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Results for “generalized finite differences”

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 1,117 records · Page 62
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Brownian dynamics of confined rigid bodies

We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust, space efficient, and easy to accumulate. We construct a system of overdamped Langevin equations in the quaternion representation that accounts for hydrodynamic effects, preserves the unit-norm constraint on the quaternion, and is time reversible with respect to the Gibbs-Boltzmann distribution at equilibrium. We introduce two schemes for temporal integration of the overdamped Langevin equations of motion, one based on the Fixman midpoint method and the other based on a random finite difference approach, both of which ensure that the correct stochastic drift term is captured in a computationally efficient way. We study several examples of rigid colloidal particles diffusing near a no-slip boundary and demonstrate the importance of the choice of tracking point on the measured translational mean square displacement (MSD). We examine the average short-time as well as the long-time quasi-two-dimensional diffusion coefficient of a rigid particle sedimented near a bottom wall due to gravity. For several particle shapes, we find a choice of tracking point that makes the MSD essentially linear with time, allowing us to estimate the long-time diffusion coefficient efficiently using a Monte Carlo method. However, in general, such a special choice of tracking point does not exist, and numerical techniques for simulating long trajectories, such as the ones we introduce here, are necessary to study diffusion on long time scales.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

Resolution requirements for velocity gradients in turbulence

Since high resolution numerical simulations of turbulent flows, or experiments at high Reynolds numbers, represent a substantial investment in resources, the estimation of the minimum resolution required for the study of a given property has been the subject of continued interest. Different properties require, in general, different resolutions, and the present paper is dedicated to the requirements for the measurement of the probability distribution functions of the velocity gradients and, in particular, of their low order moments. The deviation of these quantities from the values corresponding to a Gaussian distribution was one of the first indications of the presence of Reynolds number-dependent intermittency and has been the object of recent interest as numerical simulations have become able to explore the distribution of gradients in the low Reynolds number range, while new experiments have extended the range to increasingly high Reynolds numbers. We will use progressive filtering of the results of numerical simulations of isotropic turbulence as a model for the effect of a sensor of finite size. The numerical issues will be addressed first to ensure that the simulations are fully resolved from the point of view of the velocity gradients. This will also give us an estimate for the numerical resolution required for the different quantities.

Jimenez, Javier↗
DOE OSTI2015

Thermodynamic theory of equilibrium fluctuations

The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of non-equilibrium entropy, a fundamental equation of state in the entropy representation, and a fluctuation postulate describing the probability distribution of macroscopic parameters of an isolated system. Although these elements introduce a statistical component that does not exist in classical thermodynamics, the logical structure of the theory is different from that of statistical mechanics and represents an expanded version of thermodynamics. Based on this theory, we present a regular procedure for calculations of equilibrium fluctuations of extensive parameters, intensive parameters and densities in systems with any number of fluctuating parameters. The proposed fluctuation formalism is demonstrated by four applications: (1) derivation of the complete set of fluctuation relations for a simple fluid in three different ensembles; (2) fluctuations in finite-reservoir systems interpolating between the canonical and micro-canonical ensembles; (3) derivation of fluctuation relations for excess properties of grain boundaries in binary solid solutions, and (4) derivation of the grain boundary width distribution for pre-melted grain boundaries in alloys. The last two applications offer an efficient fluctuation-based approach to calculations of interface excess properties and extraction of the disjoining potential in pre-melted grain boundaries. Possible future extensions of the theory are outlined.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Entropy production of doubly stochastic quantum channels

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1981

Aircraft subfloor response to crash loadings

Results are presented of an experimental and analytical study of the dynamic response to crash loadings of five different load-limiting subfloors for general aviation aircraft. These subfloors provide a high-strength structural floor platform to retain the seats and a crushable zone to absorb energy and limit vertical loads. Experimental static load-deflection data and dynamic deceleration response data for the five subfloors indicated that the high-strength floor platform performed well in that structural integrity and residual strength was maintained throughout the loading cycle. The data also indicated that some of the subfloor crush zones were more effective than others in providing nearly constant load for a range of displacement. The analytical data was generated by characterizing the nonlinear crush zones of the subfloor with static load-deflection data and using the DYCAST nonlinear finite element computer program. Comparisons between experimental and analytical data showed good correlation for the subfloors in which the static deformation mode closely approximated the dynamic deformation mode.

Carden, H. D.↗
DOE OSTI2019

Reconfigurable metamaterial absorber as an optical switch based on organic-graphene control

In this paper, we have suggested an effective optical switch with the cross fractal shape. It contains the main cross element that connected to four parasitic elements by four organic’s material junctions. This absorber is modified as a tunable element by using the graphene layer which can be considered for compensating the physical distortion. Each organic and parasitic load is placed over a graphene layer. These graphene layers separated with a SiO{sub 2} thin film. We have implemented a SiO{sub 2} layer as a spacer between the graphene and metal ground layer. The organic materials are popular for their various resistances value. We have applied a bulky dielectric slab with two different conductivity values for high and low resistance (HRS and LRS). This absorber works at the range of 90–100 THz for mid-infrared spectrum and the bandwidth of 4%. In the HRS mode the reflection value is about − 35 up to − 25 dB. When the organic material switched to LRS mode, this value drastically increased to − 5 dB. The designed absorber has both the tunable and switchable attributes. We have simulated this switch by the finite integral technique method with CST microwave studio.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Broadband-antireflective hybrid nanopillar array for photovoltaic application

Subwavelength structures such as nanopillars, nanoholes, and nanodomes have recently attracted considerable attention as antireflective structures for solar cells. Recent studies on the optical property of nanopillar array revealed that the reflection minimum is related to the diameter, the pitch, and the height of nanopillars. Here, we investigate the “hybrid” nanopillar array, which is composed of different diameters of nanopillars. Finite differential time domain simulations revealed that the photogeneration in a hybrid nanopillar array is spatially heterogeneous: carriers are generated mainly in the narrower pillars for short-wavelength incident light and in the thicker pillars for long-wavelength light, respectively. Hybrid silicon nanopillar arrays fabricated by using electron beam lithography and dry etching show excellent broadband antireflection property. Hybrid nanopillar array is thus highly promising for next-generation antireflection for photovoltaic applications.

14 SOLAR ENERGY↗
DOE OSTI2016

Electron energy loss spectroscopy of plasmon resonances in titanium nitride thin films

The plasmon resonance characteristics of refractory TiN thin films were analyzed using electron energy-loss spectroscopy (EELS). A bulk plasmon resonance was observed at 2.81 eV and a weaker surface plasmon resonance peak was detected at 2.05 eV. These findings are compared to finite-difference time-domain simulations based on measured optical data. The calculated values for both the bulk and surface resonances (2.74 eV and 2.15 eV, respectively) show reasonable agreement with those measured via EELS. The amplitude of the experimentally observed surface resonance was weaker than that typically encountered in noble metal nanostructures, and this is discussed in the context of electron density and reduced spatial confinement of the resonance mode in the thin-film geometry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Investigation of the effects of metal-wire resonators in sub-wavelength array based on time-reversal technique

The resonant metalens consisting of metal-wire resonators with equally finite length can break the diffraction barrier well suited for super-resolution imaging. In this study, a basic combination constructed by two metal-wire resonators with different lengths is proposed, and its resonant characteristics is analyzed using the method of moments (MoM). Based on the time reversal (TR) technique, this kind of combination can be applied to a sub-wavelength two-element antenna array with a 1/40-wavelength interval to make the elements work simultaneously with little interference in the frequency band of 1.0-1.5 GHz and 1.5-2.0 GHz, respectively. The simulations and experiments show that analysis of MoM and the application of the resonators can be used to design multi-frequency sub-wavelength antenna arrays efficiently. This general design method is convenient and can be used for many applications, such as weakening jamming effectiveness in communication systems, and sub-wavelength imaging in a broad frequency band.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1997

Thermostructural Behavior of a Hypersonic Aircraft Sandwich Panel Subjected to Heating on One Side

Thermostructural analysis was performed on a heated titanium honeycomb-core sandwich panel. The sandwich panel was supported at its four edges with spar-like substructures that acted as heat sinks, which are generally not considered in the classical analysis. One side of the panel was heated to high temperature to simulate aerodynamic heating during hypersonic flight. Two types of surface heating were considered: (1) flat-temperature profile, which ignores the effect of edge heat sinks, and (2) dome-shaped-temperature profile, which approximates the actual surface temperature distribution associated with the existence of edge heat sinks. The finite-element method was used to calculate the deformation field and thermal stress distributions in the face sheets and core of the sandwich panel. The detailed thermal stress distributions in the sandwich panel are presented, and critical stress regions are identified. The study shows how the magnitudes of those critical stresses and their locations change with different heating and edge conditions. This technical report presents comprehensive, three-dimensional graphical displays of thermal stress distributions in every part of a titanium honeycomb-core sandwich panel subjected to hypersonic heating on one side. The plots offer quick visualization of the structural response of the panel and are very useful for hot structures designers to identify the critical stress regions.

Ko, William L.↗
NASA NTRS2019

Numerical Modeling of Boiling in a Heated Tube

This paper presents numerical models of boiling in a heated tube using the Generalized Fluid System Simulation Program (GFSSP), a finite-volume-based general-purpose flow network code developed at NASA/Marshall Space Flight Center. The heated tube is discretized into a one-dimensional array of nodes and branches to represent the flow of liquid and vapor in a tube with a prescribed pressure differential. The solid wall is also discretized into solid nodes and conductors to allow for heat transfer between the wall and the fluid. The conservation equations of mass, momentum, and energy of the fluid are solved simultaneously with the energy conservation equation for the solid wall. Two experimental configurations of fluid flowing in a vertical tube have been simulated, one with water and the other with liquid hydrogen. This paper compares experimental data with numerical predictions based on four different published correlations for boiling heat transfer coefficients. Three of these correlations are applicable to the saturated vertical flow conditions of the experiments. One of them is applicable to film boiling and has been used for the liquid hydrogen experiment, which was in film boiling regime. For the case of boiling water, the predictions of wall temperatures using the boiling heat transfer correlations agreed well with the experimental results. However, in the case of boiling hydrogen larger discrepancies were observed between the experimental data and numerical predictions.

Majumdar, Alok↗
DOE OSTI2015

Many-body localization in disorder-free systems: The importance of finite-size constraints

Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that various bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

In-situ effect in cross-ply laminates under various loading conditions analyzed with hybrid macro/micro-scale computational models

In this article, multi-scale finite element analyses based on three-dimensional (3D) hybrid macro/micro-scale computational models subjected to various loading conditions are carried out to examine the in-situ effect imposed by the neighboring plies on the failure initiation and propagation of cross-ply laminates. A detailed comparative study on crack suppression mechanisms due to the effect of embedded laminar thickness and adjacent ply orientation is presented. Furthermore, we compare the results of in-situ transverse failure strain and strength between the computational models and analytical predictions. Good agreements are generally observed, indicating the constructed computational models are highly accurate to quantify the in-situ effect. Subsequently, empirical formulas for calculating the in-situ strengths as a function of embedded ply thickness and different ply angle between embedded and adjacent plies are developed, during which several material parameters are obtained using a reverse fitting method. Finally, a new set of failure criteria for σ 22 -τ 12 , σ 22 -τ 23 , and σ 11 -τ 12 accounting for the in-situ strengths are proposed to predict laminated composites failure under multi-axial stress states. This study demonstrates an effective and efficient computational technique towards the accurate prediction of the failure behaviors and strengths of cross-ply laminates by including the in-situ effects.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Ensemble variational Fokker-Planck methods for data assimilation

Particle flow filters solve Bayesian inference problems by smoothly transforming a set of particles into samples from the posterior distribution. Particles move in state space under the flow of an McKean-Vlasov-Itˆo process. This work introduces the Variational Fokker-Planck (VFP) framework for data assimilation, a general approach that includes previously known particle flow filters as special cases. The McKean-Vlasov-Itˆo process that transforms particles is defined via an optimal drift that depends on the selected diffusion term. It is established that the underlying probability density - sampled by the ensemble of particles - converges to the Bayesian posterior probability density. For a finite number of particles the optimal drift contains a regularization term that nudges particles toward becoming independent random variables. Based on this analysis, we derive computationally-feasible approximate regularization approaches that penalize the mutual information between pairs of particles, and avoid particle collapse. Moreover, the diffusion plays a role akin to a particle rejuvenation approach that aims to alleviate particle collapse. The VFP framework is very flexible. Different assumptions on prior and intermediate probability distributions can be used to implement the optimal drift, and localization and covariance shrinkage can be applied to alleviate the curse of dimensionality. A robust implicit-explicit method is discussed for the efficient integration of stiff McKean- Vlasov-Itˆo processes. Here, the effectiveness of the VFP framework is demonstrated on three progressively more challenging test problems, namely the Lorenz ’63, Lorenz ’96 and the quasi-geostrophic equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Solitary waves in a self-gravitating opposite polarity dust-plasma medium

A more general and realistic dusty plasma model, namely, self-gravitating opposite polarity dust-plasma system (containing inertial positive and negative dust, and inertialess ions and electrons following Maxwellian distribution) is considered. The possibility for the formation of solitary electrostatic and self-gravitational potential structures in such a dust-plasma system is thoroughly examined. The standard reductive perturbation method, which is valid for small but finite amplitude solitary structures, is employed. The parametric regimes for the existence of solitary electrostatic and self-gravitational potential structures, and their basic properties (viz., polarity, amplitude, width, and speed) are found to be significantly modified by the combined effects of positively charged dust component and self-gravitational field. The applications of the present investigation in different space dusty plasma environments and laboratory dusty plasma devices are briefly discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1996

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗
DOE OSTI2019

Effect of recovery time of nonlinear absorber saturated losses on the soliton pulse structure in a fibre laser with different cavity lengths

Using numerical simulation methods, we have calculated the dependences of the pulse profile and spectrum of a ring fibre laser in the region of anomalous group velocity dispersion on the length of the laser cavity and the recovery time of the nonlinear absorber saturated losses. It is found that with increasing cavity length the laser pulse acquires a pedestal, the positions of its edges corresponding to the frequencies of the Kelly sidebands. It is shown that the finiteness of the recovery time of the saturable absorber leads to an asymmetry in the profile and spectrum of the laser pulse. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗