Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “nonlinear systems”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,261 records · Page 70
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Scalable Reduced Order Model with Discontinuous Galerkin Domain Decomposition

scaleupROM is a scalable, physics-constrained reduced order model (ROM). It aims to provide robust, accelerated physics predictions at extrapolated scales, based on the small, component-level data. This is implemented by combining projection-based ROM with discontinuous Galerkin domain decomposition, in the framework of MFEM and libROM. It currently supports the Poisson equation and Stokes flow equation, and more work is in progress toward general, nonlinear physics systems.

Chung, Seung Whan↗
DOE OSTI2021

Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

Abstract Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $$10^3{\times }$$ 10 3 × in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs. The domain of applications include both parabolic and hyperbolic PDEs, regardless of the dimension of full-order models (FOMs).

42 ENGINEERING↗
DOE OSTI2021

Alignment tolerance analysis for divided-pulse nonlinear compression

We present an analytic model that describes the output pulse after Kerr-based spectral broadening with divided-pulse nonlinear compression that includes errors in unequal pulse division, birefringent plate retardance, and thermal drift. The model shows that alignment tolerances become impractically tight at high levels of nonlinearity and that the angle of incidence on the birefringent plates can be utilized as a compensator to loosen those tolerances. We present experimental verification of the model, which is expected to be a fast and flexible tool to design future divided-pulse nonlinear compression systems.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Dual-wavelength channel GHz repetition rate mode-locked VECSEL cavities sourced from a common gain medium

Mode-locked vertical external cavity semiconductor lasers are a unique class of nonlinear dynamical systems driven far from equilibrium. We present a novel, to the best of our knowledge, experimental result, supported by rigorous microscopic simulations, of two coexisting mode-locked V-cavity configurations sourced by a common gain medium and operating as independent channels at angle controlled separated wavelengths. Microscopic simulations support pulses coincident on the common gain chip extracting photons from a nearby pair of coexisting kinetic holes burned in the carrier distributions.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

MULTISTEP AND CONTINUOUS PHYSICS-INFORMED NEURAL NETWORK METHODS FOR LEARNING GOVERNING EQUATIONS AND CONSTITUTIVE RELATIONS

In this work, we investigate the applicability and relative merit of discrete and continuous versions of physics-informed neural network (PINN) methods for learning unknown governing equations or constitutive relations in a nonlinear dynamical system. In the case of unknown dynamics, entire right-hand-side (RHS) equations of the ordinary differential equations are unknown. In the case of unknown constitutive relations, however, the RHS equations are known up to the specification of constitutive relations (that may depend on the state of the system). We use a deep neural network to model unknown governing equations or constitutive relations. The discrete PINN approach combines classical multistep discretization methods for dynamical systems with neural-network-based machine learning methods. On the other hand, the continuous versions utilize deep neural networks to minimize the residual function for the continuous governing equations. We use the case of a fedbatch bioreactor system to study the effectiveness of these approaches and discuss conditions for their applicability. Our results indicate that the accuracy of the trained neural network models is much higher for the cases where we only have to learn a constitutive relation instead of all dynamics. This finding corroborates the well-known fact from scientific computing that building as much structural information as is available into an algorithm can enhance its efficiency and/or accuracy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Progress on the Electron Gun Design for a McMillan Electron Lens in the Fermilab Integrable Optics Test Accelerator (IOTA)

This paper covers the progress made so far in designing the first McMillan electron lens for the Fermilab IOTA ring. The novel design allows for an increase in tune spread without limiting the dynamic aperture due to its integrability. Shown are simulations for an electron gun design to generate the specific required current density distribution for the nonlinear integrable system in IOTA.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

baseflow: a MATLAB and GNU Octave package for baseflow recession analysis

baseflow is a MATLAB® toolbox designed for baseflow recession analysis, a technique used in hydrologic science to infer aquifer properties from streamflow. By leveraging widely available streamflow data, baseflow can be used to estimate aquifer properties such as hydraulic conductivity and drainable porosity over the modern instrumental stream gage record. The toolbox is intended for analysis of measured streamflow values recorded on a daily timestep, and is tailored for shallow, unconfined riparian aquifers that discharge groundwater laterally into adjacent streams. Additionally, baseflow can analyze the collective behavior of individual hillslope aquifers constituting hydrologic catchments, known as “watersheds”, from a nonlinear dynamical systems perspective. The toolbox incorporates recent advances in baseflow recession analysis to enable objective estimations of aquifer properties, and their sensitivity to methodological decisions, at both hillslope and catchment scales.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Nemchinov-Dyson Solutions of the Two-Dimensional Axisymmetric Inviscid Compressible Flow Equations [Review]

We investigate the two-dimensional (2D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the 2D velocity field is space-time separable and linearly variable in each corresponding spatial coordinate, we proceed to derive an in nite family of elliptic or hyperbolic, uniformly expanding or contracting \gas cloud" solutions. Construction of specific example solutions belonging to this family is dependent on the solution of a system of nonlinear, coupled, second-order ordinary differential equations, and the prescription of an additional physical process of interest (e.g., uniform temperature or uniform entropy flow). The physical and computational implications of these solutions as pertaining to quantitative code verification or model qualification studies are discussed in some detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Multiscale modeling high-order methods and data-driven modeling

Projection-based reduced-order models (ROMs) comprise a promising set of data-driven approaches for accelerating the simulation of high-fidelity numerical simulations. Standard projection-based ROM approaches, however, suffer from several drawbacks when applied to the complex nonlinear dynamical systems commonly encountered in science and engineering. These limitations include a lack of stability, accuracy, and sharp a posteriori error estimators. This work addresses these limitations by leveraging multiscale modeling, least-squares principles, and machine learning to develop novel reduced-order modeling approaches, along with data-driven a posteriori error estimators, for dynamical systems. Theoretical and numerical results demonstrate that the two ROM approaches developed in this work - namely the windowed least-squares method and the Adjoint Petrov - Galerkin method - yield substantial improvements over state-of-the-art approaches. Additionally, numerical results demonstrate the capability of the a posteriori error models developed in this work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Accurate and Efficient Parametric Model-Order Reduction for Turbulent Thermal Transport

This project produced new algorithms and software for low-cost exploration of turbulent thermal-fluids behavior under parametric variation by using reduced-order models (ROMs). The ROMs numerically solve the governing equations for fluid motion by using a small set of basis functions (typically, N=20-200 modes) to represent the solution. The base modes are computed as optimal combinations of solutions from expensive high-fidelity "anchor-point" solutions involving millions of unknowns, which are typically generated by solving the full Navier-Stokes equations on a supercomputer. The ROM solution is itself a combination of the base modes, where the basis coefficients are determined by evolving an NxN system of nonlinear equations. The overarching idea is to use the inexpensive ROM to predict solutions under conditions where the parameters differ from the anchor-point conditions. Several ingredients are required to make ROMs useful for thermal hydraulics analysis. These include: a stable and accurate ROM that is capable of reproducing the large-scale dynamics of turbulent flow, error indicators than can guide the choice of anchor points, and low-cost mechanisms for evaluating nonlinear terms in the reduced equations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Parallel-in-Time Integration for Nonlinear Hyperbolic Problems (Final Report)

The work for the subcontract was situated in the area of parallel-in-time integration for hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. Over the past two decades, much progress has been made in this area; however, this progress has largely been limited to diffusion-dominated PDEs, with some recent success in scalar linear hyperbolic PDEs. Given the ubiquity of numerical simulations of hyperbolic PDEs throughout the sciences, in particular, nonlinear hyperbolic systems, there is a strong need to develop efficient parallel-in-time techniques for hyperbolic problems beyond simple scalar and linear cases, which is the main topic of this subcontract. The main focus of the work was to further develop and perfect coarse-grid operators for the Multigrid Reduction-inTime (MGRIT) method applied to hyperbolic PDEs that were recently proposed in PhD thesis, based on a modified semi-Lagrangian approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Cluster for Research Excellence (CRE) for Accelerator Physics

The purpose of this Cooperative Research and Development Agreement (CRADA) was to establish a Cluster of Research Excellence (CRE) for Accelerator Physics and broaden the accelerator physics collaboration between Northern Illinois University (NIU) and Fermilab. The CRE was based in both Fermilab’s Accelerator Division and in NIU’s Department of Physics. A research agenda and strategy for the CRE for Accelerator Physics included specific research topics, experiments, and research facility upgrades. The scope of the research program covered two thrusts with subtopics in the Accelerator Science Research Program utilizing the infrastructure of FAST, IOTA, the Fermilab Accelerator Complex, and the Illinois Accelerator Research Center (IARC). Specific areas of proposed exploration included: 1.Tests of novel “nonlinear integrable” systems including beam self-fields; 2.Experimental tests of phase-space diffusion and chaos in intense beams; 3.Investigate technically feasible approaches towards next generation intenseneutrino facilities; 4.Understanding optical control of charged particle beams; 5.Exploitation of bright electron beams from FAST for novel applications; 6. Conduct research into accelerator-based ‘precision science’, such as Muon g-2, EDM, Mu2e, etc.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Influence of wind turbine design parameters on linearized physics-based models in OpenFAST

Abstract. While most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear wind system equations is often important for understanding the system response and exploiting well-established methods and tools for analyzing linear systems. Linearized models are important for eigenanalysis (to derive structural natural frequencies, damping ratios, and mode shapes), controls design (based on linear state-space models), etc. In controls co-design, wherein methods often rely on linearized time-domain models of the physics, the physical structure (often called the plant) and controller are designed and optimized concurrently, so it is important to understand how changes to the physical design affect the linearized system. This work summarizes efforts done to understand the impact of design parameter variations in the physical system (e.g., mass, stiffness, geometry, and aerodynamic and hydrodynamic coefficients) on the linearized system using OpenFAST.

17 WIND ENERGY↗