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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

A Parallel Multi-Domain Solution Methodology Applied to Nonlinear Thermal Transport Problems in Nuclear Fuel Pins

This paper describes an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors is described. Details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstrating the achieved efficiency of the algorithm are presented. Furthermore, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2015

Electron Lenses for Experiments on Nonlinear Dynamics with Wide Stable Tune Spreads in the Fermilab Integrable Optics Test Accelerator

Recent developments in the study of integrable Hamiltonian systems have led to nonlinear accelerator lattice designs with two transverse invariants. These lattices may drastically improve the performance of high-power machines, providing wide tune spreads and Landau damping to protect the beam from instabilities, while preserving dynamic aperture. To test the feasibility of these concepts, the Integrable Optics Test Accelerator (IOTA) is being designed and built at Fermilab. One way to obtain a nonlinear integrable lattice is by using the fields generated by a magnetically confined electron beam (electron lens) overlapping with the circulating beam. The parameters of the required device are similar to the ones of existing electron lenses. We present theory, numerical simulations, and first design studies of electron lenses for nonlinear integrable optics.

43 PARTICLE ACCELERATORS↗
DOE OSTI2016

On the Possibility of Using Nonlinear Elements for Landau Damping in High-Intensity Beams

Direct space-charge force shifts incoherent tunes downwards from the coherent ones breaking the Landau mechanism of coherent oscillations damping at high beam intensity. To restore it nonlinear elements can be employed which move back tunes of large amplitude particles. In the present report we consider the possibility of creating a “nonlinear integrable optics” insertion in the Fermilab Recycler to host either octupoles or hollow electron lens for this purpose. For comparison we also consider the classic scheme with distributed octupole families. It is shown that for the Proton Improvement Plan II (PIP II) parameters the required nonlinear tune shift can be created without destroying the dynamic aperture.

43 PARTICLE ACCELERATORS↗
DOE OSTI2015

Development of a Nonlinear Time Domain Methodology (Part I)

The ASCE 4-2014 (draft) provides guidance in Appendix B for nonlinear time-domain soil structure interaction (NLSSI) analysis. To accommodate widespread use of NLSSI, it is necessary to develop a methodology, or a set of steps, that produce reasonable results. An NLSSI methodology opens the door to explore additional seismic behaviour at nuclear facilities such as 1) gapping and sliding, 2) inclined seismic waves coupled with gapping and sliding of foundations atop soil, 3) inclined seismic waves coupled with gapping and sliding of deeply embedded structures, 4) soil dilatancy, 5) surface waves, 4) buoyancy, 5) concrete cracking and 6) seismic isolation. This paper documents the NLSSI methodology. At a high level these steps include 1) define soil site parameters, 2) calibrate site-specific nonlinear soil constitutive model, 3) verify performance of time domain absorbing boundaries, 4) build free field soil site, 5) build 3D soil site model using the appropriate parameters 6) define design concrete material properties and develop appropriate concrete constitutive model, 7) build structural model, 8) define appropriate contact and/or friction behaviour, 9) build combined soil-structure model and run time domain models and 10) compare with SHAKE/SASSI results at increasing levels of ground motion. This paper will describe the NLSSI methodology, discuss important NLSSI considerations, and discuss its potential implementation in industry. A second paper, which is Part II, “Development of a Nonlinear Time Domain Methodology Results,” provides results comparing in-structure response from NLSSI with the linear frequency-domain program, SASSI.

42 ENGINEERING↗
DOE OSTI2017

Space-time least-squares Petrov-Galerkin projection in nonlinear model reduction.

Our work proposes a space-time least-squares Petrov-Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply Petrov-Galerkin projection in the spatial dimension and subsequently apply time integration to numerically resolve the resulting low-dimensional dynamical system, the proposed method applies projection in space and time simultaneously. To accomplish this, the method first introduces a low-dimensional space-time trial subspace, which can be obtained by computing tensor decompositions of state-snapshot data. The method then computes discrete-optimal approximations in this space-time trial subspace by minimizing the residual arising after time discretization over all space and time in a weighted ℓ 2 -norm. This norm can be de ned to enable complexity reduction (i.e., hyper-reduction) in time, which leads to space-time collocation and space-time GNAT variants of the ST-LSPG method. Advantages of the approach relative to typical spatial-projection-based nonlinear model reduction methods such as Galerkin projection and least-squares Petrov-Galerkin projection include: (1) a reduction of both the spatial and temporal dimensions of the dynamical system, (2) the removal of spurious temporal modes (e.g., unstable growth) from the state space, and (3) error bounds that exhibit slower growth in time. Numerical examples performed on model problems in fluid dynamics demonstrate the ability of the method to generate orders-of-magnitude computational savings relative to spatial-projection-based reduced-order models without sacrificing accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Nonlinearity induced synchronization enhancement in mechanical oscillators

An autonomous oscillator synchronizes to an external harmonic force only when the forcing frequency lies within a certain interval, known as the synchronization range, around the oscillator's natural frequency. Under ordinary conditions, the width of the synchronization range decreases when the oscillation amplitude grows, which constrains synchronized motion of micro- and nano-mechanical resonators to narrow frequency and amplitude bounds. The present invention shows that nonlinearity in the oscillator can be exploited to manifest a regime where the synchronization range increases with an increasing oscillation amplitude. The present invention shows that nonlinearities in specific configurations of oscillator systems, as described herein, are the key determinants of the effect. The present invention presents a new configuration and operation regime that enhances the synchronization of micro- and nano-mechanical oscillators by capitalizing on their intrinsic nonlinear dynamics.

42 ENGINEERING↗
DOE OSTI2018

Nonlinear optical frequency conversion using metamaterial arrays

A method of nonlinear wavelength generation uses a nonlinear optical medium. An input flux of pump energy is applied to one or more dielectric optical resonators. Each resonator has an optical cavity comprising the nonlinear optical medium. Each resonator has at least one Mie resonance that is excited by the input flux of pump energy. The pump energy causes the generation of converted light containing at least one converted component having a frequency attainable only through a non-linear process.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Nonlinear model-based controller for premixed charge compression ignition combustion timing in diesel engines

Advanced combustion modes, such as PCCI, operate near the system stability limits. In PCCI, the combustion event begins without a direct combustion trigger in contrast to traditional spark-ignited gasoline engines and direct-injected diesel engines. The lack of a direct combustion trigger encourages the usage of model-based controls to provide robust control of the combustion phasing. The nonlinear relationships between the control inputs and the combustion system response often limit the effectiveness of traditional, non-model-based controllers. Accurate knowledge of the system states and inputs is helpful for implementation of an effective nonlinear controller. A nonlinear controller is developed and implemented to control the engine combustion timing during diesel PCCI operation by targeting desired values of the in-cylinder oxygen concentration, pressure, and temperature during early fuel injection.

42 ENGINEERING↗
DOE OSTI2019

Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems

The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition; this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domain-specific knowledge and painstaking tuning. In this paper we introduce a deep learning framework for learning Koopman operators of nonlinear dynamical systems. We show that this novel method automatically selects efficient deep dictionaries, outperforming state-of-the-art methods. We benchmark this method on partially observed nonlinear systems, including the glycolytic oscillator and show it is able to predict quantitatively 100 steps into the future, using only a single timepoint, and qualitative oscillatory behavior 400 steps into the future.

koopman operators, machine learning, deep learning↗
DOE OSTI2020

Power supply including a nonlinear transmission line that receives a single input pulse and outputs a plurality of pulses

Technologies pertaining to a power supply that includes a nonlinear transmission line are described herein. In an embodiment, a DC power supply comprises a pulsing circuit that receives a DC input and outputs a first plurality of pulses having a first frequency to a nonlinear transmission line. The nonlinear transmission line receives the first plurality of pulses and outputs a second plurality of pulses having a second frequency that is greater than the first frequency. The second plurality of pulses is then received at an amplifier/rectifier circuit that amplifies the second pulses to increase a voltage amplitude of the pulses, and rectifies the pulses to provide a substantially constant DC output.

42 ENGINEERING↗
DOE OSTI2021

Investigation of Nonlinear Difference-Frequency Wave Excitation on a Semisubmersible Offshore-Wind Platform with Bichromatic-Wave CFD Simulations: Preprint

The natural surge and pitch frequencies of semisubmersible offshore wind platforms are typically designed to be below the wave frequencies to avoid direct excitation. However, surge or pitch resonance can be excited by the nonlinear low-frequency loads generated by irregular incident waves. Second-order potential-flow models with added Morison drag have been found to underpredict this low-frequency excitation and response. As part of the OC6 project, Computational Fluid Dynamics (CFD) simulations were performed to enable a better understanding of the low-frequency loads and the limitations of lower-fidelity models. The focus of the current paper is to set up a computationally cost-effective CFD simulation of a fixed semisubmersible platform to investigate nonlinear difference-frequency loads and establish the corresponding uncertainty in the results. Due to the high computing cost, CFD simulations of irregular waves can be challenging. Instead, simulations were performed with bichromatic waves having a shorter repeat period. A preliminary comparison with Quadratic Transfer Functions from second-order potential-flow theory shows that CFD models consistently predict higher nonlinear wave loads at the difference frequency, likely due to flow separation and viscous drag not accounted for in potential-flow theory.

2nd order↗
DOE OSTI2021

Resonance-enhanced compact nonlinear acoustic source of low frequency collimated beam for imaging applications in highly attenuating media

Acoustic signal sources include acoustic resonators that include acoustic nonlinear materials. Acoustic signals at higher frequencies are mixed in the nonlinear materials to produce a lower frequency acoustic signal. Resonance provides increased efficiency in producing acoustic signals at difference frequencies corresponding to resonance frequencies. Higher frequency acoustic signals used in nonlinear mixing are preferably at frequencies corresponding to resonance frequencies as well.

Pantea, Cristian↗
DOE OSTI2021

Constrained Block Nonlinear Neural Dynamical Models

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear dynamical models by embedding local model structure and constraints. The proposed method consists of neural network blocks that represent input, state, and output dynamics with constraints placed on the network weights and system variables. For handling partially observable dynamical systems, we utilize a state observer neural network to estimate the states of the system's latent dynamics. We evaluate the performance of the proposed architecture and training methods on system identification tasks for three nonlinear systems: a continuous stirred tank reactor, a two tank interacting system, and an aerodynamics body. Models optimized with a few thousand system state observations accurately represent system dynamics in open loop simulation over thousands of time steps from a single set of initial conditions. Experimental results demonstrate an order of magnitude reduction in open-loop simulation mean squared error for our constrained, block-structured neural models when compared to traditional unstructured and unconstrained neural network models.

Skomski, Elliott↗
DOE OSTI2021

Equations of Motion for the Vertical Rigid-Body Rotor: Linear and Nonlinear Cases

Centuries ago, the prolific mathematician Leonhard Euler (1707–1783) wrote down the equations of motion (EOM) for the heavy symmetrical top with one point fixed. The resulting set of equations turned out to be nonlinear and had a limited number of closed-form solutions.Today, tools such as transfer matrix and finite elements enable the calculation of the rotordynamic properties for rotor-bearing systems. Some of these tools rely on the “linearized” version of the EOM to calculate the eigenvalues, unbalance response, or transients in these systems.In fact, industry standards mandate that rotors be precisely balanced to have safe operational characteristics. However, in some cases, the nonlinear aspect of the EOM should be considered.The purpose of this chapter is to show examples of how the linear vs. nonlinear formulations differ. This chapter also shows how excessive unbalance is capable of dramatically altering the behavior of the system and can produce chaotic motions associated with the “jump” phenomenon.

Laos, Hector↗
DOE OSTI2022

Nonlinear hydrostatic control of a wave energy converter

Increased energy harvesting is realized using a nonlinear buoy geometry for reactive power generation. By exploiting the nonlinear dynamic coupling between the buoy geometry and the potential wideband frequency spectrum of incoming waves in the controller/buoy design, increased power can be captured in comparison to conventional wave energy converter designs. In particular, the reactive power and energy storage system requirements are inherently embedded in the nonlinear buoy geometry, therefore requiring only simple rate-feedback control.

Wilson, David G.↗
DOE OSTI2023

Improved Measurements of Nonlinear Integrable Optics Invariants at IOTA

Nonlinear integrable optics (NIO) are a promising novel approach at improving the stability of high intensity beams. Implementations of NIO based on specialized magnetic elements are being tested at the Integrable Optics Test Accelerator (IOTA) at Fermilab. One method of verifying proper implementation of these solutions is by measuring the analytic invariants predicted by theory. The initial measurements of nonlinear invariants were performed during IOTA run in 2019/20, however the covid-19 pandemic prevented the full-scale experimental program from being completed. Several important improvements were implemented in IOTA for the 2022/23 run, including the operation at higher beam energy of 150 MeV, improved optics control, and chromaticity correction. This report presents the results of improved measurements of nonlinear invariants.

43 PARTICLE ACCELERATORS↗
DOE OSTI2016

Development of Advanced Numerical Tools for the Nonlinear Seismic Analysis of Nuclear Systems

In the framework of Probabilistic Risk Assessment (PRA) of nuclear facilities, a rigorous dynamic characterization of all structural and non-structural components is of paramount concern. The common features of nuclear facilities lies in the combination of three characteristics: 1. low aspect ratio; 2. large mass; and 3. significant embedment in soil. These characteristics make the interaction between the structural system and the surrounding soil a key aspect to consider for seismic risk evaluations. The methodologies and numerical tools currently in use for simulating the seismic response of a nuclear facility with significant Soil Structure Interaction (SSI) date back to the 1970's and rely on a number of simplifying idealizations, mainly related to the characterization of the incident seismic waveforms, the assumption of linear-elastic behavior of the superstructures, and idealization of equivalent linear behavior of the supporting soils. Given this background and taking advantage of the substantial progress in computational mechanics in the last decades, the ongoing research aims at developing advanced numerical tools for the nonlinear, time history simulation of nuclear facilities. This translates into the availability of a robust nonlinear time-domain simulation tool that can accurately model the nonlinearities of coupled soil-structure systems, and whose development includes robust verification and validation. The work described herein is supported by the U.S. Department of Energy (DOE) and focuses on delivering the next-generation, high performance simulation tool in support of DOE needs and mission. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Experimental Demonstration of a Two-Dimensional Nonlinear Integrable System in a Particle Accelerator

A two-dimensional nonlinear integrable system was experimentally demonstrated at the Fermilab Integrable Optics Test Accelerator. The system was implemented by inserting a special nonlinear magnet in a conventional accelerator lattice. We characterized the system by measuring lifetimes, transverse profiles and transverse oscillation frequencies of the 150-MeV electron beam as a function of the strength of the nonlinear insert. The measured shift of the working point and the amplitude-dependent detuning were consistent with theoretical predictions. We also observed the predicted bifurcation of the stable closed orbit. A striking consequence of the system's implementation was the possibility to operate the storage ring with integer tunes without lifetime degradation. This research opens up novel ways to design particle accelerators and to stabilize particle beams.

Wieland, John [Fermilab] (ORCID:0000000289718523)↗

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