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The Mallat Scattering Transform (MST) in high energy density plasmas: a new look at nonlinear multiscale physics in HED.
Abstract not provided.
Void growth in an elastic-plastic medium.
The uniaxial deformation of an elastic-plastic medium containing a doubly periodic square array of circular cylindrical voids is studied under plane-strain conditions. Both the effects of geometrical nonlinearities resulting from large deformation and physical nonlinearities arising from plastic material behavior are included in formulating the problem. A variational principle is used as the basis for implementing a finite-element solution. Results are obtained for the change in void shape and size under increasing overall strain, the overall tensile behavior of the material with voids, and the development of the plastic zone about a void.
Theoretical study of nonlinear waves and shock-like phenomena in hot plasmas
Summaries are presented of research in basic plasma physics. Nonlinear waves and shock-like phenomena were studied which are pertinent to space physics applications, and include specific problems of magnetospheric and solar wind plasma physics.
An experimental determination of differential equations to describe simple nonlinear systems.
Ordinary differential equations experimentally determined for describing performance of existing lumped-parameter time-invariant nonlinear physical systems
Physics-Informed Active Learning With Simultaneous Weak-Form Latent Space Dynamics Identification
The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. Here, to enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared with the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5%–10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1%–7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1779x speed-up.
Development of a Single-Phase, Transient, Subchannel Code, within the MOOSE Multi-Physics Computational Framework
Subchannel codes have been widely used for thermal-hydraulics analyses in nuclear reactors. This paper details the development of a novel subchannel code within the Idaho National Laboratory’s (INL) Multi-physics Object Oriented Simulation Environment (MOOSE). MOOSE is a parallel computational framework targeted at the solution of systems of coupled, nonlinear partial differential equations, that often arise in the simulation of nuclear processes. As such, it includes codes/modules able to solve the multiple linear and nonlinear physics that describe a nuclear reactor, under normal operation conditions or accidents. This includes thermal-hydraulics, fuel performance, and neutronics codes, between others. A MOOSE-based subchannel code is a new addition to the fleet of INL-developed codes, based on the MOOSE framework. In this work, we present the derivation of the subchannel equations for a single-phase fluid, we proceed with the description of the algorithm that is used to solve these equations and describe how this algorithm was implemented within MOOSE. We also present how this code can be coupled to the BISON fuel performance code. Next, we verify the friction model and the turbulent mixing model. We calibrate the turbulent modeling parameters for momentum mixing and enthalpy mixing, C T , β. We validate the code using experimental results and last demonstrate the coupling capabilities using a simple example.
Some aspects of the Wiener theory of nonlinear systems.
Wiener theory for analysis and synthesis of nonlinear physical systems applied to non- Gaussian and Gaussian inputs
A comparison of turbulent transport in a quasi-helical and a quasi-axisymmetric stellarator
Ion-temperature-gradient-driven (ITG) turbulence is compared for two quasi-symmetric (QS) stellarator configurations to determine the relationship between linear growth rates and nonlinear heat fluxes. We focus on the quasi-helically symmetric (QHS) stellarator HSX and the quasi-axisymmetric (QAS) stellarator NCSX. In normalized units, HSX exhibits higher growth rates than NCSX, while heat fluxes in gyro-Bohm units are lower in HSX. These results hold for simulations made with both adiabatic and kinetic electrons. The results show that HSX has a larger number of subdominant modes than NCSX and that eigenmodes are more spatially extended in HSX. Furthermore, we conclude that the consideration of nonlinear physics is necessary to accurately assess the heat flux due to ITG turbulence when comparing QS stellarator equilibria.
Reentry Vehicle Flight Controls Design Guidelines: Dynamic Inversion
This report addresses issues in developing a flight control design for vehicles operating across a broad flight regime and with highly nonlinear physical descriptions of motion. Specifically it addresses the need for reentry vehicles that could operate through reentry from space to controlled touchdown on Earth. The latter part of controlled descent is achieved by parachute or paraglider - or by all automatic or a human-controlled landing similar to that of the Orbiter. Since this report addresses the specific needs of human-carrying (not necessarily piloted) reentry vehicles, it deals with highly nonlinear equations of motion, and then-generated control systems must be robust across a very wide range of physics. Thus, this report deals almost exclusively with some form of dynamic inversion (DI). Two vital aspects of control theory - noninteracting control laws and the transformation of nonlinear systems into equivalent linear systems - are embodied in DI. Though there is no doubt that the mathematical tools and underlying theory are widely available, there are open issues as to the practicality of using DI as the only or primary design approach for reentry articles. This report provides a set of guidelines that can be used to determine the practical usefulness of the technique.
Turbulent solutions of equations of fluid motion
Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence, such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations the initially nonrandom flow develops into an apparently random turbulence. The cases considered include turbulence that is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.
Turbulent solutions of the equations of fluid motion
Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used in most of the work considered. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations, the initially nonrandom flow develops into an apparently random turbulence. Thus randomness or turbulence can arise as a consequence of the structure of the Navier-Stokes equations. The cases considered include turbulence which is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A mean shear is present in some cases. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components, and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.
Turbulent solution of the Navier-Stokes equations
The unaveraged Navier-Stokes equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. Initial three dimensional cosine velocity fluctuations and periodic boundary conditions are used. No mean gradients are present. The three components of the mean square velocity fluctuations are equal for the initial conditions chosen. The resulting solution shows characteristics of turbulence, such as the nonlinear excitation of small scale fluctuations. For the higher Reynolds numbers the initially nonrandom flow develops into an apparently random turbulence.
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.
Quantification of Numerical Uncertainty via Nonlinear Dynamical Approach
Motivations (Ensure a Higher Level of Confidence in the Predictability & Reliability of Numerical Simulation for Multiscale Complex Nonlinear Fluid Problems) - The last two decades have been an era when computation is ahead of analysis & when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems & non-traditional fields (Especially when computations offer the ONLY way of generating this type of data limited simulations). - At present some of the numerical uncertainties can be explained and minimized by traditional numerical analysis and standard CFD practices. However, such practices, usually based on linearized analysis, MIGHT NOT be sufficient for strongly nonlinear and/or stiff problems. - We need a good understanding of the nonlinear behavior of numerical schemes being used as an integral part of code verification, validation and certification.
Turbulent solution of the Navier-Stokes equations
To study the nonlinear physics of incompressible turbulent flow, the unaveraged Navier-Stokes equations are solved numerically. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used. No mean gradients are present. The three components of the mean-square velocity fluctuations are equal for the initial conditions chosen. The resulting solution shows characteristics of turbulence, such as the nonlinear excitation of small-scale fluctuations. For the higher Reynolds numbers the initially nonrandom flow develops into an apparently random turbulence.
An alternative approach for MLE calculation in nonlinear continuous dynamic systems
As an important metric to tell if a nonlinear dynamic system has a singular attractor or divergent trajectory, the maximal Lyapunov exponent (MLE) can be calculated from either system models or time series of state variable measurement. However, in the real world, due to inaccurate models, measurement noise, and the fact that sometimes state variables cannot be measured directly, it is very difficult to get an accurate MLE, which limits its application in, for example, in prediction of a nonlinear physical system (e. g. power systems, etc.) behavior. To overcome these factors, this paper proposed a trajectory-estimation-based MLE calculation approach. The proposed approach addressed how to calculate the MLE when state variables cannot be accessed directly, and uncertainties in system models, as well as noise in measurements. The simulation results shows that the proposed approach is able to handle well the nonlinear measurement functions between state variables and measurements, and get better results than pure model-based approaches or measurement-based approaches in front of measurement noise and model uncertainties.
Selective nonresonant acceleration of He-3(2+) and heavy ions by H(+) cyclotron waves
The model advanced by Fisk (1978) to explain the anomalous enhancements in the abundance of some ionic species in energetic solar particle flux measurements at about 1 AU is revised by including the proper nonlinear physics of particle energization by electrostatic ion cyclotron (EIC) waves. The revised model contains two basic concepts by Fisk: the energization by EIC waves and the need for a second stage acceleration. There is no need for exciting He-4(2+) cyclotron waves, since the dominant process is nonresonant and can be accomplished by hydrogen cyclotron waves. The A/Q selectivity in the flux available for energization in the second stage process enters through the nonlinear saturation level, which in conventional theories depends on the current that drives the instabilities.