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Erratum: “Nonlinear modeling of forced magnetic reconnection in slab geometry with NIMROD” [Phys. Plasmas 24, 052508 (2017)]
The linear layer response time is evaluated inappropriately in Ref. 1. This affects analytic predictions for linear and quasilinear magnetic field penetration due to a resonant, externally applied field according to Eqs. (14) and (19) of Ref. 1, respectively. The linear layer response time for the visco-resistive regime is given according to Ref. 2 as $τ_{VR}$ =2.104$τ_{shA}$S$^{2/3}_{sh}$P$^{1/6}_{m}$, where $τ_{shA}$ ≡ $τ_A$/$k_ya$ is the local shear Alfvén time at the rational surface (called the local hydromagnetic time $τ_H$ in Ref. 2) and S sh =$Sk_ya$ is the local Lundquist number. However, Ref. 1 inadvertently omits the factor of $k_y$a in $τ_{shA}$, evaluating $τ_{VR}$ using the Alfvén time τA based on the sheared magnetic field strength at the computation boundary. The proper evaluation of $τ_{VR}$ results in a linear layer response time that is ($k_ya$) 1/3 =π -1/3 ≃0.68 shorter than that in Ref. 1. The value of the time $τ'_{VR}$ used to predict quasilinear equilibria according to Eq. (19) is shorter by the same factor. Using the correct value of $τ_{VR}$ has a direct effect on analytic predictions for the magnitude and phase of the linear penetrated field, consistent with Eq. (14) in Ref. 1. Figure 1 replaces Fig. 5 of Ref. 1, exhibiting even better agreement between NIMROD computations and analytic predictions. The highest percent difference in penetrated field magnitude is 11% and in phase is 8%.
Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction
Here, this work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.
Geometric Subspace Updates with Applications to Online Adaptive Nonlinear Model Reduction
Not provided.
Neural Network Ensemble With Embedded Hamiltonian Constraints for Modeling Nonlinear Structural Dynamics.
Abstract not provided.
Hamiltonian-Constrained Neural Networks for Modeling Nonlinear Structural Systems.
Abstract not provided.
Ensemble of Numerics-Informed Neural Networks with Embedded Hamiltonian Constraints for Modeling Nonlinear Structural Dynamics.
Abstract not provided.
Insights on the nonlinear modeling and characterization of bolted lap joint interface of beams.
Abstract not provided.
Validating a nonlinear model in a 3-axis mechanical shock environment
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Robust Bayesian Optimal Experimental Design for Misspecified Linear and Nonlinear Models
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A nonlinear model of combustion instability in liquid propellant rocket engines.
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A nonlinear model for gas chromatograph systems
Fundamental engineering design techniques and concepts were studied for the optimization of a gas chromatograph-mass spectrometer chemical analysis system suitable for use on an unmanned, Martian roving vehicle. Previously developed mathematical models of the gas chromatograph are found to be inadequate for predicting peak heights and spreading for some experimental conditions and chemical systems. A modification to the existing equilibrium adsorption model is required; the Langmuir isotherm replaces the linear isotherm. The numerical technique of Crank-Nicolson was studied for use with the linear isotherm to determine the utility of the method. Modifications are made to the method eliminate unnecessary calculations which result in an overall reduction of the computation time of about 42 percent. The Langmuir isotherm is considered which takes into account the composition-dependent effects on the thermodynamic parameter, mRo.
An application of tensor ideas to nonlinear modeling of a turbofan jet engine
An application of tensor modelling to a digital simulation of NASA's Quiet, Clean, Shorthaul Experimental (QCSE) gas turbine engine is presented. The results show that the tensor algebra offers a universal parametrization which is helpful in conceptualization and identification for plant modelling prior to feedback or for representing scheduled controllers over an operating line.
Nonstationary modulation of galactic cosmic rays in a nonlinear model
An automdel equation for the solar wind velocity is obtained in the self-consistent model. The solution of the convection-diffusion equation is obtained for the density of galactic cosmic rays at a definite dependence of the diffusion coefficient and solar wind velocity on the rigidity and distance.
Nonlinear model simplification in flight control system design
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Tensor ideas for nonlinear modeling of a turbofan jet engine: Preliminary studies
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An application of tensor ideas to nonlinear modeling of a turbofan jet engine
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