on GitHub.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Advances in relaxation and memory effects of magnetic nanoparticles for biomedical applications

Functionalized magnetic nanoparticles are pivotal in magnetic resonance imaging, computed tomography, controlled drug delivery, and hyperthermia treatments due to their exceptional magnetic relaxation and functional properties. The magnetic core composition and structure significantly affects the complex magnetic properties of these nanoparticles necessitating a thorough examination of magnetism fundamentals related to these systems. One important aspect is the ability of magnetic nanoparticles to retain previous magnetic state configurations known as memory effect, primarily governed by domain structure and magnetic anisotropy. Despite its relevance to advanced applications, comprehensive studies on magnetic relaxation and memory effects remain limited. Here, the present review aims to bridge this gap by investigating relaxation mechanisms, synthesis strategies, and applications, fostering further innovation. It investigates the memory effects and their dependence on particle composition and morphology along with key synthesis techniques for large-scale production in industrial adoption. Structured into focused sections on magnetic properties and their influence on biomedical and technological applications, this review provides essential insights into memory effects, magneto-relaxation mechanisms, influencing factors, and both experimental and theoretical methodologies. It also delves into computational modelling and AI-driven design, which are revolutionizing the prediction, discovery, and optimization of materials with tailored properties.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Alpha-relaxation by scattering and medium-range atomic correlation in simple liquids

The relaxation dynamics of liquid and glass can be studied by inelastic x-ray or neutron scattering through the intermediate scattering function F(Q, t), where Q is the momentum transfer of scattering. Because of the time-consuming nature of these measurements, F(Q, t) is usually measured only at the first peak of the structure function S(Q), and its principal decay time is referred to as the α-relaxation time τ α . τ α is generally considered to describe the relaxation time of the bulk, which is related to viscosity and is controlled by the atomic cage around an atom. Here, through simulations on metallic liquids, we show that the α-relaxation time determined by scattering experiments does not purely reflect viscosity but is influenced by changes in spatial cooperativity. We also demonstrate that atomic caging is not exerted by the nearest neighbors but involves more cooperative atomic dynamics of the atomic medium-range order.

Glass transitions↗
DOE OSTI2020

Fast Relaxation on Qutrit Transitions of Nitrogen-Vacancy Centers in Nanodiamonds

Thanks to their versatility, nitrogen-vacancy (N-𝑉) centers in nanodiamonds have been widely adopted as nanoscale sensors. However, their sensitivities are limited by their short coherence times relative to N-𝑉⁢s in bulk diamond. A more complete understanding of the origins of decoherence in nanodiamonds is critical to improving their performance. Here we present measurements of fast spin relaxation on qutrit transitions between the energy eigenstates composed of the 𝑚 𝑠 =|±1⟩ states of the N-𝑉 − electronic ground state in approximately 40-nm nanodiamonds under ambient conditions. For frequency splittings between these states of 20 MHz or less the maximum theoretically achievable coherence time of the N-𝑉 spin is approximately 2 orders of magnitude shorter than would be expected if the N-𝑉 spin is treated as a qubit. We attribute this fast relaxation to electric field noise. We observe a strong falloff of the qutrit relaxation rate with the splitting between the states, suggesting that, whenever possible, measurements with N-𝑉⁢s in nanodiamonds should be performed at moderate axial magnetic fields (>60 G). We also observe that the qutrit relaxation rate changes with time. As a result, these findings indicate that surface electric field noise is a major source of decoherence for N-𝑉⁢s in nanodiamonds.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Energy relaxation dynamics in a nodal-line semimetal

Here we study the temperature relaxation dynamics of nodal-line semimetals after a sudden excitation in the presence of acoustic and optical phonon modes. We find that the nodal line constrains the electron momenta in scattering processes, and as a result, the temperature relaxation due to acoustic phonons is exponential as a function of time. However, depending on initial conditions, other functional forms are possible. In typical pump-probe experiments, the temperature relaxation is linear due to acoustic phonons with rates that vary as ~n 1/2 with density. The temperature relaxation due to optical phonons is also linear with rates ~n -1/2 or ~n .

36 MATERIALS SCIENCE↗
DOE OSTI2024

Analytical Model for Atomic Relaxation in Twisted Moiré Materials

By virtue of being atomically thin, the electronic properties of heterostructures built from two-dimensional materials are strongly influenced by atomic relaxation. The atomic layers behave as flexible membranes rather than rigid crystals. Here we develop an analytical theory of lattice relaxation in twisted moiré materials. We obtain analytical results for the lattice displacements and corresponding pseudo gauge fields, as a function of twist angle. We benchmark our results for twisted bilayer graphene and twisted WSe 2 bilayers using large-scale molecular dynamics simulations. Our single-parameter theory is valid in graphene bilayers for twist angles 𝜃 ≳ 0.7°, and in twisted WSe 2 for 𝜃 ≳ 1.6°. Furthermore, we also investigate how relaxation alters the electronic structure in twisted bilayer graphene, providing a simple extension to the continuum model to account for lattice relaxation.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. Next, we introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods.

bound tightening↗
DOE OSTI2022

Spin relaxation rate for heavy quarks in weakly coupled QCD plasma

We compute the relaxation rate of the spin density of heavy quarks in a perturbative QCD plasma to leading-log order in the coupling constant g. The spin relaxation rate Γ s in spin hydrodynamics is shown to be Γ s ~ g 4 log(1/g)T(T/M) 2 in the heavy-quark limit T/M $\ll$ 1, which is smaller than the relaxation rate of other non- hydrodynamic modes by additional powers of T/M. We demonstrate three different methods to evaluate the spin relaxation rate: 1) the Green-Kubo formula in the spin hydrodynamic regime, 2) the spin density correlation function in the strict hydrodynamic limit, and 3) quantum kinetic theory of the spin distribution function in momentum space. We highlight the interesting differences between these methods, while they are ultimately connected to each other by the underlying Ward-Takahashi identity for the non-conserved spin density.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

On the inference of viscoelastic constants from stress relaxation experiments

Several constitutive theories have been proposed in the literature to model the viscoelastic response of materials, including widely used rheological constitutive models. These models are characterized by certain parameters ("time constants") that define the time scales over which the material relaxes. These parameters are primarily obtained from stress relaxation experiments using curve-fitting techniques. However, the question of how best to estimate these time constants remains open. As a step towards answering this question, we propose an optimal experimental design approach based on ideas from information geometry, namely Fisher information and Kullback-Leibler divergence. The material is modeled as a spring element in parallel with multiple Maxwell elements and described using a one- or two-term Prony series. Treating the time constants as unknowns, we develop expressions for the Fisher information and Kullback-Leibler divergence that allow us to maximize information gain from experimental data. Based on the results of this study, we propose that the largest time constant estimated from a stress relaxation experiment for a linear viscoelastic material should be at most one-fifth of the total time of the experiment in order to maximize information gain. Our results also provide confirmation that the equilibrium modulus of the material cannot be reliably determined from curve-fitting to data from a stress relaxation experiment.

Fisher information↗
DOE OSTI2020

A thermally-limited bubble growth model for the relaxation time of superheated fuels

Here, we propose a novel approach to evaluate the relaxation time of vapor bubble growth in the context of the flash boiling of a superheated liquid. In alternative to the empirical correlation derived from superheated water experiments almost fifty years ago, the new model describes the thermally-dominated growth of vapor bubbles in terms that are dependent on the local Jakob number (the ratio of sensible heat to latent heat during phase change) and the number density of vapor bubbles. The model is tested by plugging the resulting relaxation time into the Homogenous Relaxation Model (HRM). Flash-boiling simulations carried out with HRM are compared with n-pentane (C 5 H 12 ) injection and boil-off experiments conducted with a real-size, axial-hole, transparent gasoline injector discharging into a constant-pressure vessel. The long-distance microscopy images from the experiments, processed to derive the projected liquid volume (PLV) of the spray, provide a unique set of time-resolved validation data for direct fuel injection simulations. At conditions ranging from flaring to mild and minimal flash boiling, we show that switching to the new relaxation time improves the agreement with the measured PLV profiles with respect to the standard empirical model. Particularly at flaring conditions, the predicted increase in gas cooling caused by rapid vapor production is shown to be more consistent with the observed boil-off.

42 ENGINEERING↗
DOE OSTI2021

Tracking the evolution of processes occurring in silicon anodes in lithium ion batteries by 3D visualization of relaxation times

An unconventional electroanalytical method has been used for tracking processes in silicon anodes in lithium ion batteries: a 3D visualization of relaxation times. Impedance data of the electrodes were collected at different potentials and different cycles during cyclic voltammetry, and were treated by means of the Distribution of Relaxation Times (DRT) method. A 3D visualization of the results allowed to identify the formation of a solid electrolyte interphase on the anode, composed of two layers with different relaxation times. Such findings are not possible by conventional analysis of impedance data by modeling with equivalent circuits, nor by simple DRT alone. Additionally, it was possible to observe that the characteristic relaxation time of the lithiation of the Si anode becomes smaller upon cycling, indicating that the material experiences structural transformations that allow it to lithiate faster. The result is relevant to motivate the use of micron-sized particles in the anode.

25 ENERGY STORAGE↗