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Results for “classic nonlinearity”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

A numerical investigation of film cooling as an alternate thermal protection system for spacecraft during atmospheric reentry

Research was undertaken to determine the mass required to protect a surface during atmospheric reentry by injecting a cold gas tangentially along the surface. A consideration of this problem revealed that the boundary layer equations could be employed to approximate the most important flow configurations which occur in film cooling. However, even with this simplification, the equations to be solved are complex, nonlinear, coupled partial differential equations. Due to the relative weakness of classical methods of boundary layer analysis, finite difference methods were chosen as the best approach to the formidable problem under consideration. Instead of blindly adopting a proposed technique and trying to force it to the problem, a more systematic study was deemed to be not only desirable but necessary. A relatively basic study of the application of finite difference methods was undertaken with the objective of developing an algorithm capable of obtaining accurate solutions to film cooling problems.

Clausing, A. M.↗
NASA NTRS1982

Constitutive model development for isotropic materials

The objective is to develop a unified constitutive model for finite-element structural analysis of turbine engine hot section components. This effort constitutes a different approach for nonlinear finite-element computer codes which were heretofore based on classical inelastic methods. A unified constitutive theory will avoid the simplifying assumptions of classical theory and should more accurately represent the behavior of superalloy materials under cyclic loading conditions and high temperature environments. Model development will be directed toward isotropic, cast nickel-base alloys used for aircooled turbine blades and vanes. The contractor will select a base material for model development and an alternate material for verification purposes from a list of three alloys specified by NASA. The candidate alloys represent a cross-section of turbine blade and vane materials of interest to both large and small size engine manufacturers. Material stock for the base and alternate materials will be supplied to the Contractor by the government.

Kaufman, A.↗
NASA NTRS1986

Prediction of the long-term creep compliance of general composite laminates

An accelerated viscoelastic characterization procedure for use with polymer-based composite materials is presented which employs short term test data obtained using unidirectional specimens to predict the long term viscoelastic behavior of general composite laminates. This procedure is here illustrated using the Schapery (1966, 1969) nonlinear theory as the required viscoelastic constitutive model, as well as classical lamination theory for the lamination scheme. The technique is applied to T300/5208 graphite/epoxy.

Tuttle, M. E.↗
NASA NTRS1987

A generalized hybrid transfinite element computational approach for nonlinear/linear unified thermal/structural analysis

The present paper describes the development of a new hybrid computational approach for applicability for nonlinear/linear thermal structural analysis. The proposed transfinite element approach is a hybrid scheme as it combines the modeling versatility of contemporary finite elements in conjunction with transform methods and the classical Bubnov-Galerkin schemes. Applicability of the proposed formulations for nonlinear analysis is also developed. Several test cases are presented to include nonlinear/linear unified thermal-stress and thermal-stress wave propagations. Comparative results validate the fundamental capablities of the proposed hybrid transfinite element methodology.

Tamma, Kumar K.↗
NASA NTRS1990

Interlaminar shear stress effects on the postbuckling response of graphite-epoxy panels

The influence of shear flexibility on overall postbuckling response was assessed, and transverse shear stress distributions in relation to panel failure were examined. Nonlinear postbuckling results are obtained for finite element models based on classical laminated plate theory and first-order shear deformation theory. Good correlation between test and analysis is obtained. The results presented analytically substantiate the experimentally observed failure mode.

Engelstad, S. P.↗
NASA NTRS1990

Interlaminar shear stress effects on the postbuckling response of graphite-epoxy panels

The objectives of the study are to assess the influence of shear flexibility on overall postbuckling response, and to examine transverse shear stress distributions in relation to panel failure. Nonlinear postbuckling results are obtained for finite element models based on classical laminated plate theory and first-order shear deformation theory. Good correlation between test and analysis is obtained. The results presented in this paper analytically substantiate the experimentally observed failure mode.

Engelstad, S. P.↗
NASA NTRS2004

Application of the GRC Stirling Convertor System Dynamic Model

The GRC Stirling Convertor System Dynamic Model (SDM) has been developed to simulate dynamic performance of power systems incorporating free-piston Stirling convertors. This paper discusses its use in evaluating system dynamics and other systems concerns. Detailed examples are provided showing the use of the model in evaluation of off-nominal operating conditions. The many degrees of freedom in both the mechanical and electrical domains inherent in the Stirling convertor and the nonlinear dynamics make simulation an attractive analysis tool in conjunction with classical analysis. Application of SDM in studying the relationship of the size of the resonant circuit quality factor (commonly referred to as Q) in the various resonant mechanical and electrical sub-systems is discussed.

Regan, Timothy F.↗
DOE OSTI2021

On the generalised equipartition law

We observe that the so-called Generalised Equipartition Law for hamiltonian systems is actually valid only under specific hypotheses – unfortunately omitted in some textbooks – which limit its applicability when dealing with nonlinear systems. We introduce a new coordinate-independent generalisation which overcomes this problem and can be applied to a larger set of functions. A simple example of application is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Layer-Parallel Training of Deep Residual Neural Networks

Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be interpreted as forward Euler discretizations of a nonlinear initial value problem whose time-dependent control variables represent the weights of the neural network. Hence, training a ResNet can be cast as an optimal control problem of the associated dynamical system. For similar time-dependent optimal control problems arising in engineering applications, parallel-in-time methods have shown notable improvements in scalability. This paper demonstrates the use of those techniques for efficient and effective training of ResNets. The proposed algorithms replace the classical (sequential) forward and backward propagation through the network layers with a parallel nonlinear multigrid iteration applied to the layer domain. This adds a new dimension of parallelism across layers that is attractive when training very deep networks. From this basic idea, we derive multiple layer-parallel methods. The most efficient version employs a simultaneous optimization approach where updates to the network parameters are based on inexact gradient information in order to speed up the training process. Finally, using numerical examples from supervised classification, we demonstrate that the new approach achieves a training performance similar to that of traditional methods, but enables layer-parallelism and thus provides speedup over layer-serial methods through greater concurrency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

From Quantum Time to Manifestly Covariant QFT: On the Need for a Quantum-Action-Based Quantization

In quantum time (QT) schemes, time is promoted to a degree of freedom, allowing Lorentz covariance to be made explicit for single particles. We ask whether this can be lifted to QFT so that Lorentz covariance becomes manifest at the Hilbert-space level, rather than being hidden as in the standard canonical formulation. We address this question by proposing a second-quantized approach in which the elementary particle is the QT particle itself, leading naturally to the notion of spacetime field algebras and of quantum action. We show, however, that a naive many-body construction runs into inconsistencies. To pinpoint their origin we introduce a classical counterpart of the second-quantized formalism, spacetime classical mechanics (SCM), and prove a no-go theorem: Dirac quantization of SCM collapses back to standard QFT and therefore hides covariance. We circumvent this problem by presenting a quantum-action-based quantization that yields a spacetime version of quantum mechanics (SQM), making covariance manifest for (interacting) QFTs. Finally, we show that this resolution is tied to a genuine spacetime generalization of the notion of a quantum state, required by causality and closely connected to recent “states over time” proposals and, in dS/CFT–motivated settings, to microscopic notions of timelike entanglement and emergent time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Direct prediction of saturated neoclassical tearing modes in slab using an equilibrium approach

We demonstrate for the first time that the nonlinear saturation of neoclassical tearing modes (NTMs) can be found directly using a variational principle based on Taylor relaxation, without needing to simulate the intermediate, resistivity-dependent dynamics. As in previous investigations of classical tearing mode saturation (Loizu et al 2020 Phys. Plasmas 27 070701; Loizu and Bonfiglio 2023 J. Plasma Phys. 89 905890507), we make use of Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502), an equilibrium solver based on the variational principle of the multi-region relaxed magnetohydrodynamics (MHDs), featuring stepped pressure profiles and arbitrary magnetic topology. We work in slab geometry and employ a simple bootstrap current model J bs = C$\boldsymbol{\nabla}$p to study the bootstrap-driven tearing modes, scanning over the asymptotic matching parameter Δ' and bootstrap current strength. Saturated island widths produced by SPEC agree well with the predictions of an initial value resistive MHDs code (Huang and Bhattacharjee 2016 Astrophys. J. 818 20) while being orders of magnitude faster to calculate. Additionally, we observe good agreement with a simple analytical modified Rutherford equation, without requiring any fitting coefficients. The match is obtained for both linearly unstable classical tearing modes in the presence of bootstrap current, and NTMs, which are linearly stable but nonlinear-unstable due to the effects of the bootstrap current.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Raman-induced mode coupling in temporal waveguides formed by short solitons

We study the propagation of optical pulses trapped inside a temporal waveguide formed by two solitons in a dispersive nonlinear medium such as an optical fiber. The solitons are short enough that they decelerate as their spectra shift continuously toward the red side because of intrapulse Raman scattering. We show that the shape of a probe pulse trapped between the two solitons evolves in a periodic fashion, while its spectrum shifts toward the blue side. We develop a coupled-mode theory showing that such changes occur because of mode coupling induced by the deceleration of the short solitons, resulting in a curved waveguide. Here, a simplified two-mode model is used to introduce a single-parameter governing modal coupling and to find the condition under which coupling becomes weak enough that the probe pulse blue-shifts its spectrum without changes in its pulse shape.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation

It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly related to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Simulating non-native cubic interactions on noisy quantum machines

As a milestone for general-purpose computing machines, we demonstrate that quantum processors can be programed to efficiently simulate dynamics that are not native to the hardware. Moreover, on noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates instead of a restricted set of standard gates. We demonstrate the general methodology by solving a cubic interaction problem, which appears in nonlinear optics, gauge theories, as well as plasma and fluid dynamics. To encode the non-native Hamiltonian evolution, we decompose the Hilbert space into a direct sum of invariant subspaces in which the nonlinear problem is mapped to a finite-dimensional Hamiltonian simulation problem. Furthermore, in a three-states example, the resultant unitary evolution is realized by a product of approximately 20 standard gates, using which approximately ten simulation steps can be carried out on state-of-the-art quantum hardware before results are corrupted by decoherence. In comparison, the simulation depth is improved by more than an order of magnitude when the unitary evolution is realized as a single cubic gate, which is compiled directly using optimal control. Alternatively, parametric gates may also be compiled by interpolating control pulses. Modular gates thus obtained provide high-fidelity building blocks for quantum Hamiltonian simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

A higher-order theory for geometrically nonlinear analysis of composite laminates

A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.

Reddy, J. N.↗
DOE OSTI2026

Non-classical ion-indiffusion processes in quasi-one-dimensional ionic conductor KTiOPO4

Developments in coercive field engineering and waveguide writing via ion-exchange in the ferroelectric ionic-conductor KTiOPO4 (KTP) have led to breakthroughs within the field of nonlinear optics and quantum photonics. However, the microscopic diffusion dynamics of ion-exchange in KTP are poorly understood and show signs of non-classical diffusion dynamics. The precise control of ion-exchange gradients is critical for developing KTP into a mature, integrated nonlinear optical material but requires a level of control that, in turn, demands a deeper understanding of the ion-exchange process. We employ direct ToF-SIMS mapping to untangle the complex diffusion dynamics of the commonly used ion-exchange dopant ions: Rb, Ba, and K. We map periodic diffusion gradients of two exchanges, one dominated by Rb-ions and the other by Ba-ions. For the first time, we show the interdependent nature of the Ba- and Rb ion in the ion-exchange diffusion gradient. The low incorporation of the Ba ion is mapped and quantified, and dopant–crystal interactions are identified. This work highlights the complex diffusion dynamics of dopants in the KTP structure and lays the foundation for deterministic control of diffusion gradients for the next generation of integrated nonlinear and quantum photonic devices.

Barrett, Laura [ORNL]↗
DOE OSTI2020

Localised electromagnetic waves in a rhombic waveguide array with competing nonlinearities

We consider a model of a discrete photonic system representing a quasi-one-dimensional rhombic array of waveguides, where, in addition to the positive cubic nonlinearity, the negative quintic nonlinearity is taken into account for the material of which the central chain of the waveguides is made. The other two waveguide chains are made of an optically linear material. A continual approximation is used to obtain a solution for a system of coupled waves, which describes a wave localised in the transverse direction. In a certain special case, the competition of nonlinearities leads to the formation of a step-shaped distribution of the field intensities over the waveguides. (integrated optics)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Ultrafast nonlinear absorption of TMDC quantum dots

Here, we study theoretically absorption properties of MoS 2 quantum dots placed in an ultrashort and strong optical pulse with the duration of a few femtoseconds and the amplitude up to 1.5 V/Å. While the monolayer of MoS 2 has a bandgap of ≈ 1.8 eV, the quantum dots of MoS 2 have in-gap edge states, which open additional absorption channels. The absorbance of the system strongly depends on the amplitude of the pulse. At small amplitude, less than 0.5 V/Å, the absorbance varies by more than 20% with the frequency of the pulse. The system shows saturable absorption if the frequency of the pulse is larger than the bulk bandgap and reverse saturable absorption if the frequency of the pulse is in the bandgap. At large amplitudes, > 0.5 V/Å, of the pulse, the ultrafast absorbance of a quantum dot has a weak dependence on the pulse frequency. If the frequency of the pulse is less than the corresponding bulk bandgap, the absorbance has a nonmonotonic dependence on the pulse amplitude with the maximum at ≈ 0.5 V/Å. We also present the results for QDs of different TMDC materials, which show that at large field amplitude, > 0.5 V/Å, the absorbance is universal and has weak dependence on the type of TMDC.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗