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DOE OSTI2018

Linear and Nonlinear Optical Properties of Metal Nanocomposite Materials

The scientific theme of this award stated in its title is “Linear and Nonlinear Optical Properties of Metal Nanoparticle Composites.” The motivation for the proposal was based on prior work that highlighted unusual third-order nonlinear optical response of metal-nanoparticle composites created by Vanderbilt researchers at the Oak Ridge National Laboratory (ORNL) by implanting metal ions into fused-silica and sapphire substrates and annealing them under appropriate conditions to produce a solid solution comprising noble-metal nanoparticles embedded in an insulating matrix. For example, the well-known localized surface plasmon resonance (LSPR) of gold and silver nanoclusters and nanoparticles was known to yield enhanced effects on the nonlinear absorption and nonlinear refractive index of these materials. The project soon expanded to embrace a wider range of materials and nanostructures, including particularly vanadium dioxide with its insulator-to-metal transition, a wide variety of substrate hosts, and zinc oxide with its multi-faceted band-edge exciton that can be coupled to plasmonic degrees of freedom in silver and aluminum. We employed second- and third-order nonlinear optical spectroscopies and confocal microscopy to quantify the coupling between nanoparticles and adsorbates across interfaces. Because ORNL closed the ion-beam surface-modification facility in 2004, we then developed a nanofabrication technique combining focused ion-beam lithography and pulsed laser deposition to create ordered arrays of metal and oxide nanoparticles in various planar geometries and heterostructures. By 2008, aided by finite-difference time-domain and finite-element calculations, we began to design and fabricate plasmonic “workbenches” on which we could excite quasiparticles (e.g., excitons, phonons, plasmons) using optical signals and electrical impulses, and map the material response down to femtosecond time and nanometer length scales. We developed additional nanofabrication capabilities (e.g., dual-layer electron-beam lithography, quantum-well fabrication and multilayer magnetron sputtering and electron-beam deposition) to create a variety of novel heterostructures as model nanocomposite systems. This led to several new opportunities to study the optical properties of these composites informed by views of potential device configurations. Among the scientific themes that emerged in published papers based on new materials and nanostructures were the following: ultrafast electron dynamics in metamaterials, including ultrafast THz microscopy of the insulator-to-metal transition in VO 2 nanoparticles; plasmon-driven electron injection to promote phase transitions in VO 2 ; and second-harmonic generation in nanostructures without inversion symmetry, in particular, the Archimedean spiral with overall sub-wavelength dimensions. We also explored dimensional and structural effects in plasmonic coupling, including exciton-plasmon coupling in ZnO nanowires; exciton-plasmon coupling in structures incorporating two-dimensional dichalcogenides; and tunable plasmon-induced transparency in plasmonic heterostructures incorporating phase-changing VO 2 . Finally, it should be noted that the work on Archimedean nanospirals and plasmon-exciton coupling led directly into a current quantum-optics research project on photon correlations in diamond nanoparticles, exemplified by the first publication from that effort [Ref. [47] in the bibliography]. A more detailed account setting in the appropriate scientific context all forty-eight papers supported by this award follows.

36 MATERIALS SCIENCE↗

DOE OSTI2019

DNN Approximation of Nonlinear Finite Element Equations

We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the trained DNN to replace the coarse nonlinear operator thus avoiding the need to visit the fine level discretization in order to evaluate the actions of the true coarse nonlinear operator. The feasibility of the studied approach is demonstrated in a two level FAS (full approximation scheme) used to solve a nonlinear diffusion-reaction PDE.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, in stead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves tremendous amount of time spent on training neural networks. Another essential aspect of EnSF is its analytical update step, gradually incorporating data information into the score function, which is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. High-dimensional Lorenz systems are used to demonstrate the performance of our method. EnSF provides surprisingly impressive performance in reliably tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimension) with highly nonlinear observation processes, which is a well-known challenging problem for existing filtering methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Real-Time Nonlinear Model Predictive Controller for Multiple Degrees of Freedom Wave Energy Converters with Non-Ideal Power Take-Off

An increase in wave energy converter (WEC) efficiency requires not only consideration of the nonlinear effects in the WEC dynamics and the power take-off (PTO) mechanisms, but also more integrated treatment of the whole system, i.e., the buoy dynamics, the PTO system, and the control strategy. It results in an optimization formulation that has a nonquadratic and nonstandard cost functional. This article presents the application of real-time nonlinear model predictive controller (NMPC) to two degrees of freedom point absorber type WEC with highly nonlinear PTO characteristics. The nonlinear effects, such as the fluid viscous drag, are also included in the plant dynamics. The controller is implemented on a real-time target machine, and the WEC device is emulated in real-time using the WECSIM toolbox. The results for the successful performance of the design are presented for irregular waves under linear and nonlinear hydrodynamic conditions.

Haider, Ali S. (ORCID:0000000246513157)↗

NASA NTRS1972

Nonlinear and adaptive estimation techniques in reentry

The development and testing of nonlinear and adaptive estimators for reentry (e.g. space shuttle) navigation and model parameter estimation or identification are reported. Of particular interest is the identifcation of vehicle lift and drag characteristics in real time. Several nonlinear filters were developed and simulated. Adaptive filters for the real time identification of vehicle lift and drag characteristics, and unmodelable acceleration, were also developed and tested by simulation. The simulations feature an uncertain system environment with rather arbitrary model errors, thus providing a definitive test of estimator performance. It was found that nonlinear effects are indeed significant in reentry trajectory estimation and a nonlinear filter is demonstrated which successfully tracks through nonlinearities without degrading the information content of the data. Under the same conditions the usual extended Kalman filter diverges and is useless. The J-adaptive filter is shown to successfully track errors in the modeled vehicle lift and drag characteristics. The same filter concept is also shown to track successfully through rather arbitrary model errors, including lift and drag errors, vehicle mass errors, atmospheric density errors, and wind gust errors.

Jazwinski, A. H.↗

NASA NTRS1973

Effects of certain control-system nonlinearities on stability and pointing of an attached double-gimbal experiment package in presence of random crew-motion disturbances

The effects of two types of control-system nonlinearities, sensor deadband and actuator breakout torque, on the pointing capability of a Apollo Telescope Mount (ATM) double-gimbal experiment isolation and control system are investigated. A composite structural model of a flexible experiment package connected through frictionless double gimbals to a flexible carrier vehicle is used for this investigation. Contributions of the primary carrier control system to experiment pointing are neglected. Pointing errors onboard the experiment package due to random crew-motion input into the carrier vehicle are computed. A stability investigation is performed to verify control-system stability with nominal nonlinearities and gains. Indications are that there is no stability problem due to the nonlinearities. A nonlinearity sensitivity study is carried out to determine the effects on pointing accuracy. Its results indicate that nominal ATM control system nonlinearities limit the pointing accuracy to approximately 0.4 arc second in the presence of crew motion. Methods of reducing the error to less than 0.1 arc second are discussed.

Shaughnessy, J. D.↗

NASA NTRS1973

Nonlinear response of boron/aluminum angleplied laminates under cyclic tensile loading: Contributing mechanisms and their effects

The nonlinear response of boron/aluminum angleplied laminates subjected to cyclic loads was investigated. A procedure is outlined and criteria are proposed which can be used to assess the nonlinear response. The procedure consists of testing strategically selected laminate configurations and analyzing the results using composite mechanics. Results from the investigation show the contributions to nonlinear behavior are from: premature random fiber breaks where the ply orientation angle is small relative to the load direction, ply relative rotation at intermediate values of the ply orientation angle, and nonlinear aluminum matrix behavior at large values of the orientation angle. Premature fiber breaks result in progressively more compliant material; large ply relative rotations result in progressively stiffer material; and pronounced matrix nonlinear behavior results in no significant change in the stiffness of the initial load portion.

Chamis, C. C.↗

NASA NTRS1973

Lp-stability (1 less than or equal to p less than or equal to infinity) of multivariable nonlinear time-varying feedback systems that are open-loop unstable

A class of multivariable, nonlinear time-varying feedback systems with an unstable convolution subsystem as feedforward and a time-varying nonlinear gain as feedback was considered. The impulse response of the convolution subsystem is the sum of a finite number of increasing exponentials multiplied by nonnegative powers of the time t, a term that is absolutely integrable and an infinite series of delayed impulses. The main result is a theorem. It essentially states that if the unstable convolution subsystem can be stabilized by a constant feedback gain F and if incremental gain of the difference between the nonlinear gain function and F is sufficiently small, then the nonlinear system is L(p)-stable for any p between one and infinity. Furthermore, the solutions of the nonlinear system depend continuously on the inputs in any L(p)-norm. The fixed point theorem is crucial in deriving the above theorem.

Callier, F. M.↗

NASA NTRS1973

Nonlinear response of boron/aluminum angleplied laminates under cyclic tensile loading - Contributing mechanisms and their effects

Chamis, C. C.↗

NASA NTRS1974

Nonlinear acoustic propagation in rectangular ducts

The method of multiple scales is used to obtain a second-order uniformly valid expansion for nonlinear acoustic wave propagation in a rectangular duct whose walls are treated with a nonlinear acoustic material. The wave propagation in the duct is characterized by the unsteady nonlinear Euler equations. The results show that nonlinear materials attenuate sound more than linear materials except at high acoustic frequencies. The nonlinear materials produce higher and combination tones which have higher attenuation rates than the fundamentals. Moreover, the attenuation rates of the fundamentals increase with increasing amplitude.

Nayfeh, A. H.↗

NASA NTRS1974

Development of solution techniques for nonlinear structural analysis

Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.

Vos, R. G.↗

NASA NTRS1975

Nonlinear behavior of acoustic waves in combustion chambers

The nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber are considered. A formal framework is provided within which practical problems can be treated with a minimum of effort and expense. The general conservation equations were expanded in two small parameters, one characterizing the mean flow field and one measuring the amplitude of oscillations, and then combined to yield a nonlinear inhomogeneous wave equation. The unsteady pressure and velocity fields were expressed as syntheses of the normal modes of the chamber, but with unknown time-varying amplitudes. This procedure yielded a representation of a general unsteady field as a system of coupled nonlinear oscillators. The system of nonlinear equations was treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. The analysis is applicable to any combustion chamber. The most interesting applications are probably to solid rockets, liquid rockets, or thrust augmentors on jet engines.

Culick, F. E. C.↗

NASA NTRS1976

Nonlinear Curvature Expressions for Combined Flapwise Bending, Chordwise Bending, Torsion and Extension of Twisted Rotor Blades

The nonlinear curvature expressions for a twisted rotor blade or a beam undergoing transverse bending in two planes, torsion, and extension were developed. The curvature expressions were obtained using simple geometric considerations. The expressions were first developed in a general manner using the geometrical nonlinear theory of elasticity. These general nonlinear expressions were then systematically reduced to four levels of approximation by imposing various simplifying assumptions, and in each of these levels the second degree nonlinear expressions were given. The assumptions were carefully stated and their implications with respect to the nonlinear theory of elasticity as applied to beams were pointed out. The transformation matrices between the deformed and undeformed blade-fixed coordinates, which were needed in the development of the curvature expressions, were also given for three of the levels of approximation. The present curvature expressions and transformation matrices were compared with corresponding expressions existing in the literature.

Kvaternik, R. G.↗

NASA NTRS1977

Computation of nonlinear one-dimensional waves in near-sonic flows

A nonlinear analysis is developed for sound propagation in a variable area duct in which the mean flow approaches choking conditions. A quasi-one-dimensional model is used; results of the standard linear theory are compared with the nonlinear results to assess the significance of the nonlinear terms. The nonlinear analysis represents the acoustic disturbance as a sum of interacting harmonics. Numerical results show that the basic signal is unaffected by the presence of higher harmonics if the throat Mach number is not too large, but as the Mach number approaches unity more harmonics are needed to describe the acoustic propagation. The strong interactions among harmonics in the numerical results occur in a region which is generally consistent with the nonlinear inner-expansion region of Callegari and Myers.

Nayfeh, A. H.↗

NASA NTRS1977

Study of the use of a nonlinear, rate limited, filter on pilot control signals

The use of a filter on the pilot's control output could improve the performance of the pilot-aircraft system. What is needed is a filter with a sharp high frequency cut-off, no resonance peak, and a minimum of lag at low frequencies. The present investigation studies the usefulness of a nonlinear, rate limited, filter in performing the needed function. The nonlinear filter is compared with a linear, first order filter, and no filter. An analytical study using pilot models and a simulation study using experienced test pilots was performed. The results showed that the nonlinear filter does promote quick, steady maneuvering. It is shown that the nonlinear filter attenuates the high frequency remnant and adds less phase lag to the low frequency signal than does the linear filter. It is also shown that the rate limit in the nonlinear filter can be set to be too restrictive, causing an unstable pilot-aircraft system response.

Adams, J. J.↗

NASA NTRS1980

Nonlinear static TPS analysis

A nonlinear analysis which includes the effect of mismatch and filler bar was developed to predict the strain isolator pad reuseable surface insulation through-the-thickness interface stresses. Parametric studies were conducted for simulated shock loading on square tiles. Expected loads on an actual tile were also studied. The results indicate that when no mismatch is present, linear solutions tend to give nonconservative maximum stresses relative to the nonlinear solutions. When mismatch is present, the linear maximum stresses are only conservative at low load levels and highly nonconservative at high load levels. Although the presence of filler bar reduces maximum tensile stresses in some cases, it does not appear that the nominal dimension filler bar can reduce the nonlinear stress to a level at which the linear solution becomes conservative relative to the nonlinear solution. Moreover, on an outboard trailing edge elevon tile at descent with +20 deg flap, the linear analysis is 49% nonconservative relative to the nonlinear analysis with filler bar.

Housner, J. M.↗

NASA NTRS1980

A rapid method for the approximate determination of nonlinear solutions Application to aerodynamic flows

A method for determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameters, is developed and evaluated. The procedure consists of defining a unit perturbation by employing two or more nonlinear solutions which differ from one another by a nominal change in some geometric or flow parameter, and then using that unit perturbation to predict a family of related nonlinear solutions over a range of parameter variation. Coordinate straining is used in determining the unit perturbation to account for the movement of discontinuities and maxima of high-gradient regions due to the perturbation. Although the procedure is generally applicable, results are presented here for nonlinear aerodynamic applications. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Flows past both isolated airfoils and compressor cascades involving a variety of flow and geometry parameter changes are considered. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure. Computational time is trivial.

Stahara, S. S.↗

NASA NTRS1983

Evaluation of the effect of vibration nonlinearity on convergence behavior of adaptive higher harmonic controllers

Effect of nonlinearity on convergence of the local linear and global linear adaptive controllers is evaluated. A nonlinear helicopter vibration model is selected for the evaluation which has sufficient nonlinearity, including multiple minimum, to assess the vibration reduction capability of the adaptive controllers. The adaptive control algorithms are based upon a linear transfer matrix assumption and the presence of nonlinearity has a significant effect on algorithm behavior. Simulation results are presented which demonstrate the importance of the caution property in the global linear controller. Caution is represented by a time varying rate weighting term in the local linear controller and this improves the algorithm convergence. Nonlinearity in some cases causes Kalman filter divergence. Two forms of the Kalman filter covariance equation are investigated.

Molusis, J. A.↗