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Results for “weak solutions”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

The calculation of supersonic viscous flows using the parabolized Navier-Stokes equations

Solution of the parabolic Navier-Stokes (PNS) equations for supersonic flows is discussed, and compatibility of the PNS method with the triple-deck theory of Stewartson (1974) is demonstrated. Characteristic and stability analyses show that use of an appropriate filter on the pressure term in the x-momentum equation can suppress the departure solutions, giving the usual desired weak interaction solution. An Alternating Direction Explicit procedure, with minimal computer storage requirements compared to the full Navier-Stokes solvers, is proposed to calculate strongly interacting flows using a global iteration procedure for the PNS equations. The PNS equations are used to solve the hypersonic viscous interaction problem, and good agreement is found with experimental results.

Davis, R. T.↗
NASA NTRS1978

An interaction solution algorithm for viscous aerodynamic performance prediction

A weak-interaction solution algorithm is established for aerodynamic flow field prediction about an isolated airfoil. It requires numerical solution of differential equations governing potential flow, viscous and turbulent boundary layer flow, and the turbulent wake flow downstream of a trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. These in turn alter the viscous flow through imposed pressure gradients. Closure for turbulence is accomplished using a second order model. Numerical evaluations assess factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems as solved using a finite element algorithm.

Baker, A. J.↗
DOE OSTI2022

Weakly quasisymmetric near-axis solutions to all orders

Here, we show that the equations satisfied by weakly quasisymmetric magnetic fields can be solved to arbitrarily high order in powers of the distance from the magnetic axis. This demonstration does not consider force balance. The existence of solutions requires an appropriate choice of parameters, most notably the toroidal current or rotational transform profiles. We do not prove that the expansion converges (it is likely divergent but asymptotic), and thus, the demonstration here should not be taken as definitive proof of the existence of global solutions. Instead, we provide a systematic construction of solutions to an arbitrarily high order.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1992

Upwind schemes and bifurcating solutions in real gas computations

The area of high speed flow is seeing a renewed interest due to advanced propulsion concepts such as the National Aerospace Plane (NASP), Space Shuttle, and future civil transport concepts. Upwind schemes to solve such flows have become increasingly popular in the last decade due to their excellent shock capturing properties. In the first part of this paper the authors present the extension of the Osher scheme to equilibrium and non-equilibrium gases. For simplicity, the source terms are treated explicitly. Computations based on the above scheme are presented to demonstrate the feasibility, accuracy and efficiency of the proposed scheme. One of the test problems is a Chapman-Jouguet detonation problem for which numerical solutions have been known to bifurcate into spurious weak detonation solutions on coarse grids. Results indicate that the numerical solution obtained depends both on the upwinding scheme used and the limiter employed to obtain second order accuracy. For example, the Osher scheme gives the correct CJ solution when the super-bee limiter is used, but gives the spurious solution when the Van Leer limiter is used. With the Roe scheme the spurious solution is obtained for all limiters.

Suresh, Ambady↗
DOE OSTI2022

Midfidelity model verification for a point-absorbing wave energy converter with linear power take-off

In the preliminary design stage of a wave energy converter (WEC), researchers need fast and reliable simulation tools. High-fidelity numerical models are usually employed to study the wave-structure interaction, but the computational cost is demanding. As an alternative, midfidelity models can provide simulations in the order of real time. In this study, we operate Uppsala University’s WEC in a relatively mild sea state and model it using WEC-Sim. The model is verified based on OpenFOAM simulations. To analyze the ability of the midfidelity model to capture WEC dynamics, we investigate the system separately with 1, 2, and 3 degrees of freedom. We examine the contribution of viscous phenomena, and study both linear and weakly nonlinear solutions provided by WEC-Sim. Our results indicate that the viscous effects can be neglected in heave and surge motion, but not for pitch. We also find that the weakly nonlinear WEC-Sim solution successfully agrees with the computational fluid dynamics, whereas the linear solution could suggest misleading results.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

Mechanism of the cadherin–catenin F-actin catch bond interaction

Mechanotransduction at cell–cell adhesions is crucial for the structural integrity, organization, and morphogenesis of epithelia. At cell–cell junctions, ternary E-cadherin/β-catenin/αE-catenin complexes sense and transmit mechanical load by binding to F-actin. The interaction with F-actin, described as a two-state catch bond, is weak in solution but is strengthened by applied force due to force-dependent transitions between weak and strong actin-binding states. Here, we provide direct evidence from optical trapping experiments that the catch bond property principally resides in the αE-catenin actin-binding domain (ABD). Consistent with our previously proposed model, the deletion of the first helix of the five-helix ABD bundle enables stable interactions with F-actin under minimal load that are well described by a single-state slip bond, even when αE-catenin is complexed with β-catenin and E-cadherin. Our data argue for a conserved catch bond mechanism for adhesion proteins with structurally similar ABDs. We also demonstrate that a stably bound ABD strengthens load-dependent binding interactions between a neighboring complex and F-actin, but the presence of the other αE-catenin domains weakens this effect. These results provide mechanistic insight to the cooperative binding of the cadherin–catenin complex to F-actin, which regulate dynamic cytoskeletal linkages in epithelial tissues.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2004

Solution-Phase Processes of Macromolecular Crystallization

We have proposed, for the tetragonal form of chicken egg lysozyme, that solution phase assembly processes are needed to form the growth units for crystal nucleation and growth. The starting point for the self-association process is the monomeric protein, and the final crystallographic symmetry is defined by the initial dimerization interactions of the monomers and subsequent n-mers formed, which in turn are a function of the crystallization conditions. It has been suggested that multimeric proteins generally incorporate the underlying multimers symmetry into the final crystallographic symmetry. We posed the question of what happens to a protein that is known to grow as an n-mer when it is placed in solution conditions where it is monomeric. The trypsin-treated, or cut, form of the protein canavalin (CCAN) has been shown to nucleate and grow crystals as a trimer from neutral to slightly acidic solutions. Under these conditions the solution is composed almost wholly of trimers. The insoluble protein can be readily dissolved by weakly basic solution, which results in a solution that is monomeric. There are three possible outcomes to an attempt at crystallization of the protein under monomeric (high pH) conditions: 1) we will obtain the same crystals as under trimer conditions, but at different protein concentrations governed by the self association equilibria; 2) we will obtain crystals having a different symmetry, based upon a monomeric growth unit; 3) we will not obtain crystals. Obtaining the first result would be indicative that the solution-phase self-association process is critical to the crystal nucleation and growth process. The second result would be less clear, as it may also reflect a pH-dependent shift in the trimer-trimer molecular interactions. The third result, particularly for experiments in the transition pH's between trimeric and monomeric CCAN, would indicate that the monomer does not crystallize, and that solution phase self association is not part of the crystal nucleation and growth path. Results are presented for crystallization experiments of CCAN over the pH 6.8 to 9.6 range.

Pusey, Marc L.↗
NASA NTRS2004

The Crystallization of Canavalin as a Function of pH and NaCl Concentration

We posed the question of what happens to a protein that is known to grow as an n-mer when it is placed in solution conditions where it is monomeric. The trypsin-treated, or cut, form of the protein canavalin (CCAN) has been shown to nucleate and grow crystals as a trimer from neutral to slightly acidic solutions. Under these conditions the solution is composed almost wholly of trimers. The crystalline protein can be readily dissolved by weakly basic solution, which has been proposed to result in a solution that is monomeric. There are three possible outcomes to an attempt at crystallization of the protein under monomeric (high pH) conditions: 1) we will obtain the same crystals as under trimer conditions, but at different protein concentrations governed by the self association equilibria; 2) we will obtain crystals having a different symmetry, based upon a monomeric growth unit; 3) we will not obtain crystals. Obtaining the first result would be indicative that the solution-phase self-association process is critical to the crystal nucleation and growth process. The second result would be less clear, as it may also reflect a pH-dependent shift in the trimer-trimer molecular interactions. The third result, particularly for experiments in the transition pH's between trimeric and monomeric CCAN, would indicate that the monomer does not crystallize, and that solution phase self association is not part of the crystal nucleation and growth path. Results are presented for crystallization experiments of CCAN over the pH 6.4 to 9.6 range. Fluorescence anisotropy, light scattering, and gel filtration experiments show that the solutions are primarily trimers, with association to form larger species occurring as a function of protein concentration.

Forsythe, Elizabeth L.↗
NASA NTRS1977

An approximate calculation of the strong interaction on a transonic airfoil

This paper describes an interactive computational scheme that calculates the transonic flow field over an airfoil. The inviscid flow, the turbulent boundary layer in the weak interaction region, and the elliptic flow in the strong interaction region are computed separately, and the solutions are matched iteratively in a direct, second-order interaction scheme. The pressure distribution, obtained from a transonic, small-perturbation solution, is prescribed on the boundary layer and the Navier-Stokes equations and the ensuing displacement thicknesses are used to modify the inviscid flow. The best overall results are obtained by using a turbulence model that eliminates the eddy viscosity in the strong interaction region. Computed pressure distributions are compared with experimental data and with Navier-Stokes solutions. In weak interactions, the agreement with experimental data is very good, as it is also in strong interactions except for the pressures in the separated-flow region. There the agreement is qualitative only, and the pressure recovery is too high. The results in both cases are superior or equal to those of the Navier-Stokes solutions, and the present method is significantly faster.

Seginer, A.↗
NASA NTRS1976

Sound propagation through nonuniform ducts

Methods of determining the transmission and attenuation of sound propagating in nonuniform ducts with and without mean flows are discussed. The approaches reviewed include purely numerical techniques, quasi-one-dimensional approximations, solutions for slowly varying cross sections, solutions for weak wall undulations, approximation of the duct by a series of stepped uniform cross sections, variational methods and solutions for the mode envelopes.

Nayfeh, A. H.↗
DOE OSTI2022

Tuning Magnetic Symmetry and Properties in the Olivine Series Li 1–x Fe x Mn 1–x PO 4 through Selective Delithiation

In this work, we present the first in-depth study of the nuclear and magnetic structures of the fully lithiated LiFe x Mn 1–x PO 4 solid solutions as well as the partially delithiated Li 1– xFe x Mn 1–x PO 4 series using neutron powder diffraction. By using a weak oxidizing solution that only oxidizes Fe 2+ , we find that lithium can be removed from these olivines in a stepwise manner. Representational analysis was performed on the observed magnetic reflections and found that the lithiated solid solutions order in the magnetic space group Pnma', which is identical to triphylite (LiFePO 4 ). We report that, even when removing 20% of the lithium from the hcp lattice, the magnetic structure changes and multiple magnetic contributions are needed to fully encompass the observed magnetic order. We find that the partially delithiated x = 0.2 and 0.3 have a magnetic structure P2 1 '/n11, and when x surpasses 0.3, the magnetic structure changes to P2 1 2 1 2 1 . We give a detailed report on the effect of delithiation on magnetic order, bond distances/angles, and the super- and supersuperexchange interactions in the material. The symmetries of the magnetic order of these solid solutions are then discussed with regard to their potential as ferrotoroidic candidates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1991

A computational study of the topology of vortex breakdown

A fully three-dimensional numerical simulation of vortex breakdown using the unsteady, incompressible Navier-Stokes equations has been performed. Solutions to four distinct types of breakdown are identified and compared with experimental results. The computed solutions include weak helical, double helix, spiral, and bubble-type breakdowns. The topological structure of the various breakdowns as well as their interrelationship are studied. The data reveal that the asymmetric modes of breakdown may be subject to additional breakdowns as the vortex core evolves in the streamwise direction. The solutions also show that the freestream axial velocity distribution has a significant effect on the position and type of vortex breakdown.

Spall, Robert E.↗
NASA NTRS1997

The Effect of Three-Dimensional Freestream Disturbances on the Supersonic Flow Past a Wedge

The interaction between a shock wave (attached to a wedge) and small amplitude, three-dimensional disturbances of a uniform, supersonic, freestream flow are investigated. The paper extends the two-dimensional study of Duck et al, through the use of vector potentials, which render the problem tractable by the same techniques as in the two-dimensional case, in particular by expansion of the solution by means of a Fourier-Bessel series, in appropriately chosen coordinates. Results are presented for specific classes of freestream disturbances, and the study shows conclusively that the shock is stable to all classes of disturbances (i.e. time periodic perturbations to the shock do not grow downstream), provided the flow downstream of the shock is supersonic (loosely corresponding to the weak shock solution). This is shown from our numerical results and also by asymptotic analysis of the Fourier-Bessel series, valid far downstream of the shock.

Duck, Peter W.↗
NASA NTRS1988

Nonlinear instability of a forced baroclinic Rossby wave

The nonlinear instability of forced baroclinic Rossby waves to finite-amplitude perturbations was investigated using a simple two-layer quasi-geostrophic weakly nonlinear model and a low-order spectral model, developed for this purpose. The results were applied to a study of the interaction of planetary-scale stationary eddies with synoptic-scale transient eddies. A comparison of the energetics of the weakly nonlinear solution with that seen in observational analysis and in GCM experiments indicate three basic properties of the interaction between the two types of eddies: (1) eddy available potential energy is transferred from the planetary-scale stationary eddies to the synoptic-scale transient eddies, (2) eddy kinetic energy is transferred in the opposite direction, and (3) the eddy available potential energy transfer dominates the transfer of eddy kinetic energy. It is concluded that the simple weakly nonlinear model used in these studies does indeed capture much of the fundamental behavior of wave-wave interactions seen in the atmosphere.

Feldstein, Steven B.↗
DOE OSTI2022

Modeling the Solvation and Acidity of Carboxylic Acids Using an Ab Initio Deep Neural Network Potential

Formic and acetic acid constitute the simplest of carboxylic acids, yet they exhibit fascinating chemistry in the condensed phase such as proton transfer and dimerization. The go-to method of choice for modeling these rare events have been accurate but expensive ab-initio molecular dynamics simulations. Here, we present a deep neural network potential trained using accurate ab-initio data that can be used in tandem with enhanced-sampling methods to perform an efficient exploration of the free-energy surface of aqueous solutions of weak carboxylic acids. In particular, we show that our model captures proton dissociation and provides a good estimate of the pK a , as well as the dimerization of formic and acetic acid. This provides a suitable starting point for applications in different research areas where computational efficiency coupled with the accuracy of ab-initio methods is required.

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

Canalization of Phenotypes—When the Transcriptome is Constantly but Weakly Perturbed

Abstract Recent studies have increasingly pointed to microRNAs (miRNAs) as the agent of gene regulatory network (GRN) stabilization as well as developmental canalization against constant but small environmental perturbations. To analyze mild perturbations, we construct a Dicer-1 knockdown line (dcr-1 KD) in Drosophila that modestly reduces all miRNAs by, on average, ∼20%. The defining characteristic of stabilizers is that, when their capacity is compromised, GRNs do not change their short-term behaviors. Indeed, even with such broad reductions across all miRNAs, the changes in the transcriptome are very modest during development in stable environment. By comparison, broad knockdowns of other regulatory genes (esp. transcription factors) by the same method should lead to drastic changes in the GRNs. The consequence of destabilization may thus be in long-term development as postulated by the theory of canalization. Flies with modest miRNA reductions may gradually deviate from the developmental norm, resulting in late-stage failures such as shortened longevity. In the optimal culture condition, the survival to adulthood is indeed normal in the dcr-1 KD line but, importantly, adult longevity is reduced by ∼90%. When flies are stressed by high temperature, dcr-1 KD induces lethality earlier in late pupation and, as the perturbations are shifted earlier, the affected stages are shifted correspondingly. Hence, in late stages of development with deviations piling up, GRN would be increasingly in need of stabilization. In conclusion, miRNAs appear to be a solution to weak but constant environmental perturbations.

Lu, Guang-An↗
DOE OSTI2022

Graphene nanoplatelets reinforced cement as a solution to leaky wellbores reinforcing weak points in hydrated Portland cement with graphene nanoparticles improves mechanical and chemical durability of wellbore cements

In this work, to improve the performance of wellbore cement under subsurface environments, graphene nanoplatelets (GNPs) were added in various percentages to Class-H cement slurry. Microstructural characterization of cement slurries cured at 90 °C and 95% RH indicates that GNP modifies the microstructure of hydrated cement by reinforcing pore spaces. As a result, the mechanical properties, such as Young's modulus and axial peak stress, obtained from high temperature triaxial compression tests are significantly improved based on different percentages of added GNPs. Furthermore, the hydrated 1 × 2 inch GNP- Portland cement cores tested under simulated deep wellbore conditions of high-temperature and high pressure (HTHP), appear to have a ductile-like behavior, when compared to a typical brittle nature of Portland cement pastes. From our observations and published data on graphene resistance to fracture, GNP addition to cement is evidently enhancing the flexibility of cement. These improvements would reduce the risks associated with wellbore cement deterioration and a consequent leakage in fossil fuel production, geothermal energy production, CO 2 storage as well as long-term sealing materials in plugging and abandonment of all wellbores at the end of their service life.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for transient diffusion: Applications to forward and inverse problems in heterogeneous media

We model transient diffusion in heterogeneous materials using a novel physics-informed neural networks framework (PINNs) termed Adaptive interface physics-informed neural networks or AdaI-PINNs (Roy et al. arXiv preprint arXiv:2406.04626, 2024). AdaI-PINNs utilize different activation functions with trainable slopes tailored to each material region within the computational domain, allowing for a fully automated and adaptive PINNs approach to model interface problems with strongly and weakly discontinuous solutions. To enhance its performance in highly heterogeneous transient diffusion systems, we prescribe a suite of robust practices, including appropriate non-dimensionalization of equations, a biased sampling method, Glorot initialization, and the hard enforcement of boundary and initial conditions. Here we evaluate the efficacy of the proposed method on several benchmark forward and inverse problems. Comparative studies on one-dimensional and two-dimensional benchmark problems reveal that the modified AdaI-PINNs outperform its unmodified counterpart, achieving root-mean-square errors that are at least two orders of magnitude better in forward problems. For inverse problems, the maximum errors in the approximated diffusion coefficients by modified AdaI-PINNs are four orders of magnitude better than those of the unmodified version. Additionally, modified AdaI-PINNs demonstrate improved stability in problems with large material mismatches.

42 ENGINEERING↗