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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Point-implicit relaxation strategies for viscous, hypersonic flows

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3D, viscous, hypersonic flows in chemical and thermal nonequilibrium is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with a modified Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's symmetric total variation diminishing scheme. Newton relaxation of the fully coupled equation set is employed on a cell-to-cell basis. Under-relaxation of the inviscid and over-relaxation of the viscous contributions to the residual are implemented. Computational work is easily partitioned among many processors in an asynchronous, dynamic mode for convergence acceleration. An overview of the physical models employed herein for thermochemical nonequilibrium is included. Several test cases and comparisons with experimental data are presented involving hypersonic flow over blunt bodies which illustrate the qualitative and quantitative capabilities of this approach.

Gnoffo, P. A.↗
NASA NTRS1989

Upwind-biased, point-implicit relaxation strategies for hypersonic flowfield simulations on supercomputers

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, hypersonic flows in chemical and thermal nonequilibrium is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. The relaxation strategy is well suited for computers employing either vector or parallel architectures, and the relation between computer architecture and algorithm is emphasized. It is also well suited to the numerical solution of the governing equations on unstructured grids. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large. block tri-diagonal systems. A single relaxation step depends only on information from nearest neighbors. Predictions for pressure distributions, surface heating, and aerodynamic coefficients compare well with experimental data for Mach 10 flow over a blunt body. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium (velocity = 8917 m/s, altitude = 78 km.) over the Aeroassist Flight Experiment (AFE) configuration obtained on a multi-domain grid are discussed.

Gnoffo, Peter A.↗
NASA NTRS1990

Mathematical theory of a relaxed design problem in structural optimization

Various attempts have been made to construct a rigorous mathematical theory of optimization for size, shape, and topology (i.e. layout) of an elastic structure. If these are represented by a finite number of parametric functions, as Armand described, it is possible to construct an existence theory of the optimum design using compactness argument in a finite dimensional design space or a closed admissible set of a finite dimensional design space. However, if the admissible design set is a subset of non-reflexive Banach space such as L(sup infinity)(Omega), construction of the existence theory of the optimum design becomes suddenly difficult and requires to extend (i.e. generalize) the design problem to much more wider class of design that is compatible to mechanics of structures in the sense of variational principle. Starting from the study by Cheng and Olhoff, Lurie, Cherkaev, and Fedorov introduced a new concept of convergence of design variables in a generalized sense and construct the 'G-Closure' theory of an extended (relaxed) optimum design problem. A similar attempt, but independent in large extent, can also be found in Kohn and Strang in which the shape and topology optimization problem is relaxed to allow to use of perforated composites rather than restricting it to usual solid structures. An identical idea is also stated in Murat and Tartar using the notion of the homogenization theory. That is, introducing possibility of micro-scale perforation together with the theory of homogenization, the optimum design problem is relaxed to construct its mathematical theory. It is also noted that this type of relaxed design problem is perfectly matched to the variational principle in structural mechanics.

Kikuchi, Noboru↗
NASA NTRS1993

Relaxation schemes for Chebyshev spectral multigrid methods

Two relaxation schemes for Chebyshev spectral multigrid methods are presented for elliptic equations with Dirichlet boundary conditions. The first scheme is a pointwise-preconditioned Richardson relaxation scheme and the second is a line relaxation scheme. The line relaxation scheme provides an efficient and relatively simple approach for solving two-dimensional spectral equations. Numerical examples and comparisons with other methods are given.

Kang, Yimin↗
NASA NTRS2000

Modeling Step-Strain Relaxation and Cyclic Deformations of Elastomers

Data for step-strain relaxation and cyclic compressive deformations of highly viscous short elastomer cylinders are modeled using a large strain rubber viscoelastic constitutive theory with a rate-independent friction stress term added. In the tests, both small and large amplitude cyclic compressive strains, in the range of 1% to 10%, were superimposed on steady state compressed strains, in the range of 5% to 20%, for frequencies of 1 and 10 Hz. The elastomer cylinders were conditioned prior to each test to soften them. The constants in the viscoclastic-friction constitutive theory are determined by employing a nonlinear least-squares method to fit the analytical stresses for a Maxwell model, which includes friction, to measured relaxation stresses obtained from a 20% step-strain compression test. The simulation of the relaxation data with the nonlinear model is successful at compressive strains of 5%, 10%, 15%, and 20%. Simulations of hysteresis stresses for enforced cyclic compressive strains of 20% +/- 5% are made with the model calibrated by the relaxation data. The predicted hysteresis stresses are lower than the measured stresses.

Johnson, A.R.↗
NASA NTRS1994

Rotational Relaxation Analysis of Nitrogen in Low-Density Freejet Expansions

The phenomena of rotational relaxation of nitrogen has been examined by numerous investigators over many years. One of the experiments which has been performed examines nonequilibrium flow in low-density free jet expansions. Data have been taken in such flows using a variety of techniques, including time-of-flight methods and electron beam fluorescence spectroscopy. The direct flow properties measured in these different investigations, such as density and translational, rotational and vibrational temperatures generally show reasonable agreement. However, this kind of correlation from experiment to experiment tends to be lost when these data are analyzed to obtain rotational relaxation time or collision number. The goal of such data analyses is to generate a succinct model for rotational relaxation in nitrogen which is essential for the computation of nonequilibrium rarefied flows. The objective of the present work is to process a large body of experimental data in a consistent manner to yield relaxation model parameters of the greatest utility for flow computations.

Gochberg, Lawrence A.↗
NASA NTRS2001

Distributed Relaxation for Conservative Discretizations

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Diskin, Boris↗
NASA NTRS1997

Relaxation Revisited: A Fresh Look at Multigrid for Steady Flows

The year 1971 saw the publication of one of the landmark papers in computational aerodynamics, that of Murman and Cole. As with many seminal works, its significance lies not so much in the specific problem that it addressed| small disturbance, plane transonic flow - but in the identification of a general approach to the solution of a technically important and theoretically difficult problem. The key features of Murman and Cole's work were the use of type- dependent differencing to correctly account for the proper domain of dependence of a mixed elliptic/hyperbolic equation, and the introduction of line relaxation to solve the steady flow equation. All subsequent work in transonic potential flows was based on these concepts. Jameson extended Murman and Cole's ideas to the full potential equation with two important contributions. First, he introduced the rotated difference stencil, which generalized the Murman and Cole type-dependent difference operator to general coordinates. Second, he used the interpretation, introduced by Garabedian, of relaxation as an iteration in artificial time to construct stable relaxation schemes, generalizing the original line relaxation method of Reference. The decade of the 1970s saw an explosion of activity in the solution of transonic potential flows, which has been summarized in the review article of Caughey.

Roberts, Thomas W.↗
NASA NTRS2001

Determinants of diastolic myocardial tissue Doppler velocities: influences of relaxation and preload

Myocardial tissue Doppler echocardiography (TDE) has been proposed as a tool for the assessment of diastolic function. Controversy exists regarding whether TDE measurements are influenced by preload. In this study, left ventricular volume and high-fidelity pressures were obtained in eight closed-chest dogs during intermittent caval occlusion. The time constant of isovolumic ventricular relaxation (tau) was altered with varying doses of dobutamine and esmolol. Peak early diastolic myocardial (E(m)) and transmitral (E) velocities were measured before and after preload reduction. The relative effects of changes in preload and relaxation were determined for E(m) and compared with their effects on E. The following results were observed: caval occlusion significantly decreased E (DeltaE = 16.4 +/- 3.3 cm/s, 36.6 +/- 13.7%, P < 0.01) and E(m) (DeltaE(m) = 1. 3 +/- 0.4 cm/s, 32.5 +/- 26.1%, P < 0.01) under baseline conditions. However, preload reduction was similar for E under all lusitropic conditions (P = not significant), but these effects on E(m) decreased with worsening relaxation. At tau < 50 ms, changes in E(m) with preload reduction were significantly greater (DeltaE(m) = 2.8 +/- 0.6 cm/s) than at tau = 50-65 ms (DeltaE(m) = 1.2 +/- 0.2 cm/s) and at tau >65 ms (DeltaE(m) = 0.5 +/- 0.1 cm/s, P < 0.05). We concluded that TDE E(m) is preload dependent. However, this effect decreases with worsening relaxation.

NASA Discipline Cardiopulmonary↗
DOE OSTI2025

Uncooled GeSn MWIR Photodetectors Using Fully Relaxed Thin Triple‐Step Buffer

GeSn photodetectors monolithically grown on Ge virtual substrates demonstrate mid-wave infrared (MWIR) detection at room temperature. The lattice mismatch between GeSn and Ge causes dislocations and compressive strain, creating leakage pathways and unwanted indirect band transitions. Designed thin Ge 0.91 Sn 0.09 triple-step buffer layers of ≈175 nm total thickness reduce dislocations and enable full relaxation, showing 100% lattice relaxation and smooth surface roughness of 0.83 nm with shorter auto-correlation length in surface morphology compared to single-step buffers. Ge 1-x Sn x photodetectors (x = 0.09, 0.12, and 0.15) on triple-step buffers with n-i-p configurations achieve lattice strain relaxations of 99%, 88%, and 80%, respectively. Ge 0.91 Sn 0.09 and Ge 0.88 Sn 0.12 show gradual variation in auto-correlation amplitude, while Ge 0.85 Sn 0.15 shows an increase due to lattice mismatch. Shockley–Read–Hall recombination current dominates at low reverse bias due to mismatch-induced dislocations, while band-to-band tunneling current dominates at higher reverse bias due to narrowing bandgap under strong electric fields. Here, the photodetectors show extended spectral response with increasing Sn composition of i-GeSn active layer sandwiched by barriers. Ge 0.88 Sn 0.12 and Ge 0.85 Sn 0.15 exhibit extended wavelength cut-offs of 3.12 and 3.27 µm at room temperature, demonstrating significant potential for silicon-based MWIR applications.

GeSn↗
DOE OSTI2023

Relaxing Wrinkles in Jammed Interfacial Assemblies

Dynamic covalent bonding has emerged as a mean by which stresses in a network can be relaxed. Here, the strength of the bonding of ligands to nanoparticles at the interface between two immiscible liquids affect the same results in jammed assemblies of nanoparticle surfactants. Beyond a critical degree of overcrowding induced by the compression of jammed interfacial assemblies, the bonding of ligands to nanoparticles (NPs) can be broken, resulting in a desorption of the NPs from the interface. This reduces the areal density of nanoparticle surfactants at the interface, allowing the assemblies to relax, not to a fluid state but rather another jammed state. The relaxation of the wrinkles caused by the compression reflects the tendency of these assemblies to eliminate areas of high curvature, favoring a more planar geometry. Importantly, this enabled the generation of giant vesicular and multivesicular structures from these assemblies.

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

Reversible and Irreversible Layer Edge Relaxation in Laser–Radiation–Hardened 2D Organic–Inorganic Perovskite Crystals

The layer edge states or low energy state (LES) in 2D hybrid organic–inorganic perovskites demonstrate a prolonged carrier lifetime for better performance of optoelectronic devices. However, the fundamental understanding of LES in 2D perovskites is still inconclusive. Herein, a photoluminescence (PL) study of LES in 2D Ruddlesden–Popper perovskites is presented with n = 2 and n = 3 from their cleaved cross sections that are more stable than the natural edge. The PL measurements clearly observe reversible, and irreversible surface relaxations (case I and case II) in three laser intensity ranges, further supported by a PL excitation cycle from low to high laser intensity, and vice versa. The PL wavelength of LES is tunable with laser intensity and blueshifts with increasing laser intensity during irreversible surface relaxation process (case I). Fluorescence lifetime imaging (FLIM) shows that the LES has a longer lifetime than the band-edge emission in the sample without a photodegradation, while the BE lifetime becomes relatively longer in the area with a photodegradation. Furthermore, the presented laser tunable LES and the related irreversible relaxation process provide a new insight that can help improve the photostability in 2D perovskites and understand roles of LESs in optoelectronic device performance.

2D organic-inorganic perovskite↗
DOE OSTI2025

Regularizing the linearly extrapolated BDF2 scheme for incompressible flows with time relaxation

This paper presents a highly-efficient finite element scheme for the time relaxation model (TRM). The efficiency is achieved through the second-order BDF2 time-stepping scheme with linear extrapolation (BDF2LE). The accuracy of the scheme is also greatly enhanced through the use of the divergence-free Scott-Vogeulis finite elements, and van Cittert approximate deconvolution. A complete finite element analysis is provided, which includes rigorous proofs for the stability, well-possessedness, and convergence of both velocity and pressure solutions. Furthermore, we also demonstrate that the inclusion of the linear time relaxation term preserves the long-time stability of the unregularized BDF2LE scheme. Finally, numerical experiments are presented that demonstrate the added stability and accuracy that time relaxation can provide.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Nonlinear dielectric relaxation of polar liquids

Molecular dynamics of two water models, SPC/E and TIP3P, at a number of temperatures are used to test the Kivelson-Madden equation connecting single-particle and collective dielectric relaxation times through the Kirkwood factor. The relation is confirmed by simulations and used to estimate the nonlinear effect of the electric field on the dielectric relaxation time. We show that the main effect of the field comes through slowing down of the single-particle rotational dynamics and the relative contribution of the field-induced alteration of the Kirkwood factor is insignificant for water. Theories of nonlinear dielectric relaxation need to mostly account for the effect of the field on rotations of a single dipole in a polar liquid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Temperature Evolution of the Activation Barriers Leads to Meyer−Neldel Rules for Structural Relaxation and Transport in Polymers

Understanding activation barriers controlling structural relaxation in glass-forming liquids, molecular transport, and ionic conductivity in amorphous polymers is a grand challenge of fundamental scientific and materials engineering interest across disciplines. Over decades, intriguing but puzzling empirical correlations between the elementary time scale of activated barrier crossing and the apparent Arrhenius activation energy, the so-called Meyer−Neldel (MN) rules, have been discovered in diverse liquids and glasses. Here, in this study, we formulate and successfully apply a new experimental analysis and an explicitly dynamical theoretical framework which provides an understanding of the origin, validity, and failure of such correlations, that bridge and unify the three fields of structural relaxation, molecular transport, and ionic conductivity in liquids and quenched glasses. Distinct quasi-universal laws are predicted in equilibrated liquids and nonequilibrium glasses, consistent with experiments. Our analysis reveals that even if the relaxation appears Arrhenius over a limited temperature range, the physical activation barrier is generally temperature-dependent in polymeric systems even below glass transition temperature. In addition, we show that the approximate validity of classical MN rules hinges on a linear temperature dependence of this barrier and the temperature range probed in experiments. Our findings are relevant for controlling the activation barrier in functional soft polymeric materials relevant to molecular separations, barrier coatings, and charge transport, and also provide new constraints on the theoretical understanding of the mechanism underlying slow activated dynamics in glass-forming condensed matter.

Meyer-Neldel rules↗
DOE OSTI2026

Non-Markovian relaxation spectroscopy of fluxonium qubits

Recent studies have shown that parasitic two-level systems (TLS) in superconducting qubits, which are a leading source of decoherence, can have relaxation times longer than the qubits themselves. However, the standard techniques used to characterize qubit relaxation is only valid for measuring T 1 under the Born-Markov approximation and could mask environmental memory effects in practice. Here, we introduce two-timescale relaxometry, a technique to probe the qubit and environment relaxation simultaneously and efficiently. We apply it to high-coherence fluxonium qubits over a frequency range of 0.1-0.4 GHz, and reveal a discrete spectrum of TLS with millisecond lifetimes. Our analysis of the spectrum is consistent with a random distribution of TLS in the aluminum oxide tunnel barrier of the Josephson junction chain of the fluxonium, with a spectral and volumetric density and average electric dipole similar to previous TLS studies at much higher frequencies. Our study suggests that investigating and mitigating TLS in the junction chain is crucial to the development of various types of noise-protected qubits in circuit QED.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Linear stability analysis via simulated annealing and accelerated relaxation

Simulated annealing (SA) is a kind of relaxation method for finding equilibria of Hamiltonian systems. A set of evolution equations is solved with SA, which is derived from the original Hamiltonian system so that the energy of the system changes monotonically while preserving Casimir invariants inherent to noncanonical Hamiltonian systems. The energy extremum reached by SA is an equilibrium. Since SA searches for an energy extremum, it can also be used for stability analysis when initiated from a state where a perturbation is added to an equilibrium. The procedure of the stability analysis is explained, and some examples are shown. Because the time evolution is computationally time consuming, efficient relaxation is necessary for SA to be practically useful. An acceleration method is developed by introducing time dependence in the symmetric kernel used in the double bracket, which is part of the SA formulation described here. An explicit formulation for low-beta reduced magnetohydrodynamics (MHD) in cylindrical geometry is presented. In conclusion, since SA for low-beta reduced MHD has two advection fields that relax, it is important to balance the orders of magnitude of these advection fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Molecular basis of force-pCa relation in MYL2 cardiomyopathy mice: Role of the super-relaxed state of myosin

Here, in this study, we investigated the role of the super-relaxed (SRX) state of myosin in the structure–function relationship of sarcomeres in the hearts of mouse models of cardiomyopathy-bearing mutations in the human ventricular regulatory light chain (RLC, MYL2 gene). Skinned papillary muscles from hypertrophic (HCM–D166V) and dilated (DCM–D94A) cardiomyopathy models were subjected to small-angle X-ray diffraction simultaneously with isometric force measurements to obtain the interfilament lattice spacing and equatorial intensity ratios (I 11 /I 10 ) together with the force-pCa relationship over a full range of [Ca 2+ ] and at a sarcomere length of 2.1 μm. In parallel, we studied the effect of mutations on the ATP-dependent myosin energetic states. Compared with wild-type (WT) and DCM–D94A mice, HCM–D166V significantly increased the Ca 2+ sensitivity of force and left shifted the I 11 /I 10 -pCa relationship, indicating an apparent movement of HCM–D166V cross-bridges closer to actin-containing thin filaments, thereby allowing for their premature Ca 2+ activation. The HCM–D166V model also disrupted the SRX state and promoted an SRX-to-DRX (super-relaxed to disordered relaxed) transition that correlated with an HCM-linked phenotype of hypercontractility. While this dysregulation of SRX ↔ DRX equilibrium was consistent with repositioning of myosin motors closer to the thin filaments and with increased force-pCa dependence for HCM–D166V, the DCM–D94A model favored the energy-conserving SRX state, but the structure/function–pCa data were similar to WT. Our results suggest that the mutation-induced redistribution of myosin energetic states is one of the key mechanisms contributing to the development of complex clinical phenotypes associated with human HCM–D166V and DCM–D94A mutations.

59 BASIC BIOLOGICAL SCIENCES↗