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Results for “classic nonlinearity”

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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Solution and sensitivity analysis of nonlinear equations using a hypercomplex-variable Newton-Raphson method

Here, the classical Newton-Raphson (NR) method for solving nonlinear equations is enhanced in two ways through the use of hypercomplex variables and algebra. In particular, i) the Jacobian is computed in a highly accurate and automated way, and ii) the derivative of the solution to the nonlinear equations is computed with respect to any parameter contained within the system of equations. These advances provide two significant enhancements in that it is straightforward to provide an accurate Jacobian and to construct a reduced order model (ROM) of arbitrary order with respect to any parameter of the system. The ROM can then be used to approximate the solution for other parameter values without requiring additional solutions of the nonlinear equations. Several case studies are presented including 1D and 2D academic examples with fully functioning Python code provided. Additionally, a case of study of the catenary of an elastic cable subject to its own weight and a vertical point load. Derivatives up to 10th order were computed with respect to material, loading, and geometrical parameters. The derivatives were used to generate reduced order models of the cable deformation and reaction forces at its ends with respect to multiple input parameters. Results show that from a single hypercomplex evaluation of the cable under a single vertical point load, it is possible to generate an accurate reduced order model capable of predicting the cable deformation with 1.5 times the load in the opposite direction and with 3.5 times the load in the same direction without resolving the system of equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Numerical simulation of dispersion and nonlinear characteristics of microstructured silica fibres with a thin suspended core in a wide range of their parameters

Dispersion and nonlinear characteristics of microstructured silica fibres with a thin suspended core surrounded by three, four or six air holes have been studied theoretically in the wavelength range 1 – 2 μm. It has been shown that, owing to strong fundamental mode confinement near the core, the Kerr nonlinearity coefficient can exceed the nonlinearity coefficient of standard telecom fibre SMF28e by two orders of magnitude. The large waveguide contribution allows for effective group velocity dispersion management. Estimates are presented that demonstrate the feasibility of using suspended core fibre exhibiting Kerr nonlinearity for generating non-classical light: a state with squeezed quantum fluctuations in one of the quadrature components of a cw laser signal at a wavelength near 1.55 μm. (paper)

36 MATERIALS SCIENCE↗

NASA NTRS1990

Neural networks for function approximation in nonlinear control

Two neural network architectures are compared with a classical spline interpolation technique for the approximation of functions useful in a nonlinear control system. A standard back-propagation feedforward neural network and a cerebellar model articulation controller (CMAC) neural network are presented, and their results are compared with a B-spline interpolation procedure that is updated using recursive least-squares parameter identification. Each method is able to accurately represent a one-dimensional test function. Tradeoffs between size requirements, speed of operation, and speed of learning indicate that neural networks may be practical for identification and adaptation in a nonlinear control environment.

Linse, Dennis J.↗

NASA NTRS1983

Nonlinear effects of elastic coupling in unsymmetric laminates

Classical lamination theory predicts the room-temperature shape of all unsymmetrically laminated, elevated-temperature cure composites to be a saddle shape. Experimental observation indicates, however, that in many cases the room-temperature shape is cylindrical. In addition, a second cylindrical shape can often be obtained from the first by a simple snap-through action. It is the elastic couplings between inplane and out-of-plane deformations which are inherent in unsymmetric laminates that are responsible for the room-temperature shape. However, the couplings are so strong that geometrically nonlinear effects are produced. These are not accounted for in the classical theory. This paper reviews a theory developed to explain the effects of the coupling on laminate shape. The theory is based on a minimization of the laminate's total potential energy. The theory accounts for geometric nonlinearities. Because the problem is nonlinear, approximate solutions are sought by using a Rayleigh-Ritz procedure. Because of the observed snap-through of some laminates, stability of the predicted shapes is examined. Numerical results and some limited experimental data are presented for several laminates.

Hyer, M. W.↗

NASA NTRS1985

Periodic solutions of second-order nonlinear difference equations containing a small parameter. II - Equivalent linearization

The classical method of equivalent linearization is extended to a particular class of nonlinear difference equations. It is shown that the method can be used to obtain an approximation of the periodic solutions of these equations. In particular, the parameters of the limit cycle and the limit points can be determined. Three examples illustrating the method are presented.

Mickens, R. E.↗

DOE OSTI2023

Quantum interferometry and pathway selectivity in the nonlinear response of photosynthetic excitons

We propose a time–frequency resolved spectroscopic technique which employs nonlinear interferometers to study exciton–exciton scattering in molecular aggregates. A higher degree of control over the contributing Liouville pathways is obtained as compared to classical light. We show how the nonlinear response can be isolated from the orders-of-magnitude stronger linear background by either phase matching or polarization filtering. Both arise due to averaging the signal over a large number of noninteracting, randomly oriented molecules. We apply our technique to the Frenkel exciton model which excludes charge separation for the photosystem II reaction center. We show how the sum of the entangled photon frequencies can be used to select two-exciton resonances, while their delay times reveal the single-exciton levels involved in the optical process.

Science & Technology - Other Topics↗

DOE OSTI2020

Bayesian inference in band excitation scanning probe microscopy for optimal dynamic model selection in imaging

The universal tendency in scanning probe microscopy (SPM) over the last two decades is to transition from simple 2D imaging to complex detection and spectroscopic imaging modes. The emergence of complex SPM engines brings forth the challenge of reliable data interpretation, i.e., conversion from detected signals to descriptors specific to tip–surface interactions and subsequently to material’s properties. In this work, we implemented a Bayesian inference approach for the analysis of the image formation mechanisms in band excitation SPM. Compared to the point estimates in classical functional fit approaches, Bayesian inference allows for the incorporation of extant knowledge of materials and probe behavior in the form of corresponding prior distribution and return the information on the material functionality in the form of readily interpretable posterior distributions. We explore the nonlinear mechanical behaviors spatially in a classical ferroelectric material, PbTiO 3 . We observe the non-trivial evolution of the Duffing stiffness term and the nonlinearity of the sample surface, determine spatial clustering of the nonlinear response, and perform a Landau analysis on predicting the nonlinear coefficient, which indicates that ferroelectric behavior can be a cause of the observed results. These observations suggest that the spectrum of anomalous behaviors at the ferroelectric domain walls may be broader than previously believed and can extend to non-conventional mechanical properties in addition to static and microwave conductance.

36 MATERIALS SCIENCE↗

NASA NTRS1981

An inherent instability in fiber-reinforced composite laminates

Presented is a theory to predict the room-temperature shape of unsymmetric laminates. The theory is an extension of classical lamination theory and includes the effects of geometric nonlinearities. It is shown that the saddle shape predicted by the classical theory can actually be an unstable shape and a laminate will assume a cylindrical shape instead. The phenomena is coupled to the length, width, and thickness of the laminate.

Hyer, M. W.↗

DOE OSTI2022

Super-resonant four-photon collinear laser frequency multiplication in plasma

Resonant four-photon scattering could nearly double frequencies of intense laser pulses in plasma. However, transverse slippage between pulses presents a technological challenge, while collinear four-photon scattering is forbidden for classical light dispersion in plasma. Nonlinear renormalization of intense laser pulses can enable collinear four-photon resonance. However, such a very intensity-sensitive resonance is difficult to maintain for evolving pulses. Remarkably, there is a lower-dimensionality submanifold of the resonant four-photon manifold where the evolving pulses stay in resonance. Furthermore this could enable an all-optical frequency doubling of mildly relativistic-intense laser pulses in collinear geometry, advantageously free of the transverse slippage challenges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1972

Computation of wall effects in ventilated transonic wind tunnels.

A method for computing interference effects due to ventilated wind-tunnel walls on lifting transonic airfoils is presented. Differences between the present method based on nonlinear transonic theory and the classical correction formulae from linear subsonic theory are discussed. Computed results are presented for an NACA 0012 in solid and perforated wall tunnels. The solid wall calculations are compared with data.

Murman, E. M.↗

NASA NTRS1988

MHOST: An efficient finite element program for inelastic analysis of solids and structures

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Nakazawa, S.↗

NASA NTRS1993

Robust attitude control for Cassini spacecraft flying by Titan

This paper summarizes a few years attitude control design work on Cassini spacecraft with emphasis on the mission of Titan flyby. The study consists of modeling of the spacecraft dynamics, fuel sloshing, aerodynamic disturbance, controller design, nonlinear simulation, and establishing geometric command profiles. Both classical bang-bang control and modern robust H-infinity control have been designed and evaluated in nonlinear simulation to access the system tracking performance. Design procedures as well as their critical design issues are discussed in detail. Full model nonlinear simulations indicate that a simple 12-state H-infinity controller achieves better radar tracking performance than the classical bang-bang controller with less fuel throughout the flyby mission. Detailed robustness analysis of both designs will be published elsewhere.

Chiang, R.↗

DOE OSTI2025

Quantum critical electro-optic and piezo-electric nonlinearities

Although electro-optic (EO) nonlinearities are essential for many quantum and classical photonics applications, a major challenge is inefficient modulation in cryogenic environments. Guided by the connection between phase transitions and nonlinearity, we identify the quantum paraelectric perovskite SrTiO 3 as a strong cryogenic EO [>500 picometers per volt (pm/V)] and piezo-electric material (>90 picocoulombs per newton) at T = 5 K, at frequencies to at least 1 megahertz. Furthermore, by tuning SrTiO 3 toward quantum criticality, we more than double the EO and piezo-electric effects, demonstrating a linear Pockels coefficient above 1000 pm/V. Furthermore, our results probe the link between quantum phase transitions, dielectric susceptibility, and nonlinearity, unlocking opportunities in cryogenic optical and mechanical systems and providing a framework for discovering new nonlinear materials.

Anderson, Christopher P. [Stanford University, CA ↗

NASA NTRS1996

A Computational and Experimental Study of Nonlinear Aspects of Induced Drag

Despite the 80-year history of classical wing theory, considerable research has recently been directed toward planform and wake effects on induced drag. Nonlinear interactions between the trailing wake and the wing offer the possibility of reducing drag. The nonlinear effect of compressibility on induced drag characteristics may also influence wing design. This thesis deals with the prediction of these nonlinear aspects of induced drag and ways to exploit them. A potential benefit of only a few percent of the drag represents a large fuel savings for the world's commercial transport fleet. Computational methods must be applied carefully to obtain accurate induced drag predictions. Trefftz-plane drag integration is far more reliable than surface pressure integration, but is very sensitive to the accuracy of the force-free wake model. The practical use of Trefftz plane drag integration was extended to transonic flow with the Tranair full-potential code. The induced drag characteristics of a typical transport wing were studied with Tranair, a full-potential method, and A502, a high-order linear panel method to investigate changes in lift distribution and span efficiency due to compressibility. Modeling the force-free wake is a nonlinear problem, even when the flow governing equation is linear. A novel method was developed for computing the force-free wake shape. This hybrid wake-relaxation scheme couples the well-behaved nature of the discrete vortex wake with viscous-core modeling and the high-accuracy velocity prediction of the high-order panel method. The hybrid scheme produced converged wake shapes that allowed accurate Trefftz-plane integration. An unusual split-tip wing concept was studied for exploiting nonlinear wake interaction to reduced induced drag. This design exhibits significant nonlinear interactions between the wing and wake that produced a 12% reduction in induced drag compared to an equivalent elliptical wing at a lift coefficient of 0.7. The performance of the split-tip wing was also investigated by wing tunnel experiments. Induced drag was determined from force measurements by subtracting the estimated viscous drag, and from an analytical drag-decomposition method using a wake survey. The experimental results confirm the computational prediction.

Smith, Stephen C.↗

NASA NTRS1978

Digital set point control of nonlinear stochastic systems

A technique for digital control of nonlinear stochastic plants is presented. The development achieves a practical digital algorithm with which the closed-loop system behaves in a classical Type I manner even with gross nonlinearities in the plant structure and low signal-to-noise power ratios. The design procedure is explained in detail and illustrated by an example whose simulated responses testify to the practicality of the approach.

Moose, R. L.↗

DOE OSTI2024

Giant optical nonlinearity of Fermi polarons in atomically thin semiconductors

In this study, realizing strong nonlinear optical responses is a long-standing goal of both fundamental and technological importance. Recently, substantial efforts have been focused on exploring excitons in solids to achieve nonlinearities even down to few-photon levels. However, a crucial tradeoff arises as strong light–matter interactions require large oscillator strength and short radiative lifetime of excitons, which limits their nonlinearity. Here we experimentally demonstrate strong nonlinear optical responses with large oscillator strength by exploiting the coupling between excitons and carriers in an atomically thin semiconductor. By controlling the electric field and electrostatic doping of trilayer WSe 2 , we observe the hybridization between intralayer and interlayer excitons and the formation of Fermi polarons. Substantial optical nonlinearity is observed under continuous-wave and pulsed laser excitation, where the Fermi polaron resonance blueshifts by as much as ~10 meV. Intriguingly, we observe a remarkable asymmetry in the optical nonlinearity between electron and hole doping, which is tunable by the applied electric field. We attribute these features to the optically induced valley polarization due to the interactions between excitons and free charges. Our results establish atomically thin heterostructures as a highly versatile platform for engineering nonlinear optical response with applications to classical and quantum optoelectronics.

2d materials↗

DOE OSTI2021

Simultaneous type-I and type-II phase matching for second-order nonlinearity in integrated lithium niobate waveguide

Second-order optical nonlinearity is widely used for both classical and quantum photonic applications. Due to material dispersion and phase matching requirements, the polarization of optical fields is pre-defined during the fabrication. Only one type of phase matching condition is normally satisfied, and this limits the device flexibility. Here, we demonstrate that phase matching for both type-I and type-II second-order optical nonlinearity can be realized simultaneously in the same waveguide fabricated from thin-film lithium niobate. This is achieved by engineering the geometry dispersion to compensate for the material dispersion and birefringence. The simultaneous realization of both phase matching conditions is verified by the polarization dependence of second-harmonic generation. Correlated photons are also generated through parametric down conversion from the same device. This work provides a novel approach to realize versatile photonic functions with flexible devices.

Briggs, Ian↗

DOE OSTI2024

Extraordinary frequency stabilization by resonant nonlinear mode coupling

Here, we show that a self-sustained oscillator with a frequency-selective element operating with two nonlinearly coupled modes can achieve a level of frequency stability well beyond that available using single-mode operation. The system of interest consists of a self-sustained oscillator based on a nonlinear primary mode that is coupled via an internal resonance to a passive secondary mode. Analysis of a generic model for this resonance with both additive and multiplicative noises reveals that the stability improvements accrue from two sources: (i) nonlinear frequency veering in the primary mode, a classical analogue to quantum-level repulsion, that eliminates amplitude-to-frequency noise conversion; and (ii) phase cleaning of the oscillator through an intrinsic phase constraint arising from synchronization of the modes. This latter effect can significantly reduce the effects of intrinsic frequency fluctuations of the primary mode, which are not accessible by any known strategy using single-mode operation. The theoretical predictions are supported by experimental measurements of a microelectromechanical systems-based oscillator that demonstrate a reduction in oscillator line width of several orders of magnitude. This approach offers a means of optimizing frequency stability in self-sustained oscillators, which has direct implications for applications in timekeeping and sensing.

36 MATERIALS SCIENCE↗